Projective Geometry

With the new Blender Python API, do you think it would be possible to implement projective geometry? I would like to project a spline onto a mesh and create a spline from that projection. I have referred to this site as an example in some of my other posts, but this is what I would like to do in Blender: I will code it if I can. I just need help on some of the hurdles. I am currently looking into a geometric algebra, or Clifford algebra method of doing so.



I can live without the implementation of Geometric Algebra in Blender, but is it possible to create a curve or line above a mesh and then project it onto the surface. For example, a curve like a circle in the XY plane above a hemisphere projected onto the hemisphere in Z? Thanks.


There’s something called Retopo in the CVS that’ll fix that for you, it lets you draw meshes on the surface of other meshes, primarily used for re-making topology when a mesh is done without affecting the shape, but it’ll work for what you want, too.

You can with a script project(not really)a set of points(one mesh) to another ones,finding the nearest points(and for this you should use cambo’s octree that work very well).It’s not a real projection,but give result acceptable(at least if the mesh have many vertex).
Or you can use the intersect function to find the intersection(given a set of points and a direction(along the normals for meshes,or an arbitrary direction for curves) you can construct a set of line that can intersect with a face,but it’s slower)

BlackBoe: Is the retopo CVS build one that is already a binary for Windows?

renderdemon: I’m not sure I understand your references, but I will do some diligent forum searching when I get home.

Thanks, all.


I’m back. I did some searching through the forums and octree and cambo did not provide useful threads for me to understand your tips. I am sorry if I am thick headed, but can someone point me to more octree stuff or how I might project a series of curves made of small line segments onto a very fine mesh (2000L x 2000W vertices average)? I am at a standstill.


Retopo is a CVS tool, it works wonders, yeah. :]

How do I obtain or otherwise use Retopo? I can’t find it anywhere. Is it a script or a separate build tree of Blender? Any examples would be appreciated. Thanks.


don’t know if this will help but it’s a script to project verticies onto faces.

Thanks a lot. That may work. I’ll try it when I get home from work, and reply with the results.