The patent badge is an abbreviated version of the USPTO patent document. The patent badge does contain a link to the full patent document.
The patent badge is an abbreviated version of the USPTO patent document. The patent badge covers the following: Patent number, Date patent was issued, Date patent was filed, Title of the patent, Applicant, Inventor, Assignee, Attorney firm, Primary examiner, Assistant examiner, CPCs, and Abstract. The patent badge does contain a link to the full patent document (in Adobe Acrobat format, aka pdf). To download or print any patent click here.
Patent No.:
Date of Patent:
Jul. 30, 2019
Filed:
Mar. 30, 2018
Pixar, Emeryville, CA (US);
Theodore W. Kim, Oakland, CA (US);
Fernando Ferrari De Goes, Berkeley, CA (US);
Breannan D. Smith, Oakland, CA (US);
Pixar, Emeryville, CA (US);
Abstract
Systems, methods and articles of manufacture for rendering images depicting materials are disclosed. A stable Neo-Hookean energy model is disclosed which does not include terms that can produce singularities, or require the use of arbitrarily selected clamping parameters. The stable Neo-Hookean energy may include a length-preserving term and volume-preserving term(s), and the volume-preserving terms themselves may include term(s) from a Taylor expansion of a logarithm of a measurement of volume. The stable Neo-Hookean energy may further include an origin barrier term that increases the difficulty of reaching the origin and expands a mesh in response to a perturbation when the mesh is at the origin. Closed-form expressions of eigenvalues and eigenvectors of a Hessian of the stable Neo-Hookean energy are disclosed, which may be used in a simulation of a material to, e.g., project the Hessian to semi-positive-definiteness in Newton iterations used to determine a substantially minimal energy configuration.