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_id 6a59
authors Franklin, Randolph
year 1980
title A Linear Time Exact Hidden Surface Algorithm
source SIGGRAPH '80 Conference Proceedings. July, 1980. vol. 14 ; no. 3: pp. 117-133 : ill. includes bibliography
summary This Paper presents a new hidden surface algorithm. Its output is the set of the visible pieces of edges and faces, and is as accurate as the arithmetic precision of the computer. Thus calculating the hidden surfaces for a higher resolution device takes no more time. If the faces are independently and identically distributed, then the execution time is linear in the number of faces. In particular, the execution time does not increase with the depth complexity. This algorithm overlays a grid on the screen whose fineness depends on the number and size of the faces. Edges and faces are sorted into grid cells. Only objects in the same cell can intersect or hide each other. Also, if a face completely covers a cell then nothing behind it in the cell is relevant. Three programs have tested this algorithm. The first verified the variable grid concept on 50,000 intersecting edges. The second verified the linear time, fast speed, and irrelevance of depth complexity for hidden lines on 10,000 spheres. This also tested depth complexities up to 30, and showed that perspective scenes with the farther objects smaller are even faster to calculate. The third verified this for hidden surfaces on 3,000 squares
keywords hidden surfaces, algorithms, hidden lines, variables, grids, computer graphics, programming
series CADline
last changed 2003/06/02 11:58

_id 4418
authors Franklin, Randolph, Wu, Peter, Y. F. and Samaddar, Sumitro (et al)
year 1986
title Prolog and Geometry Projects
source IEEE Computer Graphics and Applications. November, 1986. vol. 6: pp. 46-55 : ill. includes bibliography
summary Prolog is a useful tool for geometry and graphics implementations because its primitives, such as unification, match the requirements of many geometric algorithms. During the last two years, programs have been implemented to solve several problems in Prolog, including a subset of the Graphical Kernel System, convex-hull calculation, planar graph traversal, recognition of groupings of objects, Boolean combinations of polygons using multiple precision rational numbers, and cartographic map overlay. Certain paradigms or standard forms of geometric programming in Prolog are becoming evident. They include applying a function to every element of a set, executing a procedure so long as a certain geometric pattern exists, and using unification to propagate a transitive function. This article describes the experiences, including paradigms of programming that seem useful, and finally lists those considered as the advantages and disadvantages of Prolog
keywords geometric modeling, computer graphics, PROLOG, programming
series CADline
last changed 2003/06/02 11:58

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