Trimming Local and Global Self-intersections in Offset Curves Using Distance Maps

2003 ◽  
pp. 213-222 ◽  
Author(s):  
Gershon Elber
Keyword(s):  
Offset Curves

Tool Path Optimization of 2D Contour Considering Stock Boundary

2012 ◽  
Vol 251 ◽  
pp. 169-172
Author(s):  
Fu Zhong Wu
Keyword(s):  
Present Method ◽  
Tool Path ◽  
Three Dimensional ◽  
Boundary Curve ◽  
Tool Path Generation ◽  
Path Optimization ◽  
Path Generation ◽  
Offset Curves ◽  
Measuring Machine ◽  
Tool Diameter

Based on analyzing the existing algorithms, a novel tool path generation of 2D contour considering stock boundary is presented. Firstly the boundary points of stock are obtained by three-dimensional measuring machine. And the boundary curve is constructed by method of features identifying. The stock boundary is offset toward outside with tool diameter. An enclosed region is formed between the contour curves and the offset curves of stock boundary. The tool path is generated by form of parallel spiral by offsetting the stock boundary in the enclosed region. Finally the validity of present method is demonstrated by an example.

Path Planning of Multiple UAV’s in an Environment of Restricted Regions

2005 ◽  
Author(s):  
Madhavan Shanmugavel ◽  
Antonios Tsourdos ◽  
Rafal Zbikowski ◽  
Brian White
Keyword(s):  
Path Planning ◽  
Path Length ◽  
Mathematical Property ◽  
Multiple Uavs ◽  
Safety Margins ◽  
Pythagorean Hodograph ◽  
Offset Curves ◽  
Safety Constraints ◽  
Continuous Curvature ◽  
Ph Curve

This paper describes a novel idea of path planning for multiple UAVs (Unmanned Aerial Vehicles). The path planning ensures safe and simultaneous arrival of the UAVs to the target while meeting curvature and safety constraints. Pythagorean Hodograph (PH) curve is used for path planning. The PH curve provides continuous curvature of the paths. The offset curves of the PH paths define safety margins around and along each flight path. The simultaneous arrival is satisfied by generation of paths of equal lengths. This paper highlights the mathematical property — changing path-shape and path-length by manipulating the curvature and utilises this to achieve the following constraints: (i) Generation of paths of equal length, (ii) Achieving maximum bound on curvature, and, (iii) Meeting the safety constraints by offset paths.

Fast, precise flattening of cubic Bézier path and offset curves

2005 ◽  
Vol 29 (5) ◽  
pp. 656-666 ◽  
Author(s):  
Thomas F. Hain ◽  
Athar L. Ahmad ◽  
Sri Venkat R. Racherla ◽  
David D. Langan
Keyword(s):  
Offset Curves

A Hybrid Approach to Polygon Offsetting Using Winding Numbers and Partial Computation of the Voronoi Diagram

2014 ◽  
Author(s):  
Greg Burton
Keyword(s):  
Voronoi Diagram ◽  
Recursive Algorithm ◽  
Hybrid Approach ◽  
Radius Of Curvature ◽  
Convex Polygons ◽  
Pocket Machining ◽  
Worst Case ◽  
Offset Curves ◽  
Complete Computation ◽  
Offset Curve

In this paper we present a new, efficient algorithm for computing the “raw offset” curves of 2D polygons with holes. Prior approaches focus on (a) complete computation of the Voronoi Diagram, or (b) pair-wise techniques for generating a raw offset followed by removal of “invalid loops” using a sweepline algorithm. Both have drawbacks in practice. Robust implementation of Voronoi Diagram algorithms has proven complex. Sweeplines take O((n + k)log n) time and O(n + k) memory, where n is the number of vertices and k is the number of self-intersections of the raw offset curve. It has been shown that k can be O(n2) when the offset distance is greater than or equal to the local radius of curvature of the polygon, a regular occurrence in the creation of contour-parallel offset curves for NC pocket machining. Our O(n log n) recursive algorithm, derived from Voronoi diagram algorithms, computes the velocities of polygon vertices as a function of overall offset rate. By construction, our algorithm prunes a large proportion of locally invalid loops from the raw offset curve, eliminating all self-intersections in raw offsets of convex polygons and the “near-circular”, k proportional to O(n2) worst-case scenarios in non-convex polygons.

Algebraic properties of plane offset curves

1990 ◽  
Vol 7 (1-4) ◽  
pp. 101-127 ◽  
Author(s):  
R.T. Farouki ◽  
C.A. Neff
Keyword(s):  
Algebraic Properties ◽  
Offset Curves

Tool Path Generation Based on B-Spline Wavelets

2001 ◽  
Author(s):  
Ranga Narayanaswami ◽  
Junhua Pang
Keyword(s):  
Tool Path ◽  
Fundamental Problem ◽  
Tool Path Generation ◽  
Numerical Control ◽  
Algebraic Complexity ◽  
Path Generation ◽  
Object Boundary ◽  
Machined Surface ◽  
Novel Approach ◽  
Offset Curves

Abstract Tool path generation is a fundamental problem in numerical control machining. Typical methods used for machining 2.5D objects include generation of offset contours using trimmed offset curves and zigzag sequences. The offset contours result in unnecessary detailed curves far away from the object boundary. The zigzag sequences result in frequent stops and changes in tool direction. In this paper we present a novel approach for tool path generation based on wavelet theory. The theory of wavelets naturally leads to a simple cut sequence algorithm that provides valid and efficient coverage of the machined surface. The classical analytical and algebraic complexity in tool path planning is also reduced. In this paper, curves are represented by endpoint interpolating B-splines and their corresponding wavelets. Design and manufacturing examples are also presented in this paper.

SELF-INTERSECTIONS OF OFFSET CURVES AND SURFACES

2001 ◽  
Vol 07 (01) ◽  
pp. 1-21 ◽  
Author(s):  
J. WALLNER ◽  
T. SAKKALIS ◽  
T. MAEKAWA ◽  
H. POTTMANN ◽  
G. YU
Keyword(s):  
Curves And Surfaces ◽  
Offset Curves
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