Method and apparatus for rendering using symplectic ray tracing

• US 6,999,096 B2
• Filed: 09/02/2003
• Issued: 02/14/2006
• Est. Priority Date: 09/02/2003
• Status: Expired due to Fees

• Current Assignee: National Institute of Information and Communications Technology
• Original Assignee: National Institute of Information and Communications Technology
• Inventors: Sato, Tetsu
• Primary Examiner(s): Bella, Matthew C.
• Assistant Examiner(s): Blackman, Anthony J.
• Application Number:
  US10/652,488
• Publication Number:
  US 20050046641A1
• Time in Patent Office: 896 Days
• Field of Search: 345/424, 345/427, 345/653, 345/589, 382/154
• US Class Current: 345/589
• CPC Class Codes: G06T 15/06 Ray-tracing
• CPC Class Codes: G06T 15/40 Hidden part removal

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.

Claims

1. A method for rendering using symplectic ray tracing, the method comprising:

fixing a location of observation;

fixing a view screen of observation;

practicing symplectic ray tracing;

acquiring color information where light rays cross a surface of an object; and

rendering the object according to the information acquired,

wherein practicing symplectic ray tracing includes

deriving a pre-stored Hamiltonian corresponding to the object;

acquiring all derivatives of the Hamiltonian by applying fast automatic differentiation techniques;

forming a Hamilton'"'"'s canonical equation; and

practicing symplectic integration by applying a symplectic Euler method to the formed Hamilton'"'"'s canonical equation.

2. An apparatus for rendering using symplectic ray tracing, the apparatus comprising:

a fixing section fixing a location of observation, and fixing a view screen of observation;

a practicing section practicing the symplectic ray tracing,

an information acquiring section acquiring color information where light rays cross a surface of an object; and

a rendering section rendering the object according to the color information acquired,

wherein the practicing section derives a pre-stored Hamiltonian corresponding to the object, acquires all derivatives of the Hamiltonian by applying fast automatic differentiation techniques, forms a Hamilton'"'"'s canonical equation, and then practices symplectic integration by applying a symplectic Euler method to the formed Hamilton'"'"'s canonical equation.

3. An apparatus for rendering using symplectic ray tracing as in claim 2, wherein the practicing section includes:

a forming section forming the Hamilton'"'"'s canonical equation by applying fast automatic differentiation techniques, and

a symplectic integration section practicing symplectic integration by applying the symplectic Euler method to the formed Hamilton'"'"'s canonical equation.