When creating complex surfaces in 3D modeling, topological considerations are essential for achieving clean, controllable results. Key principles include: (1) Maintaining uniform topology across cross-section curves to prevent unwanted twisting and bending of ISO curves; (2) Using rebuild or refit commands to regularize curve topology while controlling maximum deviation; (3) Understanding that surface degree is determined by control point count, with higher degrees making surfaces more difficult to control; (4) Avoiding network surfaces for complex modeling as they create excessive complexity; (5) Using poly surfaces with controlled topology for better editing flexibility; (6) Understanding curve speed and knot distribution affects surface behavior; (7) For sweep operations, maintaining regular rail and cross-section relationships prevents self-intersection problems.
Simplified Complexity - 2BHinzugefügt:
okay so if we if we try to repeat this this construction here this building for this surface using exactly the cross-section we will run into some problems okay so the topology of the single curves here is identical because they come from from the same surface that we obtained with the first execution of the loft so they all the the three curves have have six control points and degree three so when we perform the loft we will always get a degree three cross section complexity with sis six control points but the shape of this curves here and also there the geometry basically when we use it inside a lot of common and we are going to select all these lines this time by default the loft command creates a a smooth interpolation between the cross section so it doesn't get creases the only way to create quizzes using a a loft common is switching to straight sections but switching to a two section section loses the degree three interpolation between the cross section themselves so if I hit okay you see that we have this kind of surfaces they are always let's say degree three interpolations but creases or a cross section becomes inner edges so the result is going to be a poly surface and this surface I have exploded the poly surface this surface you if activate the control point it's going to have only two control points from the start cross section to the intermediate works cross section so the topology of this object here is absolutely not not good for creating this kind of object so you see that the death is not the same to prepare the construction curves and execute the loft rather then execute the loft with the my topology and eventually apply some topological editing in order to create acceptance effective then so is not like one way is is better than the other is just that there is no other possibility to create this kind of situation of course there are other ways but they are way more complex than this one for example we should consider creating something like in order for example let's concentrate on the inner stripe here so the inner stripe is a ballad that runs from this crease to the valley button here to the other crease the opposite crease right and in order to create this surface this internal surface with a traditional direct modeling matter we should at least count on I would do this with the annotation so there is no need to do it physically in vinyl we should rely at least on this curve here this curve here and then this side crease this other side crease here this valley line just want to beat this one and also in order to maintain this kind of valley aspect along the inner part of the surface if we for example take into account only these lines as this edge is straight this edge is straight and we have a flat line even if this is curved it lines on the horizontal frame then there is no need for the come for any common that you use to create this kind of valley shape okay so we will also need at least one cross section probably in the mid section of this curves like this but we are going to deal with one two and three curves in this direction and with one two and three curves in the opposite direction which leads us eventually to the only possible well it's not only it's not the only possible common but we can work only with network surfaces right here the other alternative is the patch surface but I do not recommend you use the patch surface if we want to maintain some topological control so the authority here is only the network surface which and leads us to an extremely high level of complexity for the surfaces so I don't recommend using the network surface unless you are basically performing an operation that doesn't need any additional modeling operations okay or editing operations because the level of complexity is so high that is basically way too difficult to perform any additional operation on the surface so you see that for example in order to obtain the same result we should work with poly surfaces and create each of these three surfaces you independently from the other one so we get topological differences between the three parts of the object which is not the same because here we have a unique object with a unique topology which is perfectly clean and smooth so once again you see how working with with direct topology editing like point editing also in case of surfaces is is more useful than creating a complex set of construction curves and operating directly with direct the surface model okay now as regards the loft there is another consideration that will be that you might want to do and is like it regards complexity of cross-sections we saw that sometimes like curves can become very complex like in this case okay so I'm going to use this example here in order to to analyze for example the loft creation so I'm going to take back the surface and the curve on top of it and I'm going to perform the projection once again so I will project this curve onto this surface and update this and I want a surface that starts from this line and connect to these lines here so these two lines I have a very different topology and and eventually I also want for example a another curve on top so I'm going to create a more sloth and in order to maintain exactly the same vertical alignment I'm just going to take the inner control points of this curve and move them vertically so this vertical displacement is not changing the horizontal projection of this curve if you see in this from top you see that we are not changing the horizontal behavior of the line we are just changing it from a front view or vertical view okay so these three lines basically overlap perfectly from the top perspective okay so what I want to do I want to create the loft between this curve this curve and this curve now these two curves have exactly the same topology okay besides the displacement of the control points but this one has a very complex topology because it comes from a projection so what happens if I create a loft between these these and these what happens and not of course not with straight section work it normal okay what happens is this now this is extremely problematic because the fact that the ISO curves are so much depends on the fact that the lower curve has a very high level of complexity so remember that ISO groups are not lines so what we are seeing here are a the presence of an extremely high amount of spans okay and also an uneven subdivisions of the curve in terms of other spans and knots okay and up we have these two curves with a lower level of complexity but it is normal for the loft to use the higher complexity in order to represent a best through the simplest cross section the problem is that these two curves don't have the same complexity don't have the same amount of control points north and spans so the common normally flows through these cross sections and adopts the spans and North position and therefore also the control point of the surface the best it in order to pass through these curves so this generates some unwanted behavior like for example I don't know if you can see it but this is like a twisting of the surface or a side sliding of the surface so when you see icicles doing something like this start to worry because sooner or later you will have some topological problem in terms of editing or creating some further elaborations on the surface first one for example would be these nice cuts that we created here that were perfectly aligned with the ISO curves because the icicles depended on the topology that we are controlling now we are not controlling topology here because this is an automatic interpolation so if we try to extract either curve this is the behavior that we are going to get so if we want the vertical folds or cuts we cannot do this with simply by simply extracting algebra because they will come bent like this okay so how can we how can we solve this problem well actually of course we need to obtain a more regular topology and not only a more regular topology but also because one could say okay I take the lower curve and rebuild it so rebuild it in order to have a less complex topology while actually not with four control points because as we get this kind of total deformation of the curve but eventually I don't know with 75 we already get a very good approximation of the curve eventually with this kind of maximum deviation I would eventually decrease the amount of control points and go back to a more acceptable compromise between the complexity and the precision okay so if I rebuild this and delete them but they I don't want to well no I'm not going to delete inputs so let me do something like this I'm going to take this curve and I'm going to change its color to red and so I'm going to select it once again and rebuild it with 50 control points and don't delete the input and hit okay so now we have one which is the regularization topology and I'm going to change it to blue okay so the green line is the good one and the red line is the old one and we can see that there is some difference between the two when you see the standard flickering between the columns it means that there is some difference between the two geometries so this is the curve that I want to loft together with the upper curves so loft and select the green curve this one and this one in key enter and switch to normal you see that having a more regular topology is not enough for regularizing the vertical aspect of these icicles why because the lower curve has a constant speed now because the control point will were redistributed the in an even way along the path the knot vector is uniform not vector at these two features make the speed of the curve constant but here we have two different topologies from the lower one and the speed is not exactly the same so it's the speed that makes the EIC groups bend towards the along the path okay you see that for example in the upper part of the surface you have this kind of bending of the icicle but this bending depends on this part on this different topology but if you take a look for example at the start point and end point of the ISO group on the two upper section you see that this more or less aligned vertically okay because these two section have the same speed now in order to have three curves with the same speed you also have to rebuild the upper sections now you can do this by hand like rebuilding with the rebuild command outside from the loft but you can also do something different like simplifying the cross-section curves inside the loft options so if I rebuild the whole set of cross section with the same amount of control points then I am regularizing the ISO curbs and it's interesting for example right now you see there is still some bending occurring even if they have the same topology but this is way less than the bending that we were getting before this kind of operation the only problem with executing the revealed inside the loft option is that you don't have any control on the deformation that you are getting from this rebuild so there is no maximum deviation parameter inside the loft options window so of course reducing the control point from 50 to 30 from for the lower curve is still