CN1991916B - Graphic image demonstration method and system using radiance autotransfer of low frequency lighting environment - Google Patents

Abstract

Real-time image rendering of diffuse and glossy objects in low-frequency lighting environments captures soft shadows, interreflections, and caustics. As a preprocess, a global transport simulator creates functions over the object's surface representing transfer of arbitrary, low-frequency source lighting into exiting radiance, but including global effects like shadowing and interreflection from the object onto itself. At run-time, these transfer functions are applied to the actual source lighting. Dynamic, local lighting is handled by sampling close to the object at every frame; the object can also be rigidly rotated with respect to the lighting and vice versa. Lighting and transfer functions are represented using low-order spherical harmonics. Functions for radiance transfer from a dynamic lighting environment through a preprocessed object to neighboring points in space further allow cast soft shadows and caustics from rigidly moving casters onto arbitrary, dynamic receivers.

Description

The light that is used for the low frequency lighting environment is from the graph image demenstration method and the system that shift

The application is the applying date: 2003.03.21, application number are 03107487.1, and name is called the dividing an application of application of " light that is used for the low frequency lighting environment is from the graph image demenstration method and the system that shift ".

The part that document of the present invention is revealed comprises material protected by copyright.The copyright owner has no reason to refuse your the writing that this copyright reveals and duplicates, and as shown in the patent document of patent and trademark office or the record, but keeps all copyrights in addition, whatsoever.

Technical field

The present invention relates to the computer graphic image performance technology, and illumination and the deepening that stresses to be involved in modelling object on institute's presentation graphic more.

Background technology

From area source, the illumination of soft shadows and reflection mutually has important effect in real world images is synthetic.Unfortunately, be unpractiaca at conventional method synthetic in the extensive lighting environment (comprising the Monte Carlo ray tracing, luminous energy transmission, or) during at real time demonstration in the multi-path demonstration of multiple spot light source set.(the Monte Carlo ray tracing is by except Cook, R, Porter, T and Carpenter, the distributed ray tracing of L, SIGGRAPH ' 84, outside 137-146 describes, also have Jensen, H, the combined lighting of employing photon figure, for the European graphic feature research group 1996 of demonstration, 21-30; And Kajiya, the demonstration equation of J, SIGGRAPH ' 86,143-150) (luminous energy transmits technology at Cohen, M and Wallace, the luminous energy transmission of J and real world images are synthetic, professional academic publishing industry, Cambridge, described in 1993) (various multi-path performance technologies are by except Haeberli, P, and Akeley, K, the accumulation impact damper; The hardware supported of high-quality demonstration, SIGGRAPH ' 90, outside 309-318 describes; Also have Keller, A, instant luminous energy transmit SIGGRAPH ' 97,49-56; And Segal, M, Korobkin, C, van Widenfel t, R, Foran, J, and Haeberli, P, the employing structure mapping come quick deepening and illuminating effect, SIGGRAPH ' 92,249-252.)

Real-time, the combined lighting of reality faces that three difficulties-it must be modeled to true material (BRDF complicacy) complicated, spatial variations, twocouese reflection coefficient partition function (BRDFs), it need be comprehensive (light be comprehensive) of the illumination direction hemisphere of each point, it must cause the effect of jumping/blocking, as shade, owing to from the source to the receiver along the interference reason (complicacy that light transmits) in the path of light, a lot of researchs concentrate on and expand on the BRDF complicacy (such as, level and smooth and the reflection anisotropy inequality), by incident light is expressed as direction or point and solve the comprehensive problem of light, therefore the comprehensive of light easily be simplified at some a some up-samplings BRDF parsing or tabulation with handling, but just be difficult for having handled concerning big light source.The second method sampled light of research also becomes its convolution the nuclear of different size in advance.(see, as Cabral, B, Olano, M, and Nemec, P, based on the demonstration the reflection space image, SIGGRAPH ' 99,165-170; Greene, N, environment mappings and other application of world's projection, IEEE CG﹠amp; A, 6 (11): 21-29,1986; Heidri ch, W, Seidel H, hardware-accelerated illumination and deepening SIGGRAPH ' 99,171-178; Kautz, J, Vazquez, P, Heidrich, W, and Seidel, H, the integrated scheme of filtering environment mappings in advance, for the European graphic feature research group 2000 of demonstration, 185-196; And Ramamoorthi, R, and Hanrahan, P, an effectively expression of focus ring border mapping, SIGGRAPH ' 01,497-500.) it has solved the synthtic price index of light but ignored complicacy such as the shade that light transmits, because that convolution does not assume incident light is inaccessible and do not disperse.Finally, Jing Qiao technology is as the existence of the complicacy, particularly shade that expand the light transmission.Light comprehensively become problem; These nearly all technology are not suitable for very large light source more.

Summary of the invention

Here a real-time image demonstration technology of Miao Shuing preferably resolves the complicacy that real-time light is comprehensive and light transmits.Represent this environment.Present technique lays particular emphasis on the low frequency lighting environment, this environment of expression efficiently that adopts the spherical hamonic function (SH) of low order basis not need false signal to use.An aspect of present technique is used for showing how an object disperses this light to itself or its neighbours space, weakens dispersion from refracted ray to a certain extent.For example, Fig. 8 has done contrast with a non-occlusion image of a model number of people and the automatic image of describing that is produced that shifts of light that passes through here.

Sum up described technology for simple, we have a projection, the object that the environment mappings by an infinity of scattering is lighted original hypothesis.Object covers its environment " reaction " can be seen as a transfer function, the light to outflow that mapping imports is simply finished cosine here and is increased the weight of accumulation.More complicated accumulation can be caught a recessed object and how be made and oneself shadow, and here integrand is multiplied each other by the additional transport factor of an expression along all directions visibility.

Described technical method is that a given object calculates in advance as the needed expensive simulation that transmits of the complicated transfer function of deepening.Consequent tansfer function is expressed as the vector on its plane or the matrix of an intensive series fully.Incident light does not need to be calculated in advance therebetween.In the real time demonstration afterwards, the graphic hardware incident light on the point of restricted number of can dynamically sampling, this technology converts spherical hamonic function (SH) basis with the fast calculation analysis model to, can be used as geometry such as skylight model or simple as circles.

