SkinCSE169: Computer AnimationInstructor: Steve RotenbergUCSD, Winter 2008Rendering ReviewRendering Renderable surfaces are built up from simple primitives such as triangles They can also use smooth surfaces such as NURBS or subdivision surfaces, but these are often just turned into triangles by an automatic tessellation algorithm before renderingLighting We can compute the interaction of light with surfaces to achieve realistic shading For lighting computations, we usually require a position on the surface and the normal GL does some relatively simple local illumination computations For higher quality images, we can compute global illumination, where complete light interaction is computed within an environment to achieve effects like shadows, reflections, caustics, and diffuse bounced lightGouraud & Phong Shading We can use triangles to give the appearance of a smooth surface by faking the normals a little Gouraud shading is a technique where we compute the lighting at each vertex and interpolate the resulting color across the triangle Phong shading is more expensive and interpolates the normal across the triangle and recomputes the lighting for every pixelMaterials When an incoming beam of light hits a surface, some of the light will be absorbed, and some will scatter in various directionsMaterials In high quality rendering, we use a function called a BRDF (bidirectional reflectance distribution function) to represent the scattering of light at the surface:fr(θi, φi, θr, φr, λ) The BRDF is a 5 dimensional function of the incoming light direction (2 dimensions), the outgoing direction (2 dimensions), and the wavelengthTranslucency Skin is a translucent material. If we want to render skin realistically, we need to account for subsurface light scattering. We can extend the BRDF to a BSSRDF by adding two more dimensions representing the translation in surface coordinates. This way, we can account for light that enters the surface at one location and leaves at another. Learn more about these in CSE168!Texture We may wish to ‘map’ various properties across the polygonal surface We can do this through texture mapping, or other more general mapping techniques Usually, this will require explicitly storing texture coordinate information at the vertices For higher quality rendering, we may combine several different maps in complex ways, each with their own mapping coordinates Related features include bump mapping, displacement mapping, illumination mapping…Smooth Skin AlgorithmWeighted Blending & Averaging Weighted sum: Weighted average: Convex average:10100≤≤==′∑∑==iiiiiiwwxwxRigid Parts Robots and mechanical creatures can usually be rendered with rigid parts and don’t require a smooth skin To render rigid parts, each part is transformed by its joint matrix independently In this situation, every vertex of the character’s geometry is transformed by exactly one matrixwhere v is defined in joint’s local spacevWv ⋅=′Simple Skin A simple improvement for low-medium quality characters is to rigidly bind a skin to the skeleton. This means that every vertex of the continuous skin mesh is attached to a joint. In this method, as with rigid parts, every vertex is transformed exactly once and should therefore have similar performance to rendering with rigid parts.vWv ⋅=′Smooth Skin With the smooth skin algorithm, a vertex can be attached to more than one joint with adjustable weights that control how much each joint affects it Verts rarely need to be attached to more than three joints Each vertex is transformed a few times and the results are blended The smooth skin algorithm has many other names: blended skin, skeletal subspace deformation (SSD), multi-matrix skin, matrix palette skinning…Smooth Skin Algorithm The deformed vertex position is a weighted average:()()()()∑∑=⋅=′⋅+⋅+⋅=′1...2211iiiNNwwhereworwwwvMvvMvMvMvBinding Matrices With rigid parts or simple skin, v can be defined local to the joint that transforms it With smooth skin, several joints transform a vertex, but it can’t be defined local to all of them Instead, we must first transform it to be local to the joint that will then transform it to the world To do this, we use a binding matrix B for each joint that defines where the joint was when the skin was attached and premultiply its inverse with the world matrix:1−⋅=iiiBWMNormals To compute shading, we need to transform the normals to world space also Because the normal is a direction vector, we don’t want it to get the translation from the matrix, so we only need to multiply the normal by the upper 3x3 portion of the matrix For a normal bound to only one joint:nWn ⋅=′Normals For smooth skin, we must blend the normal as with the positions, but the normal must then be renormalized: If the matrices have non-rigid transformations, then technically, we should use:()()∑∑⋅⋅=′nMnMniiiiww()()∑∑⋅⋅=′−−nMnMnTiiTiiww11Algorithm OverviewSkin::Update() (view independent processing) Compute skinning matrix for each joint: M=W·B-1(you can precompute and store B-1instead of B) Loop through vertices and compute blended position & normalSkin::Draw() (view dependent processing) Set matrix state to Identity (world) Loop through triangles and draw using world space positions & normalsQuestions:- Why not deal with B in Skeleton::Update() ?- Why not just transform vertices within Skin::Draw() ?Rig Data Flow Input DOFs Rigging system(skeleton, skin…) Output renderable mesh(vertices, normals…)[]Nφφφ...21=Φnv′′,RigSkeleton Forward Kinematics Every joint computes a local matrix based on its DOFs and any other constants necessary (joint offsets…) To find the joint’s world matrix, we compute the dot product of the local matrix with the parent’s world matrix Normally, we would do this in a depth-first order starting from the root, so that we can be sure that the parent’s world matrix is available when its needed()Njntφφφ,...,,21LL =LWW⋅=parentSmooth Skin Algorithm The deformed vertex position is a weighted average over all of the joints that the vertex is attached to: W is a joint’s world matrix and B is a joint’s binding matrix that describes where it’s world matrix was when it was attached to the skin model (at skin creation time)