Intersection testing in a ray tracing system using three-dimensional axis-aligned box

1. A method of determining, in a ray tracing system, whether a ray intersects a three-dimensional axis-aligned box, wherein the box represents a volume defined by a front-facing plane and a back-facing plane for each dimension of the three-dimensional axis-aligned box, the method comprising:

identifying which of the front-facing planes intersects the ray at a position that is furthest along a direction of the ray; and

determining whether the ray intersects the axis-aligned box in dependence on comparing (i) the position at which the ray intersects the identified front-facing plane with (ii) at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified;

wherein the method determines whether the ray intersects the box without comparing the position at which the ray intersects the identified front-facing plane with a position at which the ray intersects the back-facing plane in the dimension for which the front-facing plane was identified.

2. The method of claim 1 , wherein said steps of identifying which of the front-facing planes of the box intersects the ray at a position that is furthest along a direction of the ray and comparing (i) the position at which the ray intersects the identified front-facing plane with (ii) the at least one position at which the ray intersects one of the back-facing planes are performed without computing intersection distances to any of the planes of the box.

3. The method of claim 1 , wherein said identifying which of the front-facing planes of the box intersects the ray at a position that is furthest along the direction of the ray comprises:

performing a first front-facing test to determine which of a first front-facing plane and a second front-facing plane of the box the ray intersects furthest along the ray; and

performing a second front-facing test to determine which of the determined front-facing plane and a third front-facing plane of the box the ray intersects furthest along the ray, thereby identifying which of the front-facing planes of the box intersects the ray furthest along the ray.

4. The method of claim 1 , wherein said identifying which of the front-facing planes of the box intersects the ray at a position that is furthest along the direction of the ray comprises:

performing a first front-facing test to determine which of a first front-facing plane and a second front-facing plane of the box intersects the ray at a position that is furthest along the ray;

performing a second front-facing test to determine which of the first front-facing plane and a third front-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray;

performing a third front-facing test to determine which of the second front-facing plane and the third front-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray; and

using the results of the first, second and third front-facing tests to identify which of the front-facing planes of the box intersects the ray at a position that is furthest along the direction of the ray.

5. The method of claim 1 , wherein the step of comparing (i) the position at which the ray intersects the identified front-facing plane with (ii) the at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified comprises determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than the at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified.

6. The method of claim 5 , wherein said determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than the at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified comprises:

performing a first mixed-facing test to determine which of the identified front-facing plane and a first back-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray, wherein the first back-facing plane of the box is a back-facing plane for a first dimension of the two dimensions for which the front-facing plane was not identified;

performing a second mixed-facing test to determine which of the identified front-facing plane and a second back-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray, wherein the second back-facing plane of the box is a back-facing plane for a second dimension of the two dimensions for which the front-facing plane was not identified; and

using the results of the first and second mixed-facing tests to determine whether the position at which the ray intersects the identified front-facing plane is no further along the ray than the at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified.

7. The method of claim 5 , wherein said determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than the at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified comprises:

performing a back-facing test to determine which of a first back-facing plane and a second back-facing plane of the box intersects the ray at a position that is the least far along the direction of the ray, wherein the first back-facing plane and the second back-facing plane each have a respective dimension of the two dimensions for which the front-facing plane was not identified;

performing a mixed-facing test to determine which of the identified front-facing plane and the determined back-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray; and

using the result of the mixed-facing test to determine whether the position at which the ray intersects the identified front-facing plane is no further along the ray than the at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified.

8. The method of claim 1 , further comprising:

storing one or more intermediate results which are determined in said identifying which of the front-facing planes of the box intersects the ray at a position that is furthest along the direction of the ray; and

reading the stored one or more intermediate results for use in the step of comparing (i) the position at which the ray intersects the identified front-facing plane with (ii) the at least one position at which the ray intersects one of the back-facing planes.

9. 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 valid distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to any intersection of the ray with a point within the box,

wherein said determining whether the ray intersects the axis-aligned box further comprises using the determination of whether the maximum distance condition is satisfied.

10. 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 valid distance of the ray from the ray origin is less than or equal to a maximum distance from the ray origin to any intersection of the ray with a point within the box;

wherein said determining whether the ray intersects the axis-aligned box further comprises using the determination of whether the minimum distance condition is satisfied.

11. The method of claim 10 , further comprising determining whether a maximum distance condition is satisfied, wherein the maximum distance condition is satisfied if a maximum valid distance of the ray from the ray origin is greater than or equal to a minimum distance from the ray origin to any intersection of the ray with a point within the box;

wherein said determining whether the ray intersects the axis-aligned box further comprises using the determination of whether the maximum distance condition is satisfied; and

wherein said determining whether a maximum distance condition is satisfied and said determining whether a minimum distance condition is satisfied are performed in parallel with the step of comparing (i) the position at which the ray intersects the identified front-facing plane and (ii) the at least one position at which the ray intersects one of the back-facing planes.

12. The method of claim 1 , further comprising selectively reversing the axes for the components of the ray and the axis-aligned box, such that D i ≥0, D j ≥0 and D k ≥0, before identifying which of the front-facing planes of the box intersects the ray at a position that is furthest along the direction of the ray, wherein D i , D j and D k are the components of a direction vector of the ray in the i th , j th and k th dimensions respectively.

