Question

Hi
How can I extrude cut (like solidworks) a 3D model?
Is there an easy way or I have to do some complex calculation?

Answer 1

What you want to do is part of a discipline called Constructive Solid Geometry (CSG) and it’s about one of the trickiest subjects of 3D graphics and processing. There are several approaches how to tackle the problem:

• If you’re just interested in rendering CSG in a raytracer things get actually quite easy: At every ray/surface intersection you increment/decrement a counter. CSG combinations can also be transformed into surface count. By compariring ray intersection counter and CSG surface count you can apply the CSG operations on the traced ray

• If you’re interested on doing CSG on triangulated models, the most common approach is to build BSP trees from the geometry and apply the CSG operations on the BSP. Then from the resulting BSP you recreate the mesh. This is how it’s implemented in mesh based modellers (take a look at Blender’s source code, which does exactly this)

• CSG on analytical surfaces is extremely difficult. There are no closed solutions for the intersection of curves or curved surfaces. The best approach is to numerically find a number of sampling points in the intersection and fit a curve along the intersection. This can get numerically unstable.

• Tesselation Phase Processing (this is what I implemented (or even invented maybe) for my 3D engine): When rendering curves or curved patches on 3D hardware, one usually must tesselate them into triangular meshes before. In this tesselation phase you can test if the edges of a newly created triangle intersect with curves/curved surfaces; use a few iterations in a Newton zero crossing solver to find the point of intersection of both curves/surfaces and store this as a sampling point at the edge for both patches involved (so that the tesselation of the other surface will share its vertices’ positions with the first surface). After the first tesselation stage use a relaxation method (basically apply a Laplacian) on the vertices, while constraining them to the surface (remember that your surfaces are mathematical exact and it’s very easy to fiddle with the variables of the surface, but use the resulting positions as metric). It works very well as long as not intersections with ordinary triangulated meshes are to be considered (each triangle of the mesh had to be turned into a surface patch, slowing down the method)

You tagged this OpenGL, so to get this straight: OpenGL can’t help you there, as OpenGL is just drawing triangles, not processing complex geometry.