Reduced curvature formulae for surfaces, offset surfaces, curves on a surface and surface intersections

2015 ◽  
Vol 37 ◽  
pp. 69-84 ◽  
Author(s):  
Spiros G. Papaioannou ◽  
Marios M. Patrikoussakis
Keyword(s):  
Offset Surfaces ◽  
Surface Intersections

On the determination of starting points for parametric surface intersections

1997 ◽  
Vol 29 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Harn-Jou Yeh
Keyword(s):  
Parametric Surface ◽  
Surface Intersections

Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces

1998 ◽  
Author(s):  
Helmut Pottmann ◽  
Johannes Wallner ◽  
Georg Glaeser ◽  
Bahram Ravani
Keyword(s):  
Motion Planning ◽  
Sculptured Surfaces ◽  
Global Shape ◽  
Be Star ◽  
Offset Surfaces ◽  
Tool Motion ◽  
Curvature Information ◽  
Bivariate Functions

Abstract The paper presents a geometric investigation of collision-free 3-axis milling of surfaces. We consider surfaces with a global shape condition: they shall be interpretable as graphs of bivariate functions or shall be star-shaped with respect to a point. If those surfaces satisfy a local millability criterion involving curvature information, it is proved that this implies globally gouge-free milling. The proofs are based on general offset surfaces. The results can be applied to tool-motion planning and the computation of optimal cutter shapes.

Influence of Surface Relaxation and Multi-Dislocation Strain Field Interactions on X-ray Topographic Images of Dislocations in Semiconductor Materials

1992 ◽  
Vol 262 ◽  
Author(s):  
Jun Wu ◽  
Thomas Fannin ◽  
Michael Dudley ◽  
Vijay Shastry ◽  
Peter Anderson
Keyword(s):  
Local Stress ◽  
Surface Relaxation ◽  
Contour Analysis ◽  
Displacement Fields ◽  
X Ray ◽  
Relaxation Effects ◽  
Slip Bands ◽  
Sensitive Function ◽  
Local Slip ◽  
Surface Intersections

ABSTRACTAnalysis of the white beam synchrotron x-ray topographic contrast behavior of screw dislocations comprising slip bands in silicon, observed under low absorption conditions, is presented. For both individual and groups of dislocations, observed “Direct Image” contrast at the surface intersections of dislocation lines, on reflections for which g·b=0, could be accounted for using equi-misorientation contour analysis using displacement fields which take surface relaxation effects into account. This contrast is shown to be a sensitive function of the local stress environment. In addition, diffuse area contrast observed within and in the vicinity of slip bands on such reflections is also observed to be very sensitive to long range strain fields associated with adjacent slip bands and other defects in the local slip band environment.

Free-Form Plate Modeling Using Offset Surfaces

1988 ◽  
Vol 110 (3) ◽  
pp. 287-294 ◽  
Author(s):  
N. M. Patrikalakis ◽  
P. V. Prakash
Keyword(s):  
Boundary Representation ◽  
Free Form ◽  
Parametric Surfaces ◽  
B Spline ◽  
Spline Surfaces ◽  
Accuracy Criterion ◽  
Offset Surfaces ◽  
Representation Method ◽  
Class Of Functions ◽  
Offset Surface

This paper addresses the representation of plates within the framework of the Boundary Representation method in a Solid Modeling environment. Plates are defined as the volume bounded by a progenitor surface, its offset surface and other, possibly ruled surfaces for the sides. Offset surfaces of polynomial parametric surfaces cannot be represented exactly within the same class of functions describing the progenitor surface. Therefore, if the offset surface is to be represented in the same form as the progenitor surface, approximation is required. A method of approximation relevant to non-uniform rational parametric B-spline surfaces is described. The method employs the properties of the control polyhedron and a recently developed subdivision algorithm to satisfy a certain accuracy criterion. Representative examples are given which illustrate the efficiency and robustness of the proposed method.

Implementation of a polygonal algorithm for surface–surface intersections

1998 ◽  
Vol 34 (2) ◽  
pp. 399-412 ◽  
Author(s):  
Utpal Roy ◽  
V.Ramana Dasari
Keyword(s):  
Surface Intersections
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