How exactly is the Jacobian used to estimate this area? I'm having a hard time understanding the math going on here.
sebzhao
Is the Jacobian being used to estimate the size of the square so that you can have a mapping from screen space to texture space?
llejj
For anyone who's wondering why the Jacobian is being used, I found a chart on wikipedia that explains it pretty well. https://en.wikipedia.org/wiki/File:Jacobian_determinant_and_distortion.svg
SKwon1220
@sebzhao I think you're right about that. Correct me if I'm wrong, but I believe the Jacobian is telling us roughly the rate at which (u, v) needs to change with respect to the (x, y) plane from the mapped point in texture space to capture the same area that the screen space encapsulates in texture space. Perhaps a member of staff can chime in on this for comfirmation!
How exactly is the Jacobian used to estimate this area? I'm having a hard time understanding the math going on here.
Is the Jacobian being used to estimate the size of the square so that you can have a mapping from screen space to texture space?
For anyone who's wondering why the Jacobian is being used, I found a chart on wikipedia that explains it pretty well. https://en.wikipedia.org/wiki/File:Jacobian_determinant_and_distortion.svg
@sebzhao I think you're right about that. Correct me if I'm wrong, but I believe the Jacobian is telling us roughly the rate at which (u, v) needs to change with respect to the (x, y) plane from the mapped point in texture space to capture the same area that the screen space encapsulates in texture space. Perhaps a member of staff can chime in on this for comfirmation!