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Publication# Medial axis transformation as a solid modeling representation method for computer aided design software

Abstract

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT faces, the MAT faces being bound by sets of MAT edges, which are portions of curves lying on a surface of the MAT faces on either side of the edge, and points where several MAT faces meet are called MAT vertices. The method comprises at least defining each of the MAT vertices as points in a space domain; assigning a radius function to each of the MAT vertices, based on only a single value; defining each of the MAT edges as a curve in space; defining limits of each of the MAT edges as two MAT vertexes which lie on the curve; assigning a radius function to each of the MAT edges; defining each of MAT faces as a surface in space; defining the limits of each of the MAT faces as a MAT loop, comprising at least three MAT edges, sharing each a MAT node, whereby a direction, clockwise or counter-clockwise, of the MAT loop defines on which side of the MAT loop the MAT face will be formed; defining the MAT links as the edges which are shared by at least two MAT faces; assigning a radius function to each of the MAT faces; and defining a MAT object as a connected set of MAT faces, edges and vertices.

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Related concepts (7)

Computer-aided design

Computer-Aided Design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing. Designs made through CAD software are helpful in protecting products and inventions when used in patent applications. CAD output is often in the form of electronic files for print, machining, or other manufacturing operations.

Data structure

In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type.

Curve

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...