- #1
7thSon
- 44
- 0
Hi,
I have a limited background in differential geometry. I have a problem involving a surface mapping (from R2 to R3) which does not have a square Jacobian. I understand that for a mapping of preserved dimensionality I can compute a matrix inverse which will allow me to map tangent vector coordinates from image to domain or vice-versa.
i.e. S = (x(u,v), y(u,v), z(u,v))
I have come across some sites online that seem to cavalierly stick a column [0,0,1] and then invert, and/or utilize a matrix pseudoinverse to define an inverse for this mapping.
My question is what the heck are they doing and why? Do these pseudoinverse methods have any properties that make them useful? Perhaps my understanding is limited because I don't understand what the inverted tangent vectors mean in the domain space?
Sorry for my lack of background and thanks for any help :)
I have a limited background in differential geometry. I have a problem involving a surface mapping (from R2 to R3) which does not have a square Jacobian. I understand that for a mapping of preserved dimensionality I can compute a matrix inverse which will allow me to map tangent vector coordinates from image to domain or vice-versa.
i.e. S = (x(u,v), y(u,v), z(u,v))
I have come across some sites online that seem to cavalierly stick a column [0,0,1] and then invert, and/or utilize a matrix pseudoinverse to define an inverse for this mapping.
My question is what the heck are they doing and why? Do these pseudoinverse methods have any properties that make them useful? Perhaps my understanding is limited because I don't understand what the inverted tangent vectors mean in the domain space?
Sorry for my lack of background and thanks for any help :)