Marching Cube Algorithm

Question 1

Roughly define the marching cube algorithm:

Answer 1

1. Consider all cells defined by eight data samples.
2. Classify each voxel for each cell according to whether it lies:
   - outside the surface (value > iso value)
   - inside the surface (value <= iso value)
3. Mesh creation: Lookup the right configuration and create mesh accordingly

Question 2

For an 8 vertices object, how many different cases are there?

Answer 2

256 (2^8) cases

Question 3

How can we reduce the number of cases for a marching cube mesh creation?

Answer 3

By using symmetry and rotation to eliminate duplicates

Question 4

What are some alternatives to marching cubes?

Answer 4

• Contour tracking
• Dividing cubes

Question 5

What is contour tracking?

Answer 5

Reconstructing a surface/mesh from planar contours

Question 6

What are the main issues for contour tracking?

Answer 6

• How to find the best connection (regularization) between two contours
• How to connect multiple contours

Question 7

What is dividng cubes?

Answer 7

Subdivide a cell as long as the subdivisions project onto more than one pixel. Provides a better estimation of the isosurface

Question 8

How do we shade with the marching cube algorithm?

Answer 8

Use the triangle vertices created by the mesh with location and a normal