TL;DR
This paper investigates the isoptics of log-aesthetic curves, exploring their properties and conditions for autoisoptics, and introduces a new formula for calculating isoptic curves of tangential angle parametrized curves.
Contribution
It provides a detailed analysis of the isoptics of log-aesthetic curves and presents a novel formula for isoptic curves of tangential angle parametrized curves.
Findings
Log-aesthetic curves only coincide with their isoptics in specific cases.
A new formula for calculating isoptic curves of tangential angle parametrized curves.
The study enhances understanding of the geometric properties of log-aesthetic curves.
Abstract
The log-aesthetic curve has a significant factor in the field of aesthetic design to meet the high industrial requirements. It has much exceptional property and a large number of research papers are published, since its introduction. It can be parametrized by tangential angle, and it is autoevolute, meaning that its evolute is also a log-aesthetic curve. In this paper, we will examine the isoptics of the log-aesthetic curve and determine if it is autoisoptic as well. We will show that the log-aesthetic curve only coincides its isoptic in some specific cases. We will also provide a new formula to calculate the isoptic curve of any tangential angle parametrized curves.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Analysis Techniques · 3D Shape Modeling and Analysis · Textile materials and evaluations