Mesh Parameterization with Generalized Discrete Conformal Maps

Colin Cartade (1) , Christian Mercat , Rémy Malgouyres (1) , Chafik Samir (2)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
2 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

We introduce a new method to compute conformal parame-terizations using a recent definition of discrete conformity, and establish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can also be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section.

Mots clés: conformal parameterization; digital surfaces; Riemann map- ping theorem

Domaines: Optimisation et contrôle [math.OC]

Colin Cartade, Christian Mercat, Rémy Malgouyres, Chafik Samir. Mesh Parameterization with Generalized Discrete Conformal Maps. Journal of Mathematical Imaging and Vision, 2013, 46 (1), pp.1 - 11. ⟨10.1007/s10851-012-0362-y⟩. ⟨hal-01598210⟩