CN103366395A - Volume data non-photorealistic rendering method based on GPU (graphic processing unit) acceleration - Google Patents

Abstract

The invention relates to a volume data non-photorealistic rendering method based on GPU (graphic processing unit) acceleration. The method comprises the following steps of carrying out the direct volume rendering for medical volume data under multiple viewpoints, acquiring a plurality of rendering results, extracting a characteristic line for the two-dimensional rendering result, defining a global energy miniaturization rule, calculating a three-dimensional characteristic line, utilizing a convolution surface method to define a scalar field, clustering the three-dimensional characteristic line, utilizing a B-type curve to fit the line, and completing the stylized rendering. By utilizing the powerful calculation capacity of the GPU, the rendering speed and efficiency can be greatly improved.

Description

A kind of volume data non-photorealistic rendering method of accelerating based on GPU

Technical field

The invention belongs to non-truly playing up and the Volume Rendering Techniques field, be specifically related to the volume data non-photorealistic rendering method of accelerating based on GPU.

Background technology

Non-photorealistic rendering effectively replenishes as Realistic Rendering, its purpose does not lie in the authenticity of figure, and mainly be to produce a kind of artistic effect close with artist's work, and showing the artistic speciality of figure, it is widely applied in fields such as education, amusement, art.Yet because the three-dimensional data scale constantly increases, disposal route is day by day complicated, and the feeling of unreality volume drawing also is faced with conventional bulk and draws a same difficult problem: the contradiction of picture quality and render speed.And along with the appearance of programmable graphics hardware, become a study hotspot in this field based on the non-photorealistic rendering of GPU (Graphics Process Unit, Graphics Processing Unit).

In the nineties, the emphasis of non-photorealistic rendering research concentrates on the simulation to natural material, such as pen-and-ink drawing effect, pencil drawing effect, oil paint effect, watercolor effect etc.Winkenbach etc. introduce the concept of " stroke texture " based on three dimensions, use the surface of stroke texture padding three-dimensional model with the simulation pen-and-ink drawing.Improve the intelligibility of stick figure by omissions of detail; Simultaneously, the difference of stroke parameter can adapt to the performance of different resolution curved surface.Curtis etc. have proposed a kind of method of automatic generation watercolor.The method utilizes Kubelka-Munk color mixture mode to obtain quite real watercolor effect, but calculated amount is larger.Hertzmann etc. have proposed a kind of model from photo establishment Freehandhand-drawing effect, by using the stroke drawing image of different size and shapes, with the simulation oil paint effect.Drafting is based on the figure layer, and every one deck is selected different styles of writing, and every one deck is drawn on the basis of last layer.

From the angle of art, outline line also occupies an important position, and is the focus in NPR field for the research of outline line always.In making cartoon, for the shape of abundant expression model, outline line commonly used sketches the contours the general profile of model, and shows the key character of model with thick line, reaches the purpose that attracts audience attention.At present, the work of this respect is devoted in a lot of researchs, and wherein the most basic is the calculating of outline line.Outline line calculates the related algorithm that generally is based on pattern space and image space.Algorithm based on image space generally has: based on the outline line of Depth Map, Normal Map detection image, back side wire frame is drawn.

Main thought based on the algorithm of Depth Map is for the point that belongs to different objects, and the pixel depth value changes greatly: and for contiguous point, belong to the point on the same object, and its pixel depth value changes little.The propositions such as Decaudin utilize the outline line that comes detection image with the vector reflection.Near the face normal direction of the method hypothesis object outline line changes, and wherein the vector reflection is the image of special drafting, and what each pixel in the image was stored is the normal vector of homologue surface.

Traversal detection algorithm based on the limit directly travels through all limits, judges that sight line and face normal vector product are not less than 0, and this face is towards the front, otherwise this face is facing backwards, the method simply but inefficiency, Gooch has proposed to accelerate this algorithm by Gaussian sphere.Be that the Edge Buffer data structure traversal of utilizing that Buchanan proposes is obtained the method for outline line based on the traversal detection algorithm of face, the method only need to be known the composition limit of each face, is not having hardware-accelerated in particular cases can greatly to improve detection efficiency.

After obtaining outline line, the researcher considers how to use abundanter lines to show the shape of model, rather than the simple straight line of simple utilization.The researcher has proposed stylized silhouette rendering (Stylized Silhouette Rendering, SSR), and it is a kind of important form of expression in the non-photorealistic rendering.Can simulate various materials and draw gimmick by SSR.

Northrup etc. at first propose outline line is carried out the implementation method of stylization.At first, utilize and find out outline line with the algorithm of machine testing, then, the method for utilizing graph image to combine filters out visible outline line, and for visible outline line, the author utilizes the method for texture that characteristic curve is carried out stylization.Its main method is that characteristic edge is extended to quadrilateral along the angular bisector direction on adjacent both sides with characteristic curve, and the 2 d texture that represents unlike material is mapped in the quadrilateral.Isenberg has also proposed the algorithm of a stylized outline line.Z-buffer information when utilization is played up is judged the observability of outline line, and its cardinal principle is that outline line appears at the discontinuous place of z-depth, reaches good visual effect.

Volume Rendering Techniques is a kind of important scientific visualization technology, adopts this technology, without the characteristics algorithm of complexity, and browsing data inner structural features alternatively just.This technology is widely used in the fields such as medical science, meteorology and geology.The direct volume drawing algorithm mainly contains Ray Casting algorithm, Shear-Warp algorithm, splatting, Texture Mapping algorithm etc. at present.LevoyM etc. are divided into an octree structure with the even son of volume data recurrence, and the traversal Octree is skipped the maximum dummy section that comprises current sampling point in light projecting algorithm, reaches the effect of acceleration with this.

After the tracking of so-called unique point and match refer to obtain corresponding unique point in volume data, need to be according to some characteristics of these unique points, such as structure tensor, curvature etc., corresponding unique point fit to can the expression body data in dependency structure the characteristics of information line, such characteristic curve can have been expressed inside important structure and the feature of volume data clearly, is the important area that the user is concerned about.The Bezier method based on delta-shaped region reconstruct that Lawson etc. propose.In the ubiquity computer-aided design (CAD) of curve and surface intersection problems and processing and manufacturing, the lot of domestic and international scholar's research this problem.Anderssion etc. are from the research of starting with of the condition of curve self intersection situation, have provided the condition that the Bezier curve is avoided self intersection.Tatiana etc. have studied and have occurred the problem that the self intersection what state is removed in the two-dimensional curve moulding.

The invention belongs to non-truly playing up and the Volume Rendering Techniques field, be specifically related to the volume data non-photorealistic rendering method of accelerating based on GPU.

Summary of the invention

The technical problem to be solved in the present invention is: a kind of method of volume data being carried out non-realistic rendering is provided, and utilize the computing power of GPU hardware, improved and calculated and drafting efficient, the method is mainly utilized the two dimensional character line with vision meaning, and minimize rule according to global energy, calculate that corresponding three-dimensional feature line is also finished vector quantization and effect is drawn in stylization.

The technical scheme that the present invention solves the problems of the technologies described above is: the volume data non-photorealistic rendering method based on GPU accelerates comprises the steps:

1) extraction of two dimensional character line

Step (1), play up from a plurality of viewpoints, be specially in the XYZ cartesian coordinate system six viewpoints of positive negative direction at 3 axles, scene is carried out Ray Casting(ray cast) play up, the method is from light of viewpoint projection to each pixel, this light is in volume data in the projection process, repeatedly sample according to certain step-length, and calculating sampling is put corresponding color and opacity, until light passes volume data, this process can realize at GPU, utilize CUDA(to calculate unified equipment framework) hardware-accelerated, greatly improve rendering speed.And utilize the render to texture technology, and drawing result is rendered in a plurality of textures, obtain a plurality of two-dimentional rendering result.

Step (2), the two-dimensional effects of step (1) being desired to make money or profit process correlation technique with image, mainly is Canny operator and Contour Detect algorithm carry out characteristic curve to X-Y scheme extraction.The Canny operator also is the single order operator, and essence is to do level and smooth computing with an accurate Gaussian function, and then with locating the derivative maximal value with the first order differential operator of direction, its contribution has been to provide a kind of thinking of seeking optimum operator, has namely established optiaml ciriterion.Contour Detect mainly is to being come the continuity of calculation level by the result of calculation of Canny Detect, so just can obtaining characteristic curve in two dimension.

