MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves

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Les articles les plus proches

1. Proche* Cité par cet article Une méthode qu’il utilise Pas pertinent

   Algorithms for a Minimum Volume Enclosing Simplex in Three Dimensions

   Yunhong Zhou, S. Suri · 2002 · SIAM journal on computing (Print) · cité 32 fois · Pas encore résumé
2. Proche Pas pertinent

   A Spline-Type Extension for the Ball Basis

   Yan-Ping Wang, Wanqiang Shen, Qing-Yuan Hu · 2026 · Symmetry · Pas encore résumé

   Résumé scientifique

   In computer-aided geometric design (CAGD), the Bernstein basis was extended to the B-spline basis through knot vectors and recursive construction, shifting from a global polynomial form to a locally supported piecewise representation. The Ball basis, composed of quadratic and cubic polynomials, is similar to the Bernstein basis of degree 3. This paper proposes a generalization for a spline-type and creates a piecewise polynomial extension, called the Ball-Spline basis, consisting of symmetric polynomial segments of degrees 2, 3, 3, and 2, arranged in a symmetric structure with the highest continuity order—C1 continuity between the quadratic and cubic segments, and C2 continuity between the t…

3. Proche Cité par cet article Pas pertinent

   The Minimal Volume of Simplices Containing a Convex Body

   Daniel Galicer, Mariano Merzbacher, D. Pinasco · 2017 · Journal of Geometric Analysis · cité 5 fois · Pas encore résumé

   Résumé scientifique

   Let K⊂Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K \subset {\mathbb {R}}^n$$\end{document} be a convex body with barycenter at the origin. We show there is a simplex S⊂K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S \subset K$$\end{document} having also barycenter at the origin such that (vol(S)vol(K))1/n≥cn,\documentclass[1…

4. Proche Cité par cet article Pas pertinent

   On the convex hull of a space curve

   K. Ranestad, B. Sturmfels · 2009 · arXiv.org · preprint, non relu par les pairs · cité 51 fois · Pas encore résumé

   Résumé scientifique

   The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We express the degree of this surface in terms of the degree, genus and singularities of the curve. We present algorithms for computing their defining polynomials, and we exhibit a wide range of examples.

5. Apparenté Pas pertinent

   Fast Computation of Polynomial Data Points Over Simplicial Face Values

   T. Hamadneh, Hassan Al-Zoubi, S. Alomari · 2020 · Journal of Information & Knowledge Management · cité 7 fois · Pas encore résumé

   Résumé scientifique

   Polynomial functions F of degree m have a form in the Bernstein basis defined over l-dimensional simplex W. The Bernstein coefficients exhibit a number of special properties. The function F can be optimised by the smallest and largest Bernstein coefficients (enclosure bounds) over W. By a proper choice of barycentric subdivision steps of W, we prove the inclusion property of Bernstein enclosure bounds. To this end, we provide an algorithm that computes the Bernstein coefficients over subsimplices. These coefficients are collected in an l-dimensional array in the field of computer-aided geometric design. Such a construct is typically classified as a patch. We show that the Bernstein coefficie…

6. Apparenté Pas pertinent

   Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension

   M. Ainsworth, Manuel A. Sánchez · 2015 · SIAM Journal on Scientific Computing · cité 5 fois · Pas encore résumé

   Résumé scientifique

   The Bernstein-B\'ezier form of a polynomial is widely used in the fields of computer aided geometric design, spline approximation theory and, more recently, for high order finite element methods for the solution of partial differential equations. However, if one wishes to compute the classical Lagrange interpolant relative to the Bernstein basis, then the resulting Bernstein-Vandermonde matrix is found to be highly ill-conditioned. In the univariate case of degree $n$, Marco and Martinez showed that using Neville elimination to solve the system exploits the total positivity of the Bernstein basis and results in an $\mathcal{O}(n^2)$ complexity algorithm. Remarkable as it may be, the Marco-Ma…

7. Apparenté* Cité par cet article Pas pertinent

   On the minimal volume of simplices enclosing a convex body

   A. Kanazawa · 2014 · Archiv der Mathematik · cité 9 fois · Pas encore résumé
8. Apparenté* Pas pertinent

   B-Spline Basis Functions

   L. Piegl, W. Tiller · 1997 · cité 24 fois · Pas encore résumé

Les travaux antérieurs sur lesquels il s’appuie

1. Apparenté* Utilisé en profondeur par cet article Une méthode qu’il utilise Pas pertinent

   SLEVEs for planar spline curves

   J. Peters, Xiaobin Wu · 2004 · Computer Aided Geometric Design · cité 34 fois · Pas encore résumé
2. Apparenté* Utilisé en profondeur par cet article Une méthode qu’il utilise Pas pertinent

   General matrix representations for B-splines

   K. Qin · 1998 · Proceedings Pacific Graphics '98. Sixth Pacific Conference on Computer Graphics and Applications (Cat. No.98EX208) · cité 167 fois · Pas encore résumé
3. Apparenté* Une méthode qu’il utilise Pas pertinent

