Intersection Testing in a Ray Tracing System Using Axis-Aligned Box Coordinate Components

Application No. 19/037,551

• Filed: Jan 27, 2025
• Priority: Mar 23, 2021 — GB 2104054.8
  • Mar 23, 2022 — continuation of 11/741,655
  • Aug 29, 2023 — continuation of 12/211,135
• Examiner: LIU, GORDON G
• Assignee: Imagination Technologies Limited
• OA Round: 1 (Non-Final)

Office Action

DETAILED ACTION
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . Claims 1-20 are pending under this Office action.

Double Patenting
The nonstatutory double patenting rejection is based on a judicially created doctrine grounded in public policy (a policy reflected in the statute) so as to prevent the unjustified or improper timewise extension of the “right to exclude” granted by a patent and to prevent possible harassment by multiple assignees. A nonstatutory double patenting rejection is appropriate where the conflicting claims are not identical, but at least one examined application claim is not patentably distinct from the reference claim(s) because the examined application claim is either anticipated by, or would have been obvious over, the reference claim(s). See, e.g., In re Berg, 140 F.3d 1428, 46 USPQ2d 1226 (Fed. Cir. 1998); In re Goodman, 11 F.3d 1046, 29 USPQ2d 2010 (Fed. Cir. 1993); In re Longi, 759 F.2d 887, 225 USPQ 645 (Fed. Cir. 1985); In re Van Ornum, 686 F.2d 937, 214 USPQ 761 (CCPA 1982); In re Vogel, 422 F.2d 438, 164 USPQ 619 (CCPA 1970); In re Thorington, 418 F.2d 528, 163 USPQ 644 (CCPA 1969).
A timely filed terminal disclaimer in compliance with 37 CFR 1.321(c) or 1.321(d) may be used to overcome an actual or provisional rejection based on nonstatutory double patenting provided the reference application or patent either is shown to be commonly owned with the examined application, or claims an invention made as a result of activities undertaken within the scope of a joint research agreement. See MPEP § 717.02 for applications subject to examination under the first inventor to file provisions of the AIA as explained in MPEP § 2159. See MPEP §§ 706.02(l)(1) - 706.02(l)(3) for applications not subject to examination under the first inventor to file provisions of the AIA . A terminal disclaimer must be signed in compliance with 37 CFR 1.321(b).
The USPTO Internet website contains terminal disclaimer forms which may be used. Please visit www.uspto.gov/patent/patents-forms. The filing date of the application in which the form is filed determines what form (e.g., PTO/SB/25, PTO/SB/26, PTO/AIA /25, or PTO/AIA /26) should be used. A web-based eTerminal Disclaimer may be filled out completely online using web-screens. An eTerminal Disclaimer that meets all requirements is auto-processed and approved immediately upon submission. For more information about eTerminal Disclaimers, refer to www.uspto.gov/patents/process/file/efs/guidance/eTD-info-I.jsp.
Claims 1-20 are rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1-20 of U.S. Patent No. 11,741,655. Although the claims at issue are not identical, they are not patentably distinct from each other because they can read on to each other, see the following mapping table.

Application No. 19/037,551 (Instant Application)
U.S. Patent No. 11,741,655
1. method of determining, in a ray tracing system, whether a ray intersects a three-dimensional axis-aligned box, the method comprising:

determining whether a minimum distance condition and a maximum distance condition are satisfied, wherein the determining comprises determining whether a single distance condition is satisfied, and wherein the single distance condition is, or is mathematically equivalent to,

[AltContent: rect]

using the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box;

wherein a point on the ray is at a position O + Dt where O is a vector which represents an origin of the ray, and t represents a distance along the ray from the origin of the ray, and

wherein
D is a 3D vector defining a direction vector of the ray;

C is a 3D vector defining a position of the centre of the axis-aligned box;

H is a 3D vector representing half width values of the axis-aligned box;

tc represents a centre position defining a centre between i) tmin representing a minimum distance of the ray from the origin of the ray and ii) tmax representing a maximum distance of the ray from the ray origin; and

th represents a half width t value defining half the distance between the tmin and tmax.

1. A method of determining, in a ray tracing system, whether a ray intersects a three- dimensional axis-aligned box, the method comprising:

5. The method of claim 1, further comprising determining whether a minimum distance condition is satisfied and whether a maximum distance condition is satisfied by determining whether a single distance condition is satisfied, wherein the minimum distance condition is satisfied if a minimum distance of the ray from the ray origin is less than or equal to a maximum distance from the ray origin to an intersection of the ray direction vector with the box, wherein the maximum distance condition is satisfied if a maximum distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to an intersection of the ray direction vector with the box, and wherein a determination that the single distance condition is satisfied indicates that both the minimum distance condition and the maximum distance condition are satisfied,

wherein said using the determinations of whether the first, second and third conditions are satisfied further comprises using the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box.

6. The method of claim 5, wherein the single distance condition is, or is equivalent to,

t

c

∙
D
-
C

≤
H
+

t

h

∙
D

,

wherein D is the direction vector of the ray with components

D

x

,

D

y

, and

D

z

, wherein C is the position of the centre of the axis-aligned box with components

C

x

,

C

y

and

C

z

, wherein H is a vector representing the half widths

H

x

,

H

y

, and

H

z

, of the axis-aligned box, wherein a point on the ray is at a position
O
+
D
t

where O is a vector which represents the ray origin, and t represents a distance along the ray from the ray origin, and wherein

t

c

=

t

m
a
x

+

t

m
i
n

2

and

t

h

=

t

m
a
x

-

t

m
i
n

2

, wherein

t

m
i
n

is a Minimum value of t defining a minimum distance of the ray from the ray origin, and wherein

t

m
a
x

is a maximum value of t defining a maximum distance of the ray from the ray origin.

2. The method of claim 1, further comprising:

determining whether a first condition is satisfied, wherein the first condition is, or is equivalent to,

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;

determining whether a second condition is satisfied, wherein the second condition is, or is equivalent
to,
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132
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;

determining whether a third condition is satisfied, wherein the third condition is, or is equivalent to,

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; and

using the determinations of whether the first, second, third, and single distance conditions are satisfied to determine whether the ray intersects the axis-aligned box;

wherein
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,
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and
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, are x, y and z components of a position of the centre of the axis-aligned box relative to an origin of the ray, wherein
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,
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, and
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, are half widths of the axis-aligned box in the x, y and z dimensions, and wherein
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,
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, and
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, are x, y and z components of a direction vector of the ray.
1. A method of determining, in a ray tracing system, whether a ray intersects a three- dimensional axis-aligned box, the method comprising:

determining whether a first condition is satisfied, wherein the first condition is, or is equivalent to,

C

x

-

C

z

D

x

D

z

≤

H

z

D

x

D

z

+

H

x

;

determining whether a second condition is satisfied, wherein the second condition is, or is equivalent to,

C

y

-

C

z

D

y

D

z

≤

H

z

D

y

D

z

+

H

y

;

determining whether a third condition is satisfied, wherein the third condition is, or is equivalent to,

C

x

D

y

D

z

-

C

y

D

x

D

z

≤

H

y

D

x

D

z

+

H

x

D

y

D

z

;

using the determinations of whether the first, second and third conditions are satisfied to determine whether the ray intersects the axis-aligned box; and

outputting an indication of a result of the determination of whether the ray intersects the axis-aligned box, wherein the outputted indication is used in the ray tracing system for rendering an image of a 3D scene;

wherein

C

x

,

C

y

and

C

z

, are x, y and z components of a position of the centre of the axis-aligned box relative to an origin of the ray, wherein

H

x

,

H

y

, and

H

z

, are half widths of the axis-aligned box in the x, y and z dimensions, and wherein