13. A method of determining, in a ray tracing system, whether a ray intersects a three-dimensional axis-aligned box, wherein the box represents a volume defined by a front-facing plane and a back-facing plane for each dimension of the three-dimensional axis-aligned box, the method comprising:

identifying which of the back-facing planes intersects the ray as a position that is the least far along a direction of the ray; and

determining whether the ray intersects the axis-aligned-box in dependence on comparing (i) the position at which the ray intersects the identified back-facing plane with (ii) at least one position at which the ray intersects one of the front-facing planes for the two dimensions for which the back-facing plane was not identified;

wherein the method determines whether the ray intersects the box without comparing the position at which the ray intersects the identified back-facing plane with a position at which the ray intersects the front-facing plane in the dimension for which back-facing plane was identified.

14. The method of claim 13 , wherein said identifying which of the back-facing planes of the box intersects the ray as a position that is the least far along the direction of the ray comprises:

performing a first back-facing test to determine which of a first back-facing plane and a second back-facing plane of the box intersects the ray intersects as a position that is the least far along the direction of the ray; and

performing a second back-facing test to determine which of the determined back-facing plane and a third back-facing plane of the box intersects the ray as a position that is the least far along the direction of the ray, thereby identifying which of the back-facing planes of the box intersects the ray at a position that is the least far along the direction of the ray.

15. The method of claim 13 , wherein said identifying which of the back-facing planes of the box intersects the ray as a position that is the least far along the direction of the ray comprises:

performing a first back-facing test to determine which of a first back-facing plane and a second back-facing plane of the box intersects the ray at a position that is the least far along the direction of the ray;

performing a second back-facing test to determine which of the first back-facing plane and a third back-facing plane of the box intersects the ray at a position that is the least far along the direction of the ray;

performing a third back-facing test to determine which of the second back-facing plane and the third back-facing plane of the box intersects the ray at a position that is the least far along the direction of the ray; and

using the results of the first, second and third back-facing tests to identify which of the back-facing planes of the box intersects the ray as a position that the least far along the direction of the ray.

16. The method of claim 13 , wherein the step of comparing (i) the position at which the ray intersects the identified back-facing plane with (ii) the at least one position at which the ray intersects one of the front-facing planes for the two dimensions for which the back-facing plane was not identified comprises determining whether the at least one position at which the ray intersects one of the front-facing planes for the two dimensions for which the back-facing plane was not identified is no further along the ray than the position at which the ray intersects the identified back-facing plane.

17. The method of claim 16 , wherein said determining whether the at least one position at which the ray intersects one of the front-facing planes for the for the two dimensions for which the back-facing plane was not identified is no further along the ray than the position at which the ray intersects the identified back-facing plane comprises:

performing a first mixed-facing test to determine which of the identified back-facing plane and a first front-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray, wherein the first front-facing plane of the box is a front-facing plane for a first dimension for the two dimensions for which the back-facing plane was not identified;

performing a second mixed-facing test to determine which of the identified back-facing plane and a second front-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray, wherein the second front-facing plane of the box is a front-facing plane for a second dimension for the two dimensions for which the back-facing plane was not identified; and

using the results of the first and second mixed-facing tests to determine whether the at least one position at which the ray intersects one of the front-facing planes for the for the two dimensions for which the back-facing plane was not identified is no further along the ray than the position at which the ray intersects the identified back-facing plane.

18. The method of claim 16 , wherein said determining whether the at least one position at which the ray intersects one of the front-facing planes for the for the two dimensions for which the back-facing plane was not identified is no further along the ray than the position at which the ray intersects the identified back-facing plane comprises:

performing a front-facing test to determine which of a first front-facing plane and a second front-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray, wherein the first front-facing plane of the box and the second front-facing plane of the box each have a respective dimension of the two dimensions for which the back-facing plane was not identified;

performing a mixed-facing test to determine which of the identified back-facing plane and the determined front-facing plane of the box intersects the ray at a position that is furthest along the direction of the ray; and

using the result of the mixed-facing test to determine whether the at least one position at which the ray intersects one of the front-facing planes for the two dimensions for which the back-facing plane was not identified is no further along the ray than the position at which the ray intersects the identified back-facing plane.

19. An intersection testing module implemented in fixed function circuitry, for use in a ray tracing system, configured to determine whether a ray intersects a three-dimensional axis-aligned box, wherein the box represents a volume defined by a front-facing plane and a back-facing plane for each dimension of the three-dimensional axis-aligned box, the intersection testing module being configured to:

identify which of the front-facing planes intersects the ray at a position that is furthest along a direction of the ray; and

determine whether the ray intersects the axis-aligned box in dependence on comparing (i) the position at which the ray intersects the identified front-facing plane with (ii) at least one position at which the ray intersects one of the back-facing planes for the two dimensions for which the front-facing plane was not identified;

wherein the intersection testing module is configured to determine whether the ray intersects the box without comparing the position at which the ray intersects the identified front-facing plane with a position at which the ray intersects the back-facing plane in the dimension for which the front-facing plane was identified.

20. An intersection testing module implemented in fixed function circuitry, for use in a ray tracing system, configured to determine whether a ray intersects a three-dimensional axis-aligned box, wherein the box represents a volume defined by a front-facing plane and a back-facing plane for each dimension of the three-dimensional axis-aligned box, the intersection testing module being configured to:

identify which of the back-facing planes intersects the ray at a position that is the least far along a direction of the ray; and

determine whether the ray intersects the axis-aligned-box in dependence on comparing (i) the position at which the ray intersects the identified back-facing plane with (ii) at least one position at which the ray intersects one of the front-facing planes for the two dimensions for which the back-facing plane was not identified;

wherein the intersection testing module is configured to determine whether the ray intersects the box without comparing the position at which the ray intersects the identified back-facing plane with a position at which the ray intersects the front-facing plane in the dimension for which back-facing plane was identified.