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Nonlinear Weighted Subdivision Schemes
In this paper, we present new variants of both the de Casteljau subdivision algorithm for curves and Doo–Sabin subdivision algorithm for surfaces....
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Stochastic Geometric Iterative Method for Loop Subdivision Surface Fitting
In this paper, we propose a stochastic geometric iterative method (S-GIM) to approximate the high-resolution 3D models by finite loop subdivision...
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A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities
Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution...
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Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric
In this paper, we consider the problem of path planning in a weighted polygonal planar subdivision. Each polygon has an associated positive weight...
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Multivariate Generalized Hermite Subdivision Schemes
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for...
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Subdivision Schemes Based on Weighted Local Polynomial Regression: A New Technique for the Convergence Analysis
The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision...
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On the Complexity of the Plantinga–Vegter Algorithm
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based...
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Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach...
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Shape preserving rational [3/2] Hermite interpolatory subdivision scheme
In this paper, a new Hermite interpolatory subdivision scheme for curve interpolation is introduced. The scheme is constructed from the Rational...
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Convergence rate of a rectangular subdivision-based optimization algorithm for smooth multivariate functions
In Zheng (J. Glob. Opt. 79:431-445;2021) the authors described a global optimization algorithm for multivariate continuous functions and applied it...
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Analysis and Convergence of Hermite Subdivision Schemes
Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD...
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Clothoid fitting and geometric Hermite subdivision
We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector...
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Shape Preserving Hermite Subdivision Scheme Constructed from Quadratic Polynomial
In this paper, a Hermite interpolatory subdivision scheme is constructed from the quadratic polynomial. We show that the scheme converges and...
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Mixed hyperbolic/trigonometric non-stationary subdivision scheme
This paper proposes two novel families of non-stationary subdivision schemes with a shape parameter of hierarchically and efficiently generating...
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Branch-and-Model: a derivative-free global optimization algorithm
This paper presents a novel derivative-free global optimization algorithm Branch-and-Model (BAM). The BAM algorithm partitions the search domain...
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A Polyhedral Homotopy Algorithm for Real Zeros
We design a homotopy continuation algorithm, that is based on Viro’s patchworking method, for finding real zeros of sparse polynomial systems. The...
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A generalized combinatorial marching hypercube algorithm
We present a Generalized Combinatorial Marching Hypercubes algorithm to compute a cell complex approximation of a manifold of any dimension and...
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Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces
This survey of piecewise polynomial surface constructions for filling multi-sided holes in a smooth spline complex focusses on a class of hybrid...