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task11

Task11: Inertia Tensor

Deadline: July 1st (Thursday) at 15:00pm

preview

Setting Up

Please 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, the library DelFEM2 must be in pba-<username>/3rd_party.
Type following commands to install and update the library.

$ 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 instructor.)

3D View control

  • Alt + Left mouse drag = rotation
  • Shift + Left mouse drag = translation
  • Mouse wheel = zoom in/out

Problem1

Build the program 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

Edit main.cpp to compute the 3x3 inertia tensor of a 3D mesh. Note that the mass is distributed only on the surface of the mesh (i.e., the shape is hollow inside the mesh). The areal mass density of the surface is one. The edit is probably only necessary around line #59 adding few lines of codes.

The inertia tensor should computed for the rotation around the origin of the coordinate. (the mesh is already translated such that the center of the mass is located at the origin). The line in red, blue and green are the principal axes of the inertia tensor.

Write down the eigenvalues of the inertia tensor below (they will be shown in the standard output):

  • 1st eigenvalue:
  • 2nd eigenvalue:
  • 3rd eigenvalue:

Paste the screenshot image below:

=== paste screenshot here ===

The following slides may be useful: