An Efficient Algorithm for Circular Blending of Edges

2001 ◽  
Author(s):  
Sharad K. Jaiswal ◽  
A. Ghosal ◽  
B. Gurumoorthy
Keyword(s):  
Efficient Algorithm ◽  
Tangent Plane ◽  
Characteristic Direction ◽  
Intersection Curve ◽  
Generation Algorithm ◽  
Variable Radius ◽  
Surface Intersection ◽  
Explicit Evaluation

Abstract This paper describes a method for constructing circular blends using geometric tools. The algorithm presented in this paper is based on marching along a characteristic direction on the tangent plane to the Voronoi surface of the two surfaces being considered for blending. Starting from any point on the edge to be blended, the algorithm converges to the spine curve. The characteristic direction of marching lies on the plane containing the points in assignment and the tangent plane to the Voronoi surface. The spine curve generation algorithm presented in this paper, does not require computing offsets of surfaces or an explicit evaluation of surface-surface intersection (SSI). The algorithm presented is computationally simple and fast, and can be used for constant and variable radius circular blending of surfaces, each of which is G2 continuous. The algorithm can also be used to obtain the surface-surface intersection curve by setting the radius of blend to zero.

A NEW APPROACH FOR SURFACE INTERSECTION

1991 ◽  
Vol 01 (04) ◽  
pp. 491-516 ◽  
Author(s):  
DINESH MANOCHA ◽  
JOHN F. CANNY
Keyword(s):  
Dimensional Space ◽  
Intersection Curve ◽  
Algebraic Set ◽  
Algebraic Sets ◽  
Good Surface ◽  
Surface Intersection ◽  
Easy Problem ◽  
The Matrix ◽  
Lower Dimensional Space ◽  
Lower Dimensional

Evaluating the intersection of two rational parametric surfaces is a recurring operation in solid modeling. However, surface intersection is not an easy problem and continues to be an active topic of research. The main reason lies in the fact that any good surface intersection technique has to balance three conflicting goals of accuracy, robustness and efficiency. In this paper, we formulate the problems of curve and surface intersections using algebraic sets in a higher dimensional space. Using results from Elimination theory, we project the algebraic set to a lower dimensional space. The projected set can be expressed as a matrix determinant. The matrix itself, rather than its symbolic determinant, is used as the representation for the algebraic set in the lower dimensional space. This is a much more compact and efficient representation. Given such a representation, we perform matrix operations for evaluation and use results from linear algebra for geometric operations on the intersection curve. Most of the operations involve evaluating numeric determinants and computing the rank, kernel and eigenvalues of matrices. The accuracy of such operations can be improved by pivoting or other numerical techniques. We use this representation for inversion operation, computing the intersection of curves and surfaces and tracing the intersection curve of two surfaces in lower dimension.

A SURFACE INTERSECTION ALGORITHM BASED ON LOOP DETECTION

1991 ◽  
Vol 01 (04) ◽  
pp. 473-490 ◽  
Author(s):  
MICHAEL E. HOHMEYER
Keyword(s):  
Gauss Map ◽  
Algebraic Surfaces ◽  
Boundary Representation ◽  
Intersection Curve ◽  
Closed Loops ◽  
Detection Algorithms ◽  
Surface Intersection ◽  
Loop Detection ◽  
Intersection Algorithm ◽  
New Strategies

A robust and efficient surface intersection algorithm that is implementable in floating point arithmetic, accepts surfaces algebraic or otherwise and which operates without human supervision is critical to boundary representation solid modeling. To the author's knowledge, no such algorithms has been developed. All tolerance-based subdivision algorithms will fail on surfaces with sufficiently small intersections. Algebraic techniques, while promising robustness, are presently too slow to be practical and do not accept non-algebraic surfaces. Algorithms based on loop detection hold promise. They do not require tolerances except those associated with machine associated with machine arithmetic, and can handle any surface for which there is a method to construct bounds on the surface and its Gauss map. Published loop detection algorithms are, however, still too slow and do not deal with singularities. We present a new loop detection criterion and discuss its use in a surface intersection algorithms. The algorithm, like other loop detection based intersection algorithms, subdivides the surfaces into pairs of sub-patches which do not intersect in any closed loops. This paper presents new strategies for subdividing surfaces in a way that causes the algorithms to run quickly even when the intersection curve(s) contain(s) singularities.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Blending Cylinders and Cones using Canal Surfaces

2000 ◽  
Vol 5 ◽  
pp. 77-89 ◽  
Author(s):  
M. Kazakevičiūtė ◽  
R. Krasauskas
Keyword(s):  
Canal Surface ◽  
Variable Radius ◽  
Rolling Ball ◽  
Canal Surfaces ◽  
Rational Parameterization

There is reviewed the construction of a rational blending surface between cylinders and cones in some interlocation cases. This surface is constructed as a patch of rolling ball envelope, i.e. as a patch of tangent canal surface of rational-variable radius. This construction defines rational parameterization of a blending surface. The constructed surface is Laguerre invariant.

Energy efficient algorithm for lookup-tables on mobile devices

2016 ◽  
Vol 2016 (7) ◽  
pp. 1-6
Author(s):  
Sergey Makov ◽  
Vladimir Frantc ◽  
Viacheslav Voronin ◽  
Igor Shrayfel ◽  
Vadim Dubovskov ◽  
...  
Keyword(s):  
Mobile Devices ◽  
Efficient Algorithm ◽  
Energy Efficient ◽  
Lookup Tables

Unfoldings of the Intersected Surfaces

2019 ◽  
Vol 17 (17) ◽  
pp. 50-51
Author(s):  
Carmen Popa ◽  
Violeta Anghelina ◽  
Ruxandra-Elena Bratu
Keyword(s):  
Analytical Methods ◽  
Classical Method ◽  
Intersection Curve

AbstractThe paper proposes to establish the intersection curve and the unfoldings of three cylinders. The intersection of the curves was determined by the classical method, using the AutoCAD program, and the unfolded surfaces were realized by analytical methods. For this the Mathematica program was used.

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