In the SH basis, by expression incident light and transfer function, described technology is reduced to light accumulation simple dot-product between their coefficient vector (diffusion receptacle), or a simple linear change of the illumination factor vector by a little transition matrix (level and smooth receptacle).The low frequency lighting environment needs considerably less coefficient (9-25), makes graphic hardware result of calculation under a single-pass.Do not resemble Monte Carlo and multi-path light integrated approach, the real-time calculating of this technology can keep constant no matter light source what and much.The number that keep the real-time calculating of a constant number to depend on a large scale, level and smooth illumination limits required SH.

Described technology has showed complicated mutual reflection and the caustics of transmission effect picture in transfer function.Because these all are modeled into pre-service, have only the basic coefficients of transfer function to change, rather than real-time calculating.The described method of institute's description technique is all handled to the plane with based on the geometric configuration of volume.For more SH coefficient, this technology even can handle level and smooth receptacle (but not being high reflection) and diffusion comprises mutual reflection.As the 25SH coefficient to useful smoothly be enough.Except that transfer to the itself (crying from shifting) from the object of a rigidity, the contiguous of proximity space that this technology reduces from a rigid objects to it shifts, and allows projection soft shadows, smoothly reflection and the caustics on dynamic receiver.

Description of drawings

Fig. 1 is to be that the realtime graphic demonstration merges the block scheme of precalculated light from a computer graphical software architecture that shifts in dynamic, low frequency lighting environment.

Fig. 2 is that in the image demonstration system shifts precalculated process flow diagram certainly among Fig. 1.

Fig. 3 is the process flow diagram of the real time demonstration that a light in the image demonstration system shifts among Fig. 1.

Fig. 4 handles real-time diffusion plane from the process flow diagram that shifts in real time demonstration among Fig. 3.

Fig. 5 handles real-time smooth surfaces from the process flow diagram that shifts in real time demonstration among Fig. 3.

Fig. 6 is a block scheme for a suitable computing environment of the image demonstration system among Fig. 1.

Fig. 7 is the figure that the simulation in the calculating in advance of transfer certainly that is described among Fig. 2 is reflected mutually.

Fig. 8 describes non-that cover among Fig. 3 and by image that real time demonstration produced.

Fig. 9 describes non-that cover among Fig. 3 and by the image that real time demonstration produced, illustrates the diffusion plane from the effect of shifting.

Figure 10 describes non-that cover among Fig. 3 and by the image that real time demonstration produced, illustrates smooth surfaces from the effect of shifting.

Figure 11 has described the incident light that is used in the sampling of single-point respectively, closest point algorithms (ICP) point and a plurality of point pass through the image of the real time demonstration generation of Fig. 3 repeatedly.

Figure 12 has described the image that shifts certainly by the volume that real time demonstration produced of Fig. 3.

Figure 13 has described the image that shifts certainly by the neighborhood that real time demonstration produced of Fig. 3.

Embodiment

As shown in Figure 1, a software configuration of a computer graphic image demo system 100 provides the realtime graphic demonstration of a modelling object, and this demonstration uses employing light described here from shifting the mutual reflection of image demonstration technology and covering certainly.Common, this software configuration comprises that 120, one realtime graphic presentation engine 140 of a combined lighting simulator and a graphic presentation drive 180.More fully describe light below from shifting performance technology, combined lighting simulator 120 is carried out anticipating the stage of this technology, and it calculates light rotation shift according to 140 in advance from a geometric object module 110.This geometry module 110 can be a leg-of-mutton mesh, the microwave complex, perhaps in addition other by the performance of the geometrization of modelling object.Real time demonstration engine 140 uses and should precalculated smooth rotation shift certificate be dynamically variable illumination environment 150 and direction of observation 160 demonstrating model subject image then, and this presentation engine can selectively change or the user is set controls 170.Graphic presentation drives 180 output images to an image output device (for example: display, projector, printer etc.).

In some specific embodiments of graph image demo system, the light of simulator 120 calculates in advance and uses the image demonstration of engine 140 to carry out on single computing machine from shifting, the computing environment of describing as the 6th joint below.Common, simulator 120 can move on an independent computing machine, and this result data is transferred on the computing machine of presentation engine 140 operations then, produces graph image.

Light is always seen from the transfer technology.As a pre-service, combined lighting simulator 120 moves illumination simulation on module 110, oneself is covered and disperses light thereby how to catch the modelling object.This result is recorded in light rotation shift according in 130 as the one group of intensive vector (diffusive condition) on the module or matrix (smooth state).In the image demonstration time, presentation engine 140 is that the relevant incident light of lighting environment 150 projections is to spherical hamonic function (SH) basis (following description).Shift vector then and matrix norm V-neck V territory is applied to the illumination factor vector.If the object diffusion, thereby one of the point on this object shifts vector and gets ready and produce appropriate discrete certainly shade along with illumination factor.If this object is level and smooth, thereby a transition matrix is applied to the spherical function coefficients that illumination factor is created in a certainly discrete incident light of representative on these aspects.This function is according to twocouese reflection coefficient distribution function (BRDF) convolution of object, thereby estimates to produce based on the reflection direction of observing the final shade of the object of being demonstrated in image subsequently.

1. the review of spherical hamonic function

Definition: orthonormal basis on sphere of spherical hamonic function definition, S is similar to the fourier transform on the 1D circumference, operation parameter

Basic function is defined as

P wherein _l ^mBe relevant Legendre polynomial expression, K _l ^mBe generalized constant

$K_l^m=\sqrt{\frac{(2l+1)}{4\mathrm{\π}}\frac{(l-|m\left|\right)!}{(l+|m\left|\right)!}}$

A plural number base is formed in above-mentioned definition; A true value basis is provided by this simple institute that transforms

Low frequency basic function on the low value of I (being called the wave band index) the expression sphere.The basic function of wave band I becomes the polynomial expression of order I at x among y and the z.Assignment can be produced by simple recurrent formula.(for example: Edmonds, A, the polygonal key element in the quantum theory mechanics, Princeton University, Princeton, 1960; And ZARE, R, polygonal key element; The understanding of the aspect, space in chemistry and the physics, Wiley, New York, 1987).

Projection and transformation: because the SH basis is orthonormal, a function f by the scalar of S definition projects his coefficient by accumulation

$f_l^m=\∫f\left(s\right)y_l^m\left(s\right)\mathrm{ds}$

These coefficients provide the transformation function of n order.

