CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development1
Skeletons and Skinning
• Bones and Skeletons• Mesh Skinning
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development2
Skeletal Animation
Victoria
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development3
Skeletons
SkeletonA 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.
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development4
SkeletonsJointAllows relative movement within the skeleton. Joints are equivalent to 4x4 matrix transformations.
BoneWhat’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.
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development5
Victoria in 3DS Max
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development6
Victoria in Motionbuilder
CSE 473 Dr. Charles B. OwenFundamentals 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 (φ1…φN) 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
CSE 473 Dr. Charles B. OwenFundamentals 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.
CSE 473 Dr. Charles B. OwenFundamentals 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 = Mjoint(φ1,φ2,…,φN) 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 = MWparent
model.CopyBoneTransformsFrom(boneTransforms); model.CopyAbsoluteBoneTransformsTo(boneAbsoluteTransforms);
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development10
Skeleton Rigging
• Skeleton Rigging – Setting up the skeleton for a figure– Bones– Joints– DOF’s– Limits
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development11
Poses
Adjust DOFs to specify the pose of the skeletonWe can define a pose Φ more formally as a vector of N numbers that maps to a set of DOFs in the skeleton
Φ = [φ1 φ2 … φN]
CSE 473 Dr. Charles B. OwenFundamentals 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...
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development13
Smooth Skin Algorithm
CSE 473 Dr. Charles B. OwenFundamentals 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
vMv
This is what we did with Digger
CSE 473 Dr. Charles B. OwenFundamentals 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.
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development16
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development17
The Basic Concept1.0/0.0 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.
CSE 473 Dr. Charles B. OwenFundamentals 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.
n
iii vMwv
viw
i
iw 1with
iM
n
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.
CSE 473 Dr. Charles B. OwenFundamentals 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 0.0/1.00.5/0.50.7/0.3
• Result is a blending of the n transformations
• Algorithm names– blended skin, skeletal subspace deformation (SSD), multi-
matrix skin, matrix palette skinning…
CSE 473 Dr. Charles B. OwenFundamentals 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
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development21
Limitations of Smooth Skin
CSE 473 Dr. Charles B. OwenFundamentals 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?
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development23
Containment Binding
• Volume primitives around the bones– Boxes, cylinders, etc.– Vertex weights assigned based on which primitives it is in
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development24
Props
Often our characters will be carrying or handling somethingWe usually call this a prop
Easiest way to handle propsProp is moved by one bone
In this example the right hand bone moves the pie bazooka
CSE 473 Dr. Charles B. OwenFundamentals 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)
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development26
Manual Manipulation
How could I aim that bazooka?
What are the options?
CSE 473 Dr. Charles B. OwenFundamentals of 3D Game Development27
Manual Manipulation
Bip01 Spine1