Advanced SkinCSE169: Computer AnimationInstructor: Steve RotenbergUCSD, Winter 2008Shape Interpolation Algorithm To compute a blended vertex position: The blended position is the base position plus a contribution from each target whose DOF value is greater than 0 To blend the normals, we use a similar equation: We won’t normalize them now, as that will happen later in the skinning phase()∑−⋅+=′baseiibasevvvvφ()∑−⋅+=′baseiibasennnnφSmooth Skin Algorithm The deformed vertex position is a weighted average over all of the joints that the vertex is attached to. Each attached joint transforms the vertex as if it were rigidly attached. Then these values are blended using the weights: Where: v’’ is the final vertex position in world space wiis the weight of joint i v’ is the untransformed vertex position (output from the shape interpolation) Biis the binding matrix (world matrix of joint i when the skin was initially attached) Wiis the current world matrix of joint i after running the skeleton forward kinematics Note: B remains constant, so B-1can be computed at load time B-1·W can be computed for each joint before skinning starts All of the weights must add up to 1:∑′⋅⋅=′′−vBWv1iiiw∑=1iwLayered Approach We use a simple layered approach Skeleton Kinematics Shape Interpolation Smooth Skinning Most character rigging systems are based on some sort of layered system approach combined with general purpose data flow to allow for customizationFree-Form DeformationGlobal Deformations A global deformation takes a point in 3D space and outputs a deformed pointx’=F(x) A global deformation is essentially a deformation of space Smooth skinning is technically not a global deformation, as the same position in the initial space could end up transforming to different locations in deformed spaceFree-Form Deformations FFDs are a class of deformations where a low detail control mesh is used to deform a higher detail skin Generally, FFDs are classified as global deformations, as they describe a mapping into a deformed space There are a lot of variations on FFDs based on the topology of the control meshLattice FFDs The original type of FFD uses a simple regular lattice placed around a region of space The lattice is divided up into a regular grid (4x4x4 points for a cubic deformation) When the lattice points are then moved, they describe smooth deformation in their vicinityLattice FFDs We start by defining the undeformed lattice space:()0000,, utsxx ⋅+⋅+⋅+= utsuts10 ≤≤ s 10≤≤t 10 ≤≤u⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡=1000000 zyxzyxzyxzyxxxxuuutttsssMLattice FFDs We then define the number of sections in the 3 lattice dimensions:1 <= l,m,n <= 3 And then set the initial lattice positions: pijk0000utsxp ⋅+⋅+⋅+=nkmjliijkLattice FFDs To deform a point x, we first find the (s,t,u) coordinates: Then deform that into world space:[]11−⋅= Mxuts() () ()∑∑ ∑== =−−−⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⋅−⎟⎟⎠⎞⎜⎜⎝⎛⋅−⎟⎟⎠⎞⎜⎜⎝⎛⋅−⎟⎟⎠⎞⎜⎜⎝⎛=limjnkijkkknjjmiilffduuknttjmssil00 0111 pxArbitrary Topology FFDs The concept of FFDs was later extended to allow an arbitrary topology control volume to be usedAxial Deformations & WIRES Another type of deformation allows the user to place lines or curves within a skin When the lines or curves are moved, they distort the space around them Multiple lines & curves can be placed near each other and will properly interactSurface Oriented FFDs This modern method allows a low detail polygonal mesh to be built near the high detail skin Movement of the low detail mesh deforms space nearby This method is nice, as it gives a similar type of control that one gets from high order surfaces (subdivision surfaces & NURBS) without any topological constraintsSurface Oriented FFDsUsing FFDs FFDs provide a high level control for deforming detailed geometry Still, we must address the issue of how to animate and deform the FFD mesh The verts in the mesh can be animated with the smooth skinning algorithm, shape interpolation, or other methodsBody ScanningBody Scanning Data input has become an important issue for the various types of data used in computer graphics Examples: Geometry: Laser scanners Motion: Optical motion capture Materials: Gonioreflectometer Faces: Computer vision Recently, people have been researching techniques for directly scanning human bodies and skin deformationsBody Scanning Practical approaches tend to use either a 3D model scanner (like a laser) or a 2D image based approach (computer vision) The skin is scanned at various key poses and some sort of 3D model is constructed Some techniques attempt to fit this back onto a standardized mesh, so that all poses share the same topology. This is difficult, but it makes the interpolation process much easier. Other techniques interpolate between different topologies. This is difficult also.Body ScanningBody ScanningAnatomical ModelingAnatomical Modeling The motion of the skin is based on the motion of the underlying muscle and bones. Therefore, in an anatomical simulation, the tissue beneath the skin must be accounted for One can model the bones, muscle, and skin tissue as deformable bodies and then then use physical simulation to compute their motion Various approaches exist ranging from simple approximations using basic primitives to detailed anatomical simulationsSkin & Muscle Simulation Bones are essentially rigid Muscles occupy almost all of the space between bone & skin Although they can change shape, muscles have essentially constant volume The rest of the space between the bone & skin is filled with fat & connective tissues Skin is connected to fatty tissue and can usually slide freely over muscle Skin is anisotropic as wrinkles tend to have specific orientationsSimple Anatomical Models Some simplified anatomical models use ellipsoids to model bones and musclesSimple Anatomical Models Muscles are attached to bones, sometimes with tendons as well The muscles contract in a volume preserving way, thus getting wider as they get shorterSimple Anatomical Models Complex musculature can be built up from lots of simple primitivesSimple Anatomical Models Skin can be attached to the