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Task7: Optimization of Rotation

  • Deadline: June 17th (Thursday) at 15:00

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Setting Up

Pleae look at the following document for environment setup, creating branch, and making pull request.

In this assignment, it is necessary to install Eigen library. Please follow the following document for setting up.

Additionally, you need the library DelFEM2 installed and updated in pba-<username>/3rd_party

$ cd pba-<username> # go to the top of local repository
$ git submodule update --init 3rd_party/delfem2

(DelFEM2 is a collection of useful C++ codes written by the instructer.)

Problem1

Build the main.cpp using cmake. Run the program and take a screenshot image of the window. Paste the screenshot image below by editing this mark down document:

=== paste screenshot here ===

Problem 2

Optimize the rotation matrix R such that the sum of squared distances between the rotated source points and fixed target points are minimized. Use the Netwon's method for the energy minimization. Write some code around line #71 in the main.cpp to compute the gradient and hessian of the energy of one pair of source and target points. (The modifications are probably very little, just two lines of short codes). Once the implementation is successful, the energy should steadly decrease.

The following slides may be useful for this assignments:

Report the energy after convergence:

  • converged energy = ?????

Paste the resulting screenshot image below:

=== paste screenshot image here ===