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
f(x’)
f(x)
signed distance
f(x’)
f(x)
Outlier

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)