CN102496170A - Method for decomposing sampling task - Google Patents

Abstract

The invention provides a computer image rendering method. The method is based on a (t, s) sequence, the decomposition of a sampling task is realized through layered displacement operation. Compared with a method of carrying out grouping on the (t, s) sequence in a selected dimension so as to realize the decomposition of the sampling task, the computer image rendering method provided by the invention has the advantages that grouping is not needed to be carried out on sampling points in an additional dimension, and a generating matrix of the (t, s) sequence also has no limited condition, so that the method can be used for any type of (t, s) sequence, and the quality of the sampling points is not influenced by the quantity of parallel processing units.

Description

A kind of method that is used for the decomposition of sampling task

Technical field

The present invention relates to a kind of computer picture rendering intent, particularly a kind of rendering intent that utilizes quasi-random numbers (quasi-random numbers) to confirm sampling point position.

Background technology

Play up the field at computer picture, for simulating various effect of shadow, for example, the depth of field, motion blur, global illumination etc., need carry out evaluation to the integration with following form:

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}---\left(1\right)$

Wherein I is the unit interval, function f () by the contextual data decision of the effect that will simulate and input.Formula (1) generally can't accurately be found the solution, and in the render process of reality, always is to use the method for numerical evaluation to ask its approximate value:

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}\≈\frac{1}{N}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}f(x_i^{\left(1\right)},x_i^{\left(2\right)},...,x_i^{\left(S\right)})---\left(2\right)$

The method of confirming sampling point position

in the formula (2) can be divided into two types; One type of method that is to use random number, the another kind of method that is to use quasi-random numbers.Quasi-random numbers is a kind of distribution pattern with satisfactory texture, and the efficient higher than random number can be provided in the Integral Estimation of formula (2).

(t, s) sequence is a kind of main quasi-random numbers type, generation b system (t, s) method of the j of i some dimension component is following in the sequence:

$x_i^{\left(j\right)}=(b^{-1},b^{-2},...b^{-M})C^{\left(j\right)}\left(\begin{array}{c}{b}_0\left(i\right)\\ b_1\left(i\right)\\ \·\\ \·\\ \·\\ b_{M-1}\left(i\right)\end{array}\right)---\left(3\right)$

Wherein

For (t, s) j of sequence supports one's family into matrix (generator matrices), its coefficient

Be Galois field F _bMiddle element.b _r(i) the r bit digital of expression integer i under the b system is represented, promptly

M is selected maximal accuracy under the b system is represented.

(t, s) example of sequence comprises: Sobol sequence, Faure sequence, Niederreiter sequence and Niederreiter-Xing sequence etc.It is different that (t, s) difference of sequence is that the building method of its generator matrix is different.

Parallel computation is the another kind of method that improves formula (2) efficient, and this method is decomposed into two or more parts with the sampling to function f () in the formula (2), each part transfer to one independently parallel processing element handle:

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}\≈\frac{1}{N}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}f(x_i^{\left(1\right)},x_i^{\left(2\right)},...,x_i^{\left(S\right)})$

$=\frac{1}{N}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}\underset{i_d=0}{\overset{N_d-1}{\mathrm{\Σ}}}f(x_{i_d}^{\left(1\right)},x_{i_d}^{\left(2\right)},...,x_{i_d}^{\left(S\right)})---\left(4\right)$

Wherein,

Be the quantity of sampled point, D is the quantity of parallel processing element, N _dBe the sampled point quantity that d processing unit distributes.The different sampled point quantity that processing unit distributed can be the same or different.

Any quasi-random numbers all can directly be used for formula (2), then must do suitable conversion but will be used for formula (4).

For obtaining to use the benefit of quasi-random numbers and parallel computation simultaneously; U.S. Patent application US Patent ApplicationNo.12/432; Providing a kind of 498 open November 4 2010 date passes through (f, s) sequence is divided into groups in a selected dimension to realize the method to the decomposition of sampling task.This method mainly contains following defective:

Need an extra dimension to realize grouping to sampled point;

Used (f, s) generator matrix of sequence must be for reversible, thereby as the Niederreiter-Xing sequence this do not satisfy this condition (t, s) sequence then can't be used;

For obtaining best sampling quality, the quantity of parallel processing element must for used (f, the s) power of the radix of sequence, promptly

Satisfy D=b ^m, wherein D is the quantity of parallel processing element, b is that (when this condition did not satisfy, the quality of sampled point can descend for f, the s) radix of sequence.

