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.

Ray Tracing Free-Form B-Spline Surfaces

1986 ◽  
Vol 6 (2) ◽  
pp. 41-49 ◽  
Author(s):  
Michael A.J. Sweeney ◽  
Richard H. Bartels
Keyword(s):  
Ray Tracing ◽  
Free Form ◽  
B Spline ◽  
Spline Surfaces

An Efficient Sensing Localization Algorithm for Free-Form Surface Digitization

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Yunbao Huang ◽  
Xiaoping Qian
Keyword(s):  
Search Time ◽  
Divide And Conquer ◽  
Free Form ◽  
Point Problem ◽  
Localization Algorithm ◽  
B Spline ◽  
Divide And Conquer Algorithm ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Free Form Surface

We present a divide-and-conquer method that efficiently finds a near-optimal distribution of sensing locations for free-form surface digitization. We formulate a next-best-point problem and transform the uncertainty of a B-spline surface into a higher-dimensional B-spline surface. This technique allows the use of the convex hull and subdivision properties of B-spline surfaces in the divide-and-conquer algorithm. It thus greatly reduces the search time for determining the next best sensing location.

Intersection of Offset Surfaces of Parametric Patches

1992 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Parametric Surface ◽  
Intersection Curve ◽  
B Spline ◽  
Numerical Examples ◽  
Surface Patches ◽  
Normal Projection ◽  
Offset Surfaces ◽  
Nurbs Surfaces ◽  
Effectiveness And Efficiency ◽  
Offset Surface

Abstract In this paper, we present a new method to calculate intersection curve of offset surfaces of two parametric surface patches. This method is based on the concept of normal projection and the intersection problem is formulated with a set of tensorial differential equations. The intersection is represented in the parametric spaces of the base surfaces and no offset surface approximation is needed. Numerical examples are presented for non-uniform rational b-spline (NURBS) surfaces to illustrate the effectiveness and efficiency of the proposed approach.

Algorithm for designing free-form imaging optics with nonrational B-spline surfaces

2017 ◽  
Vol 56 (9) ◽  
pp. 2517 ◽  
Author(s):  
Rengmao Wu ◽  
José Sasián ◽  
Rongguang Liang
Keyword(s):  
Free Form ◽  
B Spline ◽  
Spline Surfaces ◽  
Imaging Optics

Parametric Surface Intersections for Geometric Modeling

1992 ◽  
Author(s):  
J.-M. Chen ◽  
Yu Wang ◽  
E. L. Guroz ◽  
Fritz B. Prinz
Keyword(s):  
Geometric Modeling ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
B Spline ◽  
Surface Intersection ◽  
Spline Surfaces ◽  
Intersection Algorithm ◽  
Intersection Curves ◽  
Surface Intersections

Abstract A surface-surface intersection algorithm is an important element in the development of a geometric modeler. This paper presents a new algorithm for calculating the intersection curves of two parametric surfaces. Combining the merits of subdivision and global exploration methods, this algorithm is efficient and robust in dealing with the issues related to small loops and singularities. This algorithm is demonstrated with examples of non-uniform rational B-spline surfaces.

scholarly journals The Similarity Comparison Algorithm of Free-Form Surfaces with Single Curvature Feature

2018 ◽  
Vol 36 (5) ◽  
pp. 1004-1012
Author(s):  
Hongshen Wang ◽  
Yurong Wang ◽  
Honghong Zhao ◽  
Jintang Yan
Keyword(s):  
Dimensional Space ◽  
Free Form ◽  
Normal Vector ◽  
Similarity Comparison ◽  
B Spline ◽  
Spline Surfaces ◽  
Similarity Algorithm ◽  
Evaluation Algorithm ◽  
Intersection Sets ◽  
Free Form Surfaces

This paper studies the shape similarity evaluation of free-form surfaces expressed by B-spline with single curvature feature and proposes a similarity evaluation algorithm based on curvature feature. Firstly, we calculate the normal vector direction of the two surfaces compared, and use it as the Z axis, so that the two surfaces are aligned on the Z axis. Then, the two surfaces are cut with planes that all perpendicular to the Z axis, and the intersection sets of two surfaces are obtained respectively. Finally, we design the similarity algorithm of plane curves to realize the similarity comparison of corresponding curves in the two sets of intersection, and which is used as the basis for evaluating the similarity between two surfaces. The algorithm transforms the problem of similarity comparison between 3D surfaces into two dimensional space by plane cutting method, and reduces the complexity of the problem effectively. The algorithm only needs to align one coordinate axis in the process of posture adjustment, so it is easy to implement. In order to test the effect of the algorithm, simulation experiments on different type of single curvature feature B-spline surfaces are carried out. The results show that the proposed similarity comparison algorithm of free-form surfaces is feasible and effective.

Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme

2017 ◽  
Vol 3 (1) ◽  
pp. 82
Author(s):  
Nga Le-Thi-Thu ◽  
Khoi Nguyen-Tan ◽  
Thuy Nguyen-Thanh
Keyword(s):  
Free Form ◽  
Subdivision Scheme ◽  
B Spline ◽  
Geometric Fitting ◽  
Arbitrary Topology ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Low Degree ◽  
Data Points ◽  
Free Form Surfaces

Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adjusted locally by a simple geometric fitting algorithm to increase the accuracy of the obtained B-spline. The reconstructed B-spline having the low degree along with arbitrary topology is interpolative to most of the given data points after some fitting steps without solving any linear system. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Results show that this approach is simple, fast, flexible and can be successfully applied to a variety of surface shapes.

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