CMSC 435/634: Introduction to Computer Graphics
Assignment 4
Mesh Fairing
Due April 15, 2024 @ 11:59 PM
The Assignment
The assignment is to write a program that performs
Mesh Fairing.
Your program will read a file in a simplified obj format and write an obj file of a smoothed mesh.
Your program should support the following usage:
./smoothing input.obj output.obj stepsize niterations
The output to the right is from
smoothing bunny.obj sbunny.obj 1 50
applied to
bunny.obj and viewed in
MeshLab.
Your program should perform niterations iterations of Laplacian smoothing. For the basic assignment use the "umbrella operator" to approxiamte the Laplacian. Initialize a vec3 (laplacian) and a double (m) for each vertex for accumulating estimates of the Laplacian and the number of incident edges. Then loop over all triangles updating the accumulators for each vertex in the triangle (this will count each edge twice, but that is okay, since you will divide by the count). Then loop over the vertices updating their position (x) to
x += stepsize * (laplacian / m)
An executable of my program is at:
~adamb/public/435/smoothing/smoothing
Extra Credit
For 50 additional points, implement implicit integration (command line option -i eps). eps is a small constant error threshold used by the linear solver. A simple LinearSolver package is in ~adamb/public/LinearSolver. implicit.cpp is some sample code to use the conjugate gradient solver assuming a Laplacian operator has been defined.
For 15 additional points, use cotangent weights (command line option -c).
./smoothing -c bunny.obj cotbunny.obj 5e-2 500
For 15 additional points, implement global volume preservation (command line option -v).
For 25 additional points, use the biharmonic operator (command line option -b).
./smoothing -b bunny.obj bibunny.obj 1e-2 200
For 50 additional points, implement Loop subdivision (command line option -s number_of_subdivision_passes).
What to turn in
Turn in this assignment electronically by pushing your source code to your proj4 GitHub directory by 11:59 PM on the day of the deadline. We will be looking for multiple checkins documenting your development process.
As always, double check that you have submitted everything we need to build and run your submission, but no generated files (.o's, executables, or images). Be sure to include a Makefile that will build your project when we run 'make', and a readme.txt file telling us about your assignment. Do not forget to tell us what (if any) help did you receive from books, web sites or people other than the instructor and TA.