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Problems of Marching Cubes

• edge intersections are computed using linear interpolation (inaccurate)
• assumes smooth isosurface: sharp features within cells are lost (aliasing problem)

Solution: Directed Distances
instead of an iso-value, store three directed distances for every vertex: exact distance to the surface crossing along every cube edge

Solution: Feature Detection / Sampling / Reconstruction
Feature Detection
based on the gradient values at the edge intersections, compute normal vectors:

find the two normal vectors which span the largest angle


find the normal which forms the smallest angle to the orthogonal direction



If , we have detected a feature.
If additionally , the current feature is a corner feature (two large opening angles). Otherwise, it is an edge feature (one large opening angle).

Feature Sampling
Find intersection point of tangent planes:


This might not have a unique solution:
Over-determined: No common intersection point. Find least-squares solution (closest to all planes).
Under-determined: Infinitely many intersection points. Find least-norm solution (closest to voxel center).
Solve using SVD:





Feature Reconstruction
Look up cell configuration from Marching Cubes table. If in a feature cell, insert feature vertex at computed position and connect with a triangle fan. Flip edges so they align with feature edges.