Closed Boundary Offset From the Medial Axis

2005 ◽  
Author(s):  
Feiqi Zhang ◽  
Terry Faddis
Keyword(s):  
Image Processing ◽  
Computer Science ◽  
Medial Axis ◽  
Tree Structure ◽  
Medial Axis Transform ◽  
B Spline ◽  
Cad Systems ◽  
Circular Arcs ◽  
Novel Method ◽  
Single Boundary

Closed boundary orthogonal offset has been a default function in many CAD systems and has applications in manufacturing engineering such as toolpath generation and computer science fields such as image processing. Most current solutions to this function are limited to the single boundary inputs composed of linear segments and circular arcs. This paper describes a novel method to generate the approximate offsets of closed boundaries directly from the associated medial axis. The method accepts both single boundaries and multi-connected boundaries as input. The local and global intersection problems are entirely avoided. An extended discrete medial axis transform construction algorithm for multi-connected boundaries is introduced. The associated tree structure storing the medial axis data is generated along with the medial axis. The discrete characteristic of the medial axis construction method also gives the offset method the advantageous potential to handle B-spline inputs.

Stable Computation of the 2D Medial Axis Transform

1998 ◽  
Vol 08 (05n06) ◽  
pp. 577-598 ◽  
Author(s):  
Guy Evans ◽  
Alan Middleditch ◽  
Nick Miles
Keyword(s):  
Medial Axis ◽  
Medial Axis Transform ◽  
Element Mesh ◽  
Alternative Representation ◽  
Circular Arcs ◽  
Straight Line ◽  
Key Points ◽  
Stable Computation ◽  
Mathematical Definitions ◽  
Biological Shape

The medial axis transform of a 2D region was introduced by Blum in the 1960's as an aid to the description of biological shape. It is an alternative representation of a region which is often more amenable to analysis. This property has led to its use in diverse fields including pattern recognition and automatic finite element mesh generation. There are two widely agreed mathematical definitions for the medial axis transform which are closely related. It is shown that these definitions are not in general equivalent, despite being so far many types of region. In this paper, precise mathematical definitions of the medial axis transform and its key points (atoms) are given, and an O(n2) algorithm for its computation via those atoms presented. This algorithm is described in terms of simple polygons whose sole boundary consists of circular arcs and straight line segments, then extended to polygons with holes. It is shown how more complex edges could be accommodated. In comparison with existing algorithms it is simple to implement and stable in the presence of geometric degeneracy.

Medial Axis Transform Method for Shape Design of Hub and Shroud Contours of Impellers

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Pengfei Wang ◽  
Xiaodong Ruan ◽  
Jun Zou ◽  
Xin Fu
Keyword(s):  
Cross Section ◽  
Medial Axis ◽  
Additional Constraint ◽  
Shape Design ◽  
Medial Axis Transform ◽  
Transform Method ◽  
Curvature Equation ◽  
Cross Section Area ◽  
Section Area ◽  
Novel Method

A novel method of designing hub and shroud contours is presented. The method, based on the medial axis transform theory in differential geometry, gives a uniform description of hub and shroud contours and the formula of cross section area. Through solving the formula of cross section area with an additional constraint, the hub and shroud contours can be determined numerically. The constraint is exposed through a curvature equation, which allows the medial axis or hub (shroud) contour to be a certain form. Using this method, various optimization criteria relating to the cross section area can be conveniently introduced into the design.

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