Animation CS418 Computer Graphics John C. Hart Keyframe Animation - PowerPoint PPT Presentation

Aug 31, 2022 •479 likes •579 views

Animation CS418 Computer Graphics John C. Hart Keyframe Animation Set target positions for vertices at key frames in animations Linearly interpolate vertex positions between targets at intervening frames Lots can go wrong (like

Animation CS418 Computer Graphics John C. Hart
Keyframe Animation • Set target positions for vertices at “key” frames in animations • Linearly interpolate vertex positions between targets at intervening frames • Lots can go wrong (like the feet) • Can be fixed by adding key frames • Piecewise linear approach to animation • Need same number and configuration of vertices at key frames for intervening frames to make sense • Often need to find correspondences between two collections of vertices A motivating example from: Sederberg & Greenwood, A Physically- Based Approach to 2-D Shape Blending, Proc. SIGGRAPH 92
Keyframe Animation • Set target positions for vertices at “key” frames in animations • Linearly interpolate vertex positions between targets at intervening frames • Lots can go wrong (like the feet) • Can be fixed by adding key frames • Piecewise linear approach to animation • Need same number and configuration of vertices at key frames for intervening frames to make sense • Often need to find correspondences between two collections of vertices A motivating example from: Sederberg & Greenwood, A Physically- Based Approach to 2-D Shape Blending, Proc. SIGGRAPH 92
Polar Decomposition • Linear affine interpolation of transformation matrices does not accommodate rotation • Let M be the upper-left 3x3 submatrix of a 4x4 homogeneous transformation matrix • Decompose: M = QS – Q : non-linearly varying part (rotation) – S : linearly varying part (scale, shear) • Initialize Q = M • Replace Q = ½ ( Q + Q -T ) until it convergence to a 3x3 rotation matrix ( Q T = Q -1 ) • Then Q contains the rotation part of M • And S = Q T M contains the scaling part • Interpolate S linearly per-element • Interpolate Q using quaternions

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