We extend Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes. We show that the measure of element distortion underlying the ODT approach can be re-expressed as a potential energy whose minimization amounts to an equidistribution of the gradient of the deformation eld, thus regularizing simultaneously the size and shape of the simplicial elements. After formulating a non-shrinking traction to favor uniform and isotropic elements at the boundary, we show that this interpretation of ODT also applies for curved meshes made of Bezier simplices. Our construction naturally promotes smoothness of the gradient of the induced geometric map inside and across elements.