deforming the the curve too much and we see that for example the surface is not connected to the actual cross-section because it is being deformed due to the decrease of the amount of control points from 50 to 30 so there is one reason why eventually I would take this lines here and perform the same rebuild outside from from the loft options so I already have a green curve here I also needed to rebuild these two guys here so I will perform a rebuild of both curve in order to keep under control the maximum mediation of course in this case I want to increase the amount of control points because I want a uniform topology for the three lines okay and so in this case I'm going to delete the input so I only get the good lines okay so the topology is now uniform I perform the loft between the green curve and this one and this one hit enter I don't need to simplify the cross-section because they already have the same topology right and so I simply hit OK now the problem what is is that I rebuilt the lower curve not the upper curve because I increased the enough the amount of control points from seven to fifty so there is absolutely no possibility that the the resulting curves are way too different from the original shapes okay but this one has been rebuilt with half the amount of the original number of control point hey am therefore the deformation was 0.007 but we are working with the tolerance of 0.001 so we obtained a deformation which is seven times more important than the lowest detailed possible form for whiner so for rhino this a green curve no longer lies perfectly on the surface which means that this Loft doesn't touch the underlying surface perfectly we're perfectly means with a lower separation than the absolute tolerance that we have here and so any operation that we try to do between these two surfaces is going to result in some well error or bad behavior for example if I take this two object and try to calculate the intersection the intersection well actually is giving us a good result this is was this was quite unexpected I was expecting a set of more open curves from this intersection eventually is because there is a maximum deviation of 0.007 but eventually this level of details that this level of separation happens in a very localized spot along the curve okay so being obtaining a maximum duration doesn't mean that you have whole portions of your curve to AB that separation so if that value or only involves a specific spot of the curves then in that case you still have enough precision in the the coincidence between this surface and this object here but if we for example repeat this with less precision so it means with less control points then eventually from this intersection you will get separated segments for the intersection okay so this is this could be one problem I'm not going to repeat a lot but you can try this if you if you want you can simply decrease the amount of on to a point for your rebuild and then take into account the value for the maximum variation but in that case but just performing this intersection would result in separate intersection lines okay so nothing case but anyway this is something that you might want to take and yeah take into consideration because the precision of the cross section can be adjusted or the repealed of the cross section can be performed outside from the left and inside of the left as well the only difference is that you don't have control over the maximum deviation which is a very important parameter another consideration is that sorry this is the the rebuilt loft okay so this is a possibility you have but you saw that obviously in the loft option window there is also another possibility for the cross section which is the reef feet now we built and with it are two different operations that they both rebuild or simplify the curves so they change the topology now what's the use of refit and you see that also feet was one of the options for the curve editing they repeat curve to tolerance which is which is actually what is happening here if it using this kind of tolerance now the reef it actually changes the shape of a curve in order for that girl to to be simplified in Rhino terms within this kind of tolerance here so let's see what for example what happens if I have a red curve which was the problematic one or the projected one okay so I have this record let's switch it back to to black so it's more visible and this is a problematic in complexity right so we want to do something with it and I don't want to rebuild it I want to repeat it right now so I'm going to take the feet common and the feet common says okay what's the pitting tolerance and the fifty tolerance is now set to the absolute tolerance of Rhino document now this is a good approach because if you say I want to or refit this curve using the absolute tolerance the topological editing that happens will respect the ocular shape of the curve within the absolute tolerance online a document so for I know there would be no difference between the a tracker and the refit curve okay let's also see if I'd know I can't so I'm going to create a new layer like layer 0 1 and give these the green color okay so I'm going to take these and refit it and say output layer is it's going to be sorry to switch to later man okay so we fit this and output layer is going to be the current layer so the refeed curve will be placed inside the layers in one okay so I leave the absolute to talk to the fitting tolerance to the absolute value I'm not going to the regime but because I want the black line to stay on default layer degree three I'm going to keep it because I don't want to change it of course and what angle tolerance we are not going to work with this right now just concentrate on the fitting tolerance okay so if I hit enter now I get two curves hey and see the control points of these curve they are extremely regular okay so worried what the common did was repealed this curve actually but fitting that the result to danisha to the original curve with a tolerance of the absolute tolerance of the of the document so I know that topologically speaking this might be the best compromise between the original weird topology and the best topology that allows to respect the absolute tolerance of our document so for Rhino there is absolutely no difference between the green curve and the black curve even if if we go very very close to this line you see that this flickering means that the curves are somehow different okay so let's see if i zoom window for example in these areas that's if we managed to see some yeah you see that there is this very very very small difference this is 1 micron basically maximum deviation okay so this is probably the best way of public building a curve according to the document tolerance 15 doesn't take into account the even distribution of control points along the path okay because it is based on fitting tolerance now fitting tolerance means that the maximum deviation must be contained inside 0.001 unit and we saw this previously with grasshopper I show that when the curve is a small curvature in order to maintain that tolerance you need more control points when the curve becomes looser they you need less control points so there is not an even distribution of control points along the path you see that in this part they are denser than in this area here okay so but this is the best apology in order to maintain that tolerance okay you have no control on the amount of hundred points so the final result for example here is saying sixty two control points okay but for example in order to observe these I'm going to take the feed curve like take it here and take this one and eventually rebuild it with the same amount of at the point 62 okay so you see that the maximum deviation is higher actually that the absolute tolerance okay very small difference but this is higher than the absolute tolerance so if I don't delete input I get this is the weird topology this is the rebuilt curve and this is the refeed curve okay so there is a slight difference with that amount of contra point between the shape of this curve and the original one this is something that Rhino could detect because the maximum maximum deviation was higher than the absolute tolerance of the top the the difference between the shape of this line and this one is undetectable for Alwine because we work inside within the absolute tolerance value Hey so any operation you performed on this topology which is way more than the original one will result in a perfect world floor or in a resort that you can foresee but when you work with this is like 5050 okay because you are you are working with a value at or a deformation which is higher than the absolute power okay so I would say that this curve for example can absolutely be being read okay so take into account these two operations now the repeat and and refit and let's go back to our loft now despite the fact that there is a refeed possibility inside the loft I would not recommend you use it so let's see why if I loft the red curve the black curve and the black curve these two always have the same topology even if we rebuilt them previously with fixed control points now if I do this and I used normal and do not simplify I start to have this kind of strange behavior even if the lines seem to be very good oriented in this moment you see that there are some icicle which are extremely close hey this means that in this areas the surface s is lower speed okay so you always aim to obtain the more regular topology possible not only for the orientation of the icicle but also also for the separation of the I suppose if you see this kind of variable separation it means that this surface is faster slower faster very slower somehow faster no and then becomes very slow here and so on okay so you don't want this and if I rebuild this well we already know a constant separation smooth surface and at constant speed and so on everything is perfect here and from this point of view I am no interested in in simplifying too much the cross the cross section because if I simplify too much I've tallied in the amount of control point too much the risk is that I work out of the limit of the absolute dominance so I prefer to increase this also to I don't know 100 okay it doesn't matter the important thing is to have a a regular topology okay well of course it matters okay if there is no need to reach these higher numbers you don't because this is going to produce some heavier geometry which is heavier to render heavier to save in your files and so on okay so you might want to also think about optimizing the size of your of your sides of your document but in general this topology is is the same is good it's as good as a simpler topology okay because it has constant speed and regular attribute orientation okay what happens if I use to repeat the rift it doesn't eliminate the problem of the difference of topology well actually it increases the problem it makes it more evident so what you should do eventually is decrease the resolution but if you decrease the resolution you don't eliminate the weird behavior because the topology bit of these three lines is way too different okay so you will always have some kind of bending of the Icicle and moreover what you get is a total separation of the actual cross-section from the original cross-section so you are almost surely working out of the limit of the absolute tolerance okay so refitting the curves inside the loft is not recommendable in general especially if you want to maintain some kind of genetic and topological control okay so as you can see I do not recommend you to perform this operation inside the loft but as we were discussing here in general this is probably the best rebuild tool that you can reuse in Pinal because it takes into account the tolerance the absolute tolerance of the document and also thanks to reorganise the control point in an intelligent smart way okay but not inside the execution of any surface creation comment okay so you might want to don't simplify if you already have the right topology