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Simplification of Articulated Meshes
Eric Landreneau Scott Schaefer
Texas A&M University
Simplification
10,000 faces 1,087,716 faces
Introduction
Articulated Meshes Eric Landreneau Scott Schaefer Texas A&M - - PowerPoint PPT Presentation
Articulated Meshes Eric Landreneau Scott Schaefer Texas A&M - - PowerPoint PPT Presentation
Simplification of Articulated Meshes Eric Landreneau Scott Schaefer Texas A&M University Introduction Simplification 1,087,716 10,000 faces faces Introduction Articulated meshes Introduction Articulated meshes
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Articulated meshes Introduction
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Articulated meshes Introduction
k k k
v M v ) ( ˆ
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Articulated meshes Introduction
k
M : Bone Transformation Matrix
k k k
v M v ) ( ˆ
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Articulated meshes Introduction
k
: Skin Weights
k
M : Bone Transformation Matrix
k k k
v M v ) ( ˆ
, 1
k k
k
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Introduction
Unsimplified
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Introduction
Unsimplified
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Introduction
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Introduction
Static simplification
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Introduction insufficient for deformable models
Static simplification
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Quadric Error Functions Basic QEF equation: : ith vertex p in mesh : normal of mth adjacent face
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QEF Edge Collapses
Qm = Quadric Error Function
(distance to plane on face m)
Qm
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QEF Edge Collapses
Q0 Q1 Q2 Q3 Q4 Q5
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QEF Edge Collapses
Q0 Q1 Q2 Q3 Q4 Q5 Qv Qv= Q0 + Q1 + Q2 + Q3 + Q4 + Q5
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QEF Edge Collapses
Qv Qv = Q0 + Q1 + Q2 + Q3 + Q4 + Q5
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QEF Edge Collapses
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QEF Edge Collapses
Qv0
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QEF Edge Collapses
Qv1
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QEF Edge Collapses
Qe Qe=Qv0 + Qv1 Qv0 Qv1
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QEF Edge Collapses
Qe
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Our Method
Example Poses
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Our Method Modify QEF Equation:
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Our Method Modify QEF Equation:
k j k k j
v M v ˆ
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Our Method Modify QEF Equation:
k j k k j
v M v ˆ
j k j k k j i T k j k k k i
v M Q v M v E ) , (
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Our Method Modify QEF Equation:
j k j k k j i T k j k k k i
v M Q v M v E ) , (
Problem: equation is quartic Solution: split into alternating quadratic equations
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Our Method Quadratic #1 – Solve for position Hold weights constant and solve for position v
v M Q M v v E
j k j k k j i T k j k k T i v
) ( min
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Our Method Hold V constant and solve for weights Quadratic #2 – Solve for weights
v M v M v M V
j k j j j
1
min
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Our Method Hold V constant and solve for weights Quadratic #2 – Solve for weights
v M v M v M V
j k j j j
1
k k
1
subject to
min
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Our Method Hold V constant and solve for weights Quadratic #2 – Solve for weights
v M v M v M V
j k j j j
1
, 1
k k
subject to
min
k
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Our Method Alternating minimization
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Results Input Poses
240,448 poly
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Results
2,000 poly 5,000 poly 10,000 poly
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Results Input Poses
206,672 poly
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Results
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Results Comparison with previous techniques
Original deCoro et al. Mohr et al. Ours
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Results
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Results
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Results
DeCoro et al.
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Results
Ours
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Results
Ours DeCoro et al.
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Results
Weight Influences
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Results
Weight reduction
Restriction to n weight influences:
- Minimize
- Prune down to n largest weights
- Minimize again
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Results
Constrained
5 weights/vertex
Unconstrained
up to 11 weights/vertex
Weight Reduction
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Results
RMS Error Comparison (METRO)
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Results
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Conclusions
- Minimizes both skin weights and vertex positions
- Easy to implement (quadratic minimization)
- Requires few example poses
- Reduces to a specified number
- f weights everywhere in the
hierarchy
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