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 of the box intersects the ray at a position that is furthest along a direction of the ray;

determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in a subset of the dimensions, wherein the subset of dimensions comprises the two dimensions for which the front-facing plane was not identified, but wherein the subset of dimensions does not comprise the dimension for which the front-facing plane was identified; and

determining whether the ray intersects the axis-aligned box in dependence on the determination of whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions,

wherein the method determines whether the ray intersects the box without performing a test to determine whether the position at which the ray intersects the identified front-facing plane is no further along the ray than 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 determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions, 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 intersects 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 said determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions 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 in the subset of dimensions;

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 in the subset of dimensions; 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 positions at which the ray intersects the back-facing planes in the subset of the dimensions.

6. The method of claim 1 wherein said determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions 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 of the box is a back-facing plane for a first dimension in the subset of dimensions, and the second back-facing plane of the box is a back-facing plane for a second dimension in the subset of dimensions;

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 positions at which the ray intersects the back-facing planes in the subset of the dimensions.

7. The method of claim 1 further comprising performing a front-facing test, a back-facing test or a mixed-facing test to determine which of a first plane and a second plane of the box intersects the ray at a position that is furthest along the direction of the ray, comprising: comparing P m,i D j ; and P n,j D i , wherein P m,i is a constant component value of the first plane in the i th dimension, wherein P n,j is a constant component value of the second plane in the j th dimension, wherein D i and D j are components of a direction vector of the ray in the i th dimension and j th dimension respectively, wherein either:

in response to determining that P m,i D j >P n,j D i , determining that the ray intersects with the first plane further along the ray than where the ray intersects with the second plane; or

in response to determining that P m,i D j <P n,j D i , determining that the ray intersects with the second plane further along the ray than where the ray intersects with the first plane,

wherein the first plane is either: (i) the front-facing plane for dimension i and has a component value of P 0,i for the i th dimension, or (ii) the back-facing plane for dimension i and has a component value of P 1,i for the i th dimension, and

wherein the second plane is either: (i) the front-facing plane for dimension j and has a component value of P 0,i for the j th dimension, or (ii) the back-facing plane for dimension j and has a component value of P 1,i for the j th dimension.

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 said determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions.

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 said determining whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions.

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. The method of claim 1 wherein the determination of whether the ray intersects the axis-aligned box is performed conservatively by rounding values determined for front-facing planes towards −∞ and rounding values determined for back-facing planes towards +∞, such that errors introduced by rounding in the determination process cannot cause a determination that the ray does not intersect the axis-aligned box if a perfectly accurate determination would have determined that the ray does intersect the axis-aligned box.

14. 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 of the box intersects the ray at a position that is the least far along a direction of the ray;

determining whether the ray intersects the front-facing planes in a subset of the dimensions at positions that are no further along the ray than a position at which the ray intersects the identified back-facing plane, wherein the subset of dimensions comprises the two dimensions for which the back-facing plane was not identified, but wherein the subset of dimensions does not comprise the dimension for which the back-facing plane was identified; and

determining whether the ray intersects the axis-aligned box using the determination of whether the ray intersects the front-facing planes in the subset of the dimensions at positions that are no further along the ray than a position at which the ray intersects the identified back-facing plane,

wherein the method determines whether the ray intersects the box without performing a test to determine whether the ray intersects the front-facing plane in the dimension for which the back-facing plane was identified at a position that is no further along the ray than a position at which the ray intersects the identified back-facing plane.

15. The method of claim 14 wherein said 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 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 at 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 at 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.

16. The method of claim 14 wherein said 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 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.

17. The method of claim 14 wherein said determining whether the ray intersects the front-facing planes in the subset of the dimensions at positions that are no further along the ray than a 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 in the subset of dimensions;

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 in the subset of dimensions; and

using the results of the first and second mixed-facing tests to determine whether the ray intersects the front-facing planes in the subset of the dimensions at positions that are no further along the ray than a position at which the ray intersects the identified back-facing plane.

18. The method of claim 14 wherein said determining whether the ray intersects the front-facing planes in the subset of the dimensions at positions that are no further along the ray than a 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 is a front-facing plane for a first dimension in the subset of dimensions, and the second front-facing plane of the box is a front-facing plane for a second dimension in the subset of dimensions;

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 ray intersects the front-facing planes in the subset of the dimensions at positions that are no further along the ray than a 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 of the box intersects the ray at a position that is furthest along a direction of the ray;

determine whether the position at which the ray intersects the identified front- facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in a subset of the dimensions, wherein the subset of dimensions comprises the two dimensions for which the front-facing plane was not identified, but wherein the subset of dimensions does not comprise the dimension for which the front-facing plane was identified; and

determine whether the ray intersects the axis-aligned box using the determination of whether the position at which the ray intersects the identified front-facing plane is no further along the ray than positions at which the ray intersects the back-facing planes in the subset of the dimensions,

wherein the intersection testing module is configured to determine whether the ray intersects the box without performing a test to determine whether the position at which the ray intersects the identified front-facing plane is no further along the ray than 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 of the box intersects the ray at a position that is the least far along a direction of the ray;

determine whether the ray intersects the front-facing planes in a subset of the dimensions at positions that are no further along the ray than a position at which the ray intersects the identified back-facing plane, wherein the subset of dimensions comprises the two dimensions for which the back-facing plane was not identified, but wherein the subset of dimensions does not comprise the dimension for which the back-facing plane was identified; and

determine whether the ray intersects the axis-aligned box using the determination of whether the ray intersects the front-facing planes in the subset of the dimensions at positions that are no further along the ray than the position at which the ray intersects the identified back-facing plane,

wherein the intersection testing module is configured to determine whether the ray intersects the box without performing a test to determine whether the ray intersects the front-facing plane in the dimension for which the back-facing plane was identified at a position that is no further along the ray than a position at which the ray intersects the identified back-facing plane.