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16
Robust Geometric Computation
, 1997
"... Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section... ..."
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Cited by 80 (14 self)
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Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section...
Recent progress in exact geometric computation.
 Journal of Logic and Algebraic Programming,
, 2005
"... ..."
Efficient Exact Geometric Predicates for Delaunay Triangulations
, 2002
"... A time efficient implementation of the exact computation paradigm relies on arithmetic filters which are used to speed up the exact computation of easy instances of the geometric predicates. Depending of what is called easy instances, we usually classify filters as static or dynamic and also some in ..."
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Cited by 18 (5 self)
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A time efficient implementation of the exact computation paradigm relies on arithmetic filters which are used to speed up the exact computation of easy instances of the geometric predicates. Depending of what is called easy instances, we usually classify filters as static or dynamic and also some in between categories often called semistatic. In this
Topological beam tracing
 In Proc. 15th ACM Symposium on Computational Geometry
, 1999
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A Generalized and Improved Constructive Separation Bound for Real Algebraic Expressions
, 2000
"... We prove a separation bound for a large class of algebraic expressions specified by expression dags. The bound applies to expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, kth root operations for integral k, and taking roots o ..."
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Cited by 6 (0 self)
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We prove a separation bound for a large class of algebraic expressions specified by expression dags. The bound applies to expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, kth root operations for integral k, and taking roots of polynomials whose coefficients are given by the values of subexpressions. The (logarithm of the) new bound depends linearly on the algebraic degree of the expression. Previous bounds applied to a smaller class of expressions and did not guarantee linear dependency.
Structural filtering: A paradigm for efficient and exact geometric programs
 Proc. 11th Canadian Conference on Computational Geometry
, 1999
"... We introduce a new filtering technique that can be used in the implementation of geometric algorithms called "structural filtering". Using this filtering techniques we gain about 20 % when compared to predicatefiltered implementations. Of theoretical interest are some results regarding th ..."
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Cited by 6 (3 self)
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We introduce a new filtering technique that can be used in the implementation of geometric algorithms called "structural filtering". Using this filtering techniques we gain about 20 % when compared to predicatefiltered implementations. Of theoretical interest are some results regarding the robustness of sorting algorithms against erroneous comparisons.
A Case Study in Algorithm Engineering for Geometric Computing
 IN PROC. WORKSHOP ON ALGORITHM ENGINEERING
, 1997
"... The goal of this paper is to prove the applicability of algorithm engineering and software design concepts to geometric computing through a vertical case study on the implementation of planar point location algorithms. The work is presented within the framework of the GeomLib project, aimed at de ..."
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Cited by 4 (2 self)
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The goal of this paper is to prove the applicability of algorithm engineering and software design concepts to geometric computing through a vertical case study on the implementation of planar point location algorithms. The work is presented within the framework of the GeomLib project, aimed at developing an easy to use, reliable, and flexible library of robust and efficient geometric algorithms. We present the criteria that have inspired the preliminary design of GeomLib and discuss the guidelines that we have followed in the initial implementation.