Distance Calculation Between a Point and a NURBS Surface

Abstract

In this paper, we consider the computation of an Euclidean shortest path between a point and a modelled curve or surface in three-dimensional space, which is one of the fundamental problems in robotics and many other areas. A new accurate algorithm for the distance-calculation between a point and a NURBS curve and its extension to the case of a point and a NURBS surface is presented. The algorithm consists of two steps, and is crucially based on appropriate projections and subdivision techniques. To solve a nonlinear polynomial system derived from the classical formulation of the distance problem, the well-known Newton-type algorithms or subdivision-based techniques first considered by Sherbrooke and Patrikalakis are used. Their modifications in conjunction with a low subdivision depth in the presented algorithms yield a verified enclosure of the solution.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP012016

Entities

People

  • Eva Dyllong
  • Wolfram Luther

Organizations

  • University of Duisburg

Tags

Communities of Interest

  • Air Platforms
  • Autonomy

DTIC Thesaurus Topics

  • Adaptive Systems
  • Algorithms
  • Computations
  • Control
  • Decomposition
  • Equations
  • Geometry
  • Intervals
  • Linear Programming
  • Motion Planning
  • Polynomials
  • Rational Functions
  • Robotics
  • Robots
  • Simplex Method
  • Technical Information Centers
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Autonomy
  • Space