Computability
Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
Exact real arithmetic formulating real numbers as functions
Research topics in functional programming
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Boundary representation modelling with local tolerances
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Handbook of logic in computer science (vol. 3)
Evaluation of a new method to compute signs of determinants
Proceedings of the eleventh annual symposium on Computational geometry
Real number computability and domain theory
Information and Computation
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Efficient exact evaluation of signs of determinants
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing exact geometric predicates using modular arithmetic with single precision
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Lazy computation with exact real numbers
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
Foundation of a computable solid modeling
Proceedings of the fifth ACM symposium on Solid modeling and applications
Domains and lambda-calculi
Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Algebraic methods and arithmetic filtering for exact predicates on circle arcs
Proceedings of the sixteenth annual symposium on Computational geometry
Theoretical Computer Science
Approximation by Interval Bezier Curves
IEEE Computer Graphics and Applications
The Appearance of Big Integers in Exact Real Arithmetic Based on Linear Fractional Transformations
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
Semantics of Exact Real Arithmetic
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Experimental study on acceleration of an exact-arithmetic geometric algorithm
SMA '97 Proceedings of the 1997 International Conference on Shape Modeling and Applications (SMA '97)
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Domain Theoretic Solutions of Initial Value Problems for Unbounded Vector Fields
Electronic Notes in Theoretical Computer Science (ENTCS)
Efficient exact arithmetic over constructive reals
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Coinductive correctness of homographic and quadratic algorithms for exact real numbers
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
From coinductive proofs to exact real arithmetic
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Coalgebraic Representation Theory of Fractals
Electronic Notes in Theoretical Computer Science (ENTCS)
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Coinductive proofs for basic real computation
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
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We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval [-1, 1]. Numerical operations are implemented in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm.