Method for generating pixel values for pixels in an image using strictly deterministic methodologies for generating sample points
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 comprises a sample point generator and a function evaluator. The sample point generator is configured to generate a set of sample points representing at least one simulated element of the simulated camera, the sample points representing elements of, illustratively, for sample points on the image plane, during time interval during which the shutter is open, and on the lens, a Hammersley sequence, and, for use in global illumination, a scrambled Halton sequence. The function evaluator configured to generate at least one value representing an evaluation of said selected function at one of the sample points generated by said sample point generator, the value generated by the function evaluator corresponding to the pixel value.
1. A computer graphics method for generating 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 method comprising:
A. a sample point generating step in which a set of sample points are generated representing at least one simulated element of the simulated camera, the sample points representing elements of a Hammersley sequence; and
B. a function evaluation step in which at least one value is generated representing an evaluation of said selected function at one of the sample points generated by said sample point generator, the value generated by the function evaluator corresponding to the pixel value;
in which the sample point generating step includes the step of generating sample position points x i representing jittered sample point positions on a subpixel grid for at least one pixel on the image plane for use by the function evaluator in evaluating the selected function; and
in which the sample point generating step includes the step of generating the sample position points x i in accordance with
x
i
=
(
s
x
+
Φ
2
(
k
)
,
s
y
+
Φ
2
(
j
)
)
=
(
s
x
+
σ
(
k
)
2
n
,
s
y
+
σ
(
j
)
2
n
)
where (s x ,s y ) are subpixel coordinates mapped onto strata coordinates
( j,k ):=( s x mod2 n ,s 2 n ),
and instance number “i” corresponds to
i=j 2 n =σ(k)
where integer permutation
σ( k ):=2 n Φ 2 ( k ) for 0≦ k <2 n
for “n” a selected integer, and
Φ b (q)
is the radical inverse function of “q” in base “b”; and
generating a display controlling electronic output from the pixel value.
2. A computer graphics method for generating 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 method comprising:
A. a sample point generating step in which a set of sample points are generated representing at least one simulated element of the simulated camera, the sample points representing elements of a Hammersley sequence; and
B. a function evaluation step in which at least one value is generated representing an evaluation of said selected function at one of the sample points generated by said sample point generator, the value generated by the function evaluator corresponding to the pixel value;
in which the sample point generating step includes the step of generating sample position points x i representing jittered sample point positions on a subpixel grid for at least one pixel on the image plane for use by the function evaluator in evaluating the selected function;
in which the simulated camera is to be provided with a shutter, and the sample point generating step includes the step of generating, for at least one sample point position on a subpixel for at least one pixel on the image plane, sample time points t i,j representing “i” points in time during a time interval t 0 to t 0 =T during which the shutter is to be open for use by the function evaluator in evaluating the selected function; and
in which the sample point generating step includes the step of generating the sample time points t i,j in accordance with
t
i
,
j
:=
t
0
+
(
Φ
3
(
i
)
⊕
j
N
T
)
·
T
where N T corresponds to a predetermined number of times at which sample time points t i,j are to be generated and
Φ b (q)
is the radical inverse function of “q” in base “b”
generating a display controlling electronic output from the pixel value.
3. A computer graphics method as defined in claim 2 in which the simulated camera is to be provided with a lens, and the sample point generating step includes the step of generating, for at least one sample point position and at least one sample time point, sample lens position points Y i,j,k representing “k” points on the lens for use by the function evaluator in evaluating the selected function.
4. A computer graphics method as defined in claim 3 in which the sample point generating step includes the step of generating the sample lens points in accordance with
y
i
,
j
,
k
=
(
(
Φ
5
(
i
+
j
,
σ
5
)
⊕
k
N
L
)
,
(
Φ
7
(
i
+
j
,
σ
7
)
⊕
Φ
2
(
k
)
)
)
where
Φ b (q,σ)
is the scrambled radical inverse function of “q” in base “b” and “⊕” refers to addition modulo a predetermined value and instance number “i” corresponds to
i=j 2 n +σ( k )
where integer permutation
σ( k ):=2 n Φ 2 ( k ) for 0 ≦k <2 n
for “n” a selected integer.
5. A computer graphics method as defined in claim 4 in which the predetermined value is “one.”