CN101763649B - Method for drawing enhanced model contour surface point - Google Patents

Abstract

A surface point drawing method that enhances the outline of the model. In the preprocessing stage, the space coordinates, normal vectors, radius, and color information of the sampling points are read and stored, and the splat template is generated according to the given number of layers, and then the threshold value specified by the user is used. Divide the sampling points into space, and obtain the k nearest neighbors of each sampling point, and finally use the k nearest neighbors to obtain the curvature of each point by the coordinate transformation method. In the running stage, first judge whether it is a contour point according to the angle between the normal vector of the sampling point and the line of sight, and if so, calculate a series of vertex coordinates that form a surface splat centered on the sampling point. If it is not a contour sampling point, use the Surface Splatting algorithm to draw: solve the Jacobian matrix of the 2D space mapping at the sampling point; then perform visibility judgment and fusion on each splat projected to the screen; use the lighting model and shade processing to calculate Spatial light intensity of a certain pixel on the screen; finally normalized. The rendering speed is fast, it can better meet real-time needs without hardware acceleration, and the rendering quality is high.

Description

A Surface Point Rendering Method for Enhanced Model Contour

technical field

The invention belongs to the technical field of computer virtual reality and computer graphics, in particular to a point drawing method in realistic drawing of computer graphics.

Background technique

Computer graphics is a subject gradually formed by applying computers to the display and rendering of graphics. From its birth to the present, it has played an increasingly important role in many fields and is playing an increasingly important role. Realistic graphics rendering is an important part of computer graphics (see Wang Jian, Discrete Point Rendering Method for Realistic Graphics, Jilin University, Master Thesis, 2006). It combines mathematics, physics, computer science and other scientific knowledge to generate photo-realistic graphics on computer graphics devices.

According to the different drawing primitives, realistic graphics drawing is divided into geometric primitive-based rendering (GBR), image-based rendering (IBR) and point-based rendering (PBR) (see Zhang Wu, point-based rendering Research and Application of Technology, Zhejiang University, Master Thesis, 2006). GBR is a traditional graphics rendering technology. It usually decomposes the scene model into triangular patches. Although it can generate highly realistic and realistic graphics, as the complexity of the object model continues to increase, the number of triangular patches representing the model also increases sharply. Its processing creates bandwidth bottlenecks and excessive floating-point calculations. IBR transforms, interpolates, and deforms images close to the viewpoint or line of sight through pre-generated images, so as to quickly obtain the scene image at the current viewpoint. It has nothing to do with the complexity of the scene, but the disadvantage is that the preprocessing time is long, a large amount of storage space is required, and obvious artifacts will be produced when the viewpoint moves. PBR performs modeling, drawing, and other graphics processing on a point-by-point basis. It abandons the traditional triangular patch representation method, only records the point information, and directly reconstructs the final image from these points. With the deepening of research and application, models and geometric scenes become more and more complex. Point elements are used as the most basic and simplest primitives. There is no need to store and maintain topology structures, which is convenient for resampling and has less redundancy. The advantages of small storage space and fast drawing speed.

Point-based rendering techniques use discrete 3D dense point clouds to represent model surfaces, and the goal is to use point elements as primitives to reconstruct a continuous, visually equivalent model surface in 3D dense point clouds. Suitable for drawing models with highly complex surface geometry or complex surface lighting details. The current mature point drawing technology has a method based on drawing speed: QSplat (Szymon Rusinkiewicz, Marc Levoy, QSplat: A Multiresolution PointRendering System for Large Meshes, Siggraph 2000, New Orleans, LA USA), which uses a hierarchical enclosing ball data structure, using Draw on fast viewshed clipping and backface culling and level of detail.

Dachsbacher et al. proposed a method to serialize the hierarchical structure into a linear array (see C.Dachsbacher, C.Vogelgsang, and M.Stamminger.Sequential point trees.Siggraph2003 Conference Proceedings), on this basis, the drawing algorithm is divided into hierarchical The traversal of the tree is converted into the traversal of the linear array, thus realizing the GPU hardware acceleration of QSplat. Method based on rendering effect: Pfister et al. first proposed to use surfel (see C.Dachsbacher, C.Vogelgsang, and M.Stamminger.Sequential point trees. Siggraph 2003 Conference Proceedings) to represent sampling points. Each point is represented as a disk tangential to the point, and the disks overlap each other to form a compact object surface. zwicker et al. applied the idea of signal processing to the drawing of points, and proposed the ellipse weighted (EWA) algorithm, which obtained high-quality drawing results (see Matthias Zwicker, Pfister.Surface Splatting.ACM Siggraph2001, Los Angeles, CA, USA) .

