  Direct mesh editing and deformation are key components in the geometric
modeling and animation pipeline. Mesh editing methods are typically framed as
optimization problems combining user-specified vertex constraints with a
regularizer that determines the position of the rest of the vertices. The
choice of the regularizer is key to the realism and authenticity of the final
result. Physics and geometry-based regularizers are not aware of the global
context and semantics of the object, and the more recent deep learning priors
are limited to a specific class of 3D object deformations. Our main
contribution is a vertex-based mesh editing method called DragD3D based on (1)
a novel optimization formulation that decouples the rotation and stretch
components of the deformation and combines a 3D geometric regularizer with (2)
the recently introduced DDS loss which scores the faithfulness of the rendered
2D image to one from a diffusion model. Thus, our deformation method achieves
globally realistic shape deformation which is not restricted to any class of
objects. Our new formulation optimizes directly the transformation of the
neural Jacobian field explicitly separating the rotational and stretching
components. The objective function of the optimization combines the approximate
gradients of DDS and the gradients from the geometric loss to satisfy the
vertex constraints. Additional user control over desired global shape
deformation is made possible by allowing explicit per-triangle deformation
control as well as explicit separation of rotational and stretching components
of the deformation. We show that our deformations can be controlled to yield
realistic shape deformations that are aware of the global context of the
objects, and provide better results than just using geometric regularizers.
