使用转换矩阵将圆柱体转换为圆锥体

Question

Working on my OpenGL ES 2.0 based graphics engine I have the following mathematical problem:

Using the algorithm for creating cylinders described here http://paulbourke.net/geometry/circlesphere/ one can create a generic cylinder mesh. I use only one cylinder mesh for all my cylinders in my application. Trough scaling of the cylinder it is possible to create new cylinders with different radius and height without altering the standard cylinder mesh (r=1,h=1).

For cones I currently create another mesh, but I had the idea that it must be somehow possible to transform a cylinder into a cone using matrix manipulation. Ideally it should be possible to create also a cylinder with a specified r1 and r2 (for the standard mesh r1=r2=1).

Any ideas how this could be possible ? I thought about a perspective matrix, but I was not successful.

Answer 1

Technically is is possible to make a truncated cone from a cylinder using projection transformation. But you must consider that projection maps vertices in to normalized device coordinates (ranged from -1.0 to 1.0). Moreover the projection transform may be not enough in case when you define your shape out of identity frustum, so you will have to use additional camera transformation as well.

Actually, you can try to bake (somehow) your main camera transformation & projection. Just place your cylinder at the certer of view area, orient its Y axis along Z axis of camera, set up appropriate FOV and bake all the transformations (including world transformation of cylinder). By multiplying all these matrices you will receive ransformation of cylinder in to a cone in normalized device coordinates.