In summary, the speed-based method does not consider transparency and anti-aliasing issues, and the rendering quality is average, while the EWA algorithm with high-quality rendering effects is based on software implementation, so it does not have real-time performance.

Contents of the invention

The technology of the present invention solves the problem: Aiming at the problems of aliasing and drawing efficiency in traditional point drawing, a surface point drawing method for enhancing the model outline is provided, which can reconstruct a continuous surface that retains high-frequency signals at the edge of the model, and at the same time It can better meet the requirements of real-time rendering.

In order to accomplish the purpose of the invention, the technical solution adopted by the present invention is: in the preprocessing stage, at first read and store information such as the spatial coordinates, normal vectors, radius, and color of the sampling point, and generate surface elements in the screen space according to the given number of layers. projection, that is, the splat template, and then space-divides the cuboid bounding box formed by the spatial coordinates of the sampling points according to the threshold specified by the user, and calculates the k neighbors of each sampling point according to the small cube grid obtained by the space division in the previous step. Finally, using k-nearest neighbors, the curvature of each sampling point, including the curvature of contour sampling points and non-contour sampling points, is solved by the coordinate transformation method.

In the running phase, when the viewpoint changes, first judge whether the sampling point is a contour point according to the angle between the normal vector of the sampling point and the line of sight. If so, combine the curvature of a contour sampling point obtained in the preprocessing stage to calculate a series of components. The vertex coordinates of the surface splat (the projection of the surface element in the screen space) centered on this sampling point. If it is not a contour sampling point, use the Surface Splatting algorithm to draw: solve the Jacobian matrix of the 2D space mapping at the sampling point; determine the visibility of each splat projected to the screen, and then for the color obtained in the first step of preprocessing , normal vector, and spatial coordinates are fused; the spatial light intensity of a certain pixel on the screen is calculated by using the illumination model and shading processing; finally, normalization is performed to eliminate the influence of Gaussian function interception and uneven distribution of sampling points on the image.

Compared with the existing method, the point drawing method of the present invention has the advantages of fast drawing speed, which can better meet real-time needs without hardware acceleration; high drawing quality, and can retain the high frequency of the edge of the model outline while anti-aliasing Signal. First of all, the Surface Splatting algorithm mainly consumes time in calculating the shape and size of the splat projected on the screen in real time. The drawing speed can be greatly improved by generating the splat template during preprocessing and selecting the template at runtime. Secondly, the Surface Splatting algorithm uses ellipse weighted average The idea is to get a high-quality splat fusion effect. Finally, the surface splat is used to draw the edge. The curvature can better preserve the details of the model edge, and the aliasing phenomenon is improved compared with the plane splat approximated by the tangent plane.

Description of drawings

Fig. 1 is the overall flowchart of the present invention;

Fig. 2 is the parameter relation of space splat and screen of the present invention;

Fig. 3 is the shape of the curved surface splat of the present invention;

Fig. 4a and Fig. 4b are the model of adding illumination calculation of the present invention;

Fig. 5 is the comparative figure of drawing effect with traditional algorithm among the present invention; A is the model drawn, and the area circled is the comparison part of traditional algorithm and the method of the present invention, and b is traditional algorithm;

Fig. 6 is the spatial coordinates, normal vector, radius and color information of the surfel centered on the sampling point in the present invention;

Fig. 7 is that the cube among the present invention is the (3*3*3) grid schematic diagram that comprises the small cube where the sampling point is located;

Fig. 8 is a schematic diagram of the calculation of the depth value of the fragment in the present invention;

FIG. 9 is a schematic diagram of visibility judgment calculation in the present invention.

Detailed ways

As shown in FIG. 1 , the implementation process of the present invention includes two parts: a preprocessing stage and a runtime stage.

The first stage: the preprocessing part. It includes five steps of reading sampling points, template generation, space division, solving k-nearest neighbors, and calculating curvature.

Step 1: Read the sampling point.

Read and store the space coordinates, normal vector, radius, color and other information of the sampling point. The position and orientation of this point on the model surface can be known through the space coordinates and normal vectors of the sampling point in the object coordinate system. The radius of the sampling point can ensure that the splat (the projection of the surface element on the two-dimensional screen) covers each other without holes, and the color information can be changed. Well presented model details.

Figure 6 shows the space coordinates, normal vector, radius and color information of the surface element (Surfel, Surface elements, surface elements) centered on the sampling point, and the radius is large enough to ensure that the splats projected to the screen cover each other without holes .

The second step: template generation.