$1\tilde{f}\left(s\right)=\underset{l=0}{\overset{n-1}{\mathrm{\Σ}}}\underset{m=-1}{\overset{l}{\mathrm{\Σ}}}{f}_l^m{y}_l^m\left(s\right)$

When the numeral growth of phase wave band n, f is approximate accordingly to be increased.Low-frequency signals can be according to the correct performance of having only of some SH wave bands.Higher frequency signals is limited by wave band by one group low order projection.(for example: no false signal level and smooth)

Projection n order comprises n ²Individual coefficient.It rewrites (2) single indices vector and basic function according to projection coefficient usually easily, by

$\tilde{f}\left(s\right)=\underset{i=1}{\overset{n^2}{\mathrm{\Σ}}}{f}_i{y}_i\left(s\right)---\left(3\right)$

Via I=l (l+1)+m+1.The evaluation of as seen transforming function S by this formula shows as n ²A simple dot-product of coefficient vector fi that forms and evaluation basic function yi (s) vector.

Primary attribute.A SH projection attribute is its constancy of taking turns; That is to provide g (s)=f (Q (s)), when Q is a rotation arbitrarily on S

$\tilde{g}\left(s\right)=\tilde{f}\left(Q\left(s\right)\right)---\left(4\right)$

This is the mobile constancy attribute that is similar to the 1D Fourier transform.In fact, this attribute means the Artifact that the SH projection causes not having false signal.The sampling example that produces as f is collected as the serial sampled point of a rotation, projection, f revolution then.

The standard quadrature on SH basis is provided at the useful attribute that S goes up any two function a and b, and their projection is satisfied

$\∫\tilde{a}\left(s\right)\tilde{b}\left(s\right)\mathrm{ds}=\underset{i=1}{\overset{n^2}{\mathrm{\Σ}}}{a}_i{b}_i.---\left(5\right)$

In other words, the product of wave band restricted function comprehensively makes a dot-product that becomes their projection coefficients.

Convolution: the kernel function h (z) that round-robin matches and the convolution of a f function are represented as h*f.Note h be necessary for circulation match (and should this can be defined as a simple function that is better than the z of s) for this result is defined within on the S, be better than the rotation group SO in higher space, as top each equation (3).The convolution projection is satisfied

${(h*f)}_l^m=\sqrt{\frac{4\mathrm{\π}}{2l+1}}{h}_l^0{f}_l^m={\mathrm{\α}}_l^0{h}_l^0{f}_l^m.---\left(6\right)$

In other words, the convolution coefficient of this projection is the simple scale product of independent projection function.This attribute provides a quick approach so that twine an environment mappings that contains hemispheric surplus medial rotation nuclear, this core is defined as h (z)=max (z, 0), with the mapping that obtains a light (as at Ramamoorthi, R, and Hanrahan, P, effective performance of luminous environment mapping, SIGGRAPH ' 01, described in the 497-500).In this example, the projection coefficient of h can obtain by using an analysis formula.This convolution attribute also can be used to produce the pre-filtering environment mappings by the kernel of precision.Notice that because h is about the circulation symmetry of z, its projection coefficient only is a non-zero when m=0.

The projection of the product of a pair of spherical function c of product projection (s)=a (s) b (s) (a known and b the unknown) can be looked at as by a matrix Projection coefficient b _jA linear transformation:

$c_i=\∫a\left(s\right)\left(b_j{y}_j\left(s\right)\right)y_i\left(s\right)\mathrm{ds}---\left(7\right)$

$=(\∫a\left(s\right)y_i\left(s\right)y_j\left(s\right)\mathrm{ds})b_j={\hat{a}}_{\mathrm{ij}}{b}_j$

Wherein, note for the sequence number j that repeats has hinted summation It is a matrix that matches.

Rotate a transformation function that is rotated by Q, f (Q (s)) can be with the linear transformation f of the projection coefficient that uses a f _iProjection.Because the attribute of rotary constant, the coefficient of each wave band is treated in this linear transformation independently.The most effective execution is finished by using a decomposition of rotating the zyz Eulerian angle of Q, uses a suitable complex loops formula.(referring to, example, Chirikjian, G, and Stein, D, the kinematic design of spherical stepper motor and replacement, Institute of Electrical and Electric Engineers machinery journal, 4 (4), 12.1999; Edmonds, A, the angular momentum in the quantum theory mechanics, Princeton University, Princeton, 1960; And ZARE, R, angular momentum; The understanding of the aspect, space in chemistry and the physics, Wiley, New York, 1987).When only relating to the low order function, the explicit rotation formula of describing in these bibliographies can be realized by using symbol to accumulate.

2. light is from shifting

Light is from shifting object O covers and disperse light to oneself the method that encapsulated.Use SH basis is crossed by light rotation Mobile Communication, (is expressed as L by the parametrization incident light first time of a p ∈ O _p(s)) represent.Therefore incident light is represented as a n ²The vector of coefficient (Lp) _iIn practice, this illumination can dynamically and sparsely be sampled near surface, perhaps only on a single point.Suppose to be that the illumination change on O is not because there be less (referring to 4.1 joints, the spatial sampling in incident light territory) in itself.Light can be calculated and very close storage on O in advance from shifting also, as shifting vector or matrix.

One is shifted vector (Mp) _iCan be used to diffusing surface and expression to producing the linear transformation that scalar withdraws from the illumination vector (being expressed as Lp ') of light, by following inner product

${L^{\′}}_P=\underset{i=1}{\overset{n^2}{\mathrm{\Σ}}}{\left(M_P\right)}_i{\left(L_P\right)}_i---\left(8\right)$

In other words, (Mp) _iEach composition represented an illumination basis function (Lp) _iTo the linear effect of covering at the p place.

A transition matrix (M _p) _IjCan be used to smooth surface and the expression linear conversion to the illumination vector, it is that a complete transfer photosphere shape function L ' p (s) produces a projection coefficient, rather than a scalar, that is:

${\left({L^{\′}}_P\right)}_i=\underset{j=1}{\overset{n^2}{\mathrm{\Σ}}}{\left(M_p\right)}_{\mathrm{ij}}{\left(L_p\right)}_j.---\left(9\right)$

Incident light and the difference of shifting between the light are L ' _p(s) comprise since O existence caused covers and dispersion effect, and L _p(s) incident illumination after expression hypothesis O is removed in scene.(M _p) _IjComposition showed incident light (L _p) _jThe illumination factor of j for shifting light L ' _p( _s) the linear effect of i coefficient.Next joint will be presented at O and go up how to obtain the transfer vector of diffusing surface and the transition matrix of smooth surface according to self-scattering.

