# Modeling and Rendering of Points with Local Geometry

 Title Modeling and Rendering of Points with Local Geometry Publication Type Journal Articles Year of Publication 2003 Authors Kalaiah A, Varshney A Journal IEEE Transactions on Visualization and Computer Graphics Volume 9 Issue 1 Pagination 30 - 42 Date Published 2003/// ISBN Number 1077-2626 Keywords differential geometry, per-pixel shading., point sample rendering, simplification Abstract We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry in the vicinity of that point. This is a more general point representation that, for the cost of a few additional bytes, packs much more information per point than the traditional point-based models. This information is used to efficiently render the surface as a collection of local geometries. To use the hardware acceleration, the DPs are quantized into $\big. 256\bigr.$ different types and each sampled point is approximated by the closest quantized DP and is rendered as a normal-mapped rectangle. The advantages to this representation are: 1) The surface can be represented more sparsely compared to other point primitives, 2) it achieves a robust hardware accelerated per-pixel shading—even with no connectivity information, and 3) it offers a novel point-based simplification technique that factors in the complexity of the local geometry. The number of primitives being equal, DPs produce a much better quality of rendering than a pure splat-based approach. Visual appearances being similar, DPs are about two times faster and require about 75 percent less disk space in comparison to splatting primitives. DOI 10.1109/TVCG.2003.1175095