Solutions to project a flat reference spline on a curved, sloped surface
by, 03-30-2012 at 09:25 PM (3050 Views)
This blog article contains two different solutions to a question posted by "Gaby424" at RFO, at this post. I found the question very interesting, and decided to study a solution. The challenge is to find a method to project a spline that is designed flat at the reference level, onto a curved, sloped surface.
The projection needs to meet two requirements:
1) The resulting 3d spline must be hosted at the surface, and
2) The resulting 3d spline must be similar to the original spline.
Notice the word "similar" in Gaby's original specifications. Later on, I learned that Gaby really meant to say "exact". That is the reason why this blog contains two different solutions.
- The first solution produces a projection that is very similar to the original.
- The second solution produces a projection that is exact.
Gaby says that the application in 'the real world' is to obtain a host for some elements of a bridge. Maybe railings, maybe beams, maybe something like the path of this railing on a bridge? I don't know exactly.
In the first solution, I found a way to project the points that define the spline to the curved surface, by selecting the points from a top 3d view, and using Pick New Host using the cursor to find a point on the curved surface. This method does project the points on the surface, and then, I can use the points to lift the spline from the reference level to the surface. However, if we zoom in really close, there is an imperfection; a very small gap between the original points and the new points at the surface. Therefore, in summary, this method creates a very approximate projection. Maybe a 95% accuracy? Let's see the first video:
This second method provides a 100% accuracy. Here, we copy the spline from the reference level to a second level, and connect the lower and upper points with vertical reference lines. Then, place points at these lines, and use "Host by intersection" to find the projection of those points at the surface. Then, lift the flat spline to be hosted by these new points. Let's see the second video:
Another example of how important it is to define specifications with precision. Did you say "similar" or did you say "exact"?
See you in our next blog...
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