CN103679780B - A kind of space target real time simulation method - Google Patents

Abstract

The present invention relates to a kind of space target real time simulation method, belong to technical field of spaceflight simulation。First the present invention builds visual Celestial Background, orbital tracking then in conjunction with extraterrestrial target, utilize the high speed that programmable processor completes position, size and color to resolve and draw, finally in conjunction with viewpoint position and user's cutting information, complete the generation of target direction roomage state。The present invention takes full advantage of parallel processing and the high accuracy floating-point operation characteristic of GPU, and acceleration effect is obvious, and real-time is good, and in expressing for roomage state, the real-time Simulation of target provides reliable means。

Description

A kind of space target real time simulation method

Technical field

The present invention relates to a kind of space target real time simulation method, belong to technical field of spaceflight simulation。

Background technology

Along with the mankind, to explore the paces of space increasingly faster, and as the important means of spacial flex target distribution directly perceived, spatial environments state, the roomage state based on Aerospace Simulation for Spacecraft is expressed of increased attention。Compared to the expression of ground situation, roomage state expresses maximum being characterized in that, and space-time unique to be described is very large, and the number of levels of the extraterrestrial target thus comprised is ten hundreds of especially, and this is a huge challenge for the real-time Simulation of target。

At present, both at home and abroad roomage state is expressed and has been carried out certain exploration by existing many units, but more concentrates on the analogue simulation of Celestial Background, specific or a small amount of extraterrestrial target, and the real-time Simulation research of extraterrestrial target is less。OpenGL, as a kind of software interface of graphic hardware, is one of current most popular 3D figure and model library, it is possible to assisted the general simulation of extraterrestrial target。But, for the real-time Simulation of extraterrestrial target, adopt OpenGL fixed function pipelines to process data and cannot meet the requirement in speed。Graphic process unit (GPU) can support T&L(TransformandLighting from hardware), have the advantages that concurrency is good and floating-point operation ability is strong, the most T&L computing of GPU can be shared, thus significantly accelerating the 3D speed rendered by graphic hardware programming (as shown in Figure 1)。Along with the range of application of GPU expands further, some general calculating tasks are transferred to GPU by shading language and run, and this be that the real time position of extraterrestrial target resolves and drafting renders and provides new thinking。

Summary of the invention

It is an object of the invention to provide a kind of space target real time simulation method, to solve to adopt OpenGL fixed function pipelines processing mode to carry out the problem that real-time Simulation extraterrestrial target causes hourly velocity to meet。

The present invention solves that above-mentioned technical problem provides a kind of space target real time simulation method, the step of this real time simulation method is as follows:

1) star place, size and brightness are calculated, and the imaging model according to fixed star picture point, draw Celestial Background；

2) utilize the position of GPU real-time resolving extraterrestrial target according to extraterrestrial target orbital tracking, and be utilized respectively size and the color of the vertex shader in GPU and fragment shader installation space target；

3) in conjunction with viewpoint position and user's cutting information, extraterrestrial target is rendered to the roomage state of target respective direction。

Described step 2) in comprising the following steps that extraterrestrial target position real-time resolving and attribute are arranged；

A. set up the relation between orientation of orbit quaternary number and track angle element, utilize quaternary number that the track profile of extraterrestrial target is described；

B. the orbital tracking in extraterrestrial target built-in properties is associated with vertex position, surface normal and texture coordinate；

C. utilize OpenGL shading language opposite vertexes tinter to be programmed, it is achieved the resolving to extraterrestrial target position, and its size is set；

D. the pel of extraterrestrial target is assembled and rasterization process, pel is decomposed into less sheet unit, and distributes different transparencys for sheet unit, in conjunction with transparency change, color of object is configured。

Relation between described step A middle orbit orientation quaternary number and track angle element is:

$q_x=\cos \frac{i}{2}\cos \frac{\mathrm{\Ω}+f}{2},q_y=\sin \frac{i}{2}\cos \frac{\mathrm{\Ω}-f}{2}$

$q_z=\sin \frac{i}{2}\sin \frac{\mathrm{\Ω}-f}{2},q_w=\cos \frac{i}{2}\sin \frac{\mathrm{\Ω}+f}{2}$

