A new method to detect projective equivalences and symmetries of rational <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e6567" altimg="si2.svg"><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:math> curves
نویسندگان
چکیده
We present a new approach to detect projective equivalences and symmetries between two rational parametric 3 D curves properly parametrized. In order do this, we introduce functions that behave nicely for Möbius transformations, which are the transformations in parameter space associated with curves. The found by first computing gcd of polynomials built from these functions, then searching special type factors, “Möbius-like”, this gcd. themselves easily computed transformations. particular, unlike previous approaches, avoid solving big polynomial systems. algorithm has been implemented Maple™ (2021), evidences its efficiency as well comparison approaches given.
منابع مشابه
Projective and affine symmetries and equivalences of rational curves in arbitrary dimension
We present a new algorithm to decide whether two rational parametric curves are related by a projective transformation and detect all such projective equivalences. Given two rational curves, we derive a system of polynomial equations whose solutions define linear rational transformations of the parameter domain, such that each transformation corresponds to a projective equivalence between the t...
متن کاملDetecting Symmetries of Rational Plane Curves
Given a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide effective methods for solving these questions without any conversion to implicit form. The underl...
متن کاملsolution of security constrained unit commitment problem by a new multi-objective optimization method
چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...
Detecting symmetries of rational plane and space curves
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space curves, our method finds the involutions in all cases, and all the rotation symmetries in the particular case of Pythagorean-hodograph curves. Our algorithm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2023
ISSN: ['0377-0427', '1879-1778', '0771-050X']
DOI: https://doi.org/10.1016/j.cam.2022.114782