for your cross section or reveal the cross section with the same topology in order to get to the - this movie and nicer topological result possible okay so this is the important part of of the last comment and as you can see everything is what it is basically determined by some topological consideration now speaking of surfaces that sweeps along the along a cross-section there are the two sweeps comments now in general I do not recommend to work with you with a sweep one way the sweep one rail is say common that only works fine and produces a control result only under very particular circumstances so for example if you have a a clear relationship between the rail and the cross section then everything works fine for example you can think of using a let's go to the front viewport and use this rectangle oh I don't need to work in the layer zero one and go back to the default layer let's create a rectangle and we can use the sweep one way to create some complex shapes with just one single execution of the comments so for example if I take a polyline starting from the midpoint here and activate the project common planner is already activated so whatever thing I do here I'm staying at the same time okay so when I want to do I go into the top viewport right now and draw around the edge of this rectangle so I go for example out here and then draw this segment segment and then this segment and I start to do something I don't know anything okay so I switched to mode are can I try to do something like these so I am basically designing something like the frame of any I don't know picture or something like that and then reach this point okay then I take this this polyline here exploded get rid of this line and join it back again so AB one closed polyline in this case which lies at half the height of this string now in this case I can use the sweep one range using this rail in this section because I know that s the situation is extremely regular and controlled what I get eventually is this perfect sweep along being the sweet one the the one way that I'm using now eventually here I would do some topological consideration in terms of is this the best topology possible for this frame I don't think so because the way that the sweep one rail worked creates for example this internal edge here at half the height of this side because the cross section is here so that the sweep starts from here and reaches down here so this is a an internal edge which is absolutely unnecessary so the opposite side has only a nicer curve here so eventually I would get rid of these two surfaces here or bony surfaces here and eventually mirror just this one here on the other side okay and the other topological problem that we have happens in the corners and because we have this edge here which is not necessary and also this one okay so we have some surface going on here splitting the whole side of this frame at this height which is useless okay we can avoid it so you see that the sweep is not producing the best result possible eventually you can take this H the well this cross section here creates some kind of a straight extension like this which is higher than the edge itself and then eventually start to mirror this 45 degree create the upper side mirror on it and have the lower side and here at least on the other hand and left the left side which are basically one single extrusion they still are poly surfaces because the cross section that we are extruding is actually a poly line with vertices okay so you always get a poly surface as a an extinction eventually what you can do in terms of topological consideration you can also avoid having these vertices here now what what would you talk to eliminate these vertices eventually the average user what what he or she would do would be using some feeling okay so I have this section here I see that this is one millimeter so eventually if I feel at all this corner with more or less the radius of point two I would get a nice smooth aspect okay so let's try and and do this with a copy of this line okay so I'm going to apply a fill at corners which is this one with a radius of point two and have this nice smooth result okay but this nice smooth result is producing this kind of a situation here the field left is a constant radius curve because it is an arc right it's a portion of a circle so we pass from a zero curvature segment which is this one straight line to a constant curvature segment to a zero curvature segment again and this happens with every single field that we perform okay so if I analyze the curvature of this line like with a curvature graph you see that this is what happens along this line okay there is zero curvature curvature constant zero curvature and so on okay now I created this as a polymer poly line with art segments so each time I clicked I was ending an arc and starting a new one so there is curvature discontinuity also in these points here what does this mean that if I take is curve okay the poly arc together with the fielitz has created a a unique polyline a unique poly a curve with curvature discontinuities all over the the segments okay so if I extrude this line and take a look at the result you see that each field becomes a surface so we still have a poly surface so we created a more complex result even if we were smoothing or rounding in but if this is not smoothing actually this is rounding the corners so three around the corners we create a discontinuous a connection between the sides okay because the pilot is a constant radius curve okay so how can we get rid of this distance you needed and eventually create a one unique smooth surface for as the exclusion of this line we cannot work with a poly curve like this one we must work with a unique curve so if I take this for example and rebuild it with I don't know 100 control points okay and delete the input and hit OK I get this line here which is basically identical to the fileted curve that I had okay and this is one single smooth line so if I extrude it I get any more complex topology of course but if I explode this extrusion I get one single surface okay so is this less complex than this one well it depends on what type of complexity you are considering having one single surface is that of a poly surface is already better for for modeling purposes okay having a higher level of complexity in terms of topological density might be lets say a increase of complexity but we have an extremely regular topology so in this case eventually I would say that piece is way better than this one okay so you see that almost always once again we are considering the sweep and we still go back to complexity control in terms of curves okay so everything is back and forth in this in this topological approach to modeling okay what other consideration that you might want to have for this surface here is that you see that the seam which is this internal edge is basically happening here on the front of your curve basically and surface as well well eventually this is a detail that we don't want to have it visible even if it doesn't matter in terms of an example of visualization like rendering and so on if I render these there is basically no visibility for this internal age right so it's not a be a visualization problem it's a topological from so having an age which is exposed like this well basically means that each discontinuous discontinuous behavior will happen in a peaceable part of your piece okay so in this case eventually I will go into this surface tools and use the closed surface seam which is basically this inner edge here in order to bring it to a invisible part of your of your model like for example I don't know here okay so you see that I have changed the the position of this internal age which is now here on the back of my model okay which means that if I hide the ISO curves so as a cop density set to disabled I see a perfectly smooth surface without any internal edges but this one which lies on the in a position that is not disturbing any process okay so you see even in this case sweep one plane also in this configuration needs some topological tweaking if you want to get to the easier or simplest result possible and also the in terms not only in terms that is not that this internal edges bother me okay is that this is a physical discontinuity between between this surface in this one which is absolutely useless that you can avoid it and in order to avoid it it's better if you work with simpler commands and with simple topologies okay now if you want to let's say get rid of this separation here you can also tweak the result of this week one way you can avoid this kind of separation but you cannot avoid this separation here now here for example if I take this object here and eventually going to the sonic tools and extract some surfaces like for example this one and this one and this no sorry this one and the upper one I can delete them I am creating an open polish surface where the only thing that it misses is one single surface so I can cap this planet hole with one surface and you can see that I get there very smooth surface from top to bottom okay but I cannot do this for example in these areas because this is not a planar hole so I cannot cut it so eventually I would have to extract these surfaces here all of them also the upper half and also this one get rid of them and now how can I rebuild this whole side for this frame with one single operation well what have you to do is eventually make a surface between this section here at the bottom and the upper section because I have straight lines here at the sides so a loft is enough okay but the problem is that as I had this kind of separation here also in the original part this is one edge and this is another age so I need first to extract these two edges oh and I see that I also have some internal discontinuity because of the field lets you see so this is a very very bad topology you see how many work I have to do because I prefer to not repealed for example the cross section curve for my sweep okay or instead of working with an extrusion I decided to work with a sweep and now I have to deal with this kind of situations here which is this one at the bottom but also this one at the top because I have exactly same topology for these ages and so I have to extract one by one all these arcs here okay and then join them together in order to have to curve and you see that well actually I'm getting for oven curls and this is in this is interesting let's see curve and it doesn't join with this one okay so now this is absolutely I was not expecting this let's go and analyze this detail I activated the control point and selected only few control point in order to zoom to selected object see Oh I missed this edge here okay there is a smaller edge because this is a dream surface okay so then there was a trimming that spitted one single edge at this height so I also need to extract this little edge now that I know also at the bottom see how much time I am wasting because of my decision to don't work with an optimized topology so I suppose it also here you see that I have this missing edge okay so now I can select this curve this curve plus the edges that I just extracted so like this and like this and join them all together into to open curves now I am I'm not going to consider it but you might already think that the topology of these curves here is it is way too problematic because it is made up of very away a huge amount of segments okay well it could be one single smooth curve with the same aspect okay I'm not going to reveal them because if I rebuild them the surface that I'm going to create build it will eventually not join well with the remaining surfaces okay so I'm not going to do this but if I perform a loft right now between these two lines what I get without simplifying anything what I get is this surface here which is one single surface from top to bottom and in the end we get this kind of topological complexity which is basically correspondent to this one more or less okay so there is no particular advantage of choosing or sticking to the sweep one rail in this case rather than performing a different operation like the one that I was doing rebuilding and basically excluding this at this new curve in order to attain a more regular topology okay so you see how many problems I had in order to regularize and simplify this kind of aspect for our frame and we still miss the upper surface which would be a mirror of this one and we can we must basically get rid of all the discontinuities that we are belong to frame okay now basically we just need to solve this problem on one side and then we mirror Mirror Mirror and we have solve all the problems but yet this is a very time-consuming process okay that we would avoid it before we decided for a different workflow okay so see how topology can it well understanding topology can also put you in the right path before starting to model okay so take this consideration not only as a guide for editing existing geometry but also before creating geometry what is the more efficient way that I can create that that jump and normally these involves some topological consideration that's say the sweep one rail I told you that it's problematic not only for this situation here but also because it's very difficult to control unless you have a very regular distribution of curves so for example in this case there is no problem in understanding that if I take a rectangular rail and a cross section like this one which is perpendicular to the rail I will get a regular frame besides the topology I would get a regular geometry okay but what happens if I use for example a completely irregular situation in regular construction lines for example a rail which is something like this which is very common in brinel so is a NURBS curve with some up and downs along the path like this okay and I want to create a sweep with this a unique rail of a curve which is something like this okay and also with some internal deformation okay so if I try to do this rail cross section I start to get some some strange result okay so for example if I turn to shaded mode you see that there is something weird happening along this Israel and this behavior is the default behavior of a sweet one rail which is called free for right now freeform is based on another topological consideration that depends on the fact that curves or NURBS curve not only have a a topology in terms of control points not vector in degree they also are oriented lines okay so a being be is an oriented line it means that it flows from one point to the other but also that when it does something like this there is some twisting going on along the path so freeform takes into account the eventual twisting occurring inside this this curve now this is something that in Rhino is it's simply invisible and it there is no possibility to to see it unless you perform once again you perform a curvature graph analysis and you get these curvature graph that we are going to display okay you see that the curvature is actually creating some kind of spiraling along this this line right because the curvature graph appears on the opposite side of the curvature circle now the curvature is simple if we want to visualize this we keep the equipment graph visible and we can visualize for example conduct a curvature analysis along the path you see that this curvature circle here is changing the orientation okay so let's disable the a snap here so you see that it changes not only its radius but also its orientation okay so this means that this curve is twisting right so orientation and twisting are basically the same aspect of one single two magical properties in this case it's not topological properties but its geometrical problem so the fact that skirt twists along the path means that the cross-section the sweeps normally are programmed to maintain the same relation between the cross section and the rail so for example if this curve connects to the rail more or less 90 degree then all the sweep will maintain all the iso curves connected 90 degree to the to do to the sweep rail but what happens with the orientation of the curve now let's go once again with grasshopper I'm going to take the red curve set one curve and that's it okay what I'm going to visualize right now is a thing called the perpendicular frame this is also a parametric analysis so I'm going to be parameter eyes once again and take a normalized slider and take c1 so this is actually the perpendicular frame to the starting point of our curve okay now if I take the curve and take this control point here and move it you see that this perpendicular frame is changing its orientation right so what does it means it means that the relationship between this curve and this line is not only the inclination between the tangent lines to this lines right but it also depends on the relationship between this curve here the cross-section and the orientation of this perpendicular friend so the perpendicular frame has its red axis pointing more or less upward okay now during the sweep I'm going to increase the preview playing sighs - Tim yeah okay so it's more visible okay now let's take a look at what happens if I flow this point and this frame along the curve right take a look at the red axis so if I start to move this the red axis is still pointing in the same direction now it's ponding more horizontally now it's pointing more downward and keeps on pointing downward okay so remember that our curve with respect to this axis here is basically more than 90 degree rotated to the left okay so if I go to the end point and see that this is rotated like this I expect my cross-section to become almost vertical here starting from horizontal and getting almost vertical so when I do the sweep one rail you see that in the end my cross-section becomes almost vertical because what is twisting is the internal perpendicular frame because there is an orientation and a twisting a going on okay so it's very difficult to control a sweep one trail with a free-form style if you don't have a regular configuration on both of the rail and of the cross section so in this case the result was totally predictable because the frame rail is a straight line rectangle okay and the cross section was perfectly perpendicular to the to the rail so the rail is not twisting because it is made up of straight lines and the cross section is perpendicular to the rail and it remains perpendicular to the rail the fact that the section is perpendicular to the rail is what makes this separation HS appear in the in the corners of our frame okay but in this particular situation you see that we get a totally uncontrollable result because we have no control over the twisting of this curve okay so free form free style free form frame style sorry is something that is very difficult to control in organic situation or or freeform situation okay that's why I normally try to avoid this kind of constructions here because they are geometrically basically uncontrollable of course you can decide for example to use the road like now the road line means that basically you make the sweet behave like if it was a road and a road for example take a mountain road okay the mountain has its no but the orientation of the road is almost always horizontal right so what this road like is saying is that the frame the frame of the of the curb doesn't rotate according to the twisty natural twisting of the curve it remains it remains road like what what like is this thing using is basically considering the vertical direction to the actual viewport which is the vertical see so if this line this cross section is horizontal according to these vertical axis it will be kept horizontal all along to sweep so you see that this line is basically never rotating around the axis of our rail okay it always keep the horizontal orientation this is something that allows creating more regular sweeps if you if you want but in in terms of a geometrical result it is very very difficult to control for example what happens in areas where the rails have higher values of curvature like for example in these capes now this is something that and you can see here what weird without we are we are obtaining okay so this is something that we still cannot control even if we switch to load like okay now this is something that is always also a problem in a more regular consider a more regular situation so for example what I'm going to do right now is draw a more regular rail like this okay so I have this red extremely regular Ray and I have a cross section which is also extremely irregular is just a straight line mode line perpendicular to the rain okay so what happens if I this curve has no twisting because all the control points lie on the same plane okay so it has some bending but not twisting okay so if five for example conduct a cryptograph analysis you see that the curve of the graph is always lying on the same XY plane so there is no twisting okay what happens if I try to do this sweep one way what's the problem in this case the problem is that this is the Ray this is the cross section and in this area here the concavity and the curvature of this whale makes this section flow the end point connected to the rain is always connected to the whale okay so it flows along the whale but the free end point of this cross section simply follows the flowing on the curve along the way so let me grab a pencil here so this is the the cross section okay so it is rotating because of the bending of the rail okay now when we reach this point this is the cross section when we reach this point the cross section is still oriented in this way because this it is thin perpendicular to the rail as it was at the start point of the way right when we get here the perpendicular is going to be this one when we are here perpendicular is this one so in order to keep the the relationship between the cross section and the rail along the sweep this is what happens so there is this opposite direction for the end point along the sweep in this area this is a self intersecting surface which is something that's extremely problematic okay so try to avoid this what can we do in order to avoid this kind of off situation well this is one problem that depends on one general consideration which we can observe not only with the sweet one train for example like in this case we can observe this problem here in many situation but they all lead to one single problem which can be analyzed using a simple offset curve okay so this problem originates at the level of a a-and offset if I try to perform an offset curve of this thing here you see that let's make the two points option okay so you see that the offset produces a smooth curve until a certain distance from this certain distance on you get this kind of intersection but now the offset is capable of doing this it trims the intersection and leaves you with a vertex so an internal discontinuity is a king basically but it's it's fundamental to understand for example what is the maximum distance for the offset in order to get to a smooth curve okay now in order to do this what you must do is take the curve and conduct a curvature analysis so right click on this if we do this curvature analysis we have access to the osculating circle which is the curvature circle but also we see these black dots and white dots the black dots are inflection points and so it means that the curvature changes its sign it goes from concavity to convexity and vice versa okay another of the white dots the white dots are given each one of these segments between black dots inside these segments there is at least one white dot and this white dot represents the smallest curvature inside these segments so this white dot here is not problematic for us because we want to offset on the other side okay so the only concave part of this curve on this side is this one between this black dot and this plateau and the smallest value of curvature I have it here so if I take this point with a snap and click with the mouse on it Rhino says the radius of curvature is six point eighty nine four four three okay so it means