Wherein q_x,q_y,q_z,q_wFor the quaternary number of track profile, Ω is right ascension of ascending node, and i is orbit inclination angle, and σ=ω+f is ascending node angular distance, and ω is the argument of perigee, and f is true anomaly。

The process utilizing the celestial coordinate system coordinate of orbital tracking resolving extraterrestrial target in described step C is as follows:

A. by mean anomaly M epoch₀, mean angular velocity n and current epoch time time, calculate mean anomaly,

M=M₀+ time*n；

B. by eccentric ratio e, according to Kepler's equations M=E-esinE, iterative eccentric anomaly E；

C. by major semiaxis a, the target coordinate at track plane right-angle coordinate is calculated,

$\left(\begin{array}{c}x\\ y\end{array}\right)=a\left(\begin{array}{c}\cos E-e\\ \sqrt{(1-e^2)\sin E}\end{array}\right);$

D. track profile quaternary number is utilized to calculate target coordinate in celestial coordinate system,

${\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)}_{\mathrm{CS}}=\left(\begin{array}{c}{\mathrm{xq}}_x^2+{\mathrm{yq}}_x{q}_y+z{q}_x{q}_z+a_0{q}_w-a_1{q}_z+a_2{q}_y\\ {\mathrm{xq}}_x{q}_y+{\mathrm{yq}}_y^2+{\mathrm{zq}}_y{q}_z+a_0{q}_z+a_1{q}_w-a_2{q}_x\\ {\mathrm{xq}}_x{q}_z+{\mathrm{yq}}_y{q}_z+{\mathrm{zq}}_z^2-a_0{q}_y+a_1{q}_x+a_2{q}_z\end{array}\right)$

Wherein $\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)=\left(\begin{array}{c}{\mathrm{xq}}_w-{\mathrm{yq}}_z\\ {\mathrm{xq}}_z-{\mathrm{yq}}_w\\ {\mathrm{yq}}_x-{\mathrm{xq}}_y\end{array}\right)$ For transition matrix, q_x,q_y,q_z,q_wFor track profile quaternary number。

In described step D for sheet unit distribution transparency model as follows:

$\mathrm{opacity}=1-\frac{{(x-x_c)}^2+{(y-y_c)}^2}{\max \{{(x-x_c)}^2+{(y-y_c)}^2\}}$

Wherein, (x, y) for sheet unit coordinate, (x_c,y_c) for pel centre coordinate。

The invention has the beneficial effects as follows: first the present invention builds visual Celestial Background, orbital tracking then in conjunction with extraterrestrial target, utilize the position of GPU real-time resolving extraterrestrial target, and utilize size and the color of the vertex shader in GPU and fragment shader installation space target, finally in conjunction with viewpoint position and user's cutting information, extraterrestrial target is rendered to the roomage state of target respective direction, thus completing the generation of object space situation。The present invention takes full advantage of parallel processing and the high accuracy floating-point operation characteristic of GPU, and acceleration effect is obvious, and real-time is good, and in expressing for roomage state, the real-time Simulation of target provides reliable means。

Accompanying drawing explanation

Fig. 1 is programmable graphics hardware streamline；

Fig. 2 is the flow chart of space target real time simulation method of the present invention；

Fig. 3 is that extraterrestrial target position resolves and attribute setup schematic diagram；

Fig. 4 is track six roots of sensation number schematic diagram；

Fig. 5 is comparison diagram before and after the transparency amendment of target patch unit；

Fig. 6 is tinter visioning procedure figure；

Fig. 7 is the real-time Simulation result figure of the dissimilar spacecraft of terrestrial space；

Fig. 8 is the analog result figure of solar system asteroid belt。

Detailed description of the invention

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is further described。

OpenGL is as a kind of software interface of graphic hardware, it is one of current most popular 3D figure and model library, it is possible to assisted the general simulation of extraterrestrial target, but, for the real-time Simulation of extraterrestrial target, adopt OpenGL fixed function pipelines to process data and cannot meet the requirement in speed。Graphic process unit (GPU) can support T&L(TransformandLighting from hardware), have the advantages that concurrency is good and floating-point operation ability is strong, the most T&L computing of GPU can be shared, thus significantly accelerating the 3D speed rendered by graphic hardware programming (as shown in Figure 1)。Along with the range of application of GPU expands further, some general calculating tasks are transferred to GPU by shading language and run, this real time position being extraterrestrial target resolves and draws to render and provides new thinking, for this, the present invention is based on above-mentioned thinking, providing the real time simulation method of a kind of extraterrestrial target, the step of this real time simulation method is as follows:

