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Related Experiment Video

Updated: Jun 23, 2026

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

An efficient solution to systems of multivariate polynomial using expression trees.

Gershon Elber1, Tom Grandine

  • 1Computer Science Department, Technion, Haifa, Israel. gershon@cs.technion.ac.il

IEEE Transactions on Visualization and Computer Graphics
|May 9, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces expression trees to represent polynomial constraints, improving scalability for geometric design problems. This method reduces exponential complexity to polynomial, enhancing the performance of subdivision solvers.

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Last Updated: Jun 23, 2026

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

Area of Science:

  • Computational Geometry
  • Computer-Aided Design (CAD)
  • Numerical Analysis

Background:

  • Subdivision-based solvers are used for polynomial constraint systems in geometric design.
  • Existing methods like binary domain subdivision and projected polyhedron methods face scalability challenges.
  • Tensor product representations lead to exponential complexity with an increasing number of variables.

Purpose of the Study:

  • To address the scalability limitations of subdivision solvers for polynomial constraint systems.
  • To introduce a novel representation for polynomial constraints that improves computational efficiency.
  • To demonstrate the practical applicability and performance benefits of the proposed method.

Main Methods:

  • Representing polynomial constraints using expression trees.
  • Analyzing the complexity reduction from exponential to polynomial.
  • Comparing the performance of expression tree representation against tensor product representation.

Main Results:

  • Expression trees effectively reduce the exponential complexity of polynomial constraints to polynomial complexity.
  • The proposed representation demonstrates improved scalability for geometric applications.
  • Empirical comparisons show performance advantages over traditional tensor product methods.

Conclusions:

  • Expression tree representation offers a scalable solution for solving polynomial constraint systems.
  • This approach enhances the efficiency of subdivision solvers in geometric design.
  • The method provides a practical alternative for complex constraint satisfaction problems.