Knot Insertion Using Forward Differences

Conformal and G1 Continuous Connection of NURBS Curves

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.756-759.3826 ◽

2013 ◽

Vol 756-759 ◽

pp. 3826-3830

Author(s):

Pei Sen Deng ◽

Shao Ping Chen ◽

Jun Cheng Shen

Keyword(s):

Knot Insertion ◽

Nurbs Curve ◽

Nurbs Curves ◽

Insertion Algorithm ◽

Vector Rotation

This paper converts a NURBS curve to piecewise rational Bézier curves by knot insertion algorithm, and then discusses the algorithm of continuous connection of NURBS curves. Meanwhile, explores the method to keep the same shape of the NURBS curves after connecting through the point translation and vector rotation theory. Finally, gives an instance to verify the validity of the algorithm.

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ON LIEB AND THIRRING TYPE DISCRETE INEQUALITIES

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.22.1991.4587 ◽

1991 ◽

Vol 22 (2) ◽

pp. 145-151

Author(s):

B. G. PACHPATTE

Keyword(s):

Independent Variables ◽

Discrete Inequalities ◽

Forward Differences

Discrete inequalities of the Lieb and Thirring type involving functions of several independent variables and their forward differences are established. The proofs given here are elementary and the results established provide new estimates on these types of inequalities.

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Smooth Surface Interpolation With Multiple Patches

Volume 1: 25th Design Automation Conference ◽

10.1115/detc99/dac-8555 ◽

1999 ◽

Author(s):

N. Adhikary ◽

B. Gurumoorthy

Keyword(s):

Smooth Surface ◽

Knot Insertion ◽

B Spline ◽

Surface Interpolation ◽

Multiple Patches ◽

Point Data ◽

C1 Continuity ◽

Knot Removal

Abstract This paper addresses the problem of interpolating point data with multiple patches. The specific issue addressed in this paper is the continuity between the patches used for interpolation. The procedure described in this paper maintains continuity by introducing an intermediate patch between the two patches used for interpolating the point data. This patch is formed by several Bezier patches that maintain continuity with the corresponding Bezier patches obtained by repeated knot insertion in the two interpolating patches. The blending Bezier patches are then converted to a blending B-spline patch by knot removal. It is shown that C1 continuity is obtained across the junction between each interpolating patch and the blending patch. The continuity, across each blending patch and the interpolation performance in the blending patch is also discussed. The paper presents results, of implementation on some typical surfaces.

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