Patrick A. Fitzhorn

A methodology for near-optimal computational superimposition of two-dimensional digital facial photographs and three-dimensional cranial surface meshes.

The authors present a methodology for human identification based on digital superimposition techniques. This methodology computes a fast, near optimal fit between a three-dimensional skull surface mesh and a two-dimensional digitized facial photograph. Since this is done digitally, (1) the photograph can be enhanced to reduce or eliminate motion blur, overexposure or underexposure, and out-of-focus distortions; (2) previous problems with skull/photograph scaling and alignment are minimized or eliminated; and (3) the photograph and skull can be numerically correlated. Two of several test cases produced from an implementation of this methodology are also presented.

Note on a Three-Dimensional Shape Grammar Interpreter

A number of two-dimensional (2D) and three-dimensional (3D) shape grammar interpreters have been developed over the years. In fact, 2D variants of such interpreters are now commonly assigned as classroom exercises. In this note, a 3D implementation is described based on a commercial solid modeling kernel and an associated functional language. A Scheme implementation of the approach is discussed and several examples are given.

A shape grammar for non-manifold modeling

Shape grammars offer a notationally rich representation for dealing with shapes defined over an algebra of points, lines, planes, and solids. Operations in the algebra are bound in subshape recognition and replacement, making them ideal candidates for design as formal solid modeling representations, and for manufacturing as shape-based feature recognizers. As well, given the topological hierarchy of the algebra of shapes, non-manifold modeling is clearly a fundamental part of shape grammars. Thus, one can work at the level of wireframe models, boundary models, and solid models. These characteristics make the shape grammars eminently suitable as a formal representation for both manifold and non-manifold representations of discrete shape.

Engineering design is a computable function

Computational abstraction of engineering design leads to an elegant theory defining (1) the process of design as an abstract model of computability, the Turing machine; (2) the artifacts of design as enumerated strings from a (possibly multidimensional) grammar; and (3) design specifications or constraints as formal state changes that govern string enumeration. Using this theory, it is shown that engineering design is a computable function. A computational methodology based on the theory is then developed that can be described as a form follows function design paradigm.

A Linguistic Formalism for Engineering Solid Modeling

Linguistic models of physical solids have been widely studied for use in the kernels of CAD/CAM systems. These models are useful because they guarantee topological correctness of computer representations of physical solids. This papers outlines a new model, based in the graph grammars, that manipulates the bounding manifolds of physical solids. Proof of topological validity of this linguistic representation scheme proceeds as follows. First, the start graph is shown to be representative of a solid, then productions in the two dimensional grammar are shown to be syntactically complete and closed in the solids. Thus one starts with a solid topology, and any application of a graph production results in a solid topology.

Language of topologically valid bounding manifolds

Abstract The kernel of a boundary-based modelling system, rooted in a formal graph language of topologically valid representations of rigid solids as connected 2-manifolds, is discussed. The representation grammar includes a syntax of face-based Euler operators and their embeddings in manifold models. Since inclusion of both elements provides necessary and sufficient conditions for solidity, topological validity of the representation scheme can be proven as follows. First the start graph is shown to be representative of a solid, then productions in the grammar are shown to be both complete and closed in the solids.

Extensions in variational geometry that generate and modify object edges composed of rational Bézier curves

Abstract Variational geometry is a powerful method for the definition and modification of geometric models, as it constrains object geometry as sets of functional constraints rather than nominal Cartesian elements. This allows one to capture design intent by specifying geometric and engineering constraints that, when resolved using a nonlinear equation solver, define the geometry of the object. The paper explores some of the issues raised when rational Bezier curves are used to generate the edges of a model, that is, specifically, the representation of basic model edges: straight lines and conics. Rational Bezier curves are investigated as they can be used to represent conics precisely in addition to being well equipped to represent and manipulate free-form curves and surfaces.

Form + Function + Algebra = Feature Grammars

Much of the current research and development in feature-based design of discrete objects is both pragmatic in nature and opportunistic in approach. We develop a formalism for features that is consistent in both enumeration and recognition as well as extensible enough to handle the complex relationships between function and form. Using the descriptive, parametric shape grammars, this paradigm is easily expanded to exploit feature set descriptions and manufacturing process planning in a unified and formal framework.

A model of hierarchical design for robotic manipulators

An interesting model of design is discussed and used to automatically design a subset of n-degree of freedom robotic manipulators. The interesting aspect of this model resides in its implementation using a hierarchical arrangement of multiple expert systems, governed and controlled by the analog of a project or design manager. This expert manager acts to divide the problem into functional units and pass information to lower level experts for resolution and convergence of the design. This paper presents the concept and investigates the number and type of expert systems required and the organization of those systems for the design of a subset of the robotic manipulators. The character and processes of the expert manager program are defined and explored. In the case of robotic design, subexpert systems may be dedicated to configuration selection, servo-motor selection, sizing the structural members, kinetic and kinematic calculations, etc. In addition, the knowledge, data base requirements and distribution are discussed. A methodology for conflict resolution between expert systems is proposed.

A dynamic approach to the robotic design cycle

The use of dynamic, high performance computer graphics equipment significantly enhances the capabilities of the engineer in the design and analysis of robotic mechanisms. This paper discusses how these enhancements should be making an impact on the engineering design methodology for robotic manipulators.