Abstract
3D digital representations have revolutionized our understanding of the world. They have become indispensable for simulating surgical operations, creating new modes of artistic expression or exploring natural resources. Algorithmic geometry is emerging at the intersection of geometry and computer science. How can we sample, represent and process complex geometric shapes ? How can we offer theoretical guarantees on the quality of approximations and the complexity of algorithms ? How can we ensure the reliability and efficiency of computer programs ? These questions arise in dimensions 2 and 3, but also in larger dimensions, for example to analyze the large masses of data essential to modern science.