2) mapping of two dimensional character alignment three-dimensional line

Step (3), two dimensional character line are the lines with obvious vision meaning in two dimension, and we think that these lines are that the line of three-dimensional is in the drop shadow effect of two dimension, so need to find the characteristic curve of every two dimensional character line corresponding three-dimensional.Yet a two-dimensional points is the projection of a lot of three-dimensional point, so problem is converted into global minimization's problem.A three-dimensional point has positional information, opacity information, and colouring information, these are the factors that need to consider in minimization problem.

Step (4), according to the minimization problem of step (3) definition, problem can be converted into the shortest route problem that is similar to the multistage multinode, utilize dynamic programming algorithm can find the solution this problem, and by the CUDA framework, every two-dimensional line distributes a thread to be responsible for calculating corresponding three-dimensional line, has so greatly accelerated counting yield.

3) cluster of three-dimensional feature line and match

Step (5), utilize the method for Convolution Surface, define a scalar field, the scalar value of this each sampled point of scalar field is the curve density of weighing in its spatial dimension, be the many and few of curve, and according to this scalar field, keep the large sampled point of scalar value, these sampled points are carried out Refinement operation, further abbreviation.

Step (6), for the sampled point after step (5) refinement, be similar to the center line of model, but these points are link information not, we adopt minimal spanning tree algorithm to come these points are connected, at first make up a figure G for these points, each node of figure represents each sampled point, and the limit of figure represents the annexation of sampled point, the weight on limit represents the distance of two points, for can utilizing the Prim algorithm, this figure makes up minimum spanning tree T, and find leaf node and bifurcation according to T, thereby can formation curve.

Step (7), the curve that obtains for step (6), owing to be each point to be connected obtain, such curve is sufficiently oily, we adopt B-spline curves that it is carried out match, originally the point on the curve is equivalent to the reference mark, can generate curve Paint Gloss like this, so that the drafting effect is more true to nature.

In a word, compare with method before, the present invention can draw rapidly volume data feeling of unreality effect and can obtain preferably effect.The present invention mainly contains 2 contributions: the first, provided a kind of method that goes out image space Calculation of Three Dimensional characteristic curve, and the method is the rendering effect from direct volume drawing, and extracts the two dimensional character line and set out, and has fast and advantage more accurately.The second, utilize the Convolution Surface method that three-dimensional curve is carried out cluster and utilizes the B batten to carry out match, so that draw effect more well with true to nature.

Description of drawings

Fig. 1 is algorithm overall flow figure;

Fig. 2 is ray cast direct volume drawing schematic diagram;

Fig. 3 is for playing up two dimensional character line design sketch;

Fig. 4 is Calculation of Three Dimensional characteristic curve synoptic diagram;

Fig. 5 is three-dimensional feature line design sketch;

Fig. 6 is the curve density field design sketch of sampled point;

Fig. 7 is to carrying out thinning effect figure in the field;

Fig. 8 is for to connect into J curve effectJ figure to the point after the refinement;

Fig. 9 is Bezier curve design sketch.

Embodiment

Further specify the present invention below in conjunction with accompanying drawing and the specific embodiment of the present invention.

For the given volume data that is comprised of voxel (the voxel grid of Fig. 2), this method may further comprise the steps for the non-photorealistic rendering of this volume data:

We arrange six viewpoints (the eye point among Fig. 2, other five viewpoints are not shown) at X step (1), Y, and the six direction that the Z coordinate axis is positive and negative carries out ray cast (Ray Casting) to scene and draws.The method is based on the algorithm of image space, each pixel from image, along light of direction of visual lines emission, light passes through whole scene, and in this process, scene sampled obtain colouring information, according to the light absorbing model color value and opacity are added up simultaneously, until light passes scene.The wherein cumulative formula of color and opacity such as formula (1) (it is synthetic to sample from the back side to the front):

$C_i^{\mathrm{\Δ}}=(1-A_{i-1}^{\mathrm{\Δ}})C_i+C_{i-1}^{\mathrm{\Δ}}$

$A_i^{\mathrm{\Δ}}=(1-A_{i-1}^{\mathrm{\Δ}})A_i+A_{i-1}^{\mathrm{\Δ}}---\left(1\right)$

C wherein, A branch represents color and opacity, light is worn in the process of penetrating in volume data, samples according to a fixed step size, has formula (2):

t＝t _start+d*delta (2)

T wherein _StartBe the intersection point initial position of light and scene, d is the radiation direction vector, and delta then is step-length.The method is accelerated based on GPU fully, has greatly accelerated rendering speed, obtains a plurality of two-dimentional rendering result, such as Fig. 3 (only having illustrated here).

