Formal specification of interactive graphics programming languages
Formal specification of interactive graphics programming languages
A functional approach to animation
Computer Graphics Forum
Modular algebraic specification of some basic geometrical constructions
Artificial Intelligence - Special issue on geometric reasoning
Interactive design with sequences of parameterized transformations
Intelligent CAD systems II: implementational issues
Metamouse: specifying graphical procedures by example
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
An OBJ3 functional specification for boundary representation
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Formal specification of topological subdivisions using hypermaps
Computer-Aided Design
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
From λσ to λν: a journey through calculi of explicit substitutions
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Algebraic specification of a 3D-modeler based on hypermaps
CVGIP: Graphical Models and Image Processing
Formal resolution of geometrical constraint systems by assembling
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Geometric construction by assembling solved subfigures
Artificial Intelligence
An Embedded Modeling Language Approach to Interactive 3D and Multimedia Animation
IEEE Transactions on Software Engineering
Functional specification and prototyping with oriented combinatorial maps
Computational Geometry: Theory and Applications
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Sketch-based pruning of a solution space within a formal geometric constraint solver
Artificial Intelligence
Computer Science Logo Style: Symbolic Computing
Computer Science Logo Style: Symbolic Computing
Algebraic Specification and Development in Geometric Modeling
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
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This paper focuses on the general parameterization in geometric modeling. We have adapted the λ-calculus formalism to an existing geometrical model which has an applicative representation: the generalized maps embedded in the plane. We investigated how this allows us to parameterize geometric objects by other objects, which can themselves be functional, rather than just by values such as size, shape or position. Thus, conditional, iterative, recursive and shared objects can be built and managed in an homogenous way. We have based the study on an interactive prototype implemented in Objective Caml. Its interface offers two consistent working views. The first interacts with geometric objects while the second interacts with the corresponding programs. We have examined in detail various higher-order operations where λ-calculus abstraction and application are used extensively to demonstrate how such objects can be built and manipulated. We will illustrate the force of our proposals using more complex constructions.