2.1 diffusion transfer

Suppose that at first O is diffusion.The simplest transfer function on a p ∈ O has showed the non-diffusion transfer of covering, and is defined as scalar function

T _DU(L _p)＝(ρ _p/π)∫L _p(s)H _Np(s)ds

Light is withdrawed from generation, and it is the invariant to the viewing angle of diffusing surface.At this, ρ _pBe the albedo of the object on p, L _pBe the incident light on the p after hypothesis O is removed in scene, N _pBe the object normal on p, and H _Np(s)=max (N _pS, 0) be cosine weighting, about N _pThe hemisphere kernel.By individually to L _pAnd H _NpCarry out the SH projection, equation (5) is simplified T _DuAn inner product for their coefficient vectors.This key element that obtains is called as light function L herein _pWith transfer function M _pIn this first simple example,

Because N _pKnown, transfer function (M _p ^DU) _iThe SH projection can be calculated in advance, the result is one and shifts vector.In fact, storage is unnecessary because simple analysis formula produces its given N _pBecause M _p ^DUBe an intrinsic low pass filter, the second rank projection (9 coefficients) is provided at a good down accuracy of (even non-level and smooth) lighting environment arbitrarily.

In order to comprise shade, we define the shade diffusion transfer and are

T _DS(L _p)＝(ρ _p/π)∫L _p(s)H _Np(s)V _p(s)ds

Wherein when a branch of ray from the direction s of p can't intersect (promptly not having crested) again with O, extra visibility function V _p(s) → { 0,1} equals 1.Cover transfer with non-, this accumulation can be used L _pSH projection and following transfer function resolve into two functions

$M_p^{\mathrm{DS}}\left(s\right)=H_{\mathrm{Np}}\left(s\right)V_p\left(s\right).---\left(10\right)$

Independent SH projection L _pAnd M _pAgain will be at T _DSOn accumulation be reduced to an inner product of coefficient vector.

It is valuable shifting now; Light rotation Mobile Communication crosses and uses a transportation simulator device to be calculated (describing in " calculating in advance from shifting " as chapters and sections below) in advance, and the result who is stored in many somes p on the O shifts vector (M _p) _iUnlike the example of front, M _p ^DSThe second rank projection may be inaccurate, even in level and smooth lighting environment because Vp can create local high-frequency illumination, for example, by covering aperture certainly.Use the 4th or the 5th rank projection to be provided at the good result of the typical mesh in the level and smooth lighting environment.For example the diffusing surface object among Fig. 9 non-covered the comparison with occlusion image.

The image of the mutual reflection of Fig. 9) and shade at last, reflect mutually in order to catch diffusion that (for example:, reflecting diffusion transfer mutually can be defined as

$T_{\mathrm{DI}}\left(L_p\right)=T_{\mathrm{DS}}\left(L_p\right)+({\mathrm{\ρ}}_p/\mathrm{\π})\∫{\stackrel{\‾}{L}}_p\left(s\right)H_{\mathrm{Np}}\left(s\right)(1-V_p\left(s\right))\mathrm{ds}$

Wherein Be the light on the s direction from O oneself itself.Unless difficulty is to send incident light from the source of infinity, light Only the given incident light on p is not known, because

Depend on the light that withdraws from, and local illumination changes on O from any point at a distance of p.If the illumination change on O is less, Lp is very approximate so, just as O by L _pIlluminated in each place.Thereby T _DIRely on L linearly _pAnd can be broken down into a product of two projection functions, as two kinds of situations in front: slight dependence and one rely on for how much.

Although precalculated mutual reflection must suppose that incident light space on O is constant, simplyr cover transfer and then do not need.Difference is to cover transfer and only relies on incident illumination on the p, yet q ≠ p, the wherein L that rely on the O are shifted in reflection at many mutually _q≠ L _pTherefore, as long as the incident light zone finally is sampled (discussion in the following joint " spatial sampling in incident light field ") fully subtly, local illumination change can be captured, and covers transfer and will be repaired.

Existence make that be difficult to explicitly represents the transfer function M of reflection mutually _p ^DI(s).Below " in advance calculate from shift " joint how calculating its projection coefficient in numerical value ground will be discussed.

2.2 smooth transfer

Certainly the transfer of smooth object can be defined similarly, but kernel function will be reduced reflection direction R of dependence (observe and rely on), rather than one (fixing) normal N.Be similar to former H kernel, light from shift can will smoothly reflect be modeled to kernel G (s, R, r), wherein " smoothness " or the broad degree of the reaction of scalar r definition mirror image.

Three similar smooth transfer functions: non-ly cover, cover and reflect mutually situation and can be defined as:

T _GU(L _p，R，r)＝∫L _p(s)G(s，R，r)ds

T _GS(L _p，R，r)＝∫L _p(s)G(s，R，r)V _p(s)ds

$T_{\mathrm{GI}}(L_p,R,r)=T_{\mathrm{GS}}\left(L_p\right)+{\∫\stackrel{\‾}{L}}_p\left(s\right)G(s,R,r)(1-V_p\left(s\right))\mathrm{ds}$

They will be output as a L at the scalar light on the R direction _pWith the function of R, their amount is all unknown on when calculating in advance.Because shifting no longer is an isolated s function, therefore can not be reduced to a simple vector of SH coefficient.

Substitute with R and r parametrization scalar and shift, a more useful decomposition is to shift incident light L _p(s) (be expressed as L ' to a complete sphere that shifts light _p(s)).Suppose that level and smooth kernel G is about R circulation symmetry, then L ' _p(s) energy and G ' _r(z)=G (s, (0,0,1), r) convolution, and on R, calculate and produce a net result.

To L ' _pTransfer show as a matrix now but not a vector.For example, smoothly covering transfer can be defined as

$M_p^{\mathrm{GS}}(L_p,s)=L_p\left(s\right)V_p\left(s\right).---\left(11\right)$

Linear actuator on Lp, its SH projection can be expressed as symmetric matrix Vp by equation (7).Even with very level and smooth illumination, along with the growth of the smoothness of O, more SH wave band is used to L _pΦ; (for example: it is effective 25 * 9) the low frequency illumination being mapped to high-frequency transfer light to the non-square matrix in these cases.

Calculating light in advance is to influence T from a critical limitation that shifts _DIAnd T _GIIn the material properties (as albedo or smoothness) of O of mutual reflection when being operation by " baking " to pretreated transfer and can not change.On the other hand, this better simply covering when shifting the permission operation of not reflecting mutually changes and/or the spatial variations on the O of material properties.If obstruction or light source are invaded the protruding shell of O, then wrong the generation.O can only move rigidly, can not be out of shape or moves a part with respect to integral body.Also to remember to suppose low illumination change on the O to correct mutual reflection.

