With a single fractional twist, the complex plane reshapes itself.
Circles become lines, infinity moves closer, and symmetry takes the lead.
#MobiusMagic #ComplexGeometry
#TwistingThePlane #ComplexAnalysis
cortexdrifter.blogspot.com/2026/01/a-sm...
Rational complex Bezier curves Alicia Cantón Pire, Leonardo Fernández Jambrina y María Jesús Vázquez Gallo, investigadores del Grupo de Investigación Geometría y sus aplicaciones del Departamento de Matemática e Informática Aplicadas a la Ingenierías Civil y Naval de las ETSI Navales y Caminos de la Universidad Politécnica de Madrid. Journal of Computational and Applied Mathematics, Volume 480, July 2026, 17246 https://doi.org/10.1016/j.cam.2025.117246 Abstract In this paper we develop the formalism of rational complex Bézier curves. This framework is a simple extension of the CAD paradigm, since it describes arcs of curves in terms of control polygons and weights, which are extended to complex values. One of the major advantages of this extension is that we may make use of two different groups of projective transformations. Besides the group of projective transformations of the real plane, we have the group of complex projective transformations. This allows us to apply useful transformations like the geometric inversion to curves in design. In addition to this, the use of the complex formulation allows to lower the degree of the curves in some cases. This can be checked using the resultant of two polynomials and provides a simple formula for determining whether a rational cubic curve is a conic or not. Examples of application of the formalism to classical curves are included. #etsinavales #caminosupm #somosupm #rationalbéziercurves #complexgeometry
Rational complex Bezier curves
Alicia Cantón , Leonardo Fernández Jambrina y María Jesús Vázquez Gallo, investigadores de la @etsinavalesupm.bsky.social y la ETSI Caminos de @upm.es
doi.org/10.1016/j.ca...
#etsinavales #caminosupm #somosupm #rationalbéziercurves #complexgeometry
