1720352
T-splines and T-NURCCs
This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T-spline control grids permit T-junctions, so lines of control points need not traverse the entire control grid. T-splines support many valuable operations within a consistent framework, such as local refinement, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The paper focuses on T-splines of degree three, which are C2 (in the absence of multiple knots). T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines and Catmull-Clark surfaces. Thus, a modeling program for T-NURCCs can handle any NURBS or Catmull-Clark model as special cases. T-NURCCs enable true local refinement of a Catmull-Clark-type control grid: individual control points can be inserted only where they are needed to provide additional control, or to create a smoother tessellation, and such insertions do not alter the limit surface. T-NURCCs use stationary refinement rules and are C2 except at extraordinary points and features.
1709850
Estimating tessellation parameter intervals for rational curves and surfaces
This paper presents a method for determining a priori a constant parameter interval for tessellating a rational curve or surface such that the deviation of the curve or surface from its piecewise linear approximation is within a specified tolerance. The parameter interval is estimated based on information about second-order derivatives in the homogeneous coordinates, instead of using affine coordinates directly. This new step size can be found with roughly the same amount of computation as the step size in Cheng [1992], though it can be proven to always be larger than Cheng's step size. In fact, numerical experiments show the new step is typically orders of magnitude larger than the step size in Cheng [1992]. Furthermore, for rational cubic and quartic curves, the new step size is generally twice as large as the step size found by computing bounds on the Bernstein polynomial coefficients of the second derivatives function.
40804986
Bounds on the Moving Control Points of Hybrid Curves
Abstract Hybrid curves provide an attractive method for approximating rational Bezier curves by polynomial Bezier curves. In this paper, several methods are provided to estimate the error bounds for the approximation to the moving control point of the hybrid curves. When the given rational Bezier curves satisfies the convergent conditions for moving control point of the hybrid curve, by these methods we can choose a hybrid curve with a certain degree such that the distance between the moving control point and a special point is less than a given error bound ϵ. So the polynomial Bezier curves to approximate the rational Bezier curve can be obtained by replacing the moving control point with the special point.
7059364
Non-uniform recursive subdivision surfaces
Doo-Sabin and Catmull-Clark subdivision surfaces are based on the notion of repeated knot insertion of uniform tensor product B-spline surfaces. This paper develops rules for non-uniform Doo-Sabin and Catmull-Clark surfaces that generalize non-uniform tensor product Bspline surfaces to arbitrary topologies. This added flexibility allows, among other things, the natural introduction of features such as cusps, creases, and darts, while elsewhere maintaining the same order of continuity as their uniform counterparts.
21588344
The mu-basis of a rational ruled surface
Abstract The mu-basis of a planar rational curve is a polynomial ideal basis comprised of two polynomials that greatly facilitates computing the implicit equation of the curve. This paper defines a mu-basis for a rational ruled surface, and presents a simple algorithm for computing the mu-basis. The mu-basis consists of two polynomials p(x,y,z,s) and q(x,y,z,s) that are linear in x,y,z and degree μ and m−μ in s respectively, where m is the degree of the implicit equation. The implicit equation of the surface is then obtained by merely taking the resultant of p and q with respect to s . This implicitization algorithm is faster and/or more robust than previous methods.
5971327
Approximate Implicitization Using Monoid Curves and Surfaces
Abstract This paper presents an approach to finding an approximate implicit equation and an approximate inversion map of a planar rational parametric curve or a rational parametric surface. High accuracy of the approximation is achieved with a relatively small number of low-degree curve segments or surface patches. By using monoid curves and surfaces, the method eliminates the undesirable singularities and “phantom” branches normally associated with implicit representation. The monoids are expressed in exact implicit and parametric equations simultaneously, and upper bounds are derived for the approximate errors of implicitization and inversion equations.
17318987
Applying regression test selection for COTS-based applications
ABB incorporates a variety of commercial-off-the-shelf (COTS) components in its products. When new releases of these components are made available for integration and testing, source code is often not provided. Various regression test selection processes have been developed and have been shown to be cost effectiveness. However, the majority of these test selection techniques rely on access to source code for change identification. In this paper we present the application of the lightweight Integrated - Black-box Approach for Component Change Identification (I-BACCI) Version 3 process that select regression tests for applications that use COTS components. Two case studies, examining a total of nine new component releases, were conducted at ABB on products written in C/C++ to determine the effectiveness of I-BACCI. The results of the case studies indicate this process can reduce the required number of regression tests at least 70% without sacrificing the regression fault exposure.
18528231
In regression testing selection when source code is not available