Rhino3d Transition Surfaces – Managing Shape and Continuity - Video Transcript

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In this video we're looking at creating and controlling transition surfaces in Rhino.

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Rhino3d Transition Surfaces Video Screenshot

Hi, this is Phil from Simply Rhino and in this video we’re going to take a look at creating and controlling transitional surfaces.

The transitional surface in this example is this blended section between the body side and the outer edge of the wheel arch. When we create a surface like this we are generally interested in not only controlling the shape of this surface, and this shape may change as the cross section moves from end to end of the wheel arch but we’re also looking at controlling the matching at either side of the new surface, so that we can produce an end result where we have a seamless match and a shape that we are fully in control of.

Before we look at ways of creating the transitional surface let’s first take a look at the ways in which continuity is both expressed and evaluated inside of Rhino. The simplest type of continuity is G0 (Zero) or Positional Continuity. This simply states that the edges of our new surface highlighted here will be within the absolute modelling tolerance of the edges of the existing surfaces so that we should be able to join these into a watertight condition. If we want to check for a watertight join we can first join the surfaces together, highlight them, go to our analysis tools, edge tools and show edges. If we only select naked edges and choose a nice bright colour for example yellow here, then the absence of any yellow along our edges here shows us that they are joined within a watertight condition. If we have a look at this surface with an environment map we’ll see that beyond the joined edges there’s no further geometric continuity so we see a very noticeable edge here. Where we want to check for conditions like this where we only have positional continuity we can use the Zebra tools: Analyse / Surface / Zebra. Where the Zebra stripes don’t run into each other, like this, then this shows us that we have at best a G0 (Zero) positional continuity.

The next step up from Positional G0 (Zero) is G1 Tangent Continuity. This starts with the premise that the G0 condition is met and adds to this the fact that the tangent direction of the adjacent surface edges is the same. This has the effect in this case of changing the shape of our transitional surface and you can see that we have a much smoother transition between the body side and the outside edge of the wheel arch. We can check for tangent continuity by using the Zebra tools and where the Zebras actually run into each other this is indicative of tangent continuity. However you’ll notice that across the curve edges there is a sharp noticeable kink or change in direction of Zebras and this again is indicative of Tangent Continuity.

The next step up from G1 Tangent Continuity is G2 Curvature Continuity this starts with the premise that the G1 Tangent Continuity is already met and adds to this the fact that as well as the tangent direction of the adjacent surface edges being the same then the radius of curvature at the edge of the surfaces is also the same. So we have a smoother transition over the surface edges. When we look at this with the Zebra tools we’ll see a subtle change in the Zebras. What we’ll see is that the Zebras still run into each other but we’ve now lost that sharp kink over the surface edges. We’ll still see that there’s quite a quick change in direction here by the shape of the Zebras but you can see that this is now much smoother.

When we look at this in terms of the reflective qualities, for example if I add an environment map to this again we’ll see a much smoother result. Sometimes the difference is quite subtle between a curvature continuous match and a tangent match, but we should be able to compare these two and see a slight difference. So if I go back to the tangent match you can see here that as I play across this surface we can see little areas where we’ve got quite a noticeable change in surface direction there.  So the tangent direction is matched but the curvature is different and this represents itself as this slightly harsher highlight. If we look at the same position here and look at this harsh highlight down here with a curvature match you’ll see this is much softer so as we play across this edge that transition is much softer and if we were to use a slightly different reflection here such as a fluorescent tube for example then we’d see a bigger difference. Here across the edges is where you can see the bigger difference with a tangent match so what we actually see on the zebras is something akin to the reflections. Now this reflection map that we’re using here, the fluorescent tube, is a very good tool to use to actually check the shape of the blend as we create this.

So now we’ve looked at actually what these basic geometric continuities are then let’s take a look at how we can create surfaces in Rhino whilst matching the tangent. Let’s take a look at how we can create these surfaces in Rhino, control the shape and match the edge conditions at the same time.

