Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Algebraic specification of a 3D-modeler based on hypermaps
CVGIP: Graphical Models and Image Processing
Some Topological Properties of Surfaces in Z3
Journal of Mathematical Imaging and Vision
Formal Specification and Theorem Proving Breakthroughs in Geometric Modeling
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Constructions: A Higher Order Proof System for Mechanizing Mathematics
EUROCAL '85 Invited Lectures from the European Conference on Computer Algebra-Volume I - Volume I
Synthesizing Proofs from Programs in the Calculus of Inductive Constructions
MPC '95 Mathematics of Program Construction
Polyhedra genus theorem and Euler formula: A hypermap-formalized intuitionistic proof
Theoretical Computer Science
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This paper is the first half of a two-part series devoted to an exemplary formal proof of a fundamental result in the field of geometry--the theorem of classification of surfaces--which has major implications in computer graphics. We study here the specification of generalized maps, a topological combinatory model for surfaces subdivisions. We show how we developed in Coq two fundamentally distinct formalizations of generalized maps, each based on one of the standard definitions, in a single common framework, then used this specification to prove for the first time their complete equivalence.