Symplectification of Circular Arcs and Arc Splines
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908486370066432 |
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| author | Gössner, Stefan |
| author_facet | Gössner, Stefan |
| contents | In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial relationships for the circular arc. Curves are considered whose neighboring circular elements each have a common end point or, in addition, a common tangent. These arc splines prove to be a one-parameter curve family, whereby this parameter can be optimized with regard to various criteria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symplectification of Circular Arcs and Arc Splines Gössner, Stefan Symplectic Geometry Computational Geometry Graphics 53D99 In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial relationships for the circular arc. Curves are considered whose neighboring circular elements each have a common end point or, in addition, a common tangent. These arc splines prove to be a one-parameter curve family, whereby this parameter can be optimized with regard to various criteria. |
| title | Symplectification of Circular Arcs and Arc Splines |
| topic | Symplectic Geometry Computational Geometry Graphics 53D99 |
| url | https://arxiv.org/abs/2508.07726 |