Counting tropical rational space curves with cross-ratio constraints
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DOI: 10.1007/s00229-021-01317-3
Abstract: This is a follow-up paper of Goldner (Math Z 297(1–2):133–174, 2021), where rational curves in surfaces that satisfy general positioned point and cross-ratio conditions were enumerated. A suitable correspondence theorem provided in Tyomkin (Adv Math… read more here.
Keywords: space curves; ratio; floor diagrams; rational space ... See more keywords
Algebraic-Trigonometric Pythagorean-Hodograph space curves
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DOI: 10.1007/s10444-018-9606-8
Abstract: We introduce a new class of Pythagorean-Hodograph (PH) space curves - called Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) space curves - that are defined over a six-dimensional space mixing algebraic and trigonometric polynomials. After providing a general definition… read more here.
Keywords: hodograph space; space; algebraic trigonometric; pythagorean hodograph ... See more keywords
Counting Integral Points Near Space Curves: A Fourier Analytic Approach
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DOI: 10.1093/imrn/rnaf200
Abstract: We establish upper and lower bounds for the number of integral points which lie within a neighbourhood of a smooth nondegenerate curve in $\mathbb{R}^{n}$ for $n\geqslant 3$. These estimates are new for $n\geqslant 4$, and… read more here.
Keywords: integral points; fourier analytic; points near; space curves ... See more keywords
A pair of kinematically related space curves
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DOI: 10.1142/s0219887818501803
Abstract: We investigate the relation between two types of space curves, the Mannheim curves and constant-pitch curves and primarily explicate a method of deriving Mannheim curves and constant-pitch curves from each other by means of a… read more here.
Keywords: mannheim curves; space; space curves; constant pitch ... See more keywords
Optimization-Driven Reconstruction of 3D Space Curves from Two Views Using NURBS
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DOI: 10.3390/math13142256
Abstract: In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging,… read more here.
Keywords: reconstruction; space curves; optimization; reconstruction space ... See more keywords