Step (2), the two-dimensional effects of step (1) being desired to make money or profit process correlation technique with image, mainly is Canny operator and Contour Detect algorithm carry out characteristic curve to X-Y scheme extraction.The Canny operator also is the single order operator, and essence is to do level and smooth computing with an accurate Gaussian function, then with locating the derivative maximal value with the first order differential operator of direction.Concrete solution procedure is as follows:

A) use the Gaussian filter smoothed image, available formula (3):

$h(x,y,\mathrm{\&sigma;})=\frac{1}{{2\mathrm{\&pi;\&sigma;}}^2}{\mathrm{\&theta;}}^{-\frac{x+\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00003473922700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{{2\mathrm{\&sigma;}}^2}}$

g(x,y)=h(x,y,σ)*f(x,y) (3)

Level and smooth to original image f (x, y) of h (x, y, σ) expression wherein, g (x, y) be the image after smoothly, " * " represents convolution.

B) with single order local derviation finite difference compute gradient amplitude and direction

C) gradient magnitude being carried out non-maximum value suppresses

D) usefulness dual threshold algorithm detects and is connected the edge

After two-dimensional effects being desired to make money or profit with the Canny rim detection, the recycling outline line detects (Contour Detect) algorithm and these unique points is further calculated the available characteristic curve that extracts, design sketch such as Fig. 4, Fig. 5, the line of same color is represented as a characteristic curve among Fig. 5.

Step (3) two dimensional character line is the line with obvious vision meaning in two dimension, and we think that these lines are that the line of three-dimensional is in the drop shadow effect of two dimension, so need to find the characteristic curve of every two dimensional character line corresponding three-dimensional.Such as Fig. 4 (a), wherein under the X-viewpoint, calculate the characteristic curve (shown in the yellow line) of a two dimension, we need to calculate curve corresponding to this line (shown in the red dotted line) in three-dimensional.Yet we notice, a two-dimensional points is the projection of a lot of three-dimensional point, that is to say that a some correspondence three-dimensional a lot of points, the green point shown in Fig. 4 (a).

This problem can be converted into global minimization's problem, and namely so that the overall Least-cost (shortest path) in all stages, this problem can be converted into shortest route problem, and shown in Fig. 4 (b), red path is the path that we need.Find the solution if use force merely, then need O (n! ) complexity.We can find the solution this problem at dynamic programming algorithm, and following equation is arranged:

Dist ^[k][x]=min{Dist[y]+Weight (x, y) }, y ∈ k+1 stage node (4)

Dist[x wherein] expression node x is to the shortest path length of terminal note, and Weight (x, y) represents node x, path between the y is because a three-dimensional point has positional information, opacity information, colouring information, these are the factors that need to consider in minimization problem.So can have:

Weight(x,y)=w1*|x.col-y.col|+w2*|x.pos-y.pos| (5)

Wherein col and pos represent respectively color RGB and opacity and locus, and w1 and w2 represent weight.We are by the CUDA framework based on GPU, and every two-dimensional line distributes a thread to be responsible for calculating corresponding three-dimensional line, has so greatly accelerated counting yield, effect such as Fig. 5.

Step (4), can see that the three-dimensional feature line that tentatively obtains can reflect preferably the structure of volume data, but these lines is also many and mixed and disorderly, therefore need to be to the further cluster of these lines.We adopt the method for Convolution Surface, define a scalar field, and this scalar field is weighed the curve density in its space certain space scope, and namely curve is many and few.Convolution Surface is defined as follows: establish P ∈ R ³, f:R ³→ R is a potential function, g:R ³→ R is the ternary function of the some geometry backbones of expression,

$g\left(P\right)=\left\{\begin{array}{cc}1,& P\&Element;\mathrm{\&Omega;}\\ 0,& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

Ω is skeleton, some Q ∈ Ω, and the potential function that is produced by skeleton Ω is defined as:

F(P)＝∫ _Ωg(Q)f(P-Q)dΩ (7)

Being write as the convolution form is

$F\left(\mathrm{PP}\right)=(f\&CirclePlus;g)\left(P\right)---\left(8\right)$

Our potential function of sampling is gaussian kernel function, as shown in Equation (9):

$f\left(x\right)=\frac{1}{\mathrm{\&sigma;}\sqrt{2\mathrm{\&pi;}}}{\mathrm{\&theta;}}^{-\frac{{(x-\mathrm{\&mu;})}^2}{{2\mathrm{\&sigma;}}^2}}---\left(9\right)$

When making up this scalar field, for each sampled point P sets up the sampling ball that radius is R, when having curve to pass through this ball, can carry out integration operation to this curve, such as formula (10), | p-q| represents 2 Euclidean distance.