D

x

,

D

y

, and

D

z

, are x, y and z components of a direction vector of the ray.
3. The method of claim 2, wherein said using the determinations of whether the first, second and third conditions are satisfied to determine whether the ray intersects the axis-aligned box comprises determining that the ray does not intersect the axis-aligned box if at least one of the first, second and third conditions is determined to be not satisfied.
2. The method of claim 1, wherein said using the determinations of whether the first, second and third conditions are satisfied to determine whether the ray intersects the axis- aligned box comprises determining that the ray does not intersect the axis-aligned box if at least one of the first, second and third conditions is determined to be not satisfied.
4. The method of claim 1, wherein the maximum distance condition is satisfied if tmax is greater than or equal to a minimum distance from the origin of the ray to an intersection of the ray direction vector with the box, and

the minimum distance condition is satisfied if tmin is less than or equal to a maximum distance from the origin of the ray to an intersection of the ray direction vector with the box, and

wherein a determination that the single distance condition is satisfied indicates that both the minimum distance condition and the maximum distance condition are satisfied.
3. The method of claim 1, further comprising determining whether a maximum distance condition is satisfied, wherein the maximum distance condition is satisfied if a maximum distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to an intersection of the ray direction vector with the box,

wherein said using the determinations of whether the first, second and third conditions are satisfied further comprises using the determination of whether the maximum distance condition is satisfied to determine whether the ray intersects the axis-aligned box.

4. The method of claim 1, further comprising determining whether a minimum distance condition is satisfied, wherein the minimum distance condition is satisfied if a minimum distance of the ray from the ray origin is less than or equal to a maximum distance from the ray origin to an intersection of the ray direction vector with the box,

wherein said using the determinations of whether the first, second and third conditions are satisfied further comprises using the determination of whether the minimum distance condition is satisfied to determine whether the ray intersects the axis-aligned box.
5. The method of claim 1, wherein C is the position of the centre of the axis-aligned box with components
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,
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and
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, wherein H is a vector representing the half widths
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,
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21
19
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, and
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, of the axis-aligned box,
and wherein
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and
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70
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.

6. The method of claim 5, wherein the single distance condition is, or is equivalent to,

t

c

∙
D
-
C

≤
H
+

t

h

∙
D

,

wherein D is the direction vector of the ray with components

D

x

,

D

y

, and

D

z

, wherein C is the position of the centre of the axis-aligned box with components

C

x

,

C

y

and

C

z

, wherein H is a vector representing the half widths

H

x

,

H

y

, and

H

z

, of the axis-aligned box, wherein a point on the ray is at a position
O
+
D
t

where O is a vector which represents the ray origin, and t represents a distance along the ray from the ray origin, and wherein

t

c

=

t

m
a
x

+

t

m
i
n

2

and

t

h

=

t

m
a
x

-

t

m
i
n

2

, wherein

t

m
i
n

is a Minimum value of t defining a minimum distance of the ray from the ray origin, and wherein

t

m
a
x

is a maximum value of t defining a maximum distance of the ray from the ray origin.

6. The method of claim 2, wherein it is determined that the ray intersects the axis-aligned box if all of the first, second, third, and single distance conditions are determined to be satisfied.
7. The method of claim 1, further comprising: determining whether a minimum distance condition is satisfied, wherein the minimum distance condition is satisfied if a minimum distance of the ray from the ray origin is less than or equal to a maximum distance from the ray origin to an intersection of the ray direction vector with the box;

determining whether a maximum distance condition is satisfied, wherein the maximum distance condition is satisfied if a maximum distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to an intersection of the ray direction vector with the box,

wherein said using the determinations of whether the first, second and third conditions are satisfied further comprises using the determination of whether the maximum distance condition is satisfied and the determination of whether the minimum distance condition is satisfied to determine whether the ray intersects the axis-aligned box,

wherein it is determined that the ray intersects the axis-aligned box if all of the first, second, third, maximum distance and minimum distance conditions are determined to be satisfied.
7. The method of claim 1, wherein said using the determinations of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box comprises determining that the ray does not intersect the axis-aligned box in response to determining that the single distance condition is determined to be not satisfied.
7. wherein it is determined that the ray intersects the axis-aligned box if all of the first, second, third, maximum distance and minimum distance conditions are determined to be satisfied.
(Note that is any of these condition is not satisfied, the ray does not intersect the axis-aligned box)
8. The method of claim 2, further comprising selectively permuting and/or reversing the x, y and z components of the ray and the axis-aligned box, such that
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85
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and
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86
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, before determining whether the first, second and third conditions are satisfied.

