Subspace gradient domain mesh deformation

Abstract

In this paper we present a general framework for performing constrained mesh deformation tasks with gradient domain techniques. We present a gradient domain technique that works well with a wide variety of linear and nonlinear constraints. The constraints we introduce include the nonlinear volume constraint for volume preservation, the nonlinear skeleton constraint for maintaining the rigidity of limb segments of articulated figures, and the projection constraint for easy manipulation of the mesh without having to frequently switch between multiple viewpoints. To handle nonlinear constraints, we cast mesh deformation as a nonlinear energy minimization problem and solve the problem using an iterative algorithm. The main challenges in solving this nonlinear problem are the slow convergence and numerical instability of the iterative solver. To address these issues, we develop a subspace technique that builds a coarse control mesh around the original mesh and projects the deformation energy and constraints onto the control mesh vertices using the mean value interpolation. The energy minimization is then carried out in the subspace formed by the control mesh vertices. Running in this subspace, our energy minimization solver is both fast and stable and it provides interactive responses. We demonstrate our deformation constraints and subspace deformation technique with a variety of constrained deformation examples.

Space Deformations, Surface Deformations and the Opportunities In-Between

“…The advantage is that the second step can be easily applied by using a non-linear method since it starts from a reasonable state and the convergence can be rather fast. A somewhat similar approach is taken by Huang et al [17] However, there the cage serves as a subspace to accelerate the non-linear optimization, and there is only one step. In such a two-step approach the cage does not need to be defined accurately around the model, nor wrap the entire model.…”

Free-Form Deformation with Rational DMS-Spline Volumes

“…• Construct the closed coarse control mesh M of the original mesh by using the method presented in [44]. The method is based on the progressive convex hull construction algorithm in [42].…”

“…The method is based on the progressive convex hull construction algorithm in [42]. For details, see [42,44].…”

Interactive and Linear Material Aware Deformations

“…Geometric deformation techniques 13,14,15,16,17,18,19,20,21,22,23,24,25 that operate directly on the meshes have become increasingly popular in recent years. These methods are both efficient and intuitive to control.…”

“…Most of the deformation methods that use linear formulations 14,15,20,21 also face the same limitation. Non-linear methods 16,24,25 that employ rotational invariant local coordinates do not have this problem, but non-linear formulations are in general less efficient.…”