Parameterization II - Computer Graphics Laboratory

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Constrained Constrained Minimization • Notation: β are (given) 3D angles angles. α i i are (unknown) 2D angles. • Objective: minimize (relative) deviation of angles: 3T ∑ 1 D ( α ) = ( α − β ) i i i i = 2 28
Constraints • All angles are positive (linear inequalities) inequalities). • Sum of angles in each triangle is π (linear equalities). • Sum of angles around each vertex is 2π (linear equalities). • All one-rings close properly (non-linear equalities). 29
Page 1 and 2: Parameterization II Some slides fro
Page 3 and 4: Fixed vs Free Boundary 3
Page 7: Cut graph 7
Page 10 and 11: Free Boundary Methods - Tactics •
Page 12 and 13: Linear Map Surgery • Singular g V
Page 14 and 15: Computing the Stretch Factors • f
Page 16 and 17: Piecewise Linear Parameterizations
Page 18 and 19: Linear Methods • the terms and ar
Page 20 and 21: Non-linear Non linear Methods • M
Page 22 and 23: Conformal Parameterization - LSCM C
Page 24 and 25: Conformal Parameterization - LSCM E
Page 26 and 27: Isotropic Parameterizations Conform
Page 30 and 31: Solving • Use non-linear solver (
Page 32 and 33: Examples LSCM ABF 32
Page 34 and 35: Linear Methods mean value conformal
Page 36 and 37: Non-Linear Non Linear Methods ABF++
Page 38 and 39: LSCM [2002] ABF++ [2005] LinABF [20
Page 40 and 41: v α i Discrete Metric Triangle edg
Page 42 and 43: What Happens to the Curvature? •
Page 44 and 45: The Flattening Algorithm for a Topo
Page 46 and 47: Comparison with Non-Linear Non Line
Page 49 and 50: Conformal Equivalence of Triangle M
Page 51 and 52: Conformal Equivalence of Triangle M

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