CS 775: Advanced Computer Graphics. Lecture 4: Skinning

Transcription

1 CS 775: Advanced Computer Graphics Lecture 4:

2

3 Binding

4 Binding Always done in a standard rest or bind pose.

5 Binding Always done in a standard rest or bind pose. Associate all skin mesh vertices to some skeleton joint(s).

6 Moving the skin vertices when the skeleton is moved. Blending the various parts of the mesh.

7 The skin is a (polygonal) mesh. A mesh is a collection of connected (polygonal) primitives.

8 Binding The skin mesh is defined in some local frame. Skin Mesh

9 Binding The skin mesh is defined in some local frame. The skeleton joints are defined in their own local frames. Let the transformation between any local frame { j} of the skeleton and the local frame of the skin be given by: Bj { j} Skeleton

10 Binding The skin mesh is defined in some local frame. The skeleton joints are defined in their own local frames. Let the transformation between any local frame { j} of the skeleton and the local frame of the skin be given by: Bj Binding Matrix or Bind Pose Matrix { j} Skeleton

11 Binding Associate a group of vertices to a single skeleton link Every vertex of the mesh that is associated to the link { j} is initially given, in the bind pose, in local skin space as vk vk { j}

12 Binding Every vertex of the mesh that is associated to the link { j} is initially given, in the bind pose, in local skin space as vk Tj {0 } Binding expresses each skin vertex in the global frame as: 0 1 v k =T j. B j. v k vj { j}

13 Deforming the mesh When the skeleton links move, T j changes. vk Tj {0 } { j}

14 Deforming the mesh But the relative position of the vertex in the local joint frame does not change. vk Tj New position of skin mesh vertex in global coordinates for the deformed skin is also given by {0 } 0 { j} v k =T j. B 1 j.vk

15 Deforming the mesh This is known as Rigid or Simple skinning. vk Tj {0 } { j}

16 Rigid Simple but low quality skinning. Large distortions happen at bends. { j 1 } Tj {0 } { j}

17 Linear Blend Vertex Blend, Skeletal Subspace deformation Associate multiple joints with vertices and blend the effect of each joint on the vertex using weights. 0 v k = w i, k T i B 1 i vk i vk {0 } { j} { j 1 }

18 Linear Blend Associate multiple joints with vertices and blend the effect of each joint on the vertex using weights. 0 v k = w i, k T i B 1 i vk i For every k, wi, k =1 and 0 w i, k 1 i vk Here i is the index over all joints associated with the vertex v k {0 } { j} { j 1 }

19 Linear Blend Deforming the mesh 0 v k = w i, k T i B 1 i vk i { j 1 } = w i,k M i v k i {0 } { j}

20 Linear Blend w i, k N i nk 0 nk = i wi, k N i nk Mesh normals i where N i is the first 3x3 submatrix of M i { j 1 } Here we have a that N i is rigid. What if it was an Affine transformation? {0 } { j}

21 Algorithm Skin::Update() 1 Compute M i =T i B 1 B for each joint. i i can be precomputed and stored. Loop through the vertices and blend positions and normals. Skin::Draw() Set matrix state to Identity Loop through skin polygons and draw using global vertex positions and normals Why separate the two?

22 Algorithm Skin::Update() (view independent processing) 1 Compute M i =T i B 1 B for each joint. i i can be precomputed and stored. Loop through the vertices and blend positions and normals. Skin::Draw() (view dependent processing) Set matrix state to Identity Loop through skin polygons and draw using global vertex positions and normals

23 Limitations of Vertex Blend Skin collapse - Bending Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation, Lewis, Cordner and Fong, SIGGRAPH 2000

24 Limitations of Vertex Blend Skin collapse Twisting (Candy Wrapper effect) Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation, Lewis, Cordner and Fong, SIGGRAPH 2000

25 Limitations of Vertex Blend Skin collapse A quick solution used to prevent collapse during bending is to dynamically add more bones Was done in many games but does not solve the problem completely.

26 Limitations of Vertex Blend Skin collapse A better solutions is to use dual quaternions Geometric with Approximate Dual Quaternion Blending, Kavan Collins, Zara and O'Sullivan, ACMTOG 2008

27 Limitations of Vertex Blend Skin Binding Containment Binding

28 Limitations of Vertex Blend Skin Binding Containment Binding Point-to-line Mapping Manual (combined with adding weights)

29 Limitations of Vertex Blend Indirect control via weights is non-intuitive Weights are added either via simple heuristic rules like wi, k Added manually Demo/Video 1 d i,k where d i, k is the distance from the skin vertex v k to the skeleton joint i

30 Limitations of Vertex Blend Skin collapse Skin Binding is difficult Indirect control via weights is non-intuitive No anatomical basis Advantages It is simple to do and so is very widely used Good starting point for more complex skinning Implementation on hardware is easy