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Related Experiment Video

Updated: Jun 2, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Boolean Operations with Prism Algebraic Patches.

Chandrajit Bajaj1, Alberto Paoluzzi, Simone Portuesi

  • 1Center for Computational Visualization, Dept. of Comp. Sc. & ICES, Univ. of Texas at Austin, USA.

Computer-Aided Design and Applications
|September 28, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel symbolic-numeric algorithm for performing Boolean operations on curved polyhedra using algebraic patches. The method approximates shapes with linear polyhedra and refines them with C(1)-continuous patches for accurate geometric computations.

Related Experiment Videos

Last Updated: Jun 2, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Computational Geometry
  • Computer-Aided Design (CAD)
  • Geometric Modeling

Background:

  • Boolean operations are fundamental in geometric modeling.
  • Representing and manipulating complex curved shapes accurately is challenging.
  • Existing methods often struggle with precision and feature representation.

Purpose of the Study:

  • To develop a robust symbolic-numeric algorithm for Boolean operations on curved polyhedra.
  • To enable precise representation and manipulation of complex geometries using algebraic patches.
  • To improve the accuracy and efficiency of geometric computations in CAD.

Main Methods:

  • Utilizes a linear polyhedron as an initial approximation.
  • Employs piecewise cubic algebraic interpolants (A-patches) for boundary representation.
  • Constructs scaffolding prisms to contain curved patches for intersection tests.
  • Generates 0-sets of trivariate polynomials for intersection detection.
  • Traces intersection curves to decompose and refine boundaries.

Main Results:

  • Successfully performs Boolean operations on curved polyhedra.
  • Achieves C(1)-continuity for interpolated patches, ensuring smooth surfaces.
  • Generates locally refined triangulations of intersecting patches.
  • Handles flat and sharp features through normal-per-face and normal-per-edge data.

Conclusions:

  • The proposed algorithm offers a precise and efficient method for Boolean operations on complex curved shapes.
  • The use of algebraic patches and scaffolding prisms enhances geometric representation accuracy.
  • This approach has significant implications for advanced CAD systems and geometric modeling research.