that if I take into account this circle the the highest value of the option of the distance is basically reaching the center of this circle in that center I already get a vertex from that Center on on the others on this side I would always get an intersection and therefore a vertex so if I consider an offset distance smaller than six point 89 I will surely get a smooth curve as an offset so let us try and see this if I take for example once again be offset curve and I was usually I was using twelve right but if I take this and set it to six and click here I get a curve which is smooth with a very complex set of control points because the curve is getting varied with a very value of Airy high value of curvature but it's still smooth okay well if I take this and make an offset oh oh sorry I think I have the cap activated so cap no six okay this is the first often offset producing a smooth curve and I am going to ask this once again to seven and click OK so here here we should have a vertex that should be this one and here it is it's a kink okay so you see that we have perfect control over the right or problematic execution of an offset and this is exactly what happens with the sweep if this line which is basically representing an offset right if this line measures something more than 6.9 and it measures 20 point 769 then it will produce a self intersecting surface so if I take a 6 offset which is this one and trim this part of the cross section and create a sweep one with this rail and this cross section then I will get this you see that is not exactly the same as the offset because there is some well we will see this in in a while but it's more or less identical so if you control the curvature of the rail you control also the needed length of the cross section in order to avoid is self intersecting problems here okay other things that that are affected by this consideration are for example the offset of a surface so the offset of a surface is a little more complex because a surface is not only one curvature value it has two curvature values which are also considered in like in combination of the two in two different ways like in terms of mean curvature and Gaussian curvature there they are two different meaning of of the curvature analysis in of a surface we are not going to discuss this because this is very very very specific and eventually you might not want to take it into account in a standard workflow but it affects some kind of particular geometric problems like I don't know like something like minimal surfaces which are a particular category of category of surfaces and other particular aspect that we are not going to discuss but anyway you see how the sweep one rail might present some problem and you always need some topological consideration you look for them for this comment to work properly okay one last consideration which has to deal with sweep with more cross more than one across sections if I go here I'm going to keep it simple right now so I'm going to take a straight rail a straight cross section and another straight cross section like this okay if I do a sweep one rail between this cross section and this cross section you see that with freeform you see that we get this kind of surface of course this is like a a executing a loft actually so if you have a one initial cross section and one final per section and you have a straight rail there is no need to create a sweet one way you can also loft the two opposite sides right but actually there are several other comments that you might want to use for example there is a simple so from two ages so for example I can take this curve and this curve enter and I get the same exact surface right so always try to use the the simplest surface creation method if you have access to it okay but if I take the surface and activate the control point I see that now using the the sweep one rate I don't get a degree three interpolation along the path okay I got a the simplest possible surface which is a four side surface by linear okay so there is no possibility of deforming the surface internal okay and this is this is curious because if the loft creates a third degree interpolation the sweep does at the end it's more complex than than the law and so this is something that I wanted to point out of course if we take a an intermediate cross section like this and we create a sweep one rail with these three lines now it's like having three lines three cross section with a loft okay so there is no way of creating a a let's say a linear interpolation okay so you see that now the opposite edge which is uncontrolled is basically treated like more or less like an interpolated curve well exactly not like an interpolated curve because if this was an interpolated curve which is this one this curve should start from here point directly in this direction here and then go and end like this you see that there is some curvature here that means that this cross section converts into this one knot with a constant speed so this interpolation is slower on the first part is faster in the center part and slower towards the end of this interpolation dysmorphia okay and the same happens between this second cross section and this third one okay but you can also activate the global shape blending the global chef blend shader blending is actually considering the interpolation the global effect of an interpolating between these T's this cross-section so it is actually behaving more like a straight interpolation like from here I must go through this point but then I must also let's say raise up raise up once again because the Third Point is up here and so I needed to prepare somehow go lower and then run towards this this direction here so you see that the free edge of the sweet one rate is very difficult to control also when you have this kind of very irregular situation here okay so you see that because it is always based unless you work with two only two cross section it is always based on a degree three interpolation which is very difficult to control you can also work on curves you see that in this case for example as there is the longitudinal guide which is the rain you can also refit the longitudinal plane now in this case as this is a straight line riff it produces no result but we fit in you already know what it means okay is it has to deal with the topological feed operation okay it by doing this what you what you produce in your surface is a different longitudinal complexity because refitting redistributes the control points and knots along the path and you will get different sets of iso curves of cross iso curves along the surface of course because remember that articles are not lines and you have a degree three interpolation so if you do this on an organic shape you will have a different distribution of not stands along the back and then you can also work with cross sections and you can reveal them and repeat them right so if you build them you will always have a web 500 points produce one single internal knot so that is always the same longitudinal I secured but it becomes a real a circle and not a visual one but if you take more control points you will have more more longitudinal icicles remember you do this only if you need it okay it's not because I like having all these lines visible is is nice visually but if you don't need it you don't do it okay by me did it meet with by meeting it means that if I get to these results is eventually because I want to activate the control point and I don't know I want to take this line of control points and this line of control points and leave all the rest untouched and so once I select these two points here I can go into selection and point selection and select for example all the points in the U Direction okay so I select all the point lines and then I go for example here in perspective and I have create this we build because I wanted to do something like this okay so even in this case topological considerations in order to get to this complex we solved but with the less amount of steps possible okay so you see that also the sweep one trail if you want to work with extremely organic shapes is way more powerful than other tools but remember it's very difficult to control and one last consideration I'm going to move this surface away and I'm going to use this reform curve which has some internal knots and stands of course and I'm going to create a sweep one with this and in this case what I'm going to do not only ever going to omit the cross section I'm also going to refit the reins and you see the effect okay so the effect is basically having a refit when when when you repeat something for example like in this case and you have no control over the fitting tolerance it means that the comment is working you see the absolute tolerance of your of your document which was 0.001 one micron that's why you get this kind of density of not lines okay because you have a huge amount of control points in this refitting okay so for example if I cancel this command going to millimeters and go on to unit settings and eventually set this to one and perform a sweet one like this with a repeat Ingram you see that the refit is way less dense than the previous one because it is using the absolute tolerance from your document okay so let's switch back to the zero point zero point zero zero questions you supposed to bake the cryptograph somehow no I mean you're gonna do it this in in vinyl you can find a way of doing this in in grasshopper so for example there is well actually I don't remember whatever but I have it do you say a component which was a script basically there was creating the criminal graph in terms of geometrical elements so you had access to the graph curve the hairs which are all the straight lines connecting to the curb and so on if I am lucky I will find it and I will share it with you guys but but I don't know I have to double check yes okay I what what do you want to do with it I it's not exactly clear but but anyway I mean I think it's extremely nice the configuration of the curvature graph the aesthetics you mean yeah exactly yeah yeah I am just an aesthetics thing yeah yeah okay okay if I if I found it I would be more than glad to share with you but I have to look for it I'm there it's quite if I don't remember wrong it's inside one very very old script so let me give me some times and eventually I will I will find it on the other hand there is the script array now the speed rail is is very important because it is a very powerful comment but in order to work with this switch away we must also perform some preliminary consideration so today we are not going to discuss the script array but we are going to take a step I don't know if further or back it depends on on how you want to see it but to me is a step forward because we are going to analyze these comment here which is the blend surface and this is going to be heavy ok so take a deep breath we have 15 minutes more or less but I will try to to be as effective as possible ok so what I'm going to do right now is creating two double curvature surfaces ok so I'm going to create a deformable plane like here and I'm going to copy it here on the right and then I'm going to activate the control point of this select them all but the surface and use a soft move common in order to create some curvature but for example in this area of the surface some curvature up like this and I'm going to do the same thing here take all the control point and use the soft move command but on this other side of the surface I'm going to create this deformation downward ok so I have two facing surfaces one has this bunch upward and one has this depression downward now what I want to do I want to create a connection between these two surfaces right we can do this in several ways ok I'm going to do it in the more effective ways which is by using the plane surface now the plane surface is like the blank curve remember the blend curve that we have used to create this kind of connections between our existing curves right where we could adjust the continuity