An adaptive iterative/subdivision hybrid algorithm for curve/curve intersection

TL;DR

This paper introduces an adaptive hybrid algorithm for curve/curve intersection that dynamically adjusts the convergence test domain, improving efficiency over fixed-domain methods.

Contribution

The paper proposes a modified algorithm that adaptively adjusts the test domain size during intersection computation, enhancing efficiency compared to fixed-domain approaches.

Findings

The adaptive algorithm is slightly more efficient than the original.

Dynamic domain adjustment reduces unnecessary subdivisions.

Improved convergence detection in curve intersection computations.

Abstract

The behavior of the iterative/subdivision hybrid algorithm for curve/curve intersection proposed in [20] depends on the choice of the domain for their convergence test. Using either too small or too large test domain may cause the test to fail to detect cases where Newton's method in fact converges to a solution, which results in unnecessary additional subdivisions and consequently more computation time. We propose a modification to the algorithm to adaptively adjust the test domain size according to what happens during the test of the parent region. This is in contrast to the original algorithm whose test domain is always a fixed multiple of the input domain under consideration. Computational results show that the proposed algorithm is slightly more efficient than the original algorithm.