Extreme simplification and rendering of point sets using algebraic multigrid

We present a novel approach for extreme simplification of point set models, in the context of realtime rendering. Point sets are often rendered using simple point primitives, such as oriented discs. However, this requires using many primitives to render even moderately simple shapes. Often, onewishes to render a simplified model using only a few primitives, thus trading accuracy for simplicity. For this goal, we propose a more complex primitive, called a splat, that is able to approximate larger and more complex surface areas than oriented discs. We construct our primitive by decomposing the model into quasi-flat regions, using an efficient algebraicmultigrid algorithm.Next, we encode these regions into splats implemented as planar support polygons textured with color and transparency information and render the splats using a special blending algorithm. Our approach combines the advantages of mesh-less pointbased techniques with traditional polygon-based techniques. We demonstrate our method on various models.