8. The method of claim 1, further comprising selectively permuting and/or reversing the x, y and z components of the ray and the axis-aligned box, such that
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85
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Greyscale

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19
85
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Greyscale
and
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, before determining whether the first, second and third conditions are satisfied.
10. The method of claim 2, wherein values of

D

x

D

z

and

D

y

D

z

are pre-computed for the ray and stored in a store, wherein the method comprises reading the values of

D

x

D

z

and

D

y

D

z

from the store for use in performing the determinations of whether the first, second and third conditions are satisfied.

9. The method of claim 1, wherein values of

D

x

D

z

and

D

y

D

z

are pre-computed for the ray and stored in a store, wherein the method comprises reading the values of

D

x

D

z

and

D

y

D

z

from the store for use in performing the determinations of whether the first, second and third conditions are satisfied.

11. The method of claim 2, further comprising reading data defining a position and a size of the axis-aligned box, and using the read data to determine

C

x

,

C

y

,

C

z

,

H

x

,

H

y

, and

H

z

, for the axis-aligned box.
10. The method of claim 1, further comprising reading data defining a position and a size of the axis-aligned box, and using the read data to determine

C

x

,

C

y

,

C

z

,

H

x

,

H

y

, and

H

z

, for the axis-aligned box.
12. The method of claim 11, wherein

C

x

,

C

y

and

C

z

, are determined by subtracting respective components of the ray origin from respective components of the read data defining the position of the centre of the box.
11. The method of claim 10, wherein

C

x

,

C

y

and

C

z

, are determined by subtracting respective components of the ray origin from respective components of the read data defining the position of the centre of the box.
13. The method of claim 2, wherein said determinations of whether the first, second and third conditions are satisfied are performed conservatively, such that any errors introduced by rounding in the determination process cannot cause a determination that a condition is not satisfied if a perfectly accurate determination would have determined that that condition is satisfied.
12. The method of claim 1, wherein said determinations of whether the first, second and third conditions are satisfied are performed conservatively, such that any errors introduced by rounding in the determination process cannot cause a determination that a condition is not satisfied if a perfectly accurate determination would have determined that that condition is satisfied.
14. The method of claim 1, further comprising outputting an indication of a result of the determination of whether the ray intersects the axis-aligned box.
15. The method of claim 1, further comprising outputting an indication of a result of the determination of whether the ray intersects the axis-aligned box.
15. The method of claim 14, wherein the outputted indication is used in the ray tracing system for rendering an image of a 3D scene.
16. The method of claim 15, wherein the outputted indication is used in the ray tracing system for rendering an image of a 3D scene.
16. The method of claim 1, wherein the axis-aligned box is an axis-aligned bounding box which bounds geometry to be rendered.
17. The method of claim 1, wherein the axis-aligned box is an axis-aligned bounding box which bounds geometry to be rendered.
17. The method of claim 1, wherein the axis-aligned box corresponds to a node of a hierarchical acceleration structure to be used for performing intersection testing in the ray tracing system.
18. The method of claim 1, wherein the axis-aligned box corresponds to a node of a hierarchical acceleration structure to be used for performing intersection testing in the ray tracing system, wherein the node is part of a bottom-level acceleration structure (BLAS) for representing geometry in an instance space, and wherein the method comprises transforming the ray into the instance space.
18. The method of claim 17, wherein the node is part of a bottom-level acceleration structure (BLAS) for representing geometry in an instance space, and wherein the method comprises transforming the ray into the instance space.
18. The method of claim 1, wherein the axis-aligned box corresponds to a node of a hierarchical acceleration structure to be used for performing intersection testing in the ray tracing system, wherein the node is part of a bottom-level acceleration structure (BLAS) for representing geometry in an instance space, and wherein the method comprises transforming the ray into the instance space.
19. An intersection testing module, for use in a ray tracing system, configured to determine whether a ray intersects a three-dimensional axis-aligned box, the intersection testing module being configured to:

determine whether a minimum distance condition and a maximum distance condition are satisfied, wherein the determining comprises determining whether a single distance condition is satisfied, and wherein the single distance condition is, or is mathematically equivalent to,

