This paper examines the efficiency of different rayshooting acceleration schemes, including the uniform space subdivision, octree and kd-tree. We use simple computational models, which assume that the objects are uniformly distributed in space. The efficiency is characterized by two measures, including the expected number of ray-object intersections needed to identify the firstly intersected object, and the expected number of steps on the space partitioning data structure. We can come to the interesting conclusion that these numbers are constant and are independent of the number of objects in the scene. The number of intersections is determined by how well the cells of the partitioning data structure enclose the objects. Such analysis helps to understand why kd-tree is better than octree and uniform space subdivision and provides hints to improve their implementation.
This paper presents a single‐pass, view‐dependent method to solve the rendering equation, using a stochastic iterational scheme where the transport operator is selected randomly in each iteration. The requirements of convergence are given for the general case. To demonstrate the basic idea, a very simple,continuous random transport operator is examined, which gives back the light tracing algorithm incorporating Russian roulette. Then, a new mixed continuous and finite‐element based iteration method is proposed, which uses ray‐bundles to transfer the radiance in a single random direction. The resulting algorithm is fast, it provides initial results in seconds and accurate solutions in minutes and does not suffer from the error accumulation problem and the high memory demand of other finite‐element and hierarchical approaches.
This paper proposes the application of a variance reduction technique called weighted importance sampling in shooting type global illumination algorithms. The sampling applied by shooting type Monte-Carlo global illumination algorithms can mimic the power transfer, but not the BRDFs at the visible target of the transfer. Consequently, these algorithms are poor in rendering visible specular surfaces. In order to eliminate these drawbacks, the BRDFs at the visible targets are taken into account as an additional weighting of the sampling density. After discussing the basic concepts we demonstrate the proposed idea with two algorithms. The first one uses conventional rays, while the second one ray-bundles to transfer the light in the scene.
Until recently, research on global illumination and photon maps in particular considered only static scenes. As hardware capabilities and acceleration techniques allow for more rapid image generation, the application of these methods for animation becomes more relevant. Techniques that retain more information about rendered frames are able to exploit coherence between frames to a larger extent. Storing all of the shooting walks, as does the photon map, is a good basis for generating a modified image more rapidly. In this paper, we describe a fast, but conservative method to verify the stored shooting walks. As a result, the cost of updating of the modified walks becomes comparable to the cost of verification, making nonconservative methods and their inherent assumptions unnecessary. In order to achieve this, we use a separation of dynamic and static objects that allows for occlusion tests limited to potentially moving objects.
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