1. calculate star place, size and brightness the imaging model according to fixed star picture point, draw Celestial Background；

2. the position of GPU real-time resolving extraterrestrial target is utilized according to extraterrestrial target orbital tracking, and the size of installation space target and color；

3., in conjunction with viewpoint position and user's cutting information, extraterrestrial target is rendered to the roomage state of target respective direction。

It is described in detail below for above three step。

1. Celestial Background is drawn

In roomage state is expressed, set up three-dimensional Celestial Background accurately, be set up spatial scene true to nature, carry out the basis of target real-time Simulation。The present invention calculates star place, size, brightness by relevant model, and in conjunction with the imaging model of fixed star picture point, utilize OpenGL to draw out position is accurate, brightness is clearly demarcated starry sky, the real-time Simulation for extraterrestrial target provides background true, reliable。This process specifically includes the calculating of the calculating of star place model, the calculating of brightness model, the calculating of the big mini Mod of fixed star and fixed star picture point imaging model。

The calculating process of star place model is as follows:

The relatively solar motion of fixed star meets certain rule, it is known that the mean place and namely available formula (1) calculates the mean place of any time fixed star voluntarily epoch of fixed star, utilizes formula (2) and then obtains fixed star t position in geocentric equatorial polar coordinate。

$\left\{\begin{array}{c}{\mathrm{\α}}_t={\mathrm{\α}}_0+{\mathrm{\μ}}_{\mathrm{\α}}(t-t_0)\\ {\mathrm{\δ}}_t={\mathrm{\δ}}_0+{\mathrm{\μ}}_{\mathrm{\δ}}(t-t_0)\end{array}\right.---\left(1\right)$

Wherein, μ_αAnd μ_δIt is fixed star respectively in declination and right ascension direction voluntarily, it is possible to read from hipparcos catalogue and obtain。

By the right ascension of fixed star, declination coordinate (α_t,δ_t) be transformed into geocentric rectangular coordinate (x, y, computing formula z) is:

$\left\{\begin{array}{c}x=r\cos {\mathrm{\α}}_t\cos {\mathrm{\δ}}_t\\ y=r\cos {\mathrm{\δ}}_t\sin {\mathrm{\α}}_t\\ z=r\sin {\mathrm{\δ}}_t\end{array}\right.---\left(2\right)$

Wherein, r is the earth distance to fixed star, and unit is light-year, utilizes the parsec in star catalogue to convert and obtains。

The calculating process of brightness model is as follows:

The brightness of fixed star quantitatively cannot show according to truth, it is considered to magnitude and vision two factors of two aspects carry out deterministic simulation by the method for linear interpolation。

B=B₀-k G(3)

Wherein, G is stellar magnitude, B₀With first the setting of k meets the brightness value after calculating and limit between scope 0.0～1.0 at OpenGL colouring information, secondly the demand of visual brightness is adjusted by basis further。Such as, the maximum magnitude of star catalogue is 13, it is contemplated that brightness controlled between 0.5～0.1, it is possible to set B₀=1.0, k=0.038。

The calculating process of the big mini Mod of fixed star is as follows:

Simulation for fixed star size quantitatively cannot show according to truth equally, and the method for employing is equal to Intensity model, namely by the size of the fixed star of line style interpolating analogue difference magnitude。

R=R₀-l G(4)

Wherein, G is stellar magnitude, being plotted in OpenGL and do not have the restriction of rigidity of fixed star size, it is possible to arrange R voluntarily according to visual experience₀And l。Such as, the maximum magnitude of star catalogue is 13, it is contemplated that fixed star size controlled between 1～3 pixel, it is possible to set R₀=3, l=0.1534。

The calculating process of fixed star picture point imaging model is:

The fixed star of infinite point is considered as the point source with certain spectral signature, therefore simulates the point spread function that picture point is optical system of star chart, and ideally its Energy distribution meets dimensional Gaussian distribution,

I (x, y)=(φ/2 π σ²)exp[-(x-x₀)²/2σ²-(y-y₀)²/2σ²] (5)

Wherein φ is the radiant power of fixed star；(x₀,y₀) for spot center position coordinates。

