We perform research in surface reconstruction from point clouds, geometry processing and geometry representations. We use parallel processing of thousands of GPU cores to enable flash geometry operations in real-time. Novel data structures are evaluated to reduce the time complexity of geometric operations, such as collision detection or occlusion-aware surface processing. In computational geometry, we prove concepts relating samples to curves and manifolds. We also research novel surface description paradigms and according operators, representing large point cloud data in a probabilistic way.