With the aim to tackle the problems of the local shape adjustment and shape control of quartic Q-Ball curves, we propose two direct subdivision algorithms for quartic QBall curves, which include coefficient subdivisio...
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ISBN:
(纸本)9781538649916
With the aim to tackle the problems of the local shape adjustment and shape control of quartic Q-Ball curves, we propose two direct subdivision algorithms for quartic QBall curves, which include coefficient subdivision and tangent subdivision. According to the two subdivision algorithms, the corresponding modeling examples are respectively given. Studies show that the sub-curves are independent and have no influence on other sub-curves in shape adjustment, which realize the local shape adjustment of the quartic Q-Ball curves and maintain the geometric meaning of shape parameters. The modeling examples show that the proposed subdivision algorithms are effective and easy to implement, which greatly improve the abilities to express complex curves in shape design by adjusting the position and shape of quartic Q-Ball curves.
This paper proposes a subdivision algorithm for quartic λ-Bézier curves with shape parameter. Firstly, the quartic λ-Bézier curves are converted to quartic traditional Bezier curves, then we solve the cont...
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ISBN:
(纸本)9781728123264
This paper proposes a subdivision algorithm for quartic λ-Bézier curves with shape parameter. Firstly, the quartic λ-Bézier curves are converted to quartic traditional Bezier curves, then we solve the control points of the sub-curved curve after the subdivision by using the traditional Bezier curves so that it can remain shape unchanged before and after subdivision, that is, the expression of the curve is the same. Finally, it can be converted to the explicit combination expression of quartic λ-Bézier curves control points. The examples show that the proposed method is effective and easy to implement, which greatly enhances the ability to constructing complex surface by using quartic generalized λ-Bézier curves.
Modern industrial manufacturing contains different kinds of surface modeling, which is processed by planar materials. For the principle of the most efficient materials using, how to optimize subdivision undevelopable ...
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ISBN:
(纸本)9783038352679
Modern industrial manufacturing contains different kinds of surface modeling, which is processed by planar materials. For the principle of the most efficient materials using, how to optimize subdivision undevelopable surface before development becomes an important topic in CAM design and manufacturing industries. The paper transforms the basic parameters of surface before subdivision, and gives the standards of subdivision surfaces. We proved the feasibility and the existence of triangle subdivision algorithm. By introducing double parameters MObius transformation, the subdivision surface is more uniform. At last, numerical examples prove that the algorithm about the approximate development of the undevelopable surfaces is effective and practical.
The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is to expand the currently limited range...
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The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is to expand the currently limited range of random polynomials that we can handle. Despite important recent progress, the available tools cannot handle random sparse polynomials and Gaussian polynomials, that is polynomials whose coefficients are i.i.d. Gaussian random variables. We initiate a condition-based complexity framework based on the norm of the cube that is a step in this direction. We present this framework for real hypersurfaces and univariate polynomials. We demonstrate its capabilities in two problems, under very mild probabilistic assumptions. On the one hand, we show that the average run-time of the Plantinga-Vegter algorithm is polynomial in the degree for random sparse (alas a restricted sparseness structure) polynomials and random Gaussian polynomials. On the other hand, we study the size of the subdivision tree for Descartes' solver and run-time of the solver by Jindal and Sagraloff (2017). In both cases, we provide a bound that is polynomial in the size of the input (size of the support plus the logarithm of the degree) not only for the average but also for all higher moments. (c) 2022 Elsevier Ltd. All rights reserved.
Classic generalized subdivision, such as Catmull-Clark subdivision, as well as recent subdivision algorithms for high-quality surfaces, rely on slower convergence towards extraordinary points for mesh nodes surrounded...
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Classic generalized subdivision, such as Catmull-Clark subdivision, as well as recent subdivision algorithms for high-quality surfaces, rely on slower convergence towards extraordinary points for mesh nodes surrounded by n > 4 quadrilaterals. Slow convergence corresponds to a contraction-ratio of ) > 0 . 5 . To improve shape, prevent parameterization discordant with surface growth, or to improve convergence in isogeometric analysis near extraordinary points, a number of algorithms explicitly adjust ) by altering refinement rules. However, such tuning of ) has so far led to poorer surface quality, visible as uneven distribution or oscillation of highlight lines. The recent Quadratic-Attraction subdivision (QAS) generates high-quality, bounded curvature surfaces based on a careful choice of quadratic expansion at the central point and, just like Catmull-Clark subdivision, creates the control points of the next subdivision ring by matrix multiplication. But QAS shares the contraction- ratio ) lambda(CC) > 1/2 of Catmull-Clark subdivision when n > 4. For n = 5 , ... , 10, , QAS, improves the convergence to the uniform ) lambda = 1/2 of binary domain refinement and without sacrificing surface quality compared to QAS.
