Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous is essentially a hybrid one that decouples continuous vertex locations from discrete topological triangulation. Unfortunately, combinatorial nature of triangulation prevents taking derivatives over space possible meshings any given surface. As result, to date, mesh processing and optimization techn...

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Preface Differential geometry is traditionally regarded as the study of smooth manifolds, but sometimes this framework is too res...

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-ti...