yys123456 / arap-deformation Goto Github PK

This is a dirty implementation of As-Rigid-As-Possible Surface Modeling (SGP2007) using uniform laplacian

Use local/global method to optimize energy at each vertex i:

local optimization (fixed p' (known) to get best R1,...,Rn, use SVD decomposition to construct each Ri):

for each i to optimize this (let pi - pj = eij, p'i - p'j = e'ij):

so we need Ri=Vi*transpose(Ui) to let the stuff in (...) to be semi-positive definite symmetric to make its trace maximum, and Ui, Vi is the SVD decomposition of: (note that eij is the edge on the origin mesh, no matter how many iterations)

global optimization (fixed R (known) to get best p1,...,pn by solving a linear system), take the derivative of (1) and assume R as constant, we can get i-th equation of the system:

solving p' and R alternatively to get the best solution of p'.

Work in vs2017 release mode, after hitting the generate solution button, shader files need to be copied into x64/Release to make it work, use command ./arap.exe your/path/to/the/mesh.obj

Press w to toggle wire mode

Press d to toggle deform/select mode

Press middle mouse button to save current mesh

Press a to display/hide anchor points

Drag left mouse button to rotate mesh

Drag right mouse button to select/deform in select/deform mode

When I use cotangent laplacian in the deformation iteration, I got really wired result, and found it hard to make it right.