Rational fixed radius rolling ball blends between natural quadrics

Dahl, Heidi; Krasauskas, Rimvydas

doi:10.1016/j.cagd.2012.06.008

Cited by 9 publications

(2 citation statements)

References 31 publications

(119 reference statements)

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“…Various time-independent methods have been proposed to blend parametric surfaces. Among them, rolling ball methods, which can be divided into constant radius [11] and variable radius [12] ones, are most widely used for rounding edges and corners of mechanical parts [13]. In addition, the potential method [14][15][16] was also proposed.…”

Section: Related Workmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

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Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

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Section: Related Workmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

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“…Various rolling-ball blending methods can be divided into constant-radius and variable-radius ones. Constant-radius rolling-ball blending methods were investigated in [6][7][8][9], and variable-radius rollingball blending methods were examined in [10][11][12].…”

Section: Related Workmentioning

confidence: 99%

A unified approach to blending of constant and varying parametric surfaces with curvature continuity

You

Tian

Tang

2018

Proceedings of Computer Graphics International 2018

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In this paper, we develop a new approach to blending of constant and varying parametric surfaces with curvature continuity. We propose a new mathematical model consisting of a vector-valued sixth-order partial differential equation (PDE) and time-dependent blending boundary constraints, and develop an approximate analytical solution of the mathematical model. The good accuracy and high computational efficiency are demonstrated by comparing the new approximate analytical solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on the continuity at trimlines, and apply the new approximate analytical solution in blending of constant and varying parametric surfaces with curvature continuity.

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