PaRas: A Rasterizer for Large-Scale Parametric Surfaces

The advantages of higher-order surfaces, such as their ability to represent complex geometry compactly and smoothly, have led to their increasing use in computer graphics. This trend underscores the importance of developing efficient rendering algorithms tailored for these representations. We introduce PaRas, a highly performant rasterizer for real-time rendering of large-scale parametric surfaces with high precision. Unlike conventional graphics pipelines that rely on hardware tessellation to convert smooth surfaces into numerous flat triangles, our method provides a highly efficient and parallel approach to directly rasterize parametric surfaces. PaRas seamlessly integrates into existing workflows, enabling smooth surfaces to be handled with the same ease as triangle meshes. To accomplish this, we formulate the rasterization of parametric surfaces as a point inversion problem, employing a Newton-type iteration on the GPU to compute precise solutions. The framework’s effectiveness is demonstrated on quartic triangular Bézier patches and rational Bézier patches, both commonly used in high-precision modeling and industrial applications. Experimental results indicate that our rendering pipeline achieves higher efficiency and greater accuracy compared to traditional hardware tessellation techniques.