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Geometric programming: a programming approach to geometric design

Geometric programming: a programming approach to geometric design,10.1145/212332.212349,ACM Transactions on Graphics,Alberto Paoluzzi,Valerio Pascucci

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Geometric programming: a programming approach to geometric design (Citations: 29)


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This article presents a functional programming approach to geometric design with embedded polyhedral complexes. Its main goals are to show the expressive power of the language as well as its usefulness for geometric design. The language, named PLASM (the Programming LAnguage for Solid Modeling), introduces a very high level approach to “constructive” or “generative” modeling. Geometrical objects are generated by evaluating some suitable language expressions. Because generating expressions can be easily combined, the language also extends the standard variational geometry approach by supporting classes of geometric objects with varying topology and shape. The design language PLASM can be roughly considered as a geometry-oriented extension of a subset of the functional language FL. The language takes a dimension-independent approach to geometry representation and algorithms. In particular it implements an algebraic calculus over embedded polyhedra of any dimension. The generated objects are always geometrically consistent because the validity of geometry is guaranteed at a syntactical level. Such an approach allows one to use a representation scheme which is weaker than those usually adopted in solid modelers, thus encompassing a broader geometric domain, which contains solids, surfaces, and wire-frames, as well as higher-dimensional objects.

Journal: ACM Transactions on Graphics - TOG , vol. 14, no. 3, pp. 266-306, 1995

DOI: 10.1145/212332.212349

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- ...Our goal is to graft this approach to field modeling onto an already established computational framework for geometric modeling with cell complexes [25]...
Antonio DiCarlo, et al. Chain-Based Representations for Solid and Physical Modeling
- ...Our goal is to apply this approach to field modeling onto an already established computational framework for geometric modeling with cell complexes (20)...
Franco Milicchio, et al. A codimension-zero approach to discretizing and solving field problems
- ...Our goal is to graft this approach to eld modeling onto an already established computational framework for geometric modeling with cell complexes [Paoluzzi et al. 1995]...
Antonio Dicarlo, et al. Solid and physical modeling with chain complexes
- ...The first prototype was developed in PLaSM, a functional design language [16,10] for rapid prototyping of geometric algorithms and applications [17]...
Antonio Dicarlo, et al. Fast computation of inertia through affinely extended Euler tensor
- ...Conversely, the design language PLaSM [10, 7, 6], a geometric extension of Backus FL [1], provides the full power of a programming language (with support for conditional, recursion, higher-level functional abstraction, etc.) while being geometry-oriented, with dimension-independent geometric primitives and operators, allowing very terse definitions of highly complex models...
Franco Milicchio, et al. A Visual Approach To Geometric Programming

Keywords (7)

Related Publications (5)

Geometric programming: a programming approach to geometric design,10.1145/212332.212349,ACM Transactions on Graphics,Alberto Paoluzzi,Valerio Pascucci

Citation Context (13)

Antonio DiCarlo, et al. Chain-Based Representations for Solid and Physical Modeling

Franco Milicchio, et al. A codimension-zero approach to discretizing and solving field problems

Antonio Dicarlo, et al. Solid and physical modeling with chain complexes

Antonio Dicarlo, et al. Fast computation of inertia through affinely extended Euler tensor

Franco Milicchio, et al. A Visual Approach To Geometric Programming

References (25)

Modification of geometric models through variational geometry (Citations: 145)

An introduction to the programming language fl (Citations: 16)

Computer graphics: principles and practice (Citations: 2925)

Constructive non-regularized geometry (Citations: 67)

Binary space partitioning trees as an alternative representation of polytopes (Citations: 24)

Citations (29)

Discrete physics using metrized chains (Citations: 2)

Chain-Based Representations for Solid and Physical Modeling (Citations: 4)

Semantic fitting and reconstruction (Citations: 3)

A codimension-zero approach to discretizing and solving field problems (Citations: 3)

Compilation of procedural models


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