[AltContent: rect]

use the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box;

wherein a point on the ray is at a position O + Dt where O is a vector which represents an origin of the ray, and t represents a distance along the ray from the origin of the ray, and wherein
D is a 3D vector defining a direction vector of the ray;

C is a 3D vector defining a position of the centre of the axis-aligned box;

H is a 3D vector representing half width values of the axis-aligned box;

tc represents a centre position defining a centre between i) tmin representing a minimum distance of the ray from the origin of the ray and ii) tmax representing a maximum distance of the ray from the ray origin; and

th represents a half width t value defining half the distance between the tmin and tmax.

1. A method of determining, in a ray tracing system, whether a ray intersects a three- dimensional axis-aligned box, the method comprising:

5. The method of claim 1, further comprising determining whether a minimum distance condition is satisfied and whether a maximum distance condition is satisfied by determining whether a single distance condition is satisfied, wherein the minimum distance condition is satisfied if a minimum distance of the ray from the ray origin is less than or equal to a maximum distance from the ray origin to an intersection of the ray direction vector with the box, wherein the maximum distance condition is satisfied if a maximum distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to an intersection of the ray direction vector with the box, and wherein a determination that the single distance condition is satisfied indicates that both the minimum distance condition and the maximum distance condition are satisfied,

wherein said using the determinations of whether the first, second and third conditions are satisfied further comprises using the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box.

6. The method of claim 5, wherein the single distance condition is, or is equivalent to,

t

c

∙
D
-
C

≤
H
+

t

h

∙
D

,

wherein D is the direction vector of the ray with components

D

x

,

D

y

, and

D

z

, wherein C is the position of the centre of the axis-aligned box with components

C

x

,

C

y

and

C

z

, wherein H is a vector representing the half widths

H

x

,

H

y

, and

H

z

, of the axis-aligned box, wherein a point on the ray is at a position
O
+
D
t

where O is a vector which represents the ray origin, and t represents a distance along the ray from the ray origin, and wherein

t

c

=

t

m
a
x

+

t

m
i
n

2

and

t

h

=

t

m
a
x

-

t

m
i
n

2

, wherein

t

m
i
n

is a Minimum value of t defining a minimum distance of the ray from the ray origin, and wherein

t

m
a
x

is a maximum value of t defining a maximum distance of the ray from the ray origin.

20. A non-transitory computer readable storage medium having stored thereon an integrated circuit definition dataset that, when processed in an integrated circuit manufacturing system, configures the integrated circuit manufacturing system to manufacture an intersection testing module for use in a ray tracing system, the intersection testing module being configured to determine whether a ray intersects a three-dimensional axis-aligned box, the intersection testing module being configured to:

determine whether a minimum distance condition and a maximum distance condition are satisfied, wherein the determining comprises determining whether a single distance condition is satisfied, and wherein the single distance condition is, or is mathematically equivalent to,

[AltContent: rect]

use the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box;

wherein a point on the ray is at a position O + Dt where O is a vector which represents an origin of the ray, and t represents a distance along the ray from the origin of the ray, and wherein
D is a 3D vector defining a direction vector of the ray;

C is a 3D vector defining a position of the centre of the axis-aligned box;

H is a 3D vector representing half width values of the axis-aligned box;

tc represents a centre position defining a centre between i) tmin representing a minimum distance of the ray from the origin of the ray and ii) tmax representing a maximum distance of the ray from the ray origin; and

th represents a half width t value defining half the distance between the tmin and tmax.
1. A method of determining, in a ray tracing system, whether a ray intersects a three- dimensional axis-aligned box, the method comprising:

5. The method of claim 1, further comprising determining whether a minimum distance condition is satisfied and whether a maximum distance condition is satisfied by determining whether a single distance condition is satisfied, wherein the minimum distance condition is satisfied if a minimum distance of the ray from the ray origin is less than or equal to a maximum distance from the ray origin to an intersection of the ray direction vector with the box, wherein the maximum distance condition is satisfied if a maximum distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to an intersection of the ray direction vector with the box, and wherein a determination that the single distance condition is satisfied indicates that both the minimum distance condition and the maximum distance condition are satisfied,

wherein said using the determinations of whether the first, second and third conditions are satisfied further comprises using the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box.

