Guaranteed Globally Injective 3D Deformation Processing

Yu Fang*1,2,3Minchen Li*1,2Chenfanfu Jiang1,2 Danny M. Kaufman3 
*Joint first authors
1University of California, Los Angeles,  2University of Pennsylvania,  3Adobe Research
ACM Transactions on Graphics (SIGGRAPH), 2021

Making dumplings: Injective Deformation Processing (IDP) enables reliable and efficient deformation with a guarantee of injectivity for a wide range of tasks. Here, applied for modeling and layout with a tetrahedral mesh, we can emulate manual steps with IDP to directly form a complex model from simple primitives in just a few steps. Once complete, we copy-paste the model. Then layout, with non-intersection enforced, provides natural variation for the copies as we nudge the plated dumplings for a final arrangement.


We extend recent advances in the numerical time-integration of contacting elastodynamics [Li et al. 2020] to build a new framework, called Injective Deformation Processing (IDP), for the robust solution of a wide range of mesh deformation problems requiring injectivity. IDP solves challenging 3D (and 2D) geometry processing and animation tasks on meshes, via artificial time integration, with guarantees of both non-inversion and non-overlap. To our knowledge IDP is the first framework for 3D deformation processing that can efficiently guarantee globally injective deformation without geometric locking. We demonstrate its application on a diverse set of problems and show its significant improvement over state-of-the-art for globally injective 3D deformation.


Source Code and Data

    author = {Yu Fang and Minchen Li and Chenfanfu Jiang and Danny M. Kaufman},
    title = {Guaranteed Globally Injective 3D Deformation Processing},
    journal = {ACM Trans. Graph. (SIGGRAPH)},
    year = {2021},
    volume = {40},
    number = {4},
    articleno = {75}

Supplemental Documents

Negative (inward) normal flow with IDP obtains shape skeletons that remain watertight, topology preserving and non-intersecting even for extreme flows.

Mousey sequence animation repair. Animation sequences often contain unacceptable and severe intersection artifacts. Here in the Mousey sequence (a and d) arms intersect both the belly and hip. IDP's clean up (b and e) removes all intersection from all frames while creating indentations on the belly and hip as pushed by the hand.

A Flower arrangement layout is created by first modeling individual flowers via folding, instancing and/or winding simple geometric primitives. We then place all modeled flowers in a vase. Deformation and contact ensure the models naturally rest against each other and the final vase geometry.