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:
Feb. 14, 2006
Filed:
Sep. 02, 2003
Tetsu Sato, Tokyo, JP;
Tetsu Sato, Tokyo, JP;
Abstract
The method for rendering using symplectic ray tracing is comprised the step of fixing the location of observation, fixing view screen of observation, practicing the symplectic ray tracing, acquiring the information of the color where the light rays cross the surface of the objects, rendering the objects according to the information of the color acquired. The symplectic ray tracing of the present invention forms the Hamilton's canonical equation by applying the fast automatic differentiation techniques with the Hamiltonian H of the objects, and practices the symplectic integration by applying the symplectic Euler method to the formed Hamilton's canonical equation. The present invention can provide the apparatus and method for rendering which can visualize the phenomena in non-homogeneously transparent object or the four-dimensional black hole space time.