Deformation using interpolation CSE 3541 Matt Boggus

Interpolation based animation Keyframe systems – in general Interpolating shapes Deforming an single shape 3D interpolation between two shapes Image morphing

Keyframing

Time-Curve interpolation Conditions: P(0) maps to Q(0) P(1) maps to Q(1) All of P maps to all of Q One to one – no two P(u) map to same Q(v) Onto – every Q(v) has a P -1 (u) value

Time-Curve interpolation Solutions: If P and Q use the same curve formation and # control points, then generate intermediate curves by interpolating the control points Supersample: Generate same number of points on P and Q, then interpolate between matching points

Object interpolation topics 1. Modify shape of one object 2. Interpolate one object into second object 3. Interpolate one image into second image

Object Modification Vertex warping 2D grid-based deforming Skeletal bending Free Form Deformations Modify the space the vertices lie in Global transforms Modify the vertices directly

Warping Vertices closer to seed are displaced more

Power functions For attenuating warping k determines how quickly increase in distance decreases warping

2D grid-based deforming Assumption: easier to deform grid points than object vertices A (global coordinates): (25.6,14.7) A (local coordinates): (5.6, 2.7) A’s Grid cell (5, 2) A’s position in cell (0.6, 0.7)

2D grid-based deforming Inverse bilinear mapping P values at corners known from grid deformation u and v are known from point’s position in original grid cell

2D grid-based deforming

2D skeleton-based bending

For each vertex, determine which line segment (or bone) it is closest to: L 2 distance to it: d relative position on the line segment: r = d 2 /d 1

2D skeleton-based bending For new vertex position on repositioned (and possibly rescaled) line segment, Interpolate r along line segment Place d units away from the line segment

Examples of artist driven deformation Point based, skeleton based, cage based From Bounded Biharmonic Weights for Real-Time Deformation by Alec Jacobson, Ilya Baran, Jovan Popovic and Olga Sorkine, appearing at SIGGRAPH &feature=related 8&feature=related

Free-Form Deformations (FFDs) 2D grid-based deformingFFDs 2D grid 3D grid tri-cubic interpolationbi-linear interpolation

FFDs Animate by passing object through FFD

Interpolate between 2 objects Correspondence problem: what part of one object to maps into what part of the other object

Interpolate between 2 objects – difficulties How to handle objects of different genus? (roughly speaking: number of holes in the model)  map to

Morphing Image blending Move pixels to corresponding pixels Example from

Morphing

Using feature lines instead of grid points