Rendering a polygonal surface with Phong normal interpolation allows shading to appear as it would for a true curved surface while maintaining the efficiency and simplicity of coarse polygonal geometry. However, this approximation fails in certain situations, especially for grazing viewing directions. Well-known problems include physically impossible reflections and implausible illumination. Some of these artifacts can be mitigated through special-case processing, although no universal or generally accepted approaches are available. In particular, all known solutions that guarantee that reflected rays will always point outward from the surface also create discontinuities in the reflection ray direction. We present a simple modification of Phong normal interpolation that allows physically plausible reflections and creates an appearance of a smooth surface. We introduce an additional scalar parameter that characterizes the deviation between per-vertex normals and per face normals and use it to adjust linearly interpolated normals. The proposed technique eliminates perceptually objectionable artifacts caused by inconsistencies between the shading and geometric normals while retaining most of the practical advantages and simplicity of the original Phong formulation.

This paper addresses the problem of computing the triangles visible from a region in space. The proposed aggressive visibility solution is based on stochastic ray shooting and can take any triangular model as input. We do not rely on connectivity information, volumetric occluders, or the availability of large occluders, and can therefore process any given input scene. The proposed algorithm is practically memoryless, thereby alleviating the large memory consumption problems prevalent in several previous algorithms. The strategy of our algorithm is to use ray mutations in ray space to cast rays that are likely to sample new triangles. Our algorithm improves the sampling efficiency of previous work by over two orders of magnitude.

We propose new approaches to ray tracing that greatly reduce the required number of operations while strictly preserving the geometrical correctness of the solution. A hierarchical "beam" structure serves as a proxy for a collection of rays. It is tested against a kd-tree representing the overall scene in order to discard from consideration the sub-set of the kd-tree (and hence the scene) that is guaranteed not to intersect with any possible ray inside the beam. This allows for all the rays inside the beam to start traversing the tree from some node deep inside thus eliminating unnecessary operations. The original beam can be further sub-divided, and we can either continue looking for new optimal entry points for the sub-beams, or we can decompose the beam into individual rays. This is a hierarchical process that can be adapted to the geometrical complexity of a particular view direction allowing for efficient geometric anti-aliasing. By amortizing the cost of partially traversing the tree for all the rays in a beam, up to an order of magnitude performance improvement can be achieved enabling interactivity for complex scenes on ordinary desktop machines.