Geometric Prediction for Compression
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This thesis proposes several new predictors for the compression of shapes, volumes and animations. To compress frames in triangle-mesh animations with fixed connectivity, we introduce the ELP (Extended Lorenzo Predictor) and the Replica predictors that extrapolate the position of each vertex in frame $i$ from the position of each vertex in frame $i-1$ and from the position of its neighbors in both frames. For lossy compression we have combined these predictors with a segmentation of the animation into clips and a synchronized simplification of all frames in a clip. To compress 2D and 3D static or animated scalar fields sampled on a regular grid, we introduce the Lorenzo predictor well suited for scanline traversal and the family of Spectral predictors that accommodate any traversal and predict a sample value from known samples in a small neighborhood. Finally, to support the compressed streaming of isosurface animations, we have developed an approach that identifies all node-values needed to compute a given isosurface and encodes the unknown values using our Spectral predictor.