A tracing algorithm for constructing medial axis transform of 3D objects bound by free-form surfaces

Medial axis transform (MAT) is a very useful shape interrogation tool in NC tool path generation for pocket milling. This paper presents a new, efficient approach to calculating MATs of planar profiles with boundaries of free-form curves. The proposed approach is mainly based on profile boundary tracing and decomposition. By studying the basic elements of MAT and their geometric properties, several algorithms of finding contact circles are developed. The boundary tracing algorithm can handle profiles with/without internal holes. For a profile without internal holes, it is continuously divided into simpler sub-profiles while travelling along the boundary, and a tree data structure is adopted to keep track of the boundary decomposition process. For a profile with internal holes, it is divided into several simple profiles without internal holes. After generating the MAT of each simple profile, the completed MAT can be found by combining these MATs. This proposed approach is implemented and some illustrative samples are presented to demonstrate its advantages.

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Computation of Shortest Paths on Free-Form Parametric Surfaces

Journal of Mechanical Design ◽

10.1115/1.2826919 ◽

1996 ◽

Vol 118 (4) ◽

pp. 499-508 ◽

Cited By ~ 30

Author(s):

T. Maekawa

Keyword(s):

Boundary Value Problem ◽

Shortest Path ◽

Medial Axis ◽

Boundary Value ◽

Shortest Paths ◽

Relaxation Method ◽

Free Form ◽

Point Boundary ◽

Parametric Surface ◽

Free Form Surfaces

Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.

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Aesthetic Curves and Surfaces in Computer Aided Geometric Design

International Journal of Automation Technology ◽

10.20965/ijat.2014.p0304 ◽

2014 ◽

Vol 8 (3) ◽

pp. 304-316 ◽

Cited By ~ 11

Author(s):

Kenjiro T. Miura ◽

◽

R. U. Gobithaasan ◽

Keyword(s):

Free Form ◽

Design Quality ◽

Aesthetic Design ◽

3D Objects ◽

Curves And Surfaces ◽

Viable Solution ◽

Main Components ◽

2D And 3D ◽

Free Form Surfaces ◽

Complex Curvature

Aesthetic shapes are usually actualized as 3D objects represented by free-form surfaces. The main components used to achieve aesthetic surfaces are 2D and 3D curves, which are the elements most basic for determining the shapes and silhouettes of industrial products. Bézier, B-Spline and NURBS are types of flexible curves developed for various design intents. These curves, however produce complex curvature functions that may undermine the formulation of shape aesthetics. A viable solution to this problem is to formulate aesthetic curves and surfaces from well-defined curvatures to improve aesthetic design quality. This paper advocates formalizing aesthetic curve and surface theories to fill the gapmentioned above, which has existed since the 1970s. This paper begins by reviewing on fair curves and surfaces. It then extensively discusses on the technicalities of Log-Aesthetic (LA) curves and surfaces and touches on industrial design applications. These emerging LA curves have a high potential for being used as standards to generate, evaluate and reshape aesthetic curves and surfaces, thus revolutionizing efficiency in developing curve and shape aesthetics.

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Contour Representation by Clustering Curvatures of the 3D Objects

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.147-149.633 ◽

2009 ◽

Vol 147-149 ◽

pp. 633-638

Author(s):

Arūnas Lipnickas ◽

Vidas Raudonis

Keyword(s):

Free Form ◽

Distance Measurements ◽

3D Object ◽

Human Foot ◽

3D Objects ◽

Large Size ◽

Contour Representation ◽

Triangulated Surfaces ◽

Curvature Estimation ◽

Free Form Surfaces

The purpose of this work is to segment large size triangulated surfaces and the contours extraction of the 3D object by the use of the object curvature value. The curvatures values allow categorizing the type of the local surface of the 3D object. In present work the curvature was estimated for the free-form surfaces obtained by the 3D range scanner. A free-form surface is the surface such that the surface normal is defined and continuous everywhere, except at sharp corners and edges [2, 5]. Two types of distance measurements functions based on Euclidian distance, bounded box and topology of surface were used for the curvature estimation. Clustering technique has been involved to cluster the values of the curvature for 3D object contour representation. The described technique was applied to the 3D objects with free-form surfaces such as the human foot and cube.

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