2. extraterrestrial target position real-time resolving and attribute are arranged

This process mainly includes utilizing quaternion representation target track, orbital tracking and built-in properties carries out variable association, target location resolves and color of object is arranged。

The process utilizing quaternion representation target track is as follows:

Description for track generally adopts six parameters such as keplerian cllipse major semiaxis, eccentricity, orbit inclination angle (shown in Fig. 4), wherein major semiaxis and eccentricity may determine that size and the shape of track, true anomaly may determine that satellite instantaneous position in orbit, and orbit inclination angle, right ascension of ascending node and the argument of perigee are then used for determining the attitude of orbital plane。Traditional description for attitude orientation adopts Eulerian angles more, but can cause occurring complicated loaded down with trivial details trigonometric function and additional singular point in equation, if using quaternary number as the parameter describing track profile, it is possible to avoid these shortcomings。

Therefore, data preparation stage will set up associating of orientation of orbit quaternary number and track angle element, it is assumed that the quaternary number describing track profile is q_x,q_y,q_z,q_w, it is as follows with the relational model of track angle element:

$q_x=\cos \frac{i}{2}\cos \frac{\mathrm{\Ω}+f}{2},q_y=\sin \frac{i}{2}\cos \frac{\mathrm{\Ω}-f}{2}$

(6)

$q_z=\sin \frac{i}{2}\sin \frac{\mathrm{\Ω}-f}{2},q_w=\cos \frac{i}{2}\sin \frac{\mathrm{\Ω}+f}{2}$

Wherein, Ω is right ascension of ascending node, and i is orbit inclination angle, and σ=ω+f is ascending node angular distance, and ω is the argument of perigee, and f is true anomaly。

By the process of orbital tracking Yu built-in properties variable association it is:

Orbital tracking refers to the one group of parameter describing celestial body (extraterrestrial target) in its track running status, current GPU only can process the primitive information such as vertex position, normal vector, texture coordinate, therefore the premise being applied to general scientific algorithm is, the relevant parameter participating in computing is stored in vertex buffer etc. to be called, therefore, orbital tracking value is stored in vertex buffer by the present invention, and each parameter is as shown in table 1 with the corresponding relation of built-in properties variable。

Table 1 orbital tracking and built-in properties incidence relation

By associating, it is possible to by the OpenGL vertex data interface of standard, from application program, orbital tracking data being sent to vertex shader program, in OpenGL, all of geometric object is finally all described as summit one group orderly。

The step utilizing the celestial coordinate system coordinate of orbital tracking solving target is as follows:

1. by mean anomaly M epoch₀, mean angular velocity n and current epoch time time, calculate mean anomaly；

M=M₀+ time*n(7)

2. according to Kepler's equations M=E-esinE, iterative eccentric anomaly E；

3. the target coordinate at track plane right-angle coordinate is calculated；

$\left(\begin{array}{c}x\\ y\end{array}\right)=a\left(\begin{array}{c}\cos E-e\\ \sqrt{(1-e^2)\sin E}\end{array}\right)---\left(8\right)$

4. track profile quaternary number is utilized to calculate target coordinate in celestial coordinate system。

${\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)}_{\mathrm{CS}}=\left(\begin{array}{c}{\mathrm{xq}}_x^2+{\mathrm{yq}}_x{q}_y+z{q}_x{q}_z+a_0{q}_w-a_1{q}_z+a_2{q}_y\\ {\mathrm{xq}}_x{q}_y+{\mathrm{yq}}_y^2+{\mathrm{zq}}_y{q}_z+a_0{q}_z+a_1{q}_w-a_2{q}_x\\ {\mathrm{xq}}_x{q}_z+{\mathrm{yq}}_y{q}_z+{\mathrm{zq}}_z^2-a_0{q}_y+a_1{q}_x+a_2{q}_z\end{array}\right)---\left(9\right)$

Wherein $\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)=\left(\begin{array}{c}{\mathrm{xq}}_w-{\mathrm{yq}}_z\\ {\mathrm{xq}}_z-{\mathrm{yq}}_w\\ {\mathrm{yq}}_x-{\mathrm{xq}}_y\end{array}\right)$ For transition matrix, q_x,q_y,q_z,q_wFor track profile quaternary number。

