Computational geometry: an introduction
Computational geometry: an introduction
Computability
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
Dynamical systems, measures, and fractals via domain theory
Information and Computation
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. 4)
Handbook of logic in computer science (vol. 3)
Towards robust interval solid modeling of curved objects
Towards robust interval solid modeling of curved objects
Algorithmic tolerances and semantics in data exchange
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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
Computable banach spaces via domain theory
Theoretical Computer Science - Special issue on computability and complexity in analysis
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Type Theory via Exact Categories
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
On The Measure Of Two-Dimensional Regions With Polynomial-Time Computable Boundaries
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Theoretical Computer Science - Mathematical foundations of programming semantics
Domain theory and differential calculus (functions of one variable)
Mathematical Structures in Computer Science
Effectively open real functions
Journal of Complexity
A Continuous Derivative for Real-Valued Functions
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Reliable Implementation of Real Number Algorithms: Theory and Practice
A computable approach to measure and integration theory
Information and Computation
Group morphology with convolution algebras
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A computational model for multi-variable differential calculus
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Computability in computational geometry
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Geometric interoperability via queries
Computer-Aided Design
Hi-index | 5.23 |
Solid modelling and computational geometry are based on classical topology and geometry in which the basic predicates and operations, such as membership, subset inclusion, union and intersection, are not continuous and therefore not computable. But a sound computational framework for solids and geometry can only be built in a framework with computable predicates and operations. In practice, correctness of algorithms in computational geometry is usually proved using the unrealistic Real RAM machine model of computation, which allows comparison of real numbers, with the undesirable result that correct algorithms, when implemented, turn into unreliable programs. Here, we use a domain-theoretic approach to recursive analysis to develop the basis of an effective and realistic framework for solid modelling. This framework is equipped with a well defined and realistic notion of computability which reflects the observable properties of real solids. The basic predicates and operations on solids are computable in this model which admits regular and non-regular sets and supports a design methodology for actual robust algorithms. Moreover, the model is able to capture the uncertainties of input data in actual CAD situations.