Summary of the invention

The invention provides a kind of computer picture rendering intent, this method is based on (f, s) sequence realize the decomposition to the sampling task through the hierarchical replacement operator.

Realize the scheme of technical purpose of the present invention, may further comprise the steps:

The integration that needs evaluation during (A) for rendering image

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}$

Use the method for numerical evaluation to ask its approximate value, may further comprise the steps:

To be decomposed into two or more parts to the sampling of function f (), each part transfer to one independently parallel processing element handle

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}\≈\frac{1}{N}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}\underset{i_d=0}{\overset{N_d-1}{\mathrm{\Σ}}}f(x_{i_d}^{\left(1\right)},x_{i_d}^{\left(2\right)},...,x_{i_d}^{\left(S\right)});$

Wherein,

Be the quantity of sampled point, D is the quantity of parallel processing element, N _dBe the sampled point quantity that d processing unit distributes, the different sampled point quantity that processing unit distributed can be the same or different; (B) confirm variable described in the step (A)

The method of value, 0≤i wherein _d≤N _d-1,1≤d≤D may further comprise the steps:

Will $(x_{i_d}^{\left(1\right)},x_{i_d}^{\left(2\right)},...,x_{i_d}^{\left(S\right)})$ Be grouped into $(x_{i_d}^{(p_0+1)},...x_{i_d}^{\left(p_1\right)},x_{i_d}^{(p_1+1)},...,x_{i_d}^{\left(p_2\right)},...,x_{i_d}^{(p_q+1)},...,x_{i_d}^{\left(p_{q+1}\right)}),$ P wherein ₀=0, p _Q+1=s, 0＜p _V+1-p _v≤s _Max, 0≤v≤q, s _MaxBe selected largest;

For set of variables

0≤v≤q wherein, confirm that the method for its value may further comprise the steps:

$x_{i_d}^{(p_v+\mathrm{\Δ})}=h_{\mathrm{\Δ}}\left({\tilde{i}}_{i_d,d}^{\left(v\right)}\right),$ 0≤v≤q，1≤Δ≤p _v+1-p _v；

${\tilde{i}}_{i_d,d}^{\left(v\right)}={\mathrm{\π}}_v(i_{d}D+d),$ 0≤v≤q；

Wherein,

h _j(i) :=(b ^-1, b ^-2..., b ^-M) C ^(j)(b ₀(i), b ₁(i) ..., b _M-1(i)) ^T, wherein

Be that (t, s) j of sequence supports one's family into matrix to a b system, b _r(i) the r bit digital of expression integer i under the b system is represented, promptly

M is selected maximal accuracy under the b system is represented;

π _v() is the hierarchical replacement operator, to an integer

Wherein

$b_{M-1}^{\left(v\right)}\left(x\right)=(b_{M-1}\left(x\right)+{\mathrm{\ξ}}_v),\mathrm{mod}b$

$b_{M-2}^{\left(v\right)}\left(x\right)=(b_{M-2}\left(x\right)+{\mathrm{\ξ}}_{v,b_{M-1}\left(x\right)}),\mathrm{mod}b$

$b_{M-3}^{\left(v\right)}\left(x\right)=(b_{M-3}\left(x\right)+{\mathrm{\ξ}}_{v,b_{M-1}\left(x\right),b_{M-2}\left(x\right)}),\mathrm{mdb}$

$b_0^{\left(v\right)}\left(x\right)\stackrel{\stackrel{\stackrel{\·}{\·}}{\·}}{=}(b_0\left(x\right)+{\mathrm{\ξ}}_{v,b_{M-1}\left(x\right),b_{M-2}\left(x\right),...,b_1\left(x\right)}),\mathrm{mod}b$

ξ wherein _v, ξ _{V, 0}, ξ _{V, 1}..., ξ _{V, b-1}, ξ _{V, 0,0}..., ξ _{V, b-1, b-1}..., ξ _{V, b-1}..., b-1,0≤v≤q is separate random number.

The present invention has the following advantages:

(t, s) sequence realize the decomposition to the sampling task through the hierarchical replacement operator owing to the present invention is based on; With through to (t, s) sequence divides into groups the method for the decomposition of sampling task to be compared realizing in a selected dimension, the present invention need not divide into groups to sampled point in an extra dimension; To (t, s) the also unrestricted condition of the generator matrix of sequence can be used for the (t of any kind; S) sequence, the quality of sampled point also do not receive the influence of parallel processing element quantity.

