Algebraic Splats Representation for Point Based Models

The primitives of point-based representations are independent but are rendered using surfels, which approximate the immediate neighborhood of each point linearly. A large number of surfels are needed to convey the exact shape. Higher-order approximations of the local neighborhood have the potential to represent the shape using fewer primitives, simultaneously achieving higher rendering speeds. In this paper, we propose algebraic splats as a basic primitive of representation for point based models. An algebraic splat based representation can be computed using a moving least squares procedure. We specifically study low order polynomial splats in this paper. Quadratic and cubic splats provide good quality and high rendering speed using far fewer primitives on a wide range of models. They can also be rendered fast using ray tracing on modern GPUs. We also present an algorithm to construct a representation of a model with a user-specified number of primitives. Our method to generates a hole-free representation parametrized by a smoothing radius. The hole-free representation reduces the number of primitives needed by a factor 20 to 30 on most models and by a factor of over 100 on dense models like David with little or no drop in visual quality. We also present a two-pass GPU algorithm that ray-traces the algebraic splats and blends them using a Gaussian weighting scheme for smooth appearance. We are able to render models like David at upwards of 200 fps on a commodity GPU using algebraic splats.