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# Spline cage mathematics

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Hello all, I am working on a modelling application written in C# and using DirectX 9. I have got various features working such as parametric curves and surfaces. To make it useful, I need to implement a spline cage definition of a surface. I have two questions: 1. What kind of splines does 3DS Max use when one defines a "spline cage"? It looks like a spline cage is made up of Bezier curves, which can be degenerate so you can have a straight line and curvature discontinuties. However, I am wondering if it's more general and permits a spline cage to be composed of different types of spline. Is the underlying spline type actually NURBS? 2. Does anyone know where I can find a mathematical treatment of spline cages and the conversion to a surface? My problem is that I can easily see how a patch can be bounded by 4 curve segments, but I'm not sure how a patch can be bounded by 3 curve segments. I am guessing that two of the corners have the same position, so that the patches bounded by 3 curves are really degenerate patches bounded by 4 curves. Is this right? thanks for any pointers Tom

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Ok, I think I found out what I'm after: a surface bounded by 4 curves is a Coons Patch, and more generally, when bounded by 'n' curves it is a Gordon Surface. There is precious little information about these constructs on the net though...

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