A null-object detection algorithm for constructive solid geometry
Communications of the ACM
An Adaptive Parallel Algorithm for Display of CSG Objects
CONPAR '86 Conference on Algorithms and Hardware for Parallel Processing
Sculptured Surface Shapes using Inner and Outer Bounded Models
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
An algorithm and data structure for 3D object synthesis using surface patch intersections
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Refinement methods for geometric bounds in constructive solid geometry
ACM Transactions on Graphics (TOG)
Computing CSG tree boundaries as algebraic expressions
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Handling geometric objects with free form curves in spatial databases
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
IEEE Transactions on Knowledge and Data Engineering
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A boundary-evaluation algorithm for constructive solid geometry is presented for representations in which the primitives can be bounded by complex surfaces (such as splines) as well as by simpler polynomial surfaces. A fundamental part of the algorithm is the spatial decomposition of each primitive in a way that yields three planar bounded volumes, one containing the primitive (outer set), one contained within the primitive (inner set), and the third being the set difference of the first two, containing the boundary of the primitive. A positive feature of this approach is that the geometric coverage can be extended to any family of solid primitives for which an initial inner-solid-outer-solid segmentation and a subdivision procedure can be devices. Satisfying these two requirements ensures that the resulting primitive definitions are in the canonical form necessary for evaluation. Therefore the cost in terms of software development of adding primitive types does not depend on the number or type of existing primitives.