Ambiguity Problem

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 Vis91)
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
Asymptotic Decider (3)
(Sa, Ta)
(1,1)
(0,0)
Asymptote
8
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). Lets look at Nielon and
Hamanns paper