Marching Cubes

• 3D version of Marching Squares
• Cell consists of 8 node values: (i+{0,1}, j+{0,1}, k+{0,1})
• 1. Consider a cell
• 2. Classify each vertex as inside or outside
• 3. Build an index
• 4. Get edge list from table[index]
• 5. Interpolate the edge location
• $x=i+\frac{(c-v[i])}{(v[i+1]-v[i])}$
• 6. Compute gradients
• Finite Differences Central
• 7. Consider ambiguous cases
• Midpoint Decider
• Asymptotic Decider
• 8. Go to next cell
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Limitations

• Produces many triangles
• Cannot represent sharp edges
• Produces “ugly” (thin) triangles
• Produces ringing artifacts!