Said process requires over GLSL and is translated into " language " that tinter may identify which, then transfers to GPU to carry out high-speed parallel computing, and GLSL has numerous characteristics similar to C++ and Java, and the key code of corresponding above step is as follows:

Floatsma=gl_Vertex.x;// major semiaxis

Floatecc=gl_Vertex.y;// eccentricity

FloatM0=gl_Vertex.z;// epoch mean anomaly

Floatnu=gl_Normal.x;// mean angular velocity

FloatM=M0+time*nu;// calculate mean anomaly

floatE=M;

for(inti=0;i<4;i+=1)

E=M+ecc*sin (E);// iterative cycles seeks eccentric anomaly 4 times

Vec3position=vec3 (sma* (cos (E)-ecc), sma* (sin (E) * sqrt (1.0-ecc*ecc)), 0.0);" // satellite is at the coordinate of track plane right-angle coordinate for n；

Gl_Position=gl_ModelViewProjectionMatrix*vec4 (position, 1.0);Output coordinate after the conversion of // model view projections；Additionally, program utilizes self-defining uniform variable by target sizes " incoming " vertex shader program, by gl_PointSize assignment is completed the setting to target sizes。

Utilize GLSL programming that color of object is configured

After having processed summit, the whole attributes being associated with each summit will be determined completely, and after pel assembling and rasterisation, pel will be broken down into less sheet unit, and these sheet units are corresponding to the pixel of target frame relief area。And sheet unit processor is a programmable unit processing sheet unit value and associated data, it is possible to being used for performing traditional graphic operation, the present invention passes through the setting to color of object of the GLSL programming realization。

Shown in figure as left in Fig. 5, the sheet unit that the pel after rasterizing is formed is combined as square distribution, and real imaging model is circular distribution, and from inside to outside color is gradually shallow, formula (10) can be adopted to distribute different transparencys for sheet unit for this and realize。

$\mathrm{opacity}=1-\frac{{(x-x_c)}^2+{(y-y_c)}^2}{\max \{{(x-x_c)}^2+{(y-y_c)}^2\}}$

Wherein, (x, y) for sheet unit coordinate, (x_c,y_c) for pel centre coordinate, shown in figure as right in Fig. 5, sheet unit transparency according to square linearly the changing of centre slice unit distance, pel entirety from inside to outside transparency is gradually lowered, and color is gradually shallow, meets target imaging model。Program utilizes self-defining uniform variable by color of object " incoming " sheet unit coloration program, in conjunction with transparency change by gl_FragColor assignment is completed the setting to color of object。

Create GLSL tinter object and they are chained up creating can perform step required for coloration program as shown in Figure 6。

1. tinter object is created；

2. successful com shader code；

3. create a coloration program, and suitable tinter object is linked in program；

4. use tinter to carry out summit or fragment processes。

Graphic hardware could be started after such a step be accelerated processing, and finally be efficiently completed calculating coordinate and attribute setting。

3. the real-time Simulation of extraterrestrial target

The present invention uses the real-time Simulation that OpenGL 3 d graphic library and Qt programming language achieve target to draw, the Celestial Background with accurate time-space relationship and brightness degree is drawn out first with existing mature technology, then the position of GPU real-time resolving extraterrestrial target is utilized according to extraterrestrial target orbital tracking, size and color are set, as shown in Figure 1, in the process that pipeline is drawn, pel assembling, rasterisation, depth test etc. operate and are still completed by the pipeline of fixing function。Therefore, it is also desirable to complete the cutting of scene according to viewpoint position, target projection is to high performance display the most at last, completes extraterrestrial target simulation。

The experimental verification of the space target real time simulation method that the present invention expresses for roomage state:

In order to verify feasibility and the suitability of target real time simulation method that the present invention proposes, with " roomage state expression " for background, the dissimilar spacecraft of milky way galaxy asteroid belt and terrestrial space is carried out real-time Simulation verification experimental verification: be in the simulation system of core input time in the process of the present invention, target sizes and color are set, after adjusting the parameters such as viewpoint position, generated corresponding optical signalling by work station and show on high resolution displays, its result is as follows: Fig. 7 is the real-time Simulation result of nearly ten thousand dissimilar spacecrafts of terrestrial space, different classes of spacecraft target has been carried out the differentiation of color and size by test。Fig. 8 is the analog result of solar system asteroid belt, increases simulation step length, and the position of asteroid target constantly changes in time, shows smoothness。