At last, note as diffusion transfer defined above produces light leaving the back, surface because it is by the standard hemisphere institute convolution of cosine weighting when smooth transfer generation light is incident on the surface, and by local BRDF institute convolution to produce the last light that withdraws from.To level and smooth O, also may toast into a fixing BRDF, make the convolution that when operation, does not need with G, except the restriction of dirigibility.

Fig. 9 for example the non-of a clear smooth surface object covers, covers and mutual reflected image.

3. calculate in advance from shifting

Contrast Fig. 2 now, by use the SH basis (" the reference illumination environment " of simulation) on infinite range as transmitter, the light that illumination simulator 120 (Fig. 1) calculates the modelling object in a combined lighting simulation 200 in advance shifts (being also referred to as " shift in advance certainly and calculate ") certainly, and this combined lighting simulation 200 is an object O execution.This simulation is by the unknown spherical n rank SH parametrization of incident light L; That is n, ²Individual unknowm coefficient L _iAlthough this Simulation result may be by using SH basic function y _i(s) be each L as a projector _iCalculate independently, they will be more effective for same Time Calculation.This reference illumination environment (infinity spherical L) will be when operation by reality about O, L _pIncident light substitute.

Simulation 200 starts from a path (" shade path " 202), and simulation is from leaving L and the direct direct shade that arrives the path of sampled point p ∈ O.At subsequently path (" reflex path mutually " 204), reflection increases mutually, and expression is from the path that L begins, arrive at p (Lp, LDp, LDDp, etc.) L is in the O bounce-back many times before.On every path, accumulation of energy is on each sampled point on p surface.Large-scale transmitter (that is, low-frequency SH basis) makes to assemble and upgrades more effective than projection-type.

In order to catch the direction scope on sampled point p ∈ O, simulation produces huge (10k-30k), accurate random direction set { S _d, S _d∈ S.This simulation also is at each direction S _dOn all SH basic function calculating in advance.This S _dDirection is organized in the branch sheaf space, this minute sheaf space be by pair assign to 1-＞2 with an initial icosahedron be refined into spherical triangle of the same area (1-＞4 segmentations do not cause with the plane on the same trigonum of the same area on sphere) formation.6 to 8 segmentation grades are used in this simulation, create 512 to 2048 spaces.Each space is included in a S of its inside on each stratum level _dTable.

First or shade path 202, to each p ∈ O, simulation 200 connect (on 211) those by the direction that begins from a p of object self-blocking.This simulation is in the normal N of hemisphere upthrow ejaculation about p _pShadow ray, use level to go selected direction outside hemisphere.An inaccessible position 1-V is used in this simulation _p(S _d) connect each direction S _d, point out S _dWhether in hemisphere and with O, intersect once more (that is, being covered certainly) by O.An inaccessible position also joins with layering space correlation, points out any one S of portion within it _dWhether in obturation.To such an extent as to all being connected us, self-blocking direction and space can on them, carry out further reflex path mutually; Direct sunshine next from environment is only accepted in non-completely dead-air space/sampling.

Then, on 212, simulation 200 is shifted light for some p accumulation.At diffusing surface, at each some p ∈ O, simulation is also by the SH projection M according to equation (10) _pCalculate and shift vector.At smooth surface, simulation is calculated transition matrix by the SH projection Mp from equation (11).In arbitrary situation, the result represents by the parameterized light of collecting on p of L.Be used for calculating the SH projection of transfer by the S that samples in direction _dOn numerical value accumulation performed, use following rule to be summarised as the transfer of an accumulation:

Subscript O refers to numeral repeatedly.Vector M _pOr matrix M _pBefore the shade path, be initialized to 0 at each point on p, then on each p with all S _dAddition.This rule obtains by the equation (1) of use diffusion transfer accumulation and the equation (7) of smooth transfer accumulation.

According to shown in Figure 7, mutual reflex path 204 subsequently passes has the space that inaccessible position is provided with, and this obturation position is accumulated at the shade path and is provided with during mutual reflection on 221 is shifted.Substitute shadow ray, analog transmissions is returned the ray of transfer from withdrawing from illumination on O.If ray (p, S _d) and some q ∈ O (the wherein the most close p of q) is crossing in addition, we are at direction-S _dThe light that middle sampling is withdrawed from from q.Following update rule is used, and subscript b wherein is that the bounce-back path repeats:

Shown on the shade path 202, at direction S _dOn, before gathering transfer, shift vector or matrix is that O begins mutual reflex path 204 by initialization.The diffusion rule originates from T _DIDefinition and equation (1); Smoothing regulation is from T _GIDefinition and equation (6) and (7) in obtain.In smooth transfer definition, middle factor representative is from before the path of upspringing, b-1, the light that turns back to p that sends from q.Because M _qThe storage incident light, it must be on q with the BRDF of O mutually convolution obtain at-S _dWithdraw from light on the direction, on k, produce a summation.a _kBe the k time convolution coefficient, represent by single index." reflection " symbol reflects second first vector parameters about it simply.Observation equation formula (7) has hinted (M _p) _IjBe a symmetric matrix, because it is made up of two spherical function products for the crested smooth transfer; For mutual reflection smooth transfer is incorrect.

Shown in 230, mutually reflex path 204 repeats, up to meeting an ending standard, when for example the gross energy of given path is fallen under the important limit.For typical material, reflection is subdued very quick mutually.Consider reflection mutually from the transfer summation of all paths of upspringing subsequently.

Perhaps, this simulation simple surface that allows in O that strengthens as mirror.Simulation is not recorded in the transfer of similar surfaces.Substitute, the ray of bump minute surface always reflects and propagates subsequently up to arriving at non-specular surface.Thereby, continuously repeatedly path can be represented as (L[S] ^*P, L[S] ^*D[S] ^*P, L[S] ^*D[S] ^*D[S] ^*P, etc.), wherein D is a diffusion or smoothly upsprings, and upsprings and S is a mirror image.It captures the caustics on diffusion or the level and smooth receiver, reacts illumination change dynamically.

