biVector forum

Projections of quadrics and conics onto a plane

Despite being a beginner in geometric algebra, I’m finding it to be a great fit for navigation.

I have found that I can apply most ideas without trouble (largely thanks to this forum and the coffeeshop on Github), yet one important piece still hasn’t fallen in place. While I have explored the 3D projective GA and conformal GA, I have not yet found how to project a conic (circle or ellipse) in 3D space (really, it’s a flattened, degenerate quadric) onto a camera image plane, which should be an ellipse. I can do this in 3D projective space with regular vector algebra, and can do it in the 2D case with points and lines, but the 3D case eludes me.

First, is 3D CGA appropriate, or do I need the QCGA?

Any thoughts on the general direction or any specific papers?

Thank you!