CN103473803A - Rendering method based on aeolotropy spherical Gaussian function - Google Patents

Abstract

The invention relates to the technical field of three-dimensional image processing, in particular to a rendering method based on an aeolotropy spherical Gaussian function. The rendering method includes the steps that (S11) fitting is carried out on a light source and a bidirectional reflection distribution function by means of the aeolotropy spherical Gaussian function; (S21) spherical distortion from a semivector to the incidence direction is carried out on the bidirectional reflection distribution function represented by the aeolotropy spherical Gaussian function; (S31) by means of multiplication closure of the aeolotropy spherical Gaussian function, the distorted bidirectional reflection distribution function is multiplied by the light source to obtain a distribution function; (S41) the distribution function obtained in the step (S31) is integrated to obtain the final rendering color, wherein the aeolotropy spherical Gaussian function is a novel spherical Gaussian function provided by the rendering method based on the aeolotropy spherical Gaussian function. The rendering method can remarkably improve the rendering frame rate, and therefore real-time rendering is better achieved.

Description

Rendering intent based on anisotropy sphere Gaussian function

Technical field

The present invention relates to the three-dimensional computer-generated image processing technology field, be specifically related to a kind of rendering intent based on anisotropy sphere Gaussian function.

Background technology

The efficient succinct expression of spherical function is all the computer graphics application all the time, especially plays up the pith in application; For example, in order better to realize the purpose of real-time rendering complex environment illumination reflecting effect, in prior art, a lot of research has all adopted the sphere Gaussian function to come analog light source, bidirectional reflectance distribution function and visibility function efficiently to calculate the illumination transmission.Why selecting the sphere Gaussian function is mainly to consider its good nature: for example, express the frequency domain scope wide, so the sphere Gaussian function can be expressed the signal of any frequency band well; There is rotational invariance; For its integration, all there are Analytical Expression etc. in the product between the sphere Gaussian function, convolution; These character are all the key factors in the real-time rendering application.

Sphere Gaussian function of the prior art is isotropic, take anisotropic while being main true distribution function expressing, and normal the employing utilizes a plurality of sphere Gaussian functions to carry out the method for approximate expression.This expression that utilizes a plurality of sphere Gaussian functions is called as and mixes the sphere Gaussian function.Under certain accuracy requirement, true distribution function anisotropic degree is higher, and needed sphere Gaussian function is just more; Yet, because each function mixed in the sphere Gaussian function is not mutually orthogonal, the product calculation of the mixing sphere Gaussian function of two n items needs O (n ²) complexity.Therefore, when needs utilization mixing sphere Gaussian function, express real anisotropy distribution function while being played up, usually need balance accuracy and performance, can the raising of playing up frame per second be impacted like this, be unfavorable for that real-time rendering better realizes.

Summary of the invention

(1) technical matters that will solve

The object of the invention is to for the deficiencies in the prior art, a kind of real-time rendering method of the anisotropy sphere Gaussian function based on brand-new is provided, thereby reach, improve the technique effect of playing up frame per second.

(2) technical scheme

Technical solution of the present invention is as follows:

A kind of rendering intent based on anisotropy sphere Gaussian function comprises step:

S11. utilize anisotropy sphere Gaussian function to carry out matching to light source and bidirectional reflectance distribution function;

S21. the bidirectional reflectance distribution function of being expressed by anisotropy sphere Gaussian function is carried out to the sphere distortion of semivector to incident direction;

S31. utilize the multiplicative closed of anisotropy sphere Gaussian function, the bidirectional reflectance distribution function after distortion and light source are multiplied each other and obtain a distribution function;

S41. the distribution function obtained in step S31 is carried out to integration and obtain the final color of playing up;

Wherein, the geometric definition of described anisotropy sphere Gaussian function is:

$G(v;[x,y,z],[\mathrm{\λ},\mathrm{\μ}],c)=c\·S(v;z)\·e^{-\mathrm{\λ}{(v\·x)}^2-\mathrm{\μ}{(v\·y)}^2};$

Wherein, z, x, y is three main shafts perpendicular to each other; λ and μ are respectively the bandwidth of x and y axle, and meet λ > 0, μ > 0; The amplitude that c is function; Level and smooth S (v; Z)=max (vz, 0), v is vector of unit length, a bit on the representation unit ball;

The algebra definition of described anisotropy sphere Gaussian function is:

$G(v;A)=S(v;z)\·e^{{-v}^T\mathrm{Av}};$

Wherein, A is 3 * 3 real symmetric matrixs, the unit character vector that the minimal characteristic root that z is A is corresponding.

