One approach to drawing implicit 2D curves using interval analysis and Runge Method type.

Анотація

Implicit curve approximation stands as a foundational task in both mathematics and computer graphics. Numerous approaches have been introduced to tackle this problem, from algebraic techniques to numerical methods. Among these, interval analysis has gained significant attention. Its strength lies in its inherent ability to provide guaranteed bounds, ensuring a robust estimate of the curve's location, a feature not consistently offered by many other methods. In this paper, we introduce an enhancement to the curve approximation algorithm, building upon the established foundation set by the [1] algorithm. Our primary objective is to optimize efficiency, with a particular emphasis on improving the boundary intersection determination. Our ambition is to speed up implicit curve approximation by using Runge method [2] instead of more traditional approach of using Newton method.