# Hierarchical Deformation of Locally Rigid Meshes

A method of applying deformations based on constraints to vertices in a high-resolution mesh. The deformation is calculated quickly by deforming a low-resolution base mesh, and adding details that match the deformation.

## BibTeX

@article{Manson:2011:HDLRM,
author    = {Josiah Manson and
Scott Schaefer},
title     = {Hierarchical Deformation of Locally Rigid Meshes},
journal   = {Computer Graphics Forum},
volume    = {30},
number    = {8},
year      = {2011},
pages     = {2387--2396},
}



## Abstract

We propose a method for calculating deformations of models by deforming a low-resolution mesh and adding details while ensuring that the details we add satisfy a set of constraints. Our method builds a low-resolution representation of a mesh by using edge collapses and performs an as-rigid-as-possible deformation on the simplified mesh. We then add back details by reversing edge-collapses so that the shape of the mesh is locally preserved. While adding details, we deform the mesh to match the predicted positions of constraints so that constraints on the full-resolution mesh are met. Our method operates on meshes with arbitrary triangulations, satisfies constraints over the full-resolution mesh, and converges quickly.

## Supplemental Materials

local_rigid.avi

A movie demonstrating the method described in the paper.

eg2012-hierarchical.zip

The slides and movies used for the presentation at Eurographics 2012.

## Figures

An example like the armadillo man. A mesh is shown on the left, followed by deformations with base meshes of 200, 500, 2000 vertices, and unsimplified. Using more vertices makes the mesh deform more like a rubber skin.

Deformations of a dragon (bottom, middle) from the rest pose (top) are shown with constraints shown as yel- low spheres

A comparison of the bumpy plane example using our method at 200 (top) and 500 (bottom) vertices in Q0. The low-resolution meshes are shown on the left, with the full-resolution meshes on the right.

This grid of images compares deformations produced by a variety of methods in challenging configurations. The constraints in the first row are moved purely by a translation, while the remaining rows contain a bend or twist. The columns from left to right are the resulting meshes after performing (a) no deformation, (b) PriMo [BPGK06], (c) thin shells with deformation transfer [BSPG06], (d) gradient based editing [ZRKS05], (e) Laplacian-based editing with implicit optimization [SCOL*04], (f) rotation invariant coordinates [LSLCO05], (g) our method.

The deformation of a cylinder collapsed to 100 vertices using a plane distance metric [GH97] (left), and using a point distance metric [ACSE05] (right). The top shows the simplified meshes, and the bottom shows the result after adding details.