4. the demonstration time of running of light transfer

The many somes p that the simulation of describing 200 (Fig. 2) just is provided on the body surface go up a module of catching the light transfer, show as vector or matrix.With reference now to Fig. 3,, real time demonstration engine 140 (Fig. 1) uses this module in the process 300 subsequently when an operation, calculates the light of transfer certainly of object in the presentation process of the object realtime graphic on a selection lighting environment and direction of observation.Fig. 4 and Fig. 5 divide other process 300 according to as the operation of diffusion and smooth surface the time to come elaborate process stream respectively.

In process 300, presentation engine 140 is carried out following action when operation: 310, according near the sampled point P of SH basis one or more O _iLast calculating incident light { L _Pi; In 320, rotate these L _PiTo the coordinate structure of O and mix them and (as follows) produce an incident light L on O _pA territory, and in 330-390, on each the some p on the O to (L _p) _iCarry out a linear change and obtain to withdraw from light.The action 350 on, this linear change be diffusing surface with (M _p) _iA dot product (equation (8)), or the action 360 on, be smooth surface with (M _p) _yA matrix-vector multiplication (equation (9)).Smooth surface has further action 370 and 380, and the BRDF convolution of the light vector that obtains from multiplication 360 and O on p is wherein estimated observing on the reflection direction R that relies on subsequently.

In action 310, the presentation engine 140 computing environment mapping in advance of can packing into, the analysis lighting module in the evaluation software perhaps uses graphic hardware to come sampled light, as the expression to the incident light of selecting lighting environment.Being rotated in the spherical hamonic function review of the 1st joint of action 320 narrated, and it is carried out once each object, rather than to each p.Rotation is performed, because shift to be to use the common coordinate system of O is stored.If O moves rigidly, many transfer functions of the rotation O that compares are at L _PiLast rotation minority gloss sample makes that it will be more effective arranging with O.

For diffusing surface, a simple realization of action 350 is the transfer vector and the dot products of execution in a summit veil on each summit of storage.This shifts vector and also can be stored in the structure mapping, rather than each summit, and uses a pixel to hide and calculate.Because coefficient is the number that symbol is arranged, not always in [1,1] scope, DirectX 8.1 pixel veils (V1.4) or its OpenGL equivalent (by the ATI expansion) can be used, because they provide [8,8] one in a big way.In one implementation, the pixel veil only needs 8 instructions to go to carry out dot product and store L in constant register _pProjection coefficient.

For coloured environment or the simulation of diffusion color on O, 3 paths are performed, and each is at r, and g carries out independent dot product for one in the b passage.Otherwise a path is just enough.

For level and smooth transfer certainly, the matrix conversion from equation (9) can be performed in software, because in current summit or pixel veil, transition matrix may can not be operated too greatly.The result be (L ' _p) _i, the some p place on O shifts the SH coefficient of light.In a pixel veil, enough one of convolution 370 energy simply are cosine power (the protruding lobe of Phong) the kernel execution of G, and calculate the result on reflection direction R subsequently.The result can be write as

$\underset{i=1}{\overset{n^2}{\mathrm{\Σ}}}{\mathrm{\α}}_i{G}_i^{*}\left(\underset{j=1}{\overset{n^2}{\mathrm{\Σ}}}{\left(M_p\right)}_{\mathrm{ij}}{\left(L_p\right)}_j\right)y_i\left(R\right)---\left(12\right)$

High SH mapping to the 5th rank can be calculated in current graphic hardware.

4.1 the spatial sampling in incident light territory

For one of dynamic sampling incident light simple and effective method is central point up-sampling incident light at O.For the local lighting of handling on O changes, one more accurate technique at a plurality of somes up-sampling incident lights.As a pre-service, given input requisite number point of destination uses ICP (repetition closest approach) algorithm just can obtain one group of good sampled point (reference, Linde, Y, Buzo, A, and Gray, R, an algorithm that is used for the design of vector quantum, IEEE communication journal COM-28,1980,84-95).This produce near the O, on O equally distributed one group of representational some P _i, can be when operation at these some place sampling incident lights.Presentation engine 140 can also be calculated the coefficient at each p point place on O in advance, and this calculates the photosphere L that mixes from result's sampling _PiThereby each contribution be created in an incident light territory on the O, be represented as L in the past _p

Figure 11 describe by sampling incident light in a single-point, ICP point and multiple sampling and during with the operation of Fig. 3 process 300 demonstrate resulting image.

4.2 at graphic hardware up-sampling SH light

In a dynamic scene, graphic hardware is used for catching gloss sample { L effectively _Pi.For this reason, according to each P corresponding to 6 faces of three-dimensional mapping ball shape parameter _iDemonstrate 6 images.O itself must be removed from these demonstrations.Integration in user's formula (1), three-dimensional map image are mapped on their the SH coefficient.

More effective, for by the basic function of differential solid horn weighting computation structure in advance,

Each is all calculated on the three-dimensional mapping parameters of s.Subsequently this as a result integration become structure B _l ^m(s) with the sampling L that catches _p(s) a simple dot product on.

Desirable, this calculating can be performed on graphic hardware.Selectable, because accuracy and can't make inner product on hardware, the sampled light image can be by retaking of a year or grade and projection in software subsequently.In this case, the resolution that reduces the retaking of a year or grade image as much as possible will be helpful.

The SH mapping of low order is shone upon with the solid of low-down resolution and is calculated, and supposes their quilts band limit accurately.For example, can be come projection with 64 * 4 images with the spherical signal that is limited to the 6th rank, these images have about 0.3% general case square error and about 1% worst condition square error, wherein by the hypothesis specific power signal error (that is, the integrated square on sphere is 1 signal) of standardizing.(more accurately, the general case error is the integrated square difference between signal reference and that rebuild, all cell power signals average.The worst condition error is identical integration mistake, but is for worst condition cell power signal.) for 6 * 8 * 8 mappings, this mistake reduces to 0.003% average and 0.02% worst condition.Unfortunately, type signal is not spherical band limit.Another analyzes demonstration, supposes bilinearity reconstruction continuously on the 2D image of sampling, uses the mapping on the 6th rank of 6 * 8 * 8 images to produce 0.7% and 0.2% average and worst condition square error, and produces 0.2% and 0.5% error at 6 * 16 * 16 o'clock.

