1. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development1 Skeletons and Skinning Bones and Skeletons Mesh Skinning

2. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development2 Skeletal Animation Victoria

3. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development3 Skeletons Skeleton A pose-able framework of joints arranged in a tree structure. An invisible armature to manipulate the skin and other geometric data of the character. Does not actually render.

4. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development4 Skeletons Joint Allows relative movement within the skeleton. Joints are equivalent to 4x4 matrix transformations. Bone What’s the difference between a joint and a bone? Nothing really, and XNA uses the term bone for a joint. Sometimes bones includes a length or actual geometry Skeleton bones are identical in function to the bones you used for Digger.

5. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development5 Victoria in 3DS Max

6. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development6 Victoria in Motionbuilder

7. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development7 DOFs Degree of Freedom (DOF) A variable φ describing a particular axis or dimension of movement within a joint Joints typically have around 1-6 DOFs (φ 1 …φ N ) Can have more (up to 9 for affine) Changing the DOF values over time results in the animation of the skeleton Rigid body transformations: 6DOF Arbitrary rotations: 3DOF

8. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development8 Skeleton Posing Process 1.Specify DOF values for the skeleton 2.Traverse the hierarchy using forward kinematics to compute the world matrices 3.Use world matrices to deform skin & render The matrices can also be used for other things such as collision detection, FX, props, etc. 1-2 is what we did for Digger. #3 is new.

9. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development9 Forward Kinematics Each joint computes a local matrix M based on the DOFs and some formula representative of the joint type: Local matrix M = M joint (φ 1,φ 2,…,φ N ) boneTransforms[b] = Matrix.CreateScale(boneScales[b]) * Matrix.CreateFromQuaternion(bone.Rotation) * Matrix.CreateTranslation(bone.Translation); Then, world matrix W is computed by concatenating M with the world matrix of the parent joint World matrix W = MW parent model.CopyBoneTransformsFrom(boneTransforms); model.CopyAbsoluteBoneTransformsTo(boneAbsoluteTransforms);

10. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development10 Skeleton Rigging Skeleton Rigging – Setting up the skeleton for a figure – Bones – Joints – DOF’s – Limits

11. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development11 Poses Adjust DOFs to specify the pose of the skeleton We can define a pose Φ more formally as a vector of N numbers that maps to a set of DOFs in the skeleton Φ = [φ 1 φ 2 … φ N ]

12. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development12 Joint Types Rotational – Hinge: 1-DOF – Universal: 2-DOF Around two axis – Ball & Socket: 3-DOF Euler Angles Quaternions Translational – Prismatic: 1-DOF – Translational: 3-DOF (or any number) Compound – Free – Screw – Constraint – Etc. Non-Rigid – Scale – Shear – Etc. Design your own...

13. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development13 Smooth Skin Algorithm

14. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development14 Rigid Parts are Easy Robots and mechanical creatures – Rigid parts, no smooth skin – Each part is transformed by its joint matrix Every vertex of the character’s geometry is transformed by exactly one matrix where v is defined in joint’s local space This is what we did with Digger

15. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development15 What happens with Skinned Characters? The mesh is deformed by the bones, but not “rigidly”. Instead, it is a flexible bend.

16. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development16

17. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development17 The Basic Concept 1.0/0.0 0.0/1.00.5/0.5 0.7/0.3 Each vertex can be moved by 1-4 bones, with each bone having a weight.

18. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development18 Mathematics of mesh skinning Where: is the number of matrices. is the vertex position. is the weight associated. is a transformation matrix. with Each vertex is multiplied by several “weighted” transformation matrices and the results are added together. The transformation matrix indicates how that bone has been moved.

19. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development19 Smooth Skin A vertex can be attached to more than one joint/bone with adjustable weights that control how much each joint affects it – Rarely more than 4 – Definitely no more than 4 in XNA 1.0/0.0 0.0/1.00.5/0.5 0.7/0.3 Result is a blending of the n transformations Algorithm names – blended skin, skeletal subspace deformation (SSD), multi- matrix skin, matrix palette skinning…

20. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development20 Limitations of Smooth Skin Smooth skin is very simple and quite fast, but its quality is limited – Joints tend to collapse as they bend more – Very difficult to get specific control – Unintuitive and difficult to edit Still, it is common in games and commercial animation! If nothing else, it is a good baseline upon which more complex schemes can be built

21. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development21 Limitations of Smooth Skin

22. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development22 Bone Links Bone links are extra joints inserted in the skeleton to assist with the skinning – Instead of one joint, an elbow may be 2-3 joints – Allows each joint to limit the bend angle! – Why does this help?

23. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development23 Containment Binding Volume primitives around the bones – Boxes, cylinders, etc. – Vertex weights assigned based on which primitives it is in

24. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development24 Props Often our characters will be carrying or handling something We usually call this a prop Easiest way to handle props Prop is moved by one bone In this example the right hand bone moves the pie bazooka

25. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development25 How I determined the numbers Matrix bazMat = Matrix.CreateRotationX(MathHelper.ToRadians(109.5f)) * Matrix.CreateRotationY(MathHelper.ToRadians(9.7f)) * Matrix.CreateRotationZ(MathHelper.ToRadians(72.9f)) * Matrix.CreateTranslation(-9.6f, 11.85f, 21.1f) * Model.GetBoneAbsoluteTransform(handBone); X value is +90 to get from 3DS coordinates (Z is up) to our coordinates (Y is up)

26. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development26 Manual Manipulation How could I aim that bazooka? What are the options?

27. CSE 473 Dr. Charles B. Owen Fundamentals of 3D Game Development27 Manual Manipulation Bip01 Spine1