Self-affinities of planar curves: towards unified description of aesthetic curves
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916334961426432 |
|---|---|
| author | Kumagai, Shun Kajiwara, Kenji |
| author_facet | Kumagai, Shun Kajiwara, Kenji |
| contents | In this paper, we consider the self-affinity of planar curves. It is regarded as an important property to characterize the log-aesthetic curves which have been studied as reference curves or guidelines for designing aesthetic shapes in CAD systems. We reformulate the two different self-affinities proposed in the development of log-aesthetic curves. We give rigorous proof that one self-affinity actually characterizes log-aesthetic curves, while another one characterizes parabolas. We then propose a new self-affinity which, in equiaffine geometry, characterizes the constant curvature curves (the quadratic curves). It integrates the two self-affinities, by which constant curvature curves in similarity and equiaffine geometries are characterized in a unified manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-affinities of planar curves: towards unified description of aesthetic curves Kumagai, Shun Kajiwara, Kenji Differential Geometry 53A15, 93B51, 65D18 In this paper, we consider the self-affinity of planar curves. It is regarded as an important property to characterize the log-aesthetic curves which have been studied as reference curves or guidelines for designing aesthetic shapes in CAD systems. We reformulate the two different self-affinities proposed in the development of log-aesthetic curves. We give rigorous proof that one self-affinity actually characterizes log-aesthetic curves, while another one characterizes parabolas. We then propose a new self-affinity which, in equiaffine geometry, characterizes the constant curvature curves (the quadratic curves). It integrates the two self-affinities, by which constant curvature curves in similarity and equiaffine geometries are characterized in a unified manner. |
| title | Self-affinities of planar curves: towards unified description of aesthetic curves |
| topic | Differential Geometry 53A15, 93B51, 65D18 |
| url | https://arxiv.org/abs/2407.17008 |