Please answer the following two questions that pertain to Lecture 17 and Lecture 18.

  1. A variant of Marching Cubes, called Marching Tetrahedra, uses a similar procedure that examines each (tetrahedral) cell locally to construct the isosurface. Just as in Marching Cubes, where we first described the stencils relative to quadrilateral faces, we can describe the stencils for Marching Tetrahedra through their triangular faces. First enumerate, up to symmetry, the cases associated with triangular faces. Next, enumerate, up to symmetry, the cases associated with tetrahedral cells. For both lists, be sure to note the number of vertices above/below the isovalue as well as shape of the isosurface within the face/cell. A picture is not necessary, but may help.

  2. Marching Cubes, done carefully, can produce a closed, manifold surface that has boundary only at the boundary of the volume. Explain why the output will be a manifold, specifically describing what properties are necessary for the algorithm to guarantee it.

Grading

Submit your quiz in a folder called quizzes in your git repo. Within this folder create a file Q06.txt that has your answers.

For each question, I’m expecting an answer of 150 words or less. Aim to answer each question in a single paragraph.

I plan to grade your answer on a scale of 0-5, where 5 indicates that you completely answered all portions of the question. Thus, you will receive a score of 0-10 for this quiz. This score will be scaled to the total value of this quiz for your final grade (1%).