In an illustrative is carried out, 6 * 16 * 16 images of from hardware, extracting.Though always correct in the point sampling demonstration, the aliasing of 2D image still is exactly a problem, because above analysis uses the bilinearity from point sampling to rebuild as reference.In order to reduce aliasing, three-dimensional map image can be carried out a boxlike and filter a large amount of the extraction by super sampling (for example, by a factor 2) on each dimension on hardware before retaking of a year or grade and projection.The basic function structure is also by super sampling, and anticipates with an identical method as one and to extract in a large number.As a gloss sample, comprise retaking of a year or grade and SH mapping, this illustrative execution about 1.16 milliseconds of cost on a PIII-933 computer with ATI Radeon 8500.

4.3 the transfer certainly of volume-based model

Shifting certainly on volume data used the framework identical with the surface.Change when this precalculated model permission that obtains moves illumination is accompanied by correctly covering and reflection mutually under any low frequency lighting environment.Figure 12 illustrates the image of a cloud model, uses volume from shifting to this image, and a volume rotation of process 300 moves variations (description after this) and catches cloud model itself is covered and dispersed light during with operation.

Follow the surface to shift, a pre-treatment step uses the SH basic function as the light of transmitter simulation on volume.For reflection not mutually cover transfers (that is, directly covering), simulate each volumetric pixel p from the transmitter focused energy to volume, passed the path attenuation of volume by this, at direction S _dGoing up required numerical integration can be represented as

${\left(M_p\right)}_i^0+=A(p\→p+{\mathrm{Ds}}_d)y_i\left(s_d\right)$

Wherein (p-＞q) is the volume overall attenuation of the path from p to q along the path to A, and D is up to ray (p, S _d) withdraw from three-dimensional distance.In order to comprise mutual reflection, simulation is traversed each volumetric pixel p and along random direction S _dDisperse its transfer forward.This shifts along S _dAll volumetric pixel q are precipitated up to withdrawing from volume, service regeulations

${\left(M_q\right)}_i^b+=A(p\→q){\left(M_p\right)}_i^{b-1}$

More path on volume produces further non-direct bounce-back.

Demonstration is performed by traditional approach: describe segment on the 3D volume by order from back to front, adopt alpha to synthesize and consider the transparency.Each fragment is the 2D image that comprises the sampling of shifting vector.A pixel shader thing compute illumination coefficient and need cover dot product between the transfer vector of each segment.

5. the contiguous of light shifts

Contiguous transfer is thrown light on respect to parameterized low frequency and is calculated the influence of an object O to its adjacent ambient in advance.Figure 13 illustrates the image in the adjacent waveforms field that the contiguous transfer variation (description subsequently) of hang-gliding projection soft shadows presentation process 300 (Fig. 3) to simulation 200 (Fig. 2) and operation the time catches.Transmitting simulation is identical with the simulation of shifting certainly of calculating in advance in shifting at the 3rd joint, but takes place in the 3d space point of O at one, rather than on it.In when operation, one arbitrarily recipient R can be placed on and remove to catch shade, reflection and O in this volume and under the situation of not knowing R in advance, project caustics on the R.For example, mobile automobile O can be on a Zone R territory cast shadow.Cast shadow and illumination also can respond illumination and change; For example, mobile light moves soft shadows on R.This is by considering smooth transfer and allowing dynamic lighting to conclude the volume of light (for example, referring to Greger, G, Shirley, P, Hubbard, P, and Greenberg, D, luminous volume, IEEE computer graphical and application, 6 (11): 21-29,1986).

Because in calculation procedure in advance, R is unknown, the neighbouring body of O accumulates a transition matrix of storage rather than a vector.This in addition also be correct in the diffusion recipient because do not know the normal of R in advance.

In an execution, simulator calculates the transition matrix M on each point in a simple 3D grid that surrounds O in advance _pIn when operation, in software, carry out matrixing and upload result to graphic hardware on presentation engine each point in volume from equation (9).The result be one comprise the transfer light that is applied to R (L ' _p) _iA volume structure of coefficient.

Subsequently, in a pixel shader thing, this shifts light and is used to the recipient of throwing light on.A diffusion recipient is by the hemisphere H of user's formula (6) with cosine weighting ^*Come this light of convolution, and the SH projection of result of calculation on the normal vector of R subsequently.Level and smooth recipient carries out equation (12).

The recipient calculates in advance from shifting, and has brought O and R not to share the difficulty of a common coordinate system.Therefore, in the dense set of the transfer of two objects sampling must rotate to arrange with another one dynamically.Let it be to the greatest extent, and complicacy is O (n ⁴), be the same with the complicacy of the matrix conversion of in equation (9), carrying out, that operation of the speed ratio of higher-order projection is more expensive.Improve hardware and will solve this difficulty rapidly.

Be compared to from shifting, the contiguous transfer produces some additional approximate errors.Be difficult to combination from a plurality of contiguous transfer object cast shadows or light to identical recipient.Not that the local lighting variation that exists because of O or R also is a problem; The illumination of passing the whole proximity of O must be quite stable so that accurate result is provided.The error of especially, for example losing shade will occur when the pressure of the object by O and the R enter the proximity of O.The proximity of O must also be enough big, so that surround the cast shadow or the light that may be incident upon arbitrarily on the R.Yet according to previous methods, contiguous transfer seizure effect can not be obtained in real time.

6. computing environment

Fig. 6 illustrates the example of a general suitable computing environment (600), and the illustrative embodiment here may be performed in this environment.This computing environment (600) does not plan to advise any restriction to usable range of the present invention or function, because present invention may be realized in different universal or special computing environment.

As shown in Figure 6, computing environment (600) comprises at least one processing unit (610) and storer (620).In Fig. 6, this most basic configuration (630) is included in the dotted line.Processing unit (610) is carried out and is calculated executable instruction, and may be reality or virtual processor.In a multiprocessing system, multiplied unit is carried out the calculating executable instruction and is improved processing power.Storer (620) can be the storer (for example, register, impact damper, random access memory etc.) of volatibility, non-volatile storer (for example, ROM (read-only memory), electricallyerasable ROM (EEROM), flash memory etc.) or these some combinations of two.Storer (620) storage realizes having the software (680) of light from the graph image demonstration of shifting.

A computing environment can have supplementary features, and for example, computing environment (600) comprises reservoir (640), one or more input equipments (650), and one or more output devices (660), and one or more communication connects (670).An interlocking frame (not shown), for example network interconnection of bus, controller or computing environment (600) assembly.Typically, the operating system software (not shown) provides the operating environment of other software of operation in computing environment (600), and the activity of the assembly of Coordination calculation environment (600).As what mentioned, the computing environment expectation comprises graphics process hardware and software, for example DirectX and OpenGL function library and ATI Radeon or Nvidia GeForce video card.

Reservoir (640) may comprise disk, tape or magnetic tape cassette for movably or immovable, CD-ROM, CD-RW, DVD, or any other can be used to canned data and can be in computing environment (600) accessed medium.Storer (640) storing software (680), the instruction of this software carries out image demo system (Fig. 1).

Input equipment (650) may be an input equipment that can contact, for example keyboard, mouse, writing pencil or trace ball, and a voice-input device, a scanning device, or other provide the equipment that is input to computing environment (600).For sound, input equipment (650) can be a sound card or the similar audio input device of accepting the analog or digital form.Output device (660) may be a display, printer, loudspeaker or other equipment from the output of computing environment (600) are provided.

Communication connection (670) makes at a communication media and becomes possibility to the communication on the another one computational entity.Communication media transmits such as computer executable instructions, compressed audio or video information signal, or the information of other data in a modulated digital signal and so on.A modulated message signal is such signal, and its one or more feature is provided with along with the information in signal or changes.As an example, rather than restriction, communication medium comprises the wired or wireless technology by electricity, light, radio frequency (RF), infrared, sound or the execution of other carriers.

This invention can be described in the conventional environment of computer-readable media.Computer-readable media is any useable medium, and it can be accessed in computing environment.As an example, rather than restriction, for computing environment (600), computer-readable media comprises storer (620), reservoir (640), communication media and top any combination.

This invention can be described in the conventional environment of computer executable instructions, for example is included in the program module those, truly or on the virtual processor carries out a target in a computing environment.Normally, program module comprises the routine carrying out special duty or realize special abstract data type, program, storehouse, object, class, assembly, data structure etc.The function of this program module can be according to desired combined or separately in program module among the different embodiment.The computer executable instructions of program module can be performed in this locality or distributed computing environment.

In order to state, describe in detail and use similar " determining ", " obtaining ", " adjusting " and terms such as " application " remove to be described in a calculating operation in the computing environment.These terms are abstract to the height of computing machine executable operations, can not obscure with the performed behavior of people.Carry out and change corresponding to the actual computer operating basis of these terms.

Described and illustrational principle of the present invention with reference to an illustrative embodiment, be to be appreciated that illustrative embodiment can change under the situation that does not break away from this principle on structure and details.It must be understood that here program, processing or the method described do not relate to or be limited to any specific calculations environmental form, except as otherwise noted.The dissimilar operations that may be used or carry out of various universal or special computing environment according to the instruction of describing herein.All unit of the illustrative embodiment that shows in software may be implemented on hardware, and vice versa.

Consider that principle of the present invention may be incorporated on many possible embodiment, we require with might be below claim and the invention that all is considered as us of all embodiment in the equivalent scope thereof.

Claims (6)

1. computer implemented method of demonstrating the computer graphic image of a geometric modeling object plane in real time, method comprises:

For at least one sampled point in the lighting environment calculates the source lighting data;

According to being the precalculated smooth transferring data in a plurality of positions on the modelling object surfaces, calculated source lighting data are carried out a linear transformation, be that a direction of observation obtains the data that withdraw from light from these positions, the light transferring data of expression photoresponse be included in reference under the low frequency lighting environment in overall situation transmission effect to the locational modelling object of source light;

According to the image that light is created in the modelling object that has under the lighting environment on the direction of observation that covers that withdraws from from the position;

Under the level and smooth situation of modelling object surfaces, carry out linear transformation and comprise:

A matrix-vector multiplication of execution source light vector and precalculated smooth transition matrix, this source light vector is illustrated in the source light of sampled point, and this light transition matrix is represented the photoresponse of a position on this modelling object smooth surface;

A matrix-vector multiplied result and a bidirectional reflectance distribution function of this position on modelling object smooth surface are carried out convolution; With

Estimate the convolution results on the direction of observation.

2. the method for claim 1, it is characterized in that, under the diffusing surface situation of modelling object, carry out the dot product that linear transformation comprises a calculating source light vector and a precalculated light transfer vector, source light and precalculated light that the source light vector is illustrated in a sampled point shift the photoresponse of vector representation position on the diffusing surface of modelling object.

3. the method for claim 1 is characterized in that, under the level and smooth situation of modelling body surface, carries out linear transformation and comprises:

For at least one sampled point in the lighting environment calculates the source light vector;

Determine withdrawing from light, represent the data of photoresponse of this position and a bidirectional reflectance distribution function of this position from the direction of observation of this position as a function of source light vector.

4. the method for claim 1 is characterized in that, under the level and smooth situation of modelling object surfaces, carries out linear transformation and comprises:

For at least one sampled point in the lighting environment calculates the source light vector;

Determine the transfer light of this position according to the source light vector and the data of the photoresponse of this position of expression; With

Determine the light that withdraws from from the direction of observation in this position according to the transfer light of this position and bidirectional reflectance distribution function.

5. computer implemented method of demonstrating the computer graphic image of a smooth surfaces on a geometric model object in real time, method comprises:

Projection light to one a spherical hamonic function basis produces an illumination factor vector at least one position of modelling object under a lighting environment;

Will be from the function that light is defined as an illumination factor vector that withdraws from of a direction of observation of at least one position on the smooth surfaces, the photoresponse of a precalculated smooth transition matrix data representation is included in one with reference to the following overall situation transmission effect at least one locational smooth surface to source light of low frequency lighting environment;

Calculating is covered the smooth surface of at least one locational modelling object;

Generation has an image of the smooth surface of the modelling object that covers;

Wherein, be that a direction of observation is determined to withdraw from light and comprised:

For carrying out a matrix-vector multiplication of illumination factor vector and precalculated smooth transition matrix at least one position on the smooth surface, precalculated smooth transition matrix is represented photoresponse, is included in reference to the following overall situation transmission effect at least one locational smooth surface to source light of low frequency lighting environment.

A matrix-vector multiplied result and a bidirectional reflectance distribution function of this position on modelling object smooth surface are carried out convolution; With

Calculate the convolution results on the direction of observation.

6. method as claimed in claim 5 is characterized in that, determines that the light that withdraws from the direction of observation comprises:

Light is withdrawed from the matrix that calculates the light transition matrix in advance-vector product calculating according at least one position on described illumination factor vector and the smooth surface, calculate the light transition matrix in advance and represent photoresponse, be included in reference to following the overall situation transmission effect of low frequency lighting environment at least one locational smooth surface to source light.

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