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Ambiguity Problem

Learn how to fix ambiguous faces in marching cubes cases to ensure a consistent triangulation. Explore the Asymptotic Decider method by Nielson and Hamann for resolving mismatches. Detailed explanation of Bilinear Interpolation over faces and applying the asymptotic decider to expand cases. Dive into Nielson and Hamann's paper for a comprehensive understanding.

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Ambiguity Problem

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  1. Ambiguity Problem Certain Marching Cubes cases have more than one possible triangulation Mismatch!!! Hole! + + Case 6 Case 3 + +

  2. The Problem Ambiguous Face : a face that has two diagonally oppsed points with the same sign + + Connecting either way is possible

  3. To fix it … Match!!! + + Case 6 Case 3 B + + The goal is to come up with a consistent triangulation

  4. Solutions There are many solutions available – we present a method called: Asymptotic Decider by Nielson and Hamann (IEEE Vis’91)

  5. Asymptotic Decider Based on bilinear interpolation over faces B11 B01 (s,t) B00 B01 B10 B11 1-t t B(s,t) = (1-s, s) The contour curves of B: {(s,t) | B(s,t) = a } are hyperbolas B00 B10

  6. Asymptotic Decider (2) (1,1) Where the hyperbolas go through the cell depends on the values at the corners, I.e., B00, B01, B10, B11 (0,0)

  7. If a < B(Sa, Ta) Asymptotic Decider (3) (Sa, Ta) (1,1) (0,0) Asymptote

  8. If a > B(Sa, Ta) Asymptotic Decider (4) (Sa, Ta) (1,1) (0,0) Asymptote

  9. Asymptotic Decider (5) (Sa, Ta) (1,1) Sa = B00 - B01 B00 + B11 – B01 – B10 Ta= B00 – B10 B00 + B11 – B01 – B10 B(Sa,Ta) = B00 B11 + B10 B01 B00 + B11 – B01 – B10 (0,0)

  10. Asymptotic Decider (6) Based on the result of asymptotic decider, we expand the marching cube case 3, 6, 12, 10, 7, 13 (These are the cases with at least one ambiguious faces). Let’s look at Nielon and Hamann’s paper…

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