Three Step Geometric Pipeline

1
Three Step Geometric Pipeline
2
Volumetric Modeling

• Grid sampling of an implicit surface
• Generate surface by zero-crossing interpolation

inside surface
outside surface
surface
3
Marching Cubes Algorithm

• Lorensen and Cline(87)
• f (x) given to each vertex x
• if , vertex x is outside of the
  object.
• if , vertex x is inside of the
  object.
• Generate triangles to meet the above rule

4
Compute Scalar Value

• Naive Algorithm
• Compute the magnitude compute the distance f(x),
  to the nearest object surface from x
• Compute the sign determine whether the point is
  inside or outside of the object

5
Consensus Surface Algorithm

• Compute consensus surface comparing using the
  location and surface normal
• Compute f(x) by averaging signed-distances

6
Octree-based Voxel Splitting

• If subdivide the current octant
• The octree reduces the computation O(n3) to O(n2)