Embodiment

Below in conjunction with embodiment the present invention is elaborated.

Table 1 has been listed the C++ example code that calculates 2 system Niederreiter sequences:

Table 1

In code shown in the table 1, maximal accuracy is made as 32.The reason of setting a maximal accuracy is, in numerical evaluation, and both can not the also unnecessary calculating of carrying out infinite precision.

In code shown in the table 1, largest is made as 12 dimensions.The effect of setting largest is, on the one hand, calculate (t, s) data of the generator matrix that need use of sequence need be stored in the computer-readable medium in advance, and any equipment in the reality all can not the unlimited many data of storage; On the other hand, though the quality of quasi-random numbers is superior to random number, along with the increase of dimension, the quality of quasi-random numbers can descend gradually, thus in reality the infinite dimensional quasi-random numbers of also unnecessary use.

(choosing of largest will decide according to the maximal accuracy of its mass parameter (quality parameters) t and setting for t, s) sequence, and its principle is that the mass parameter of selected largest should not surpass the maximal accuracy of setting to different.

Table 2 has been listed 2 system Sobol sequences, Niederreiter sequence and the mass parameter of Niederreiter-Xing sequence in different dimensions.The little expression quality of this more parameters is high more, and minimum is 0.

Table 2

Dimension	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	20
																	Sobol	0	0	1	3	5	8	11	15	19	23	27	31	35	40	45	71
Niederreiter	0	0	1	3	5	8	11	14	18	22	26	30	34	38	43	68
																	Niederreiter-Xing	0	0	1	1	2	3	4	5	6	8	9	10	11	13	15	21

Can find out from last table; For 2 system Sobol sequences and Niederreiter sequence, if maximal accuracy is made as 32, then largest should be elected 12 dimensions as; Because the Sobol sequence of 12 dimensions and the mass parameter of Niederreiter sequence are respectively 31 and 30; Do not surpass 32, and the Sobol sequence of 13 dimensions and the mass parameter of Niederreiter sequence are respectively 35 and 34, have surpassed 32.

Use (t, s) sequence need be set a largest, when the dimension of the required sampled point of rendering image surpasses this setting value; Need be to (t; S) sequence number of sequence is carried out a hierarchical replacement operator, and the sequence number after the displacement can be used for, and former (t, s) sequence generates new component.In addition, also to use this hierarchical replacement operator to the decomposition of sampling task.Table 3 has been listed the C++ example code of realizing this hierarchical replacement operator:

Table 3

Table 4 has been listed based on 2 system Niederreiter sequences, realizes the C++ example code of the decomposition of sampling task has wherein been used at code shown in table 1 and the table 3 through the hierarchical replacement operator:

Table 4

Table 5 has been listed the C++ example code of code shown in the use table 4 in render process:

Table 5

In code shown in the table 4, to each divide into groups all to have used identical (t, s) sequence of all dimensions of sampled point component; I.e. 2 system Niederreiter sequences; Remove to use identical (t, s) sequence also can be used radix identical but (t, s) sequence that type is different outward; For example, 2 system Niederreiter-Xing sequences.Though the quality of Niederreiter-Xing sequence is superior to Sobol sequence and Niederreiter sequence; But there is a restriction in the use; Promptly must confirm total sampling dimension in advance; Thereby suitable play up as image in a kind of blanket method, if but the dimension of current group is known and do not have the more sampling of higher-dimension, then available Niederreiter-Xing sequence replacement Niederreiter sequence is to obtain better rendering effect.

It is a kind of that (t, s) expansion of sequence is referred to as randomization (t, s) (randomized (t, s) sequences) its role is to estimate the error size of integral approach value to sequence.Though needn't go to estimate the error size of integral approach value during rendering image; But this method of randomization is used in the flaw of alleviating in the playing up of animation in the image; The pictures different frame uses different random numbers that sampled point is carried out randomization in promptly animation being played up, to desalinate the flaw pattern that possibly exist.

