TL;DR
This paper introduces a novel approach to aesthetic interpolation by applying the golden section, presenting three methods for different degrees, and proposing new concepts like golden cuspidal and domed hills to enhance visual appeal.
Contribution
It presents the first systematic integration of golden section principles into interpolation methods, including three specific techniques and new aesthetic concepts.
Findings
Demonstrated the effectiveness of golden section in interpolation aesthetics
Provided comparative examples showing improved visual harmony
Proposed new aesthetic concepts for interpolation curves
Abstract
For the classic aesthetic interpolation problem, we propose an entirely new thought: apply the golden section. For how to apply the golden section to interpolation methods, we present three examples: the golden step interpolation, the golden piecewise linear interpolation and the golden curve interpolation, which respectively deal with the applications of golden section in the interpolation of degree 0, 1, and 2 in the plane. In each example, we present our basic ideas, the specific methods, comparative examples and applications, and relevant criteria. And it is worth mentioning that for aesthetics, we propose two novel concepts: the golden cuspidal hill and the golden domed hill. This paper aims to provide the reference for the combination of golden section and interpolation, and stimulate more and better related researches.
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Taxonomy
TopicsAesthetic Perception and Analysis · Computer Graphics and Visualization Techniques · Advanced Numerical Analysis Techniques