As can be seen from the test results, the space target real time simulation method speed that the present invention expresses for roomage state is fast, highly reliable, effect is true to nature, take full advantage of GPU estimated performance parallel, efficient, it is possible to for the target simulation that the expression offer of future space situation is real-time。

Claims (4)

1. a space target real time simulation method, it is characterised in that the step of this analogy method is as follows:

1) star place, size and brightness are calculated, and the imaging model according to fixed star picture point, draw Celestial Background；

2) utilize the position of GPU real-time resolving extraterrestrial target according to extraterrestrial target orbital tracking, and be utilized respectively size and the color of the vertex shader in GPU and fragment shader installation space target；

3) in conjunction with viewpoint position and user's cutting information, extraterrestrial target is rendered to the roomage state of target respective direction；

Described step 2) in comprising the following steps that extraterrestrial target position real-time resolving and attribute are arranged；

A. set up the relation between orientation of orbit quaternary number and track angle element, utilize quaternary number that the track profile of extraterrestrial target is described；

B. the orbital tracking in extraterrestrial target built-in properties is associated with vertex position, surface normal and texture coordinate；

C. utilize OpenGL shading language opposite vertexes tinter to be programmed, it is achieved the resolving to extraterrestrial target position, and its size is set；

D. the pel of extraterrestrial target is assembled and rasterization process, pel is decomposed into less sheet unit, and distributes different transparencys for sheet unit, in conjunction with transparency change, color of object is configured。

2. space target real time simulation method according to claim 1, it is characterised in that the relation between described step A middle orbit orientation quaternary number and track angle element is:

$q_x=cos\frac{i}{2}cos\frac{\mathrm{\&Omega;}+f}{2},q_y=\sin \frac{i}{2}cos\frac{\mathrm{\&Omega;}-f}{2}$

$q_z=sin\frac{i}{2}\sin \frac{\mathrm{\&Omega;}-f}{2},q_w=cos\frac{i}{2}\sin \frac{\mathrm{\&Omega;}+f}{2}$

Wherein q_x,q_y,q_z,q_wFor the quaternary number of track profile, Ω is right ascension of ascending node, and i is orbit inclination angle, and σ=ω+f is ascending node angular distance, and ω is the argument of perigee, and f is true anomaly。

3. space target real time simulation method according to claim 1, it is characterised in that the solution process of described step C Spatial Object position is as follows:

A. by mean anomaly M epoch₀, mean angular velocity n and current epoch time time, calculate mean anomaly, M=M₀+ time*n；

B. by eccentric ratio e, according to Kepler's equations M=E-esinE, iterative eccentric anomaly E；

C. by major semiaxis a, the target coordinate at track plane right-angle coordinate is calculated,

$\left(\begin{array}{c}x\\ y\end{array}\right)=a\left(\frac{\cos E-e}{\sqrt{(1-e^2)\sin E}}\right);$

D. track profile quaternary number is utilized to calculate target coordinate in celestial coordinate system,

${\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)}_{CS}=\left(\begin{array}{c}{\mathrm{xq}}_x^2+{\mathrm{yq}}_x{q}_y+{\mathrm{zq}}_x{q}_z+a_0{q}_w-a_1{q}_z+a_2{q}_y\\ {\mathrm{xq}}_x{q}_y+{\mathrm{yq}}_y^2+{\mathrm{zq}}_y{q}_z+a_0{q}_z+a_1{q}_w-q_2{q}_x\\ {\mathrm{xq}}_x{q}_z+{\mathrm{yq}}_y{q}_z+{\mathrm{zq}}_z^2-a_0{q}_y+a_1{q}_0+a_2{q}_z\end{array}\right)$

WhereinFor transition matrix, q_x,q_y,q_z,q_wFor track profile quaternary number。

4. space target real time simulation method according to claim 1, it is characterised in that as follows for the transparency model of sheet unit distribution in described step D:

$opacity=1-\frac{{(x-x_c)}^2+{(y-y_c)}^2}{\max \{{(x-x_c)}^2+{(y-y_c)}^2\}}$

Wherein, (x, y) for sheet unit coordinate, (x_c,y_c) for pel centre coordinate。