SCALe-invariant Integral Surfaces

Extraction of skeletons from solid shapes has attracted quite a lot of attention, but less attention was paid so far to the reverse operation: generating smooth surfaces from skeletons and local radius information. Convolution surfaces, i.e. implicit surfaces generated by integrating a smoothing kernel along a skeleton, were developed to do so. However, they failed to reconstruct prescribed radii and were unable to model large shapes with fine details. This work introduces SCALe-invariant Integral Surfaces (SCALIS), a new paradigm for implicit modelling from skeleton graphs. Similarly to convolution surfaces, our new surfaces still smoothly blend when field contributions from new skeleton parts are added. However, in contrast with convolution surfaces, blending properties are scale-invariant. This brings three major benefits: the radius of the surface around a skeleton can be explicitly controlled, shapes generated in blending regions are self-similar regardless of the scale of the model and thin shape components are not excessively smoothed out when blended into larger ones.