We use PN-triangles to improve the quality of isosurfaces extracted by marching cubes. Our contribution is a pure-GPU solution for smoothed isosurfaces, combining GPU isosurface extraction with tessellation shaders for PN-triangles. The marching cubes algorithm was first introduced to reconstruct isosurfaces of implicit functions in a uniformly sampled space. Curved PN-triangles [Vlachos et al. 2001], or PN-triangles for short, is a fast way of generating smooth surfaces using limited local geometric information, such as per-vertex positions, and normals.

Surface curvature is used in a number of areas in computer graphics, including texture synthesis and shape representation, mesh simplification, surface modeling, and nonphotorealistic line drawing. Most real-time applications must estimate curvature on a triangular mesh. This estimation has been limited to CPU algorithms, forcing object geometry to reside in main memory. However, as more computational work is done directly on the GPU, it is increasingly common for object geometry to exist only in GPU memory. Examples include vertex skinned animations and isosurfaces from GPU-based surface reconstruction algorithms. For static models, curvature can be precomputed and CPU algorithms are a reasonable choice. For deforming models where the geometry only resides on the GPU, transferring the deformed mesh back to the CPU limits performance. We introduce a GPU algorithm for estimating curvature in real time on arbitrary triangular meshes. We demonstrate our algorithm with curvature-based NPR feature lines and a curvature-based approximation for an ambient occlusion. We show curvature computation on volumetric data sets with a GPU isosurface extraction algorithm and vertex-skinned animations. We present a graphics pipeline and CUDA implementation. Our curvature estimation is up to ~18x faster than a multithreaded CPU benchmark.

Surface curvature is used in a number of areas in computer graphics, including texture synthesis and shape representation, mesh simplification, surface modeling, and non-photorealistic line drawing. Most real-time applications must estimate curvature on a triangular mesh. This estimation has been limited to CPU algorithms, forcing object geometry to reside in main memory. However, as more computational work is done directly on the GPU, it is increasingly common for object geometry to exist only in GPU memory. Examples include vertex skinned animations and isosurfaces from GPU-based surface reconstruction algorithms.