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.

Fast Deformation for Modelling of Musculoskeletal System

“…External forces at vertices are also expressed as an energy function. A product of these two functions gives the deformation energy function whose minimisation, which is done by solving an over-constrained system of linear or non-linear equations, yield the new positions of vertices in the deformed mesh (Huang et al, 2006), (Zhou et al, 2005). We note that gradient domain deformation techniques are usually designed for direct mesh editing, where only a small part of surface is subject to external forces, which is again something uncommon in our context.…”

“…We note that gradient domain deformation techniques are usually designed for direct mesh editing, where only a small part of surface is subject to external forces, which is again something uncommon in our context. Our method is based on the gradient domain deformation technique described in (Huang et al, 2006). In contrast to original description, however, it does not assume that the mesh skeleton, whose change triggers the deformation of surface mesh, is fully inside the volume of the mesh.…”

“…This method is based on that described by (Huang et al, 2006) where volume preserving deformation is achieved by forming a system of non-linear equations that is solved by an iterative Gauss-Newton method with Lagrange multipliers. The main changes done to the original description were to adapt conditions and the computation process to our input data and goals.…”

Video-based Capturing and Rendering of People

“…Following a similar line of thinking, [40,9] propose a mesh-based inverse kinematics framework based on pose examples with potential application to mesh animation. Recently, [37] presents a multi-grid technique for efficient deformation of large meshes and [19] presents a framework for performing constrained mesh deformation using gradient domain techniques. Both methods are conceptually related to our algorithm and could also be used for animating human models.…”

A new framework for behavior modeling of organs and soft tissue using the Boundary-Element Methods

“…We seek an approach that is physically-based, like the finite-element methods (FEM), but achieves a speed comparable to that of the efficient kinematic methods [8,5,4,10], popular in the computer graphics and animation industry. The research makes the following contributions:…”