$f\left(P\right)={\&Integral;}_{\mathrm{\&Omega;}}\frac{1}{\mathrm{\&sigma;}\sqrt{2\mathrm{\&pi;}}}{\mathrm{\&theta;}}^{-\frac{{|F-Q|}^2}{{2\mathrm{\&sigma;}}^2}}\mathrm{d\&Omega;}---\left(10\right)$

And according to this scalar field, keep the large sampled point of scalar value, give over to further abbreviation.Take effect the fruit Fig. 6, wherein the whiter point of color represents that this point curve density value is higher, namely more curves are at this near zone.

Step (5), for step (4) the interior sampled point of must showing up, still more, we adopt thinning algorithm that these are put further abbreviation, therefrom extract the point that can react the volume data structure.Thinning algorithm is similar to the process of " stripping onion ", through peeling off from level to level, from original image, remove some points, but still to keep original shape, until obtain the skeleton of image, it can be used for two dimensional image and three-dimensional data, for the purpose of the present invention, whether a sampled point should be deleted, depends on following condition:

A) this some point on surface whether, this judgement is the space 26-neighbours' attribute according to this point.

B) this point can not be a curve starting point or terminal point.

C) delete this point and can not change Euler characteristic (Euler characteristic), for example, delete this point and can not cause former data to produce the cavity.

D) delete this point and can not change UNICOM's associated number, associated number refers in the 3*3*3 field of this point, with the number of being connected the graphics component that a little connects.

If satisfy above condition, then we can delete this sampled point, until all points all can not delete, so remaining point is exactly the point on our center line that needs.Fruit Fig. 7 takes effect.

Point after the refinement that the corresponding step of step (6) (5) is tried to achieve can access this center line, but these somes link information not, we adopt minimal spanning tree algorithm to come these points are connected, and step is as follows:

A) at first for these points make up a figure G (V, E), V represents sampled point, and E represents the annexation of sampled point.The weight on limit represents the Euclidean distance of two points, if two some distances are excessive, then thinks unconnected.

B) utilize the Prim algorithm to make up minimum spanning tree T for figure G, in the method, this figure is undirected unconnected graph, so have many trees.

C) according to these minimum spanning trees, find leaf node and bifurcation, and traverse tree, calculate the node of each curve process, thus formation curve.

Suppose wherein certain minimum spanning tree shown in Fig. 8 (a), then wherein red point then is bifurcation and leaf node, then can segmentation creating curve path:

Curve 0: comprise node 1-2-3; Curve 1: comprise node 3-4-5; Curve 2: comprise node 3-6-7; Curve 3: comprise node 1-8; Curve 4: comprise node 8-9-10; Curve 5: comprise node 8-13-14; Curve 6: comprise node 8-11-12.Design sketch is seen Fig. 8 (b).

The curve that step (7) obtains for step (6), owing to be each point to be connected obtain, such curve is sufficiently oily, and we adopt B-spline curves that it is carried out match, and what we adopted is the Bezier curve.

Suppose to provide position, n+1 reference mark: P _k=(x _k, y _k, z _k), k can get 0 to n here.These are named a person for a particular job to mix and produce lower column position P (u), are used for describing P ₀And P _nBetween approach the path of Bezier polynomial function:

$P\left(u\right)={\mathrm{\&Sigma;}}_{k=0}^n{P}_k{\mathrm{BEZ}}_{k,n}\left(u\right),0\&le;u\&le;1---\left(11\right)$

Bezier mixed function BEZ _{K, n}(u) be the Bernstein polynomial expression:

BEZ _k，n(u)＝C(n，k)u ^k(1-u) ^n-k (12)

Here, parameters C (n, k) is binomial coefficient:

$C(n,k)=\frac{n|}{k\left|(n-k)\right|}---\left(13\right)$

In the present invention, originally the point on the curve is equivalent to the reference mark of Bezier curve, then utilizes formula (11) (12) (13) interpolation calculation to go out more point, can generate curve Paint Gloss like this, so that the drafting effect is more true to nature, design sketch is seen Fig. 9.

