Generating an image using sample points determined on a sub-pixel grid offset using elements of a low-discrepancy sequence
View Patent ↗A computer graphics system generates a pixel value for a pixel in an image, the pixel being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer graphics system being configured to generate the pixel value for an image using a selected ray-tracing methodology in which simulated rays are shot from respective ones of a plurality of subpixels in the pixel, each subpixel having coordinates (s x ,s y ) in the image plane The computer graphics system comprises a sample point generator and a function evaluator. The sample point generator is configured to map subpixel coordinates (s x ,s y ) onto strata coordinates (j,k):=(s x mod 2 n ,s y mod 2 n ), from which a ray is to be shot, in accordance with x i = ( s x + σ ( k ) 2 n , s y + σ ( j ) 2 n ) where “i” is an instance number for the ray generated as i=j2 n +σ(k), where integer permutation σ(k):=2 n Φ b (k) for 0≦k<2 n for selected “n,” where Φ b (x) is a radical inverse function given by Φ b : N 0 → I x = ∑ j = 0 ∞ a j ( x ) b j ↦ ∑ j = 0 ∞ a j ( x ) b - j - 1 , where ( a j ) j = 0 ∞ is the representation of “x” in a selected integer base “b”. The function evaluator is configured to evaluate a selected function using the strata coordinates generated by the sample point generator, the value generated by the function evaluator corresponding to the pixel value.
1. A computer program product for use in connection with a computer to enable the computer to generate a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer program product being configured to enable the computer to generate the pixel value for an image using a selected ray-tracing methodology in which simulated rays are shot from respective ones of a plurality of subpixels in the pixel, each subpixel having coordinates(s x , s y ) in the image plane, the computer program product comprising a computer-readable medium having encoded thereon:
A. computer-readable program instructions executable to provide a sample point generator module configured to enable the computer to map subpixel coordinates (s x , s y ) onto strata coordinates
( j,k ):=( s x mod 2 n ,s y mod 2 n ),
from which a ray is to be shot in accordance with
x
t
=
(
s
x
+
σ
(
k
)
2
n
,
s
y
+
σ
(
j
)
2
n
)
,
where “i” is an instance number for the ray generated as i=j2 n +σ(k),
where integer permutation
σ( k ):=2 n Φ b ( k ) for 0 ≦k <2 n
for selected “n,” where φ b (x) is a radical inverse function given by
Φ
b
:
N
0
->
I
x
=
∑
j
=
0
∞
a
j
(
x
)
b
j
↦
∑
j
=
0
∞
a
j
(
x
)
b
-
j
-
1
,
where
(α j ) j=0 ∞
is the representation of“x” in a selected integer base “b”; and
B. computer-readable program instructions executable to provide a function evaluator module configured to enable the computer to generate at least one value representing an evaluation of a selected function using the strata coordinates generated by said computer under control of the sample point generator module, the value generated by the computer under control of the function evaluator module corresponding to the pixel value.