Boundary to CSG Conversion

Description:

Conversion of boundary representations (b-rep) to Constructive Solid Geometry (CSG) representations is well understood as a mathematical problem that has been solved and fully implemented for restricted geometric domains. Loosely, the procedure induces a set of primitives from a given boundary representation that are used to partition the space into Boolean atoms (cells) that classify either in or out with respect to the solid. The union of those atoms that classify in is optimized using geometric and Boolean algebra techniques to obtain efficient (often minimal) CSG representation of the solid. 

The union of those atoms that classify inis optimized using geometric and Boolean algebra techniques to obtain efficient (often minimal) CSG representation of the solid. Below you can find detailed technical information on the problem and the approach, full implementation of the procedure for three-dimensional solids bounded by natural quadric surfaces, and some examples illustrating the power of the method.

• {ln:csg-example 'Examples}
• {ln:Technical Overview 'Technical Background}
• {ln:Software 'Software}
• Online conversion service (coming soon)

Boundary to CSG conversion technology can be extended to deal with conversion and consistency problems in parametric feature-based modeling and other constructive representations.

For more information on this and other types of representation conversion technology, please contact Prof. This email address is being protected from spambots. You need JavaScript enabled to view it. .

Moving Parts and Assembly

Description:

In this work we propose a set-theoretic characterization of the design space of solutions for the class of problems of moving parts subjected to spatial containment and contact constraints. Our proposed characterization of the design space relies on the fundamental notion of {ln:equivalence 'equivalence classes} of mechanical parts that identifies all parts satisfying a given contact function, and hence it is most useful in the conceptual stage of mechanical design [2, 1]. More specifically, we propose the concept of the maximal part satisfying given spatial constraints as a basis for the formulation of a new set-theoretic approach to designing moving parts based on a `material shrinking' paradigm [2]. Within this formulation, the design proceeds by eliminating only the material whose presence would violate given spatial constraints, and results in the largest part satisfying containment and contact constraints.

The computational tools developed in this research for systematic product development and efficient modification of mechanical parts build on the novel concept of {ln:unsweep 'unsweep} , which is dual to the general sweep operation [5, 6, 4]. We also showed that unsweep operation and the standard set complement induce a disjoint {ln:decomp 'decomposition} of space [3] describing a computational framework that treats motion as an integral part of the model.

In practical terms, the proposed characterization of the contact problem enables the systematic exploration of the design space using fully defined representatives of the functionally equivalent class of parts. Furthermore, we showed that such exploration may be performed using standard tools from geometric modeling, and without assuming any particular parametrization that necessarily restrict both the design space and possible computational techniques for exploring feasible designs.

Finally, a different aspect of this research seeks to understand spatial properties and {ln:comb-struct 'combinatorial structure} of mechanical parts in terms of simple interacting constructs related to part functionality and manufacturing processes [7, 8, 9]. 

Interactive Physics Editor

Description:

 The long term focus of our work is to unify geometric and physical computations and languages, and to develop a  modeling framework where both geometric and physical models are maintained simultaneously.  This in turn requires developing a fundamentally new  combinatorial and algorithmic infrastructure, as described below.

• {ln:vision 'The Vision}
• {ln:comp-rep 'Computer Representation}
• {ln:Modeling Process}
• {ln:System Tutorial}
• {ln:Future directions}

Parametric Solid Modeling

Description:

The main goal of this research work is to provide a broad theoretical framework, investigate systematic methods and algorithms, and develop prototype systems for modeling parametric and variational family of parts. Please follow the links below to learn more about the problems and solutions in parametric modeling.

•   {ln:limitations 'Limitations in current CAD systems}

•   {ln:problems 'Problems in modeling part families}

•   {ln:solutions 'Solutions and methodology}

Are these two solids in the same parametric family?  

People:

• This email address is being protected from spambots. You need JavaScript enabled to view it.
• This email address is being protected from spambots. You need JavaScript enabled to view it.