Preferably, after described step S11, also comprise:

S12. judge whether to consider observability: be to go to step S13, otherwise go to step S14;

S13. the observability function is sampled;

S14. judge whether to consider two sizes: be to go to step S15, otherwise go to step S21;

S15. the normal direction distribution of microcosmic is carried out to matching;

The normal direction of the microcosmic that S16. will be expressed by anisotropy sphere Gaussian function distributes and carries out with macroscopical plane bidirectional reflectance distribution the bidirectional reflectance distribution function that convolution obtains two sizes.

Preferably, in described step S21, utilize that second-order differential is constant carries out the sphere distortion of semivector to incident direction to the bidirectional reflectance distribution function of being expressed by anisotropy sphere Gaussian function.

Preferably, after described step S31, also comprise:

S32. judge whether to consider observability: otherwise go to step S41, be to go to step S42;

S42. the distribution function obtained in step S31 is combined with the observability function, calculated product is divided and is obtained the final color of playing up.

(3) beneficial effect

At first the present invention provides a kind of brand-new anisotropy sphere Gaussian function, rendering intent provided by the present invention is based on above-mentioned brand-new anisotropy sphere Gaussian function, than the rendering intent based on mixing the sphere Gaussian function in prior art, can significantly improve and play up frame per second, thereby can better realize real-time rendering; In addition, anisotropy sphere Gaussian function provided by the present invention and character thereof can also be for other application of graphics, even other fields.

The accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the rendering intent based on anisotropy sphere Gaussian function that provides of the embodiment of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described further.Following examples are only for the present invention is described, but are not used for limiting the scope of the invention.

At first a kind of brand-new anisotropy sphere Gaussian function is provided in the present embodiment:

The geometric definition of described anisotropy sphere Gaussian function is:

$G(v;[x,y,z],[\mathrm{\λ},\mathrm{\μ}],c)=c\·S(v;z)\·e^{-\mathrm{\λ}{(v\·x)}^2-\mathrm{\μ}{(v\·y)}^2};$

Wherein, z, x, y is three main shafts perpendicular to each other; λ and μ are respectively the bandwidth of x and y axle, and meet λ > 0, μ > 0; The amplitude that c is function; Level and smooth S (v; Z)=max (vz, 0), v is vector of unit length, a bit on the representation unit ball;

The algebra definition of described anisotropy sphere Gaussian function is:

$G(v;A)=S(v;z)\·e^{{-v}^T\mathrm{Av}};$

Wherein, A is 3 * 3 real symmetric matrixs, the unit character vector that the minimal characteristic root that z is A is corresponding, level and smooth S (v; Z)=max (vz, 0), v is vector of unit length, a bit on the representation unit ball.

A kind of rendering intent based on above-mentioned brand-new anisotropy sphere Gaussian function also is provided in the present embodiment, and as shown in fig. 1, this rendering intent mainly comprises step:

S11. utilize anisotropy sphere Gaussian function to carry out matching to light source and bidirectional reflectance distribution function; Adopt the mixture model of anisotropy sphere Gaussian function to be similar to: at first according to the local maximum of sampling function, determine initial anisotropy sphere Gaussian function, recycling L-BFGS-B(is with the BFGS algorithm of boundary constraint) etc. method solve.

Optionally, can also comprise step S12-step S16 after step S11:

S12. judge whether to consider observability: be to go to step S13, otherwise go to step S14;

S13. the observability function is sampled;

For example, adopt the cube sampling, utilize sphere tape symbol distance function express and data are carried out to PCA(Principal Component Analysis, pivot analysis) compression;

S14. judge whether to consider two sizes: be to go to step S15, otherwise go to step S21;

S15. the normal direction distribution of microcosmic is carried out to matching;

The normal direction of the microcosmic that S16. will be expressed by anisotropy sphere Gaussian function distributes and distributes and carry out the bidirectional reflectance distribution function that convolution operation obtains considering two sizes of micromechanism with macroscopical plane bidirectional reflectance;

S21. the bidirectional reflectance distribution function of being expressed by anisotropy sphere Gaussian function is carried out to the sphere distortion operation of semivector to incident direction;

Preferably, in above-mentioned steps S21, can utilize that second-order differential is constant carries out the sphere distortion of semivector to incident direction to the bidirectional reflectance distribution function of being expressed by anisotropy sphere Gaussian function; For example, the method that can propose in 09 year with reference to Wang Jia equality people, by keeping second-order differential constant, derive the anisotropy sphere Gaussian function after distortion; This distortion conversion is applied to bidirectional reflectance distribution function, it is transformed to the incident direction space.