level the desired continuity level that we wanted now this is exactly the same you have blend surface it asked for the first age which is this one and it asks for the second age which is this one and it creates this kind of nice connection surface how does it work when exactly like like the curves if I want position I get this simply straight cross-section connecting the two opposite edges it is like using a sweep to rail if you think about it because you have the two rails which are the opposite edges and then you have this line coming up from the blend which is basically a connection line created with the desired level of continuity now if I increase tangency tangency I get as a result this kind of continuity we're just two control points are involved which defined the initial tangent and the final tangent for our connection surface actually what we are creating is a connection a tangent control point all along the edges of the two existing surfaces so you see for example that if I confirm this and take a look at the topology of this you see that I have this line of control points and then I have another line of control points here at the bottom okay so of course as we are dealing with two-dimensional objects well sorry a surface is a two-dimensional object in terms of topology so it's a a two-dimensional domain okay of course this is a three-dimensional object right but it is in terms of topology it only has two dimensions because it has no thickness okay so when we work with two dimensions like in this case one single control points converts into a control point line okay it's like when we were working with kings and Kings lines okay here is the same so we have a blank surface that connects with tangency all along these two edges now let's make a few considerations here because this is very very important okay that's why I was saying we are taking a step forward because this common is very complex so the result that we get it's a surface that is basically touching the existing two with tangency continuity if we take for example a zebra analysis these simple analysis oh by the way this is flipped okay this zebra analysis tells us what level of continuity we have between the selected surfaces okay I'm going to adjust the mesh just with simple control in order to have a smoother aspect of our stripes okay so tangency continuity in terms of zebra analysis is represented by stripes that flow from one surface to another corresponding black with black white with white but tangency means that there is some angle between one stripe coming from one surface and the same stripe coming from the other surface so if you see this regular connection black with black but you see this break line then it means you only have tangent continuity okay so as you can see simple analyses give you the information of the type of continuity you have but this is visual analysis so it might be tricky because depending on the orientation that you will take for example like this it seems like that the stripes flows perfectly along this connection line but it is not so the zebra analysis you better move around and see if you get this kind of situation if you get this kind of situation at least from one point of view then it means you don't have a higher level of continuity then the visible one okay so we get a connection surface with several control point in this direction because they come from the original curve the original plane sorry and on the cross section we got four control points now when you create a surface like in this case with an amount of four control points let's take a look at the degree of this surface so if I try to rebuild it Rhino says we have ten by four control points and we have three by three you three which is basically the degree in the edges direction depends on the degree of the original surfaces right but the cross section degree which is in this case is B the pre one depends on the amount of control points and the amount of control points depends on the level of continuity that we want so if we sect tangency tangency we need two control points plus two control points for total and we get three as the degree in this direction what happens if I take let's copy this here let's get rid of this okay and let's repeat the blank surface between this edge and this edge now let's not visualize the interior shapes well no let's consider integration because it keeps us like a smoother connection okay but it doesn't affect actually it depends only if you want to have a local control over the the inner part of the surface okay and you see that the interior shapes are set in with all constants of each control point of your original surfaces this is what happens okay but it doesn't matter in this case if the important thing is another one so if I say for example curvature tangency okay now curvature needs one two three control points on the h1 and two control points on h2 okay so if I hit OK I get this surface here now this surface has this topology so it has 500 points in the cross-section direction but we flipped it quickly I just want to avoid the orange I don't want to take into account V U and V Direction okay so if I perform a similar analysis but now on this thing here I'm going to zoom analyze everything so you see that now even if I move around it's more difficult for me to let's say see here that I have some kind of breaking lines you see on this side because this side was connected with curvature continuity right so you see that the spread always for flow smoothly from one surface to another to the other one well in this case I still get this breaking line okay so in terms of civil analysis everything works perfectly right we were expecting this what happens if we analyze this surface and we take a look for example at this degree V is actually made up of 500 points but if we take up the degree it says for now this is something that it's absolutely problematic okay we said that we don't want to work with with degree which is higher than 3 normally okay and we are seeing that the blend common sets the degree according to the number of control point that's the only thing that you can do so when you define the amount of control point automatically you have a degree which is equal to the amount of control point minus one so you can imagine what happens if I take a blank surface between these and these and set these two g44 and eventually avoid some self-intersection along the way okay like this so if I do this I have an extremely continuous relation along 1 & 2 right but I have 1 2 3 4 5 6 7 8 9 10 control points in this direction okay so of course I get perfect smooth continuity between geometric continuity between these surfaces you see there is absolutely no possibility that some break appears along these stripes right but topologically I have a huge problem here because he finalized this from a topological point of view you see that I have degree 9 okay now the Green Line causes many problems okay where many problems means that for example let's see how can we quickly explain this remember that we considered these basic rules when working with control points right so initial tangent and interior tangency a flat portion passage through a point and so on right so here we are getting to a surface which has some higher degree okay so let's take a look at what happens no we're not with the surface because it's more difficult we should conduct a similar analysis each time that we do something let's do this with a curve right so if I take a curve and let's say I take a NURBS curve with one two three four five six seven control points right and I know that if I have a curve with degree three I can take three control points and displace them and be tangent to the line that connects these three points right so if I have this line prepared with with the right apology and I want this line to reach for example this height I can simply take this line take these three points and move them until they have exactly the same height of the point that I want right so it's a it's easy to produce some control deformation with degree three curves right what happens if i take another NURBS curve with degree but I'm not going to use the green line but but but degree five okay so I'm going to use the three five I know that I must provide at least six control points in order to maintain the degree five okay so I'm going to use quite a bunch of control points I don't even care about how many control points right but I have this curve which has degree five and I take this control point here let me get rid of the gumbo so I get this control point here I take three of them and I want to move them here now if I do this this thing you see that I think I am passing through this point on reaching the height of this point but I don't you see that the curve stops at a lower level than the level of this point so if I draw for example a line from this point horizontally I see that the control point of my curve is lying exactly at the same height of this intermediate point but the curve is not reaching this height this is because if you have a degree three curve he this enough to work with tweet control points and they'll line them along a line to have the curve tangent to that line but if you want with a degree 5 curve you need to align 500 points and even if you're lying for you will see that there is some very small difference between these two lines but if I take the fifth one then the curve becomes tangent to the line here exactly in the not contained between these five control points so if I for example try to use an insert not common so I can well can let me get rid of this point here let me hide it so I don't have anything any visible point but now if I try to add a note to this curve you see that here we have a not appearing this is the tangency point okay and I had to move five control points in order to make this curve be tangent to this line okay so if you think about this in terms of surfaces it means that you have no college achill control over a degree nine surface the amount of control point that you will need on a degree nine surface to produce some kind of control like this should be huge and basically uncontrollable so that's why it's preferable to work with degree three surfaces the problem is and we are going to discuss this tomorrow as the first thing now that we know how the blank surface and the blank curve also so also the blank curve works like this so if I try to blend this line with this one and I do for example this adjustable curve blank between DS and DS and I select G for and G for continuity and take this curve and analyze this with a rebuild you see that the actual degree is nine okay so the blank s it it can only work starting from the desired level of continuity it doesn't know what you want to do with the internal not vector the only thing that it can do is create a one span curved so there is no inner not in this curve with a full multiplicity not here so five control point here and another for multi basically not here so other five cuts at one here so it means basically that the degree is absolutely a consequence only of the control the amount of on short ones okay chat is it possible to have a curvature continuity between two surfaces deal at individual yes of course but not with the blank surface so the blank surface well think about it in this way okay if you try to blend surface this with this okay and you select tangency tangency you don't have curvature continuity right but use you have in this case a degree three surface which is what you want to get right so the moment you select curvature either along one or along two or in both cases you are increasing the degree of the surface in the cross direction so if I do this I will get three plus two control points and I get a for a degree for surface if I do this I get a degree five surface because I have three plus three five six one zero point degree five okay because this is a one span curve okay so the degree is affected only by the amount of control points now it it is also true that