Curves of constant width and Zindler curves: Duality and algebraic equations

• David Rochera ^[1]
  1. [1] Basque Center for Applied Mathematics

     Basque Center for Applied Mathematics

     Bilbao, España

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 139-142
• Idioma: inglés
• Enlaces
  • Texto Completo Libro
• Resumen

  • The relationship between curves of constant width and Zindler curves with offsets and front track curves is described and generalized to non-convex shapes. A one-toone correspondence between hedgehogs of constant width and standard generalized Zindler curves is provided in terms of a projective hedgehog. With this idea, given a family of projective hedgehogs defined by trigonometric polynomials as support functions, an explicit method to compute algebraic equations for the associated curves of constant width and Zindler curves is possible. This extends the methodology used by Rabinowitz and Martinez-Maure in particular constant width curves to generate a full family of algebraicequations, both of curves of constant width and Zindler curves.