S31. utilize the multiplicative closed of anisotropy sphere Gaussian function, the bidirectional reflectance distribution function after distortion and light source are carried out to combination, the bidirectional reflectance distribution function after soon distortion and light source multiply each other and obtain a distribution function;

S41. the distribution function obtained in step S31 is directly carried out to integration and obtain the final color of playing up;

Optionally, after described step S31, also comprise:

S32. judge whether to consider observability: otherwise go to step S41, be to go to step S42;

S42. the distribution function obtained in step S31 is combined with the observability function, calculated product is divided and is obtained the final color of playing up; Thereby utilize the general sphere Gaussian function of the constant calculating of integration and the equivalence of anisotropy sphere Gaussian function to obtain playing up color;

For example, by the anisotropy sphere Gaussian function obtained in step S31, by size (surface integral of function) constant method, be approximately bandwidth and be

the general sphere Gaussian function of equivalence of (bandwidth that wherein λ and μ are former anisotropy sphere Gaussian function); The method of then utilizing Wang Jia equality people to propose in 09 year is calculated the final color of playing up to integrated value.

It should be noted that: the rendering intent based on anisotropy sphere Gaussian function provided in the present embodiment is only a kind of implementation method of the present invention, can also be by increasing or reduce step, selecting step to combine to realize the present invention etc. in practical application.

The anisotropy sphere Gaussian function of rendering intent provided by the present invention based on brand-new, than the rendering intent based on mixing the sphere Gaussian function in prior art, can significantly improve and play up frame per second, thereby can better realize real-time rendering; In addition, anisotropy sphere Gaussian function provided by the present invention and character thereof can also be for other application of graphics, even other fields.

Above embodiment is only for illustrating the present invention; and be not limitation of the present invention; the those of ordinary skill in relevant technologies field; without departing from the spirit and scope of the present invention; can also make a variety of changes and modification, therefore all technical schemes that are equal to also belong to protection category of the present invention.

Claims (4)

1. the rendering intent based on anisotropy sphere Gaussian function, is characterized in that, comprises step:

S11. utilize anisotropy sphere Gaussian function to carry out matching to light source and bidirectional reflectance distribution function;

S21. the bidirectional reflectance distribution function of being expressed by anisotropy sphere Gaussian function is carried out to the sphere distortion of semivector to incident direction;

S31. utilize the multiplicative closed of anisotropy sphere Gaussian function, the bidirectional reflectance distribution function after distortion and light source are multiplied each other and obtain a distribution function;

S41. the distribution function obtained in step S31 is carried out to integration and obtain the final color of playing up;

Wherein, the geometric definition of described anisotropy sphere Gaussian function is:

$G(v;[x,y,z],[\mathrm{\λ},\mathrm{\μ}],c)=c\·S(v;z)\·e^{-\mathrm{\λ}{(v\·x)}^2-\mathrm{\μ}{(v\·y)}^2};$

Wherein, z, x, y is three main shafts perpendicular to each other; λ and μ are respectively the bandwidth of x and y axle, and meet λ > 0, μ > 0; The amplitude that c is function; Level and smooth S (v; Z)=max (vz, 0), v is vector of unit length, a bit on the representation unit ball;

The algebra definition of described anisotropy sphere Gaussian function is:

$G(v;A)=S(v;z)\·e^{{-v}^T\mathrm{Av}};$

Wherein, A is 3 * 3 real symmetric matrixs, the unit character vector that the minimal characteristic root that z is A is corresponding.

2. rendering intent according to claim 1, is characterized in that, after described step S11, also comprises:

S12. judge whether to consider observability: be to go to step S13, otherwise go to step S14;

S13. the observability function is sampled;

S14. judge whether to consider two sizes: be to go to step S15, otherwise go to step S21;

S15. the normal direction distribution of microcosmic is carried out to matching;

The normal direction of the microcosmic that S16. will be expressed by anisotropy sphere Gaussian function distributes and carries out with macroscopical plane bidirectional reflectance distribution the bidirectional reflectance distribution function that convolution obtains two sizes.

3. rendering intent according to claim 2, is characterized in that, in described step S21, utilizes that second-order differential is constant carries out the sphere distortion of semivector to incident direction to the bidirectional reflectance distribution function of being expressed by anisotropy sphere Gaussian function.

4. according to the described rendering intent of claim 2 or 3, it is characterized in that, also comprise after described step S31:

S32. judge whether to consider observability: otherwise go to step S41, be to go to step S42;

S42. the distribution function obtained in step S31 is combined with the observability function, calculated product is divided and is obtained the final color of playing up.

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