Energy constraints on parameterized models
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
LAPACK: a portable linear algebra library for high-performance computers
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Dynamic simulation of non-penetrating flexible bodies
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Dynamic deformation of solid primitives with constraints
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Matrix animation and polar decomposition
Proceedings of the conference on Graphics interface '92
Matrix computations (3rd ed.)
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Eigenvalues of a symmetric 3 × 3 matrix
Communications of the ACM
A modeling system based on dynamic constraints
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Constraints methods for flexible models
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Collision Detection and Response for Computer Animation
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Dynamic real-time deformations using space & time adaptive sampling
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Fast animation and control of nonrigid structures
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Interactive skeleton-driven dynamic deformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Robust treatment of collisions, contact and friction for cloth animation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Physically-Based Simulation of Objects Represented by Surface Meshes
CGI '04 Proceedings of the Computer Graphics International
A virtual node algorithm for changing mesh topology during simulation
ACM SIGGRAPH 2004 Papers
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Meshless deformations based on shape matching
ACM SIGGRAPH 2005 Papers
Dynamic Simulation of Articulated Rigid Bodies with Contact and Collision
IEEE Transactions on Visualization and Computer Graphics
Hybrid simulation of deformable solids
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
FastLSM: fast lattice shape matching for robust real-time deformation
ACM SIGGRAPH 2007 papers
A mass spring model for hair simulation
ACM SIGGRAPH 2008 papers
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Efficient elasticity for character skinning with contact and collisions
ACM SIGGRAPH 2011 papers
Real-time large-deformation substructuring
ACM SIGGRAPH 2011 papers
Solid simulation with oriented particles
ACM SIGGRAPH 2011 papers
Robust real-time deformation of incompressible surface meshes
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Physical material editing with structure embedding for animated solid
Proceedings of Graphics Interface 2012
Interactive authoring of simulation-ready plants
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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In physical simulation, it is frequently useful to define constraints between deformable objects, ensuring that one object follows another. Existing techniques for enforcing these constraints define the relationship between the objects using barycentric coordinates, a linear combination of vertices. While simple to implement and understand, barycentric coordinates have one important drawback: for stability, weights must be non-negative, which limits the types of constraints that can be defined. We introduce the Point Cloud Glue, which uses the nearest fit rigid rotation (the Procrustes transform) to the deformable object's particles. Our key contribution is to demonstrate that we can differentiate through this minimization in a numerically stable manner, allowing our method to be used in many constrained dynamics systems including those based on bindings/embeddings and those based on Lagrange multipliers. We demonstrate the flexibility of our method through several examples.