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Related Concept Videos

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Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
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Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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3D Modeling of Dendritic Spines with Synaptic Plasticity
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Published on: May 18, 2020

Spherical DCB-spline surfaces with hierarchical and adaptive knot insertion.

Juan Cao1, Xin Li, Zhonggui Chen

  • 1School of Mathematical Sciences, Xiamen University, Xiamen, China. Juancao@xmu.edu.cn

IEEE Transactions on Visualization and Computer Graphics
|September 21, 2011
PubMed
Summary

This study introduces a new surface fitting method using spherical Delaunay configuration B-splines (DCB-splines) to accurately reconstruct genus-0 objects into smooth spline surfaces. The approach ensures high-quality reconstruction for reverse engineering and shape modeling applications.

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Area of Science:

  • Computer Graphics
  • Geometric Modeling
  • Computational Geometry

Background:

  • Reconstructing complex 3D shapes from data is crucial for various applications.
  • Existing methods often struggle with accuracy, smoothness, and efficiency for genus-0 objects.
  • Parametric spline surfaces offer desirable properties but require robust fitting schemes.

Purpose of the Study:

  • To develop a novel, practical, and accurate surface fitting scheme for genus-0 objects.
  • To introduce a new non-tensor-product spline: the spherical Delaunay configuration B-spline (DCB-spline).
  • To enable automatic reconstruction into a continuous parametric spline surface with bounded error.

Main Methods:

  • Developed a spherical generalization of Delaunay configuration B-splines (DCB-splines).
  • Implemented an efficient method for computing Delaunay configurations on a sphere.
  • Utilized a hierarchical and adaptive knot-insertion strategy guided by surface geometry and fitting error.

Main Results:

  • Successfully reconstructed genus-0 models into single spherical spline representations.
  • Achieved tightly bounded root mean square error within user-specified tolerances.
  • Demonstrated global smoothness and absence of auxiliary knots in the reconstructed surfaces.

Conclusions:

  • The proposed DCB-spline framework provides an effective and accurate method for surface fitting.
  • The hierarchical and adaptive approach enhances fitting quality and efficiency.
  • The method shows significant promise for reverse engineering and shape modeling.