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A Survey of Geometric Data Structures for Ray Tracing
, 2001
"... Ray tracing is a computer graphics technique for generating photorealistic images. To determine the color at each pixel of the image, one traces the path traversed by each ray of light arriving at the pixel back through several reflections and/or refractions. The most timeconsuming phase of a ray ..."
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Ray tracing is a computer graphics technique for generating photorealistic images. To determine the color at each pixel of the image, one traces the path traversed by each ray of light arriving at the pixel back through several reflections and/or refractions. The most timeconsuming phase of a ray tracer is ray traversal, which determines for each of a large number of rays, the first object met by that ray. Many data structures have been proposed to accelerate this process. This survey describes and compares the construction and traversal algorithms for a variety of commonly used data structures from practitioner’s point of view.
TOPOLOGICAL EFFECTS ON MINIMUM WEIGHT STEINER TRIANGULATIONS
"... Abstract. Let mwt(X) denote the sum of the Euclidean edge lengths of a minimum weight triangulation of a point set X ∈ R 2. We investigate a curious property of some npoint sets X, which allow for an (n + 1) st point P (called a Steiner point) to give mwt(X ∪ {P}) < mwt(X). We call the regions o ..."
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Abstract. Let mwt(X) denote the sum of the Euclidean edge lengths of a minimum weight triangulation of a point set X ∈ R 2. We investigate a curious property of some npoint sets X, which allow for an (n + 1) st point P (called a Steiner point) to give mwt(X ∪ {P}) < mwt(X). We call the regions of the plane where such a P reduces the length of the minimum weight triangulation Steiner reducing regions. We demonstrate by example that these Steiner reducing regions may have many disconnected components or fail to be simply connected. By examining randomly generated point sets, we show that the surprising topology of these Steiner reducing regions is more common than one might expect. 1.