In order to reconstruct spatial curves from discrete electronic sensor data, two alternative C Pythagorean–hodograph (PH) quintic spline formulations are proposed, interpolating given spatial data subject to prescribed contraints on the arc length of each spline segment. The first approach is concerned with the interpolation of a sequence of points, while the second addresses the interpolation ...

The stability of a soil slope is usually analyzed by limit equilibrium methods, in which the identification of the critical slip surface is of principal importance. In this study the spline curve in conjunction with a genetic algorithm is used to search the critical slip surface, and Spencer’s method is employed to calculate the factor of safety. Three examples are presented to illustrate the r...

We present a new method for computing intersections of two parametric B-Spline curves. We use an intersection of the control polygons as an approximation for an intersection of the curves in combination with knot insertion. The resulting algorithm is asymptotically Newton-like, but without the need of a starting value. Like Newton’s method, it converges quadratically at transversal intersection...

We consider the problem of fitting B-spline curves and surfaces to point clouds on taking real world obstacles into account at the same time. Therefor, we describe the fitting problem as optimization problem and employ an iterative procedure to solve it. The presence of obstacles poses constraints on this minimization process. We examine two families of obstacles: first, the point cloud itself ...

A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces Sm Δ and S t n Δ over a domain D with a partition Δ, the Bezout number BN m,r;n,t;Δ is defined as the maximum finite number of the common intersection points of two arbitrary piecewise algebraic curves f x, y 0 and g x, y 0, where f x, y ∈ Sm Δ and g x, y ∈ Sn Δ . In ...

Problem statement: The objective of this study is to compare the methods for approximating the positions of twist fiber in yarn structures. Computer Aided Design (CAD) is applied using parametric equation, spline curve and NURBS curve. The ideal twist fiber and fiber migration are studied in 3 dimensions. Approach: The fiber positions in yarn structures were measured by trace fiber technique. T...

This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In particular, when one bicubic tensor-product B-spline patch is associated with each facet of a quadrilateral mesh with n-valent vertices and we do not want seg...

Abstract. This paper presents an efficient and sufficient algorithm to approximate general interpolating Spline curve which goes through the given set of design-data points by using asymptotic iterative B-spline curves. Firstly, the given set is considered as the control points of a B-spline, to create the initial approximate curve, then the iterative grade is built based on the error between t...

Given a polygonal channel between obstacles in the plane or in space, we present an algorithm for generating a parametric spline curve with few pieces that traverses the channel and stays inside. While the problem without emphasis on few pieces has trivial solutions, the problem for a limited budget of pieces represents a nonlinear and continuous (‘infinite’) feasibility problem. Using tight, t...

The effect of the modification of knot values on the shape of B-spline curves is examined in this paper. The modification of a knot of a Bspline curve of order k generates a one-parameter family of curves.This family has an envelope which is also a B-spline curve with the same control polygon and of order k 2 1: Applying this theoretical result, three shape control methods are provided for cubi...