Embedded deformation for shape manipulation

Abstract

We present an algorithm that generates natural and intuitive deformations via direct manipulation for a wide range of shape representations and editing scenarios. Our method builds a space deformation represented by a collection of affine transformations organized in a graph structure. One transformation is associated with each graph node and applies a deformation to the nearby space. Positional constraints are specified on the points of an embedded object. As the user manipulates the constraints, a nonlinear minimization problem is solved to find optimal values for the affine transformations. Feature preservation is encoded directly in the objective function by measuring the deviation of each transformation from a true rotation. This algorithm addresses the problem of "embedded deformation" since it deforms space through direct manipulation of objects embedded within it, while preserving the embedded objects' features. We demonstrate our method by editing meshes, polygon soups, mesh animations, and animated particle systems.

Anisotropic deformation for local shape control

“…Mesh manipulation based on the transfer of per-triangle deformation gradients was introduced by Sumner and Popović [9]. In the same fashion, arbitrary affine transformations applied to nodes to provide direct and intuitive deformation were presented by Sumner et al [10]. More recently, modeling methods for articulated, organic shapes based on polar and quad representations have been presented in Refs.…”

Elastic Fragments for Dense Scene Reconstruction

“…where N (p) is the set of neighbors of p in G i , and R ′ p is a rotation transform that maps the local tangent frame of p to the local tangent frame of p ′ [28,30]. R ′ p thus represents the local rotational effect of T at p. The intuition behind this formulation is that R ′ p corrects for the rotation induced by T, so the linear least-squares term…”

Shape manipulation using physically based wire deformations

“…deforming the whole length of all profile wires (Figure 8b), (2). deforming a part of all profile wires (Figure 8c), (3).…”

“…Space deformation techniques [1][2][3] deform 3D models by warping the surrounding space. They are suitable for global shape manipulation.…”