Hello all,
I started working in 3D mesh parameterization (mapping a triangle mesh from 3D space to 2D space ). In this study, what i know is that we have 3 criteria to measure the parameterization distortion: 1) isometric (length preserving), 2) comformal (angle preserving), 3) equiareal ( area preserving).
Suppose that we have a function mapping F from 2D to 3D. The distortion using above criteria is calculated using derivatives of F in each triangle ( singular values of matrix Jacobian of F ).
Because the area of a triangle can be calculated using its base and height. So, to measure distortion of each triangle, i will only compare the height and the base of this triangle in 3D and 2D. What is wrong if i measure the parameterization distortion by this simple way rather than above complex methods?
Thank you so much for all explanation!
Hoping this doc helps u. Good luck.
http://people.eecs.berkeley.edu/~jrs/meshpapers/ShefferPraunRose.pdf
Dear Van-Toan Cao,
I hope this article to be helpful.
Best Luck
Khaled
http://www.mrl.nyu.edu/~dzorin/geom02/lectures/lect09.pdf
Dear Van-Toan Cao,
I think I cannot help you, but I have one question for you: are you just interested in triangles or also quads?
best luck
Filippo
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