Defining a stretching and alignment aware quality measure for linear and curved 2D meshes

Abstract

We define a regularized shape distortion (quality) measure for curved high-order 2D elements on a Riemannian plane. To this end, we measure the deviation of a given 2D element, straight-sided or curved, from the stretching and alignment determined by a target metric. The defined distortion (quality) is suitable to check the validity and the quality of straight-sided and curved elements on Riemannian planes determined by constant and point-wise varying metrics. The examples illustrate that the distortion can be minimized to curve (deform) the elements of a given high-order (linear) mesh and try to match with curved (linear) elements the point-wise alignment and stretching of an analytic target metric tensor.