Wherein, step (1) (3) (4) (7) is calculated all and is realized with CUDA, can utilize the powerful computing power of GPU, has greatly improved efficient.

The software platform that the realization of this paper algorithm is used is Microsoft visual studio2010 and OpenGL, has used CUDA to accelerate the counting yield of parallel algorithm.Hardware platform is 3.4GHz Inter (R) Core (TM) i7-2600CPU, 4GB internal memory and NVIDIA GeForce GTX570GPU.The method design sketch as shown in Figure 9.Output screen resolution is 512*512, the three-dimensional size of volume data is 256*256*128, wherein utilize light projecting algorithm to carry out direct volume drawing, and utilize time of Canny operator and outline line detection algorithm Two-dimensional characteristic curve the chances are 0.70s, utilize dynamic programming to find the solution three-dimensional feature line time corresponding to two-dimensional line the chances are 1.22s, utilize the Convolution Surface method to make up the density field time probably for 5.26s, wherein refinement is carried out in the field, and the time of last match is 1.60s probably.

Claims (5)

1. a volume data non-photorealistic rendering method of accelerating based on GPU totally comprises the steps:

(1) from a plurality of viewpoints, utilize Direct Volume Rendering Techniques that volume data is drawn, obtain a plurality of rendering result, namely generate two dimension and play up picture;

(2) utilize Canny operator detected characteristics point, outline line detection method algorithm carries out extract minutiae and characteristic curve to two-dimentional rendering result, and definition global minimization rule, finds the solution three-dimensional character line corresponding to two dimensional character line;

(3) for characteristic curve being reached the purpose of cluster, utilize Convolution Surface technology defining scalar field, weigh the curve density in the spatial sampling space of points zone, and this is carried out Refinement operation, and utilize annexation to obtain curve;

(4) curve of step (3) carries out the B-spline curves match, and finishes stylization and draw.

2. the volume data non-photorealistic rendering method of accelerating based on GPU according to claim 1, it is characterized in that step (1) comprising: from X, Y, the positive and negative direction of principal axis of Z arranges 6 cameras, volume data is carried out direct volume drawing, adopt Ray Casting light projection method, this process can realize at GPU, utilizes and calculates the hardware-accelerated of unified equipment framework CUDA, greatly improve rendering speed, and utilize PBO, FBO technology render to texture, and be saved in two-dimentional rendering result.

3. the volume data non-photorealistic rendering method of accelerating based on GPU according to claim 1, it is characterized in that step (2) comprising: in two-dimentional rendering result, utilize Canny operator and Contour Detect method picture to be carried out the extraction of characteristic curve, acquisition is at the characteristic curve of two dimension, these characteristic curves are that the characteristic curve of three-dimensional is in the drop shadow effect of two dimension, so need to find the characteristic curve of every two dimensional character line corresponding three-dimensional, and definition two dimensional character line is to global minimization's rule of three-dimensional feature line, this rule comprises color, opacity, the locus factor, and utilize the dynamic programming on the GPU to find the solution, obtain a series of three-dimensional feature lines;

4. the volume data non-photorealistic rendering method of accelerating based on GPU according to claim 1, it is characterized in that step (3) comprising: for can be to the purpose of often and relatively more assorted three-dimensional feature line cluster, adopted the method for Convolution Surface, the defining scalar field, the density that characterizes an inner curve is many and few; According to this scalar field, keep the large sampled point of scalar value, and utilize thinning method to obtain the sampled point of further abbreviation, to between these sampled points apart from design of graphics G, and ask the minimum spanning tree T of figure G, and detect leaf node and bifurcation according to T, thus further formation curve.

5. the volume data non-photorealistic rendering method of accelerating based on GPU according to claim 1, it is characterized in that step (4) comprising: the curve to step (3) carries out the refinement operation, adopt B spline-fitting method, point on the virgin curve is as the reference mark, calculate more interpolation point, obtain B-spline curves, and these curves are drawn, so that curve is more smooth.

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