even if you select curvature curvature and you already have a degree five surface you have curvature continuity okay if I select g3 g3 I still have curvature continuity I have more than that but I still have curvature continuity okay so the blank surface and the black curve they don't allow controlling the degree because they only allow controlling the geometric property not a topological property okay so yes you can still have this but you you must perform something like this well let's do it at once okay so tomorrow we will start with another you want a degree three surface and then you take tangency tangency in order to create the first version of this connection okay of course it doesn't have curvature continuity but it is degree three okay and it approximates the connection with some higher level of continuity more than that you can also create this blank surface dynamically because you have access to the sections okay interior shapes with or without interior shapes you still have tangency continuity but the problem is that this line is basically straight and this line has very few curvature that is more curvature and so the tangency along the line 1 and line 2 can become very very very local okay so you still are capable of seeing some kind of sudden light variation which basically indicates the presence of a crease even if locally topologically you still have tangency continuity right but the presence of this thing here allows to distribute one interior shape with correspondence to each control point coming from the two opposite edges okay so if you if you have this you have access to a whole range of plane surfaces because you can simply change the shape of one section at a time and you can create a different blank surface also extreme blind surfaces like paranhos this kind of will be thing here okay but anyway you shape the surface as you please because you know that you are working with a point a degree three surface and you get the pretty preliminary saw okay now you want curvature continuity but you have a surface degree three with just four control points in this direction so if you want curvature continuity for example along h1 which is here on the left you need one control point here another control point and also the third control point here must be used in order to create curvature continuity along h1 if you do this there is no possibility that you have curvature continuity along h2 because you would need another two control points that you don't have okay so in order to have curvature curvature continuity you still must have six control point but a degree three surface so we created the degree three surfaces we still means the amount the right amount of control points so what are we going to do right now we are going to add a not line we have four control points we need six control points so we need to not lines okay so if I do this and I add a not line of course in this direction because I want another line of control points and another line of control points so I get these for example md's okay so now I still have a degree three surfing's but if I activate the control point I see that I have one two three four five and six okay so once I have these I still have tangency continuity here and here because I'm not changing the orientation of the direction of the first line of control points they still are danger but we miss the position of the curvature control point how can we do this as we were doing with the match comma that we were using here there is a match for the surface now I go into here surface tool and there is this is the blend and this is the match so what I want to do I want to match the untrimmed surface edge to change is here we have both edges so when I click here I must select not this edge which belongs to this surface I must select the other one which belongs to our internal surface so I want to match this edge with the edge of the surface to match which is going to be the other one and I want to match it with curvature continuity okay I don't need to preserve curvature continuity on the other end because I don't have a curvature continuity on the other end so I am NOT going to consider this right now okay so I simply say okay that's it now I have curvature continuity along this edge if I perform a zebra analysis between these two object I should see something like curvature continuity as I don't well actually yeah this is something very weird that's happening here because you see this kind of thicker in here this means that in this case we not there is not even tangency continuity okay so something I need something weird right now that I don't recall let me double check what I did with the match which is the only new operation that I did let me see if I did it correctly right so much surface I want to match this edge with the opposite edge so now I am considering curvature you see that actually considering curve yeah now it's now it's it's working so I did something weird before I don't know what but you see that now for example see this deformation here this deformation of curves because I'm taking the third line of control points and placing them well he is placing them in the correct position in order to have curvature continuity along these days and this part and of course this is changing the shape of our surface see what happens with these control points okay so this is quite a a problem right now so in this case for example if I don't want to affect the opposite end of the surface yes I must take into account to preserve the opposite continuity okay at least like this so this reduces the the formation of the control point but still you see that we have this kind of weird situation why we have this thing here it's because let me take a step back oh I think I did also the insert not thing that's why something weird is is happening so let me recover yeah this thing you see well when I was about to point out is that I place they not line very close to this edge here so M was create a span very small span another span here at the center and a very small span here this irregular span is actually bringing in the third line of control points way too deep inside the surface but I want for example this the surface to be curvature continuous with this edge here in in this area so I need for example to add a couple of not lines in order to have a couple of control points line close to that page and eventually another couple of not lines here so in this case I will have three control points in this area which will be used to create the curvature continuity and three control points in these areas which will be used to control the curvature continuity here in general I can do this because in general the original surface tangency tangency was already smooth enough with the edges and surfaces okay so in this case what I'm going to do I'm going to match this inner edge with this one why I get this weird result oh yeah nature speculoos this point yeah okay so yeah in this case this basically is due to the fact that my inner surface let me double check this this has this kind of orientation so red is moving toward the right premium white are oriented properly as you can see but I finalized this yeah you see that red and green are not in the same orientation okay so that's why the merging was happening in a weird way so in this case if I don't want to reorient the surfaces what I can sorry what I can do is basically tell vinyl to use simply the closest point for our Comment to work not taking into account the orientation okay so I can do this and I can also in order to be sure match the opposite edge you see that there is some change going on in this area preserving the other end curvature which is right now already a curve a computer continuity and you see that now we get a a disco breeze this surface is still degree three as you can see in the B direction and it has it should have let's double check with a zebra analysis it should have curvature continuity or you still have some artifact here and I know I don't know if this depend on no I think this is actually a problem a real genetic problem this is kind of weird I think it depends on the match I'm doing something weird with a match let me see if I can do it again like matching this with these I want to curvature curvature I don't want to do an average surfaces because if I do average surfaces it is going to match the two surfaces together also adjusting the shape of this one and I don't want to lose this this shape here no there is nothing wrong with this also I'm not refining the DHS so basically these values here are not being taken into account so you see average surface is also changing this one no it can be set properly I don't understand why this is creating this kind of strange result also I'm going to copy this and do let's go back to this one which should be tangent tangent at we double check if there is something weird happening already in the oh yeah it's the plane that is working he's not working properly yeah it's the blend in this case that it's creating this kind of a problem that's why the match is not is not actually working we get a problematic situation from the blend itself let me double check why so let's blend this this with this once again I selected tangency tangent seats it should be already enough let's see with the zebra analysis even asks ok now now it's working you can see that now if I move like this you see that there is black with black with some breaking line here okay so I don't know what I did before sorry about that but in this case for example I would eventually add not lines along this surface here like a couple of not lines like this I am creating a a regular spans as you can see so we get this and now I will match I will match this edge with this one matches by closest point so we can simply match corresponding points genetic points along the edges curvature curvature and then match this edge to this one with curvature curvature as well so eventually now within signal analysis we should get double continuity but we still have some tangency going on here now on them yeah you see that there is some breaking going on still but at least we don't have yet but it's very smooth on this area but at least we don't have this kind of g0 continuity as you can see so this is the way that you basically adjust the continuity with the degree so the bend engine is not affected by the direction of the surfaces a ancient sea tangency will be less angel error I don't know but you said it is a little bit strange when we are doing the zipper analysis yeah zebra analysis I wouldn't rely on the zebra analysis one how can because because it's visual analysis but regarding your question being is the surface orientation important for the continuity properties of the blend no because tangency is a genetic condition before being a topological condition so if you want this new surface be tangent to the adjacent one this surface will have its control points it's line of control points created in order to keep tangency and oriented according to the direction of the surface which responses to the first control point of your new blank surface so the orientation is not important in that case but it can affect some some operation like for example in the match as you saw because the match tends to consider that of the edges in topology the match for example also has some kind of options that are based on edges in topology like for example if you take a look at these preset of Ice Cube direction now as a good direction to to someone that doesn't know the real meaning of a circle means only oh okay I want this black line to correspond to this black line but we know that if we preserve isotope direction we are talking about knots spans and so on match target isotope direction also it depends on the actual surface ice cubes or target isotope direction okay so this this basically depends on adjust this basically says that you want to set the geometric property but also taking into account the topological property of the surfaces there are involved okay so there