authors 
Pasko, A.A., Adzhiev, V.D., Sourin, A.I. and Savchenko, V.V. 
year 
1995 
title 
Function representation in geometric modeling: concepts, implementation and applications 
source 
The Visual Computer, 11 (8) 429446 
summary 
Geometric modeling using continuous real functions of several variables is discussed. Modeling concepts include sets of objects, operations and relations. An object is a closed point set of ndimensional Euclidean space with a defining inequality f x x xn ( , ,..., ) 1 2 0 °Ÿ . Transformations of a defining function are described for the settheoretic operations, blending, offsetting, bijective mapping, projection, Cartesian product and metamorphosis. Inclusion, point membership and intersection relations are described. In the implemented interactive modeling system, we use highlevel geometric language that provides extendibility of the modeling system by input symbolic descriptions of primitives, operations and predicates. This approach supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxelbased objects, deformable and other animated objects. Application examples of aesthetic design, collisions simulation, NC machining, range data processing, and 3D texture generation are given. 
series 
journal paper 
full text 
file.pdf (106,571 bytes) 
references 
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last changed 
2003/04/23 13:50 
