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<p><b>Abstract</b>—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 <it>Differential Points</it> (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 <tmath>$\big. 256\bigr.$</tmath> 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.</p>
Differential geometry, simplification, point sample rendering, per-pixel shading.

A. Varshney and A. Kalaiah, "Modeling and Rendering of Points with Local Geometry," in IEEE Transactions on Visualization & Computer Graphics, vol. 9, no. , pp. 30-42, 2003.
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