Assignment 5 [Coding]: Geodesic Distance (Due 4/27)

Note: For the final assignment, you can do either this assignment or A6. Overall, you just need to be sure you completed A0 and A1, as well as 3 of the assignments A2–A6 (your choice which ones).

For the coding portion of this assignment, you will implement the heat method, which is an algorithm for computing geodesic distance on curved surfaces. All of the details you need for implementation are described in Section 3 of the paper, up through and including Section 3.2. Note that you need only be concerned with the case of triangle meshes (not polygon meshes or point clouds); pay close attention to the paragraph labeled “Choice of Timestep.”

Please implement the following routines in:

1. projects/geodesic-distances/heat-method.[js/cpp]:
   1. constructor
   2. computeVectorField
   3. computeDivergence
   4. compute

Notes

• Refer to sections 3.2 of the paper for discretizations in Algorithm 1 (page 3).
• Recall that our Laplace matrix is positive semidefinite, which might differ from the sign convention the authors use.
• The tests for computeVectorField and computeDivergence depend on the A and F matrices you define in your constructor. So if you fail the tests but your functions look correct, check whether you have defined the flow and laplace matrices properly.
• Your solution should implement zero Neumann boundary conditions (which are the “default behavior” of the cotan Laplacian) but feel free to tryout other Dirichlet and Neumann boundary conditions on your own.

Submission Instructions

Please submit your source files as usual to Gradescope by 5:59pm ET..