A relatively simple way of creating a transition surface between these two existing surfaces is to use the Blend Surface tool. From the Surface menu we go to Blend Surface, I have got some Command line options here, which I’m going to leave at Default, then I’m going to pick the two edges in question. Then I’m going to Enter, or right click, and I’ll get into the preview mode for the tool. So the Blend Surface tool is an interactive tool, it’s slider based so I can move these sliders to change the end bulge and therefore the shape of the blended surface and I can also set a different continuity on for example edge 1 than I have on edge 2. Now this tool also gives me the ability to use edge matching beyond the G2 curvature matching that we looked at earlier on in the video. So for example if I set edge 1 to G3 or flow continuity you’ll see that we get another control point here and the analogy here is that if you consider the G2 blend on this side being analogist to a degree 3 surface so that there is a curvature continuous transition across this edge then the G3 match on this side is analogist to a degree 4 surface so there is a constant rate of change of curvature going into the blend and then a G4 match will have a constant rate of change of the rate of change of curvature so it’s analogist to a degree 5 surface. Now the position, tangency and curvature matches can be considered absolute and are measurable. The G3 and G4 matches can be considered as being aesthetic improvements over the G2 curvature match so there is not a way in which we can analyse these and say there is definitely a G3 or G4 condition. So the best way to look at these is with the environment map tools. If we go back to looking at the slider based tools we can lock both of the sliders together here and control the end bulge of both edges at the same time. With surfaces like this we’re probably looking to have less of a S shape that we would have at the default position of 1 and maybe more of a taughter surface here. Now when we do this using the slider tools alone what will happen is that we’ll get most of the shape right across the majority of the blend but where we have more local shape change going on at the ends we might actually compromise the shape at the ends by merely using the sliders. So we can also use these handles that we get here and these allow us to adjust the shape locally by moving the control points on the handles. Now these handles are set up so we can move these points without changing the inherent continuity across here and we can also should we wish add more handles along the blend so we can add more local shape change. Now you might want to avoid adding too many of these because the blend shape might become more complex but in this case for example then it would be a fairly obvious place to add another handle might be at the top of the blend here. So we do this by adding shapes, make sure here that we’ve got the perpendicular snap on, maybe snap to a mid snap on one edge and find a perpendicular point on another edge and snap to that and this gives us the ability to add a handle. We can then for example say that against edge 1 you might want to step up the continuity and then we can start to play a little with the shape change here. So maybe I’ll just slightly raise this shape up a little here and certainly up here maybe give this blend a little more room to work in so I’ll just give this a bit more shape here. Now you may need to do this iteratively by closing the blend tool and then looking at the result with the environment map. One of the things you’ll see with this shape is that when you step up the continuity here from G2 to G3 is that it just means that the shape transitions a little better into the side of the wheel arch. Typically things to look out for here is that we get a constant or a fairly good progression of this highlight as we move down the wheel arch here, we kind of want to see the same thing going on in the back. Now we can see here we have a little bit of trouble going on here where the surface maybe got a little bit of a ripple in it here. One of the reasons for this is that we’ve got a shorter gap here in which to create the bend than here and at the top of the bend so this is an area that needs work here. Now we would go on and do more with the blend surface tool but another way that we can do this and possibly a preferred way might be to use the two rail sweep tool.

The two rail sweep tool will give us a nice taut surface that generally is free from local inflections. Now if we use the two surface edges as our rails then we first of all need to put in some cross sections and a very useful tool in creating these cross sections is the adjustable curve blend tool. This is found on the curve tools here and it’s ‘Adjustable Curve Blend’. For these edges here we can just click up on the surface edges and build the appropriate surface blend. Like the blend surface tool this tool has the ability to match up to G4 and I’m going to pick a G3 match here on the curve that goes into the wheel arch outer and G2 curvature to match to the body side. Again I can adjust these handles whilst the tool is live without fear of losing the continuity. So I can add another blend here, swap the edges around here, and this is kind of where I want to just add a little more shape to this blend, it was a little bit too flat before which is why we were getting the ripple in the surface at the end. Gradually nudge this curve round, take a look at that. If we want to add additional cross sections in the centre here we can do this fairly easily now it may be helpful here to draw a straight line first of all and take this straight line from for example a mid point to a perpendicular point. Next up we can use the adjustable curve blend tool again but this time we can use the edge option and we can pick anywhere on these edges and then slide the blend into position by snapping to the end of the straight line and then I can go into the appropriate blend here and start to adjust the shape of the blend. So with this we want to keep the shape of this blend quite flat at the top here. Ok once I’ve got my cross sections set up I can then run the Sweep 2 Rails tool – pick the two rails and then pick the cross sections. I can match the edges for curvature here, just because we have the 3 curves already set up to match for curvature doesn’t actually ensure that our edges will match for curvature here so adding this will help to ensure my edges match correctly. There’s a maintain height option here on the sweep like there is with a lot of the tools here but you can see that in this case it’s making a small difference but let’s have a look at what it’s doing down here, yes it’s making a very small difference here so I’ll leave that off for the moment and let’s just have a look at how that looks. Again we’ve got not a bad progression of the highlight here, let’s have a look at what happens on the back, again the back now is slightly better you can see how this shape now progresses better and I think we’ve lost the crease here. You can see that as we go up the wheel arch here the shape gets tighter here and then it gradually smooth’s out here so we get more definition if you like in this corner here at the top of the wheel arch and then we lose that definition as we go down the edges and this is a way of removing that kink in the surface. So again this may be something of an iterative process in using two rail sweep but it’s a very controllable process and it will give us a very taut surface that is free from local inflections. It’s always helpful to look at this in a rendered mode as well with a reflective material, I’m going to match the material of my blend and it’s helpful as well to add context to this because then the shape and the form that you are looking at when you see this in context it all makes a lot more sense. So use any of the surface analysis tools here until you are happy with the result. The idea with these tools of course is that we want to create a surface which is not too over complex.

