Spherical harmonics scaling

• US 7,663,623 B2
• Filed: 12/18/2006
• Issued: 02/16/2010
• Est. Priority Date: 12/18/2006
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Corporation
• Inventors: Zhou, Kun, Wang, Jiaping, Guo, Baining, Lin, Stephen
• Primary Examiner(s): Chauhan; Ulka
• Assistant Examiner(s): Hajnik; Daniel F
• Application Number:
  US11/612,394
• Publication Number:
  US 20080143719A1
• Time in Patent Office: 1,156 Days
• Field of Search: None
• US Class Current: 345/426
• CPC Class Codes: G06T 15/55 Radiosity

Abstract

A method, device and system is provided for providing global illumination of a scene. For example, global illumination may be provided in a rendered 3-dimensional image that may contain objects and/or light sources. Radiance functions or visibility functions may further be represented by scaling of spherical harmonics functions in the spherical harmonics domain. For example, scaling of spherical harmonics coefficients corresponding to a spherical function may be performed based on a spherical harmonics scaling transformation matrix based on an angular scaling function.

Claims

1. A method for scaling a spherical harmonics function, the method comprising:

storing, in a memory communicatively coupled to a processor, computer-executable instructions for performing the method;

executing the instructions on the processor;

according to the instructions being executed;

receiving spherical function;

converting the spherical function to a spherical harmonics representation;

generating a matrix-vector product comprising the spherical harmonics representation based on a spherical harmonics scaling transformation matrix, wherein the matrix-vector product is equivalent to M·

S_r^T, M being the spherical harmonics scaling transformation matrix and S_r^T being the spherical harmonics representation corresponding to the spherical function, wherein r indicates a radius of the spherical harmonics representation, and T indicates a transpose of S, and wherein M is equal to;

2. The method of claim 1 wherein the spherical harmonics scaling transformation matrix comprises a plurality of zero elements and a plurality of non-zero elements.

3. The method of claim 2 wherein the number of non-zero elements in the spherical harmonics scaling transformation matrix is based on an order of the spherical harmonics representation.

4. The method of claim 3 wherein the number of non-zero elements in the spherical harmonics scaling transformation matrix is equal to N(2N²+1)/3, wherein N is the order of the spherical harmonics representation.

5. The method of claim 1 wherein the spherical harmonics scaling transformation matrix comprises a number of elements proportional to an order of the spherical harmonics representation.

6. The method of claim 1 wherein the spherical harmonics representation includes a vector containing spherical harmonics coefficients.

7. The method of claim 1 wherein η

(θ

) comprises one of sin θ and

sin τ

(θ

)τ

′

(θ

).

8. The method of claim 7 wherein the spherical function is a visibility function and η

(θ

) comprises sin θ

.

9. The method of claim 7 wherein the spherical function is a radiance function and η

(θ

) comprises sin τ

(θ

)τ

′

(θ

).

10. The method of claim 1 wherein the spherical harmonics scaling transformation matrix comprises zero elements and non-zero elements and wherein the scaling includes reducing the matrix-vector product based only on the non-zero elements of the spherical harmonics scaling transformation matrix.

11. A computer-readable medium containing computer-executable code wherein execution of the computer-executable code performs the following steps:

receiving a spherical function and an angular scaling function for rescaling the spherical function;

projecting the spherical function into a spherical harmonics domain, wherein projecting the spherical function includes converting the spherical function to a vector comprising spherical harmonics coefficients; and

scaling the spherical function in the spherical harmonics domain, wherein the spherical function is associated with a region and scaling includes one of shrinking or enlarging the region to generate a scaled region, wherein the scaling includes generating a matrix-vector product based on the vector and a spherical harmonics scaling transformation matrix;

wherein the matrix-vector product is equal to M·

S_r^T, M being the spherical harmonics scaling transformation matrix and S_r^T being a vector comprising coordinates corresponding to the projected spherical function in the spherical harmonics domain, wherein r indicates a radius of the spherical harmonics representation, and T indicates a transpose of S.

12. The computer-readable medium of claim 11 wherein the spherical harmonics scaling transformation matrix is based on the angular scaling function.

13. The computer-readable medium of claim 11 wherein M is equal to:

14. A system for generating global illumination effects in a computer-generated environment, the system comprising:

an input for receiving a spherical function corresponding to an illumination-based area; and

a processor for performing the following steps;

converting the spherical function into a vector comprising spherical harmonics coefficients;

determining a spherical harmonics scaling transformation matrix corresponding to a scaling function;

computing a matrix-vector product comprising the vector and the spherical harmonics scaling transformation matrix; and

scaling the spherical function in a spherical harmonics domain based on the matrix-vector product;

wherein the spherical harmonics scaling transformation matrix is equal to;

15. The system of claim 14, wherein:

determining the spherical harmonics scaling transformation matrix corresponding to the scaling function is determined such that;

the spherical harmonics scaling transformation matrix comprises a plurality of zero elements and a plurality of non-zero elements;

the number of non-zero elements in the spherical harmonics scaling transformation matrix is based on an order of the spherical harmonics representation; and

the number of non-zero elements in the spherical harmonics scaling transformation matrix is equal to N(2N²1)/3, wherein N is the order of the spherical harmonics representation; and

the matrix-vector product is equivalent to M·

S_r^T, wherein M is the spherical harmonics scaling transformation matrix and S_r^T is the spherical harmonics representation corresponding to the spherical function, and wherein r indicates a radius of the spherical harmonics representation, and T indicates a transpose of S.