We present a novel algorithm for optimal control of nonlinear systems based on a subdivision algorithm. The algorithm presented in this paper is an alternative to a set-oriented approach for optimal feedback stabiliza...
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We present a novel algorithm for optimal control of nonlinear systems based on a subdivision algorithm. The algorithm presented in this paper is an alternative to a set-oriented approach for optimal feedback stabilization. We compare the proposed algorithm to the set-oriented approach, contrast these two approaches, and use examples to show that the new algorithm produces comparable results. Also, we demonstrate by example that we receive a precomputed optimal solution. The main contribution of the paper is understanding how cost function improves with further subdivision of state space and smaller memory footprint of the final solution in comparison with set-oriented approach. Copyright (c) 2012 John Wiley & Sons, Ltd.
This paper gives the first algorithm for finding a set of natural epsilon-clusters of complex zeros of a regular triangular system of polynomials within a given polybox in (C)n, for any given epsilon > 0. Our algor...
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This paper gives the first algorithm for finding a set of natural epsilon-clusters of complex zeros of a regular triangular system of polynomials within a given polybox in (C)n, for any given epsilon > 0. Our algorithm is based on a recent near-optimal algorithm of Becker et al. (Proceedings of the ACM on international symposium on symbolic and algebraic computation, 2016) for clustering the complex roots of a univariate polynomial where the coefficients are represented by number oracles. Our algorithm is based on recursive subdivision. It is local, numeric, certified and handles solutions with multiplicity. Our implementation is compared to with well-known homotopy solvers on various triangular systems. Our solver always gives correct answers, is often faster than the homotopy solvers that often give correct answers, and sometimes faster than the ones that give sometimes correct results.
In this paper we consider the Voronoi diagram of a finite family of parallel half-lines, with the same orientation, constrained to a compact domain D-0 subset of R-3, with respect to the Euclidean distance. We present...
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In this paper we consider the Voronoi diagram of a finite family of parallel half-lines, with the same orientation, constrained to a compact domain D-0 subset of R-3, with respect to the Euclidean distance. We present an efficient approximation algorithm for computing such VD, using a subdivision process, which produces a mesh representing the topology of the VD in D-0. The computed topology may not be correct for degenerate configurations or configurations close to degenerate. In this case, the output is a valid partition, which is close to the exact partition in Voronoi cells if the input data were given with no error. We also present the result of an implementation in Julia language with visualization using Axl software (***) of the algorithm. Some examples and analysis are shown.
Toric surface patches are a class of multi-sided surface patches that can represent multi sided domains without mesh degeneration. In this paper, we propose an improved subdivision algorithm for toric surface patches,...
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Toric surface patches are a class of multi-sided surface patches that can represent multi sided domains without mesh degeneration. In this paper, we propose an improved subdivision algorithm for toric surface patches, which subdivides an N-sided toric surface patch into N rational tensor product Bezier surface patches. By the proposed subdivision algorithm, a C-k-continuous spline surface composed of piecewise toric surface patches is subdivided into a set of rational tensor product Bezier surface patches with Gk-continuity. Additionally, after subdivision, toric surface patches are compatible with CAD systems. Combining the subdivision algorithm with the classical knot insertion algorithm of nonuniform rational B-splines, we develop a novel h-refinement scheme for isogeometric analysis with planar toric parameterizations. Several numerical examples are given to demonstrate the effectiveness and numerical stability of the presented method. (C) 2022 Elsevier B.V. All rights reserved.
This paper focuses on generating smooth trajectories for a wheeled nonholonomic mobile robot using piecewise Bezier curves with properties ideally suited for this purpose. The developed algorithm generates smooth moti...
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This paper focuses on generating smooth trajectories for a wheeled nonholonomic mobile robot using piecewise Bezier curves with properties ideally suited for this purpose. The developed algorithm generates smooth motion trajectories with C-2 continuous curvature. We consider a teleoperated wheeled mobile robot in an indoor environment with ceiling cameras for operator visibility. The motion trajectory is constrained by the operator-specified via points and path width. A method to automatically generate a trajectory based on only these two inputs is proposed and demonstrated. To improve the trackability of the mobile robot, we adopted a Bezier subdivision method and inserted a quintic Bezier segment into high-curvature areas. The proposed algorithm can be used for real-time obstacle-avoidance trajectory generation because it allows trajectory subdivision and arbitrarily setting of the second derivative at the start point. Simulation and experimental results demonstrate the effectiveness of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.
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