Alfred Schmitt, Heinrich Muller, and Wolfgang Leister. Ray tracing algorithms --- theory and practice. In R. A. Earnshow, editor, Theoretical Foundations of Computer Graphics and CAD, pages 997--1030. Springer-Verlag, Berlin Heidelberg, 1988. NATO ASI Series, Vol. F40.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is still far from resolved. When the origin of the query ray is fixed and the objects are the faces of a polyhedral terrain, then an efficient solution exists [12] For arbitrary query rays, we know of only three results in the literature. The first result is due to Schmitt, Mfiller and Leister [25]; they show that a set of axis parallel polyhedra in space can be preprocessed into a data structure of size O(n a polylog n) such that a query takes O(log a n) time. They also present an O(n polylog n) size structure with O(n 65) query time. The second result is by Chazelle et al. 7] They ....

....in axis parallel polyhedra. In this case it is possi ble to obtain O(log n) query time after O(n 2 ) preprocessing, by using the recently developed recursive partition trees of Chazelle et al. 9] instead of the conjugation trees of Dobkin and Edelsbrunner [14] in the second structure of [25]. In fact, anything between near linear storage and roughly O(x ) query time and near quadratic storage and polylogarithmic query time is possible. We take a different approach and obtain a structure using the same amount of preprocessing time and space, namely O(n2 ) but with a query time of ....

[Article contains additional citation context not shown here]

A. Schmitt, H. Milllet and W. Leister, Ray Tracing Algorithms -- Theory and Practice, in: R.A. Earnshaw (ed.), Theoretical Foundations of Computer Graphics and CAD, NATO ASI Series, Vol. F40, Springer-Verlag, 1988, pp. 997-1030.

....coordinates that runs in O(log n) time but requires only O(n ) storage space. Pellegrini, on the other hand, investigated global rays and came to the conclusion that tracing m rays among n triangles can be done in roughly O(m ) time [Pel93] The paper of Schmitt, Muller and Leister [SML88] contains space querytime lower bounds for ray shooting iso oriented rectangles. One of their propositions states that it is possible to preprocess n iso oriented rectangles within P (n) O(npolylogn) time into a data structure of size O(npolylogn) so that an arbitrary ray query for a closest ....

Alfred Schmitt, Heinrich Muller, and Wolfgang Leister. Ray tracing algorithms --- theory and practice. In R. A. Earnshow, editor, Theoretical Foundations of Computer Graphics and CAD, pages 997--1030. Springer-Verlag, Berlin, Heidelberg, 1988. NATO ASI Series, Vol. F40. 35

....reflecting surfaces the problem is complicated by the effect of the reflected light. The basic geometric content of image rendering is computing ray surfaces intersections. This is known to be an expensive computation and many methods are used in graphics to speed up the computation [Gla89, SML88, AK87] A widely used approach is the substitution for complex objects of a hierarchy of objects forming a chain of inclusions [KK86, Rot82] The external object is very simple (a cube or a sphere) and checking the ray object intersection takes O(1) time. If the ray hits the external object the ....

....from a (proper or improper) point. On line single source ray shooting queries can be solved in O( p n log n) time using O(n log n) space and O(n 3=2 log fl n) preprocessing by modifying the implicit planar point location method of Agarwal [Aga90a] Aga90b] Schmitt, Muller and Leister [SML88] consider the case when the objects are iso oriented rectangles, they give several algorithms with different trade off between query time and space. In the off line case they use O(m 0:82 n 0:59 log O(1) n) time and O(m log O(1) m) n) storage. On line 3 queries are solved in O(log ....

A. Schmitt, H. Muller, and W. Leister. Ray tracing algorithms - theory and practice. In R.A. Earnshaw, editor, Theoretical Foundations of Computer Graphics and CAD, pages 997--1030. NATO ASI, Springer Verlag, 1988.

....n sufficiently large) and a small constant fl. On line single source ray shooting queries can be solved in time O( p n log n) using O(n log n) space and O(n 3=2 log fl n) preprocessing by modifying the implicit point location method of Agarwal [Aga89a] Aga89b] Schmitt, Muller and Leister [SML88] consider the case when the objects are isoriented rectangles, in the batched case they use O(m 0:82 n 0:59 log c n) time and O(m log c m n) storage. For the problem involving any polygonal scene and any set of rays only the trivial O(mn) bound is known. Ray shooting (also called ray ....

....is known. Ray shooting (also called ray tracing) is widely used in graphics to simulate the effect of a light source on surfaces, and to simulate reflection and refraction of light. Ray tracing is an expensive computation and most of the method used in graphics to speed up the computation [Gla89] SML88] AK87] do not perform well in the worst case. The result presented in this paper (Sections 7 and 8, Theorem 9) although not yet practical because of the huge constants involved, is the first examples of ray shooting algorithm with a sublinear cost per ray, for any set of triangles and rays. ....

[Article contains additional citation context not shown here]

A. Schmitt, H. Muller, and W. Leister. Ray tracing algorithms - theory and practice. In R.A. Earnshaw, editor, Theoretical Foundations of Computer Graphics and CAD, pages 997--1030. NATO ASI, Springer Verlag, 1988.

....is used to find the plane in front of the origin of the ray. Later, the linear update of the active list does not require any floating point operations any more. 4 Performance Measurements 4. 1 Previous Studies Studies of the efficiency of space subdivisions have been made by Schmitt et al. [30], who analize worst case time bounds of ray tracing and by Devillers [10] who compares grid, octree and macro regions. A comparison of space subdivision algorithms and hierarchical bounding volumes is discussed by Scherson and Caspary [29] Unfortunately, those studies give not a lot of examples ....

A. Schmitt, H. Muller, and W. Leister. Ray tracing algorithms --- theory and practice. In R. A. Earnshaw, editor, Theoretical Foundations of Computer Graphics and CAD, volume F40 of NATO ASI, pages 997--1030. Springer-Verlag, 1988.

No context found.

Alfred Schmitt, Heinrich Muller, and Wolfgang Leister. Ray tracing algorithms --- theory and practice. In R. A. Earnshow, editor, Theoretical Foundations of Computer Graphics and CAD, pages 997--1030. Springer-Verlag, Berlin Heidelberg, 1988. NATO ASI Series, Vol. F40.

No context found.

Schmitt, Alfred, Heinrich Muller, and Wolfgang Leister. "Ray Tracing Algorithms --- Theory and Practice." Theoretical Foundations of Computer Graphics and CAD, NATO ASI Series, Vol. F40, Springer-Verlag, 1988, p. 997-1030. f5g

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