Table 6 has been listed the C++ example code that on the basis of code shown in the table 4, has increased the randomization step:

Table 6

Claims (4)

1. a computer picture rendering intent is characterized by, and may further comprise the steps:

The integration that needs evaluation during (A) for rendering image

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}$

Use the method for numerical evaluation to ask its approximate value, may further comprise the steps:

To be decomposed into two or more parts to the sampling of function f (), each part transfer to one independently parallel processing element handle

$\underset{I}{\∫}...\underset{I}{\∫}f(x^{\left(1\right)},x^{\left(2\right)},...,x^{\left(S\right)}){\mathrm{dx}}^{\left(1\right)}{\mathrm{dx}}^{\left(2\right)}...{\mathrm{dx}}^{\left(S\right)}\≈\frac{1}{N}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}\underset{i_d=0}{\overset{N_d-1}{\mathrm{\Σ}}}f(x_{i_d}^{\left(1\right)},x_{i_d}^{\left(2\right)},...,x_{i_d}^{\left(S\right)});$

Wherein,

Be the quantity of sampled point, D is the quantity of parallel processing element, N _dBe the sampled point quantity that d processing unit distributes, the different sampled point quantity that processing unit distributed can be the same or different;

(B) confirm variable described in the step (A)

The method of value, 0≤i wherein _d≤N _d-1,1≤d≤D may further comprise the steps:

Will $(x_{i_d}^{\left(1\right)},x_{i_d}^{\left(2\right)},...,x_{i_d}^{\left(S\right)})$ Be grouped into $(x_{i_d}^{(p_0+1)},...x_{i_d}^{\left(p_1\right)},x_{i_d}^{(p_1+1)},...,x_{i_d}^{\left(p_2\right)},...,x_{i_d}^{(p_q+1)},...,x_{i_d}^{\left(p_{q+1}\right)}),$ P wherein ₀=0, p _Q+1=s, 0＜p _V+1-p _v≤s _Max, 0≤v≤q, s _MaxBe selected largest;

For set of variables

0≤v≤q wherein, confirm that the method for its value may further comprise the steps:

$x_{i_d}^{(p_v+\mathrm{\Δ})}=h_{\mathrm{\Δ}}\left({\tilde{i}}_{i_d,d}^{\left(v\right)}\right),$ 0≤v≤q，1≤Δ≤p _v+1-p _v；

${\tilde{i}}_{i_d,d}^{\left(v\right)}={\mathrm{\π}}_v(i_{d}D+d),$ 0≤v≤q；

Wherein,

h _j(i) :=(b ^-1, b ^-2..., b ^-M) C ^(j)(b ₀(i), b ₁(i) ..., b _M, b _M-1(i)) ^T, wherein

Be that (t, s) j of sequence supports one's family into matrix to a b system, b _r(i) the r bit digital of expression integer i under the b system is represented, promptly

M is selected maximal accuracy under the b system is represented;

π _v() is the hierarchical replacement operator, to an integer

Wherein

$b_{M-1}^{\left(v\right)}\left(x\right)=(b_{M-1}\left(x\right)+{\mathrm{\ξ}}_v),\mathrm{mod}b$

$b_{M-2}^{\left(v\right)}\left(x\right)=(b_{M-2}\left(x\right)+{\mathrm{\ξ}}_{v,b_{M-1}\left(x\right)}),\mathrm{mod}b$

$b_{M-3}^{\left(v\right)}\left(x\right)=(b_{M-3}\left(x\right)+{\mathrm{\ξ}}_{v,b_{M-1}\left(x\right),b_{M-2}\left(x\right)}),\mathrm{mod}b$

$b_0^{\left(v\right)}\left(x\right)\stackrel{\stackrel{\stackrel{\·}{\·}}{\·}}{=}(b_0\left(x\right)+{\mathrm{\ξ}}_{v,b_{M-1}\left(x\right),b_{M-2}\left(x\right),...,b_1\left(x\right)}),\mathrm{mod}b$

ξ wherein _v, ξ _{V, 0}, ξ _{V, 1}..., ξ _{V, b-1}, ξ _{V, 0,0}..., ξ _{V, b-1, b-1}..., ξ _{V, b-1 ..., b-1}, 0≤v≤q is separate random number.

2. like the said method of claim 1., also comprise, each of all dimensions of sampled point component divided into groups to use identical (t, s) identical but (t, s) sequence that type is different of sequence or radix.

3. like the said method of claim 1., wherein, said (t, s) sequence comprises Sobol sequence, Faure sequence, Niederreiter sequence and Niederreiter-Xing sequence.

4. like the said method of claim 1., wherein, said (t, s) sequence also comprises randomized (t, s) sequence.