Another potential solution is to use Network Surface. Network Surface is generally better suited for surfaces where we have a lot of local shape change and undulation and is less well suited to the type of surface we’re trying to create here. If I use exactly the same set of curves that we used for the sweep two rail example let’s see what we can do with network surface. So it’s Surface and Curve Network and we pick the four boundary curves and the one interior curve and enter. Now Network Surfaces allows you where possible to match to all the boundary edges but of course we’ve only got two surfaces here, D and B, to which we can match curvature continuous. If we preview the surface you can see that unlike the sweep this produces a very complex surface because this fits the edge curves to a tolerance and although we can slacken off the interior curves here we still end up with a very complex surface and you’ll see that if I add another decimal place here and preview that my surface becomes even more dense. So I run the risk of not being able to join these edges together yet still have a complex surface, part of the problem of course of having this complex surface is that we’ll get undulations across this surface. We can see this is if we go into our environment map and we choose our fluorescent tube result, you can see here that with exactly the same set of curves that we used to create a quite smooth swept result that here we have particularly around this area here we have a really nasty looking surface. On an average it’s not bad around the top here but when we look closely at this you can see we’ve got some issues around here. So the fact that Network Surface produces this dense topology that isn’t necessarily that well related to the overall shape means that it’s a great surface for things like terrain and objects where we have a lot of local shape change but it’s not a good surface solution for something like this where we want to have a simple taut surface that produces a very clean result.

Another way of looking at this and particularly if you wanted a single span surface as a result of creating the transition surface is to make sure that both of the edges that we’re working against here are untrimmed edges and that this cross section and this cross section have the same number of control points. So here we’ve got an adjustable curve blend that is matched for curvature continuity at each end and we’ve got surface edges that are both untrimmed. These surfaces are both degree 5 as well with the minimum number of control points. So to build a single span surface across here we can use 2 Rail Sweep and we can build this and then turn on the simple sweep. The simple sweep will, if the geometry permits, allow us to build a surface that has the same number of control points as the rails and the cross section. In this case it will produce a surface that’s degree 5 with 6 control points in both directions. However when we use simple sweep you’ll disable the matching options, so for example here when you look at this with an environment map on we’ll see that we’ve lost the matching here. The matching though is something we can recover using the surface tools, so we can go to Surface Edit Tools and Match and we can hit the Multiple Match option and we can choose the surface to change, which is the wheel arch surface that we’ve just created and the surface to match to, which is the body side, and then Enter. Then we can select the next surface to change and the next surface to match to and enter and then when we’re done with the edges we can enter again to get into preview mode, we can choose curvature continuity and as long as we don’t have refine match turned on here we won’t add any control points when we create the matching. Now because our surface edges were already close enough to each other we should be able to actually join the result of this into a watertight condition and we should also have a solution that looks pretty smooth. Now it should be said that it’s quite difficult to produce both of these surfaces as single span surfaces to start off with, so this would only be the sort of thing you would do if you were entirely certain that you needed a surface with a minimum number of control points here for the wheel arch component.

So from the solutions we’ve looked at perhaps the blend surface solution and the Sweep 2 Rails solution are the most appropriate solutions on this case. The single span solution probably requires too much effort to produce a surface that is anywhere near as good as the sweep 2 rail example we have here and the network surface solution simply doesn’t produce a surface with the desired continuity. So this as I’ve said is the Sweep 2 Rail solution that we looked at earlier on, it’s a fairly quick and reliable method of creating a smooth transitional surface.

I hope you’ve enjoyed this video and please look out for further tutorials in this series.

 

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