   Global Optimization with Polynomials and the Problem of Moments

   J. Lasserre · 2000 · SIAM Journal on Optimization · cité 2 947 fois · Pas encore résumé
4. Apparenté* Pas pertinent

   Bounding the Distance between 2D Parametric Bézier Curves and their Control Polygon

   M. Karavelas, P. Kaklis, K. Kostas · 2004 · Computing · cité 16 fois · Pas encore résumé
5. Apparenté* Pas pertinent

   Structure of the convex hull of a space curve

   V. Sedykh · 1986 · Journal of Soviet Mathematics · cité 21 fois · Pas encore résumé

Les articles qui le citent

1. Apparenté Cité par cet article Utilisé en profondeur par cet article Une méthode qu’il utilise Pas pertinent

   MADER: Trajectory Planner in Multiagent and Dynamic Environments

   Jesús Tordesillas, J. How · 2020 · IEEE Transactions on robotics · cité 263 fois · Pas encore résumé

   Résumé scientifique

   This article presents MADER, a 3-D decentralized and asynchronous trajectory planner for UAVs that generates collision-free trajectories in environments with static obstacles, dynamic obstacles, and other planning agents. Real-time collision avoidance with other dynamic obstacles or agents is done by performing outer polyhedral representations of every interval of the trajectories and then including the plane that separates each pair of polyhedra as a decision variable in the optimization problem. MADER uses our recently developed MINVO basis to obtain outer polyhedral representations with volumes 2.36 and 254.9 times, respectively, smaller than the Bernstein or B-Spline bases used extensive…

2. Apparenté Pas pertinent

   $\mathcal {C}^{n}$ Trajectory Generation in 3D Under Arbitrary Bounds on Curvature and Higher-Order Curvature Derivatives

   Samer Raed Aldabbas, A. T. Çetin, M. Abu-Khalaf et al. · 2026 · IEEE Robotics and Automation Letters · Pas encore résumé

   Résumé scientifique

   We propose a method to solve the general problem of generating a trajectory in 3D space that is <inline-formula><tex-math notation="LaTeX">$\mathcal {C}^{n}$</tex-math></inline-formula> continuous, and satisfies given bounds on the curvature <inline-formula><tex-math notation="LaTeX">$\kappa _{\text{max}}$</tex-math></inline-formula>, and its higher-order derivatives <inline-formula><tex-math notation="LaTeX">$\dot{\kappa }_{\text{max}}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$\ddot{\kappa }_{{\text{max}}}$</tex-math></inline-formula>, up to <inline-formula><tex-math notation="LaTeX">$\kappa _{{\text{max}}}^{(n-2)}$</tex-math></inline-formula> where <inline-f…

3. Apparenté Pas pertinent

   Trajectory Planning Based on MINVO Basis for Autonomous Vehicles in Lane Change Scenarios

   Zixuan Fan, Jin-Xian Wu, Li Dai et al. · 2023 · Cybersecurity and Cyberforensics Conference · cité 2 fois · Pas encore résumé

   Résumé scientifique

   This paper focuses on the problem of collision-free lane change for autonomous vehicles under dynamic obstacle road scenarios and proposes a new trajectory planning algorithm for autonomous vehicles. With the goals of dynamics feasibility, comfort, and safety in mind, we develop a B-spline-based trajectory planning method capable of generating trajectories which satisfy all the desired objectives. Specifically, (i) the maximum velocity, the maximum acceleration and the maximum curvature of the trajectory are taken into account explicitly to ensure the comfort of the ride and the traceability of the planned path; (ii) MINVO basis is used to obtain outer polygon representations with minimum ar…

4. Apparenté Pas pertinent

   DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

   Kun Cao, Muqing Cao, Sheng-Hai Yuan et al. · 2021 · IEEE Robotics and Automation Letters · cité 20 fois · Pas encore résumé

   Résumé scientifique

   This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent multiple polynomial segments as in literature, we take a new perspective from state-space representation such that the linear equation reduces to a finite horizon control system with a fixed state dimension and the required continuity conditions for consecutive polynomials are automatically satisfied. Consequently, the constrained trajectory generation problem (both with and without time optimization) can be converted to a discrete-time finite-horizon optimal con…

5. Apparenté Utilise cet article en profondeur Pas pertinent

   Perception-Aware Based Quadrotor Translation and Yaw Angle Planner in Unpredictable Dynamic Situations

   Han-Xuan Zhang, Ju Huo, Yu-Long Huang et al. · 2025 · IEEE Transactions on Aerospace and Electronic Systems · cité 14 fois · Pas encore résumé

   Résumé scientifique

   In this article, we offer a perception-aware quadrotor translation and yaw angle planner approach to solve the navigation problem for a quadrotor with limited field of view (FOV) in unpredictable dynamic situations. Our method is developed based on the static obstacle avoidance method Ego-Planner. First, we establish an environmental perception module based on a depth sensor. This module categorizes obstacles into static and dynamic types, tracking and predicting the trajectories of dynamic obstacles. Second, we introduce the minimum volume enclosing polynomial curves basis instead of B-spline basis to solve the problem of conservative convex hull generated by existing planning methods based…