6. The method of claim 5, wherein the single distance condition is, or is equivalent to,

t

c

∙
D
-
C

≤
H
+

t

h

∙
D

,

wherein D is the direction vector of the ray with components

D

x

,

D

y

, and

D

z

, wherein C is the position of the centre of the axis-aligned box with components

C

x

,

C

y

and

C

z

, wherein H is a vector representing the half widths

H

x

,

H

y

, and

H

z

, of the axis-aligned box, wherein a point on the ray is at a position
O
+
D
t

where O is a vector which represents the ray origin, and t represents a distance along the ray from the ray origin, and wherein

t

c

=

t

m
a
x

+

t

m
i
n

2

and

t

h

=

t

m
a
x

-

t

m
i
n

2

, wherein

t

m
i
n

is a Minimum value of t defining a minimum distance of the ray from the ray origin, and wherein

t

m
a
x

is a maximum value of t defining a maximum distance of the ray from the ray origin.

Claim 1 of the instant application is drawn to a method of determining, in a ray tracing system, whether a ray intersects a three-dimensional axis-aligned box, the method comprising: determining whether a minimum distance condition and a maximum distance condition are satisfied, wherein the determining comprises determining whether a single distance condition is satisfied, and wherein the single distance condition is, or is mathematically equivalent to,
[AltContent: rect]

using the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box; wherein a point on the ray is at a position O + Dt where O is a vector which represents an origin of the ray, and t represents a distance along the ray from the origin of the ray, and wherein D is a 3D vector defining a direction vector of the ray; C is a 3D vector defining a position of the centre of the axis-aligned box; H is a 3D vector representing half width values of the axis-aligned box; tc represents a centre position defining a centre between i) tmin representing a minimum distance of the ray from the origin of the ray and ii) tmax representing a maximum distance of the ray from the ray origin; and th represents a half width t value defining half the distance between the tmin and tmax.

While the exact wordings of claims 1 and 5-6 of the ‘655 patent may not be the same as that of claim 1 of the instant application, but there is no significant difference in scope between the claim 1 of the instant application and the claim 1 claims 1 and 5-6 of the patent ‘655. Therefore, claim 1 of the instant application cannot be considered patentably distinct over claims 1 and 5-6 of the ‘655 patent.

Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.

The claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more. Claims 1-20 are directed to an abstract idea. The claim(s) does/do not include additional elements that are sufficient to amount to significantly more than the judicial exception. The rationale for this determination is explained below:
Claim 1-20 are rejected under 35 U.S.C 101 because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more. Claim 1-14 and 17-20 are directed to an abstract idea that manipulate the ray vectors in various mathematical steps involved in the geometrical and distance analysis to determine if the ray intersects with the axis-aligned box based on the ray vector and the box center position and box dimension (sizes).
The following analysis of facts of this particular patent application follows the rationale suggested in the "Federal Register Notice: 2019 Revised Patent Subject Matter Eligibility Guidance " (OG Notices: January 7, 2019, available from the US PTO website at https://www.govinfo.gov/content/pkg/FR-2019-01-07/pdf/2018-28282.pdf).
The Guidelines states:
Limitations that were found not to be enough to qualify as ‘‘significantly
more’’ when recited in a claim with a judicial exception include (P6):
• An additional element merely recites the words ‘‘apply it’’ (or an
equivalent) with the judicial exception, or merely includes instructions to
implement an abstract idea on a computer, or merely uses a computer as
a tool to perform an abstract idea;
• an additional element adds insignificant extra-solution activity to
the judicial exception;
• an additional element does no more than generally link the use of a judicial
exception to a particular technological environment or field of use.
In the instant case, at least one embodiment of the claimed invention is merely about the ray vector manipulations of revering the ray vector component Dx, Dy, and Dz to make all these three vector components non-negative, the axis-aligned box half size Hx, Hy, Hz (half the box size in x, y, z direction, respectively), and coordinate of the box center Cx, Cy, Cz respectively, determining a distance between the point in the ray and the center of the box using vector subtraction, and test if the distance satisfies a condition to determine if the ray intersect the axis-aligned box. These are just Mathematical operations (coordinate geometry analysis in essence) in vector manipulations.
Claim 1, and the similar independent claims 19-20, recites a process of a few steps. Thus, the claim is directed to a process which is a statutory category under 35 U.S. C 101. (Step 1: YES)
The claim is then analyzed to determine whether it is directed to any judicial exception.
The claim recites the steps of ray vector manipulations and determining whether a minimum distance condition and a maximum distance condition are satisfied, wherein the determining comprises determining whether a single distance condition is satisfied by position vector algebra operations (subtraction), and wherein the single distance condition is, or is mathematically equivalent to
PNG
media_image1.png
38
424
media_image1.png
Greyscale
.
The steps of determining the distance between the point on the ray, and the center of the axis-aligned box, the maximum and minimum distance constraints for the ray within the volume of the axis-aligned box with the box center coordinates (Cx, Cy, and Cx) and the half length, width, and depth of the axis-aligned box (Hx, Hy, and Hz) are geometric deterministic "Mathematical Relationships/Formulas". Thus, the claim is directed to a judicial exception. (Step 2A: YES).
The claim is then analyzed to determine whether the claim as a whole amount to significantly more than the judicial exception.
The claim recites “using the determination of whether the single distance condition is satisfied to determine whether the ray intersects the axis-aligned box; wherein a point on the ray is at a position O + Dt where O is a vector which represents an origin of the ray, and t represents a distance along the ray from the origin of the ray, and wherein D is a 3D vector defining a direction vector of the ray; C is a 3D vector defining a position of the centre of the axis-aligned box; H is a 3D vector representing half width values of the axis-aligned box; tc represents a centre position defining a centre between i) tmin representing a minimum distance of the ray from the origin of the ray and ii) tmax representing a maximum distance of the ray from the ray origin; and th represents a half width t value defining half the distance between the tmin and tmax.”, which are all descriptions of the mathematical terms to distance condition formula, and they are insignificant extra solutional data gathering. Thus, these limitations are mathematical, and adds insignificant extra- solution activity to the judicial exception.
The limitation “ray tracing system” in the preamble is an intended use recitation for where the method is to be practiced, but it is not relied upon in the body of the claims, it would not constitute a practical application. The ray tracing system would have to be brought into the body of the claims to at least argue a practical application under step 2A prong 2- e.g., by the ray tracing system meaningfully using the result of the transformation to display a particular visual result. Thus, the term “ray tracing system” in the preamble does not make the claim significant more than an abstract idea.
The claim does not recite additional elements that amount to significantly more than the judicial exception. Even when viewed as a combination, the additional elements fail to transform the exception into a patent-eligible application of that exception. (Step 2B: No)
The claim is "directed to" a judicial exception. Further, the claim as a whole does not recite any more additional limitations. Therefore, the independent Claim 1, its related dependent claims 2-14 and 17-18 which each dependent claim adds new limitations that do not amount to have significant effects to transform the exception into a patent-eligible application of that exception, and the independent claims 19-20, are directed to an abstract idea and is rejected under 35 USC§ 101. However, the dependent claims 15-16 recite the extra steps to render the axis-aligned box and the scene based on the intersection testing result that are significantly more than the judicial exception, thus, the claims 15-16 are not “101” rejected.

Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure. Aila, etc. (US 8564589 B1), Karras, etc. (US 20180182158 A1), and Sowizral, etc. (US 20020033835 A1).

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/GORDON G LIU/ Primary Examiner, Art Unit 2618

Prosecution Timeline

• Jan 27, 2025: Application Filed
• Jul 27, 2026: Non-Final Rejection mailed — §101 (current)