Computer Animation Algorithms and Techniques Chapter 4 Interpolation-based animation

Interpolation based animation Key-frame systems – in general Interpolating shapes Deforming an single shape 3D interpolation between two shapes Morphing – deforming an image

Keyframing – interpolating values

Keyframing keys, in-betweens track-based Avars – articulation variables Sample interface for specifying interpolation of key values and tangents as segment boundaries.

Keyframing curves

Time-Curve interpolation Implement using surface patch technology Two key frames showing a curve to be interpolated.

Time-Curve interpolation Establish point correspondence

Time-Curve interpolation Define time – space-curve “patches” Interpolate in one dimension for curve (spatially) Interpolate in other dimension temporally

Object interpolation 1. Modify shape of object interpolate vertices of different shapes Correspondence problem Interpolation problem 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 vertices directly OR Modify the space the vertices lie in Global transforms

Warping

Power functions For attenuating warping effects

Space Warping Deform the object by deforming the space it is in Two main techniques:  Nonlinear Deformation  Free Form Deformation (FFD) Independent of object representation

2D grid-based deforming Assumption Easier to deform grid points than object vertices

2D grid-based deforming Inverse bilinear mapping (determine u,v from points)

2D grid-based deforming

Global Transformations Common linear transform of space In GT, Transform is a function of where you are in space

Global Transformations

z below z min : no rotation z between z min, z ma x : Rotate from 0 to Q z above z min : rotate Q

Compound global transformations

Nonlinear Global Deformation Objects are defined in a local object space Deform this space using a combination of:  Non-uniform Scaling  Tapering  Twisting  Bending

Nonlinear Global Deformation

Good for modeling [Barr 87] Animation is harder

Free Form Deformation (FFD) Deform space by deforming a lattice around an object The deformation is defined by moving the control points Imagine it as if the object were encased in rubber

Free Form Deformation (FFD) The lattice defines a Bezier volume Compute lattice coordinates Alter the control points Compute the deformed points

FFD Example

Free-Form Deformations: Continuity As in Bezier curve interpolation Continuity controlled by coplanarity of control points

FFDs: alternate grid organizations

FFDs: Bulging & Bending

FFDs:hierarchical

FFDs – as tools to design shapes

FFD Animation Animate a reference and a deformed lattice referencedeformedmorphed

FFDs Animate by passing over object

FFD Animation Animate the object through the lattice referencedeformedmorphed

FFDs Animate by passing object through FFD

FFDs Exo-muscular system Skeleton -> changes FFD -> changes skin

FFD: Examples From “Fast Volume-Preserving Free Form Deformation Using Multi-Level Optimization” appeared in ACM Solid Modelling ‘99

FFD: Examples From “Fast Volume-Preserving Free Form Deformation Using Multi-Level Optimization” appeared in ACM Solid Modelling ‘99

FFD: Examples From “Fast Volume-Preserving Free Form Deformation Using Multi-Level Optimization” appeared in ACM Solid Modelling ‘99

Interpolate between 2 objects Correspondence problem: what part of one object to map into what part of the other object. Some surface-based approaches Slice along one dimension; interpolate in other two Map both to sphere Recursively divide into panels How to handle objects of different genus? Volumetric approaches with remeshing

Object interpolation

Object interp.

Object interpolation For cylinder-like objects

Object interpolation 1. Map to sphere 2. Intersect arc-edges 3. Re-triangulate 4. Remap to object shapes 5. Vertex-to-vertex interpolation Spherical mapping to establish matching edge-vertex topology