A fast geometric multigrid solver for simulating elastic deformation of animated characters using an octree mesh discretization.
A method andsystem for simulation of deformation of elastic materials are disclosed herein. A matrix-free geometric multigrid method utilizing a direct coarse grid discretization is presentedfor the solution of linear systems resulting from an octree discretization of the equations of corotational linear elasticity. The diagonal component of the stiffness matrix needed for the multigrid smoother is calculated without generating the stiffness matrix. The use of an incomplete linear octree data structure supports the efficient simulation of objects with complicated boundaries. Furthermore, the method is robust to large deformations, making it suitable for character skinning applications in computer animation.
BRIEF DESCRIPTIONOF THE DRAWINGS(1) In order to reasonably describe and illustrate those innovations, embodiments, and/or examples found within this disclosure, reference may be made to one or more accompanying drawings. The additional details or examples used to describe the one or more accompanying drawings should not be considered as limitations to the scope of any of the claimed inventions, any of the presently described embodiments and/or examples, or the presently understood best mode of any innovations presented within this disclosure.(2) FIG.1 is a simplified block diagram of a system for creating computer graphics imagery (CGI) and computer-aided animation that may implement or incorporate various embodiments or techniques for simulating deformation.(3) FIG. 2 is a flowchart of a method for simulating deformation in one embodiment.(4) FIG. 3A is an illustration depicting rigging associated with a computer-generated character in one embodiment.(5) FIG. 3B is an illustration depicting a lattice embedding a mesh representing skin of the computer-generated character of FIG.3A in one embodiment.(6) FIG. 3C is an illustration depicting a pose for the mesh representing skin of the computer-generated character of FIG. 3A that may be produced in one embodiment.(7) FIG. 4 is a flowchart of a method for determining response of a continuum representation of a material for posing a mesh representing skin of the computer-generated character of FIG. 3A in one embodiment.(8) FIG.
1.A method for deforming computer-generated objects, the method comprising: receiving at one or more computer systems, information identifying a computer-generated object; receivinginformation identifying a space partitioning tree grid associated with the computer-generated object; receiving information identifying a set of material properties for the computer generated object; receiving kinematic information associated with the computer-generated object; calculating a diagonal component of a stiffness matrix as the combination of an auxiliary component and a Laplacian component; determining a response of a continuum representation of a material at one or more cells forming the space partitioning tree grid according to the set of material properties and the kinematic information associated with the computer-generated object based on the diagonal component of the stiffness matrix associated with a stabilized energy discretization over the one or more cells of the space partitioning tree grid utilizing a one point quadrature at each of the one or more cells; and generating information configured to deform the computer generated object from a first configuration to a second configuration based on the determined response of the continuum representation of the material.
10. A non-transitory computer-readable medium storing computer-executable code for deforming computer-generated objects, the non-transitory computer-readable medium comprising: code for receiving at one or more computer systems, information identifying a computer-generated object; code for receiving information identifying a space partitioning tree grid associated with the computer-generated object; code for receiving information identifying a set of material properties for the computer generated object; codefor receiving kinematic information associated with the computer-generated object; code for calculating a diagonal component of a stiffness matrix as the combination of an auxiliary component and a Laplacian component; code for determining a response of a continuum representation of a material at one or more cells forming the space partitioning tree grid according to the set of material properties and the kinematic information associated with the computer-generated object based on the diagonal component of the stiffness matrix associated with a stabilized energy discretization over the one or more cells of the space partitioning tree grid utilizing a one point quadrature at each of the one or more cells; and code for generating information configured to deform the first object from a first configuration to a second configuration based on the determined response of the continuum representation of the material.
19. A method for deforming computer-generated objects, the method comprising: receiving at one or more computer systems, information identifying a computer-generated object; receiving information identifying a space partitioning tree grid associated with the computer-generated object; receiving information identifying a set of material properties for the computer generated object; receiving kinematic information associatedwith the computer-generated object; determining a response of a continuum representation of a material at one or more cells forming the space partitioning tree grid according to the set of material properties and the kinematic information associated with the computer-generated object based on a diagonal component of a stiffness matrix associated with a stabilized energy discretization over the one or more cells of the space partitioning tree grid utilizing a one point quadrature at each of the one or more cells, wherein the space partitioning tree grid comprises an octree grid formed by a plurality of hexahedral cells having different sizes, and wherein each of the cells forming the octree grid has eight nodes, wherein determining the response of the continuum representation of a material at one ormore of the cells forming the octree grid according to the set of material properties andthe kinematic information associated with the computer-generated object based on a calculated diagonal component of a stiffness matrix further comprises: identifying a first cell of the octree grid having a first size; identifying a second cell of the octree grid having a second size, wherein the second cell is smaller than the first cell, and wherein the first cell and the second cell are adjacent; and identifying a hanging node of the second cell, wherein the hanging node is at a location on the first cell but not co-located with anode of the first cell; and generating information configured to deform the computer generated object from a first configuration to a second configuration based on the determined response of the continuum representation of the material.