are operations that depends also on topology and operations that do not depends on topology there is one particular comment that I don't know if we are going to talk about it because it's a very strange which is the patch that works in a totally free way but suddenly it allows to adapt to exactly the same topology that you have for let's say an underline we were eventually we were going to see these because is the only way to control somehow the topology of a patch surface but anyway it's a very strange comment it's very unlikely that you will use in your production processes other questions okay quick off-topic question how do you sketch in Rhino with the marker pen never beat never we do you are talking about the marker pen that I was using to underline some things it is not from Rhino it is from the zoom platform so I can create annotations with this thing here okay but it is this is not mine this is the zoom platform that allows to do this okay guys are there any you're welcome Jose are you any any other questions I have to yes I know wait wait wait wait wait wait Beto he never asks anything okay in the previous case is it possible to okay what do you mean by blend or merge what is fonder in this case because if you want to join them you can do this I cannot read the question no you don't but I don't but I do ah okay Oh funky superficial okay I think this is merge merge surfaces so it's this this thing here now yes you can do this but also consider that if you merge these with piece you are taken into account for example smooth yes tolerance zero zero zero one you are not taking into account the the initial topology so for example you can always merge theme but you need to adjust the topology previous to this operation because for example if you have let's say that we do things in the worst possible way so we create for example a blend like from here to here we position position right and we get this now you can merge surfaces you can still use the merge command in order to merge these two here and to merge these two here and get to us one single surface but this change of direction in in this area it's harder than this one because here we tweaked the continuity before the geometric agility before merging the surfaces while here don't so in this case you get always a smooth surface but with a less smooth aspect let's say it so one in this case you can take perfect smooth result if you deal if you do things properly ok and this is important in Casey you are doing this because you want to work with one single surface this is an important step but I do recommend that you don't get rid of the original surfaces so always maintain at least I do not know man that you maintain at least this and this the inner one can be also always recreated with a blend but always keep these two object here safe somewhere before merging them because when you merge everything you don't have access to the original surfaces and eventually you don't that you are you won't be able to recreate this kind of connection now this is also a very simple connection right so eventually if you want this mood aspect there is no need to keep the history of your modeling workflow but if you work with something more extreme like I don't know blending these with these in order to create something like something like a wavy behavior like I don't know taking this point and doing something like this and something like this oh I cannot do this because this will create some self-intersection but I can take eventually the third control point and move it away from no what did I do okay let's reset everything but this is quite complex because we have a symmetric or anti-symmetric surfaces so let me let me do this this way okay so that would be clearer so I'm going to take the straight done before you finish the explanation could you repeat quick the question so we can follow ah the question was if it was still possible to merge the surfaces and merging the surfaces gives us as a result one single surface one single continuous surface instead of three separated surfaces or 140 surface okay so the the goal is to have one single surface in order to perform an easier topological operations okay but in this case I wanted to point out that it's important to save the inputs before merging surfaces because if you perform some some let's say complex blend operation okay like this and and you create some let's say complex scenarios like this one well this is not a not so regular if I remove ages and I only add a shape like here in the midpoint for example like here now I have control over one a single cross-section besides the initial and last first section so let's say I think I create this blank surface here okay which is quite complex already and it's very difficult to recreate it okay unless I know exactly what I was doing so before merging things I would save these two before merging these these surfaces because once you merge them okay you get one single surface which is perfectly continuous not continuous along this connection pages okay so you should eventually go back and do undo undo undo until you get back to the original surfaces and eventually they will repeat the plank okay so I do recommend that that when you merge things you always save a copy of the original object that you are merging okay you're welcome and one consideration we are merging but if we take into account the topology it's important to double-check that you don't have control points coincident with the ISO curves because this would mean a king you see that merging creates a perfect smooth connection that was that that was what I was saying right now so it means that you have no internal discontinuity along this this surfaces once they are merged okay so it means that this is one unique surface flowing in this areas okay very important okay so it means that you completely lose the original objects okay once you have this kind of smooth it's like when you extend a a line so example if I have this this line here and I try to work with an extent common you know that the extension can be created with several options if you create any extension like straight extension art extensions you still have the possibility to go back to the original curve but if you use a smooth extension I am going to point out the position of the actual end point if I extend this curve and also the position of these control points here okay if I extend this curve with a smooth extension like this you see that I completely lost the previous end point and together with the previous end point I also lost the correspondent control point so if I do this is somehow like merging two surfaces I completely lost the original input okay so when you when you create some some smooth continuous geometry you always lose the original one so pay attention then and create a copy if you don't want to lose it okay like in this case now I have a copy here so I I didn't care but you see that we have reached to a totally new object okay any other questions I can do this last yeah so it yeah don't go to channel okay so basically the first one is just something that I was thinking follow with the direction a like I feel like that rebuild the rebuild common and the rebuild not uniform and repeat are quite similar on the behavior and yes yes just because of the speed is the only difference the tolerance that you cannot controlling the rebuild about you when or is something well well it's only the tolerance is like the tolerance is not important but tolerances is very extremely important so let's say that you have this kind of very complex shape like this and you have two options as we saw which is basically we feet and we build on uniform so if you do this you have access to request the tolerance and you give more or less more or less 35 control points more or less what maximum actually and eventually the common can use less control points and depending on the on the tolerance you might or might not reach this amount of control points and they are distributed more densely along the curve where you have more curvature okay so if you on the other end if you refit this it asks only for yeah it does for for 15 tolerance the degree that you want you see that there is no control over the amount of control points okay so in this case you see that you lack some some information you see so you have no control over the control points so you the risk is that you get a completely different topology now remember that the amount of control points is also important because it determines the amount of knots and the amount of spans so if you don't control the amount of control point the risk is that you get different set of spans between two curves and if you want for example to work with I sweep two rails you should have the an equivalent topology for the two rates in order to avoid twisting of the of the of the surface and different speed along the ways okay so it's important to consider the right common between rebuild non uniform and we feet it depends on on the type of work and the type of work flow that you are into if you are working for example with in a sweep two rail I would recommend that you rebuild non uniform because this gives you the possibility at least to control more or less that two different rail will receive more or less the same amount of nuts and and therefore of spans okay while if you work with the repeat you don't know how many control points and spans you will have okay so the difference is in between tolerance amount control point spans and therefore the ball weighs Oh and the other last to question the first is really quick a unite you mentioned a type of su phrase that is the only surface or I don't know if it's the only Bible so phrase but it depends on the degree depends of on how many cultural balls you have what was the name of that soup race it's a blank surface okay so it's only the plain service that the nicer case for how it is created it only deep as it creates a single spam surface as the blank curve it only creates a single spanker so the moment you create a single spanker the amount of contra points only affects the degree okay that that was read clear and they in the last I mean now going a bit low with the level because we spoke a lot of things really deep if I opening grasshopper day a curve for a editor and then you go under spline from tight I understand that spline is the category that contain both NURBS polyline and interpolate curve was actually actually actually if you go here which what point curve okay and you yeah yeah but if you go here control point curve and you are going to create a spline right actually you are deliciously a tiny nerves which is a basis spline non-uniform rational basis plan okay and if you change the agree to one you are trading at 49 which is an applying okay so that's why you will find all the the types of curves of free form curves inside the supplying group so it's correct to say that the only difference is the degree know the only difference if the differences are the degree the amount of control point and I don't know the sector now they are always together district they always always always together and you can work with two simple comments like this one's here for example that each time you use for example enormous curve you are assuming that you want a uniform for it not vector for example if you take the NURBS curve you are off you are only asked for vertices which are concha points and degree it automatically builds the not vector like a uniform not vector okay if you want to work with the not vector there is the other NURBS curve common which is the PW key which asks for control points and not vector okay the degree is automatically set to three because this is the default degree of course and the interpolate one it can only generate polyline right the interpret is this one yes no this generates a is a smooth curve if you give degree carry each other yeah yeah okay so that's said that's it for now he gay okay questions are more than welcome guys you
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