In order to eliminate the holes between the sampling points, the sampling points are represented as surfels (reconstruction kernels) in the object space, and this step is used to calculate the shape of the space splat projected to the screen. Figure 2 shows the splat shape of the tangent plane projected onto the screen. According to the number of layers specified by the user, the radius of the sampling points read and stored in the first step is divided into n ₁ , the larger n ₁ is, the more splat templates are, and the better the drawing effect is; the radius r _i of the i-th layer =( r _max -r _min )/n ₁ i, r _max , r _min respectively represent the maximum radius and minimum radius of the sample point read, the angle between the tangent plane of the sample point and the screen is θ, 0≤θ<90, and θ Divide it into n2 intervals, the angle between the ellipse and the x-axis of the screen space is ω, 0≤ω<180, divide ω into n3 intervals, then n1 n2 n3 splat templates can be generated, the process of template generation is as follows:

(1) Traversing the n1 intervals generated by the radius, for the i-th interval of the radius, perform the operation of the second step;

(2) For n2 and n3 intervals, traverse with the step size of deltang, and for the jth interval in n2 and the kth interval in n3, execute the operation of the third step to generate a template;

分别为采样点P法向量的投影在屏幕空间x、y轴的分量；(3) For a certain pixel point (x, y) in the matrix whose coordinates of the lower left corner and the upper right corner are respectively (-r _i , -r _i ) and ( _ri , r _i ), if it satisfies (x·cosω _k -y·sinω _k ) ² /(r _i ·cosθ _j ) ² +(y·cosω _k +x·sinω _k ) ² /r _i ² ≤1, then this pixel is covered by splat, traversing all pixels in the matrix , which is to calculate the shape of this ellipse; the angle between the ellipse and the x-axis of the screen space $\mathrm{\&omega;}=\arctan \frac{{\stackrel{\&Right\; Arrow;}{\mathrm{no}}}_{\mathrm{p\&beta;x}}}{{\stackrel{\&Right\; Arrow;}{\mathrm{no}}}_{\mathrm{p\&beta;y}}}$ ,in

Respectively, the components of the projection of the normal vector of the sampling point P on the x and y axes of the screen space;

(4) Perform steps (1), (2), and (3) in a loop until all intervals have been traversed once, and all splat templates can be generated

The third step: space division.

The cuboid bounding box of the sampling point is obtained from the spatial coordinates read in the first step. According to the side length a specified by the user, this bounding box is divided into m·n·l small cubes, m, n, and l are x, y respectively , the number of small cubes on the z-axis; the hash table HashList[m n l] that uses the chain address method to deal with conflicts stores the points in each cube; solves the index of each sampling point in the x, y, and z directions i is n _x , n _y , n _z , where n _x represents the index of a small cube where a sampling point is located in the x direction, n _y represents the index of a small cube where a sampling point is located in the y direction, and n _z represents a certain The index of the small cube where the sampling point is located in the z direction, where 0≤n _x <m, 0≤n _y <n, 0≤n _z <l, stored in

Step 4: Solve k-Nearest Neighbors

Find all adjacent points in the relevant grid (3*3*3) of the small cube where a sampling point is located, perform insertion sorting according to the order of the distance between the sampling point and the adjacent points from small to large, and select the first k points to store in the adjacency In the table, k here is set by the user, and is used to calculate the curvature of the local area in the following steps, and is generally set to 20--30.

As shown in Figure 7, this cube is a (3*3*3) grid including the small cube where the sampling point is located, and the central small cube is the cube where the sampling point is located. Knowing the index number of this small cube, you can know (3* 3*3) Indexes of all small solids in the grid, the spatial coordinates of all adjacent points in these small solids can be found in the hash table, so the distance between the sampling point and the neighboring points can be calculated.

Step 5: Calculate the curvature.

The process of calculating the curvature according to the coordinate transformation method is as follows:

(1) Project k neighboring points onto the tangent plane of the sampling point, select the unit vector from the sampling point to the farthest projection point as the u axis, and calculate the vector v by cross multiplying u and the normal vector, so as to calculate the u of the neighboring point , v value and the coordinate value h in the direction of the normal vector;

(2) According to the u, v and h coordinate values, in the local adjacent area of the sampling point, use the least square method to carry out paraboloid fitting. The fitted paraboloid is s(u, v)=au^2+bu*v+cv^2, and the coefficients a, b, and c can be obtained by using the least square method;

(3) The average curvature of the fitted paraboloid at the origin is the sampling point curvature, and the average curvature=a+c;

The second stage: the runtime part. First judge whether it is a contour sampling point. If the angle between the normal vector and the line of sight is within the range of [ε, 90], it is a contour point. Otherwise, it is not a contour point and needs to be processed separately. Therefore, it is divided into two sub-stages: surface splat drawing and Surface Splatting drawing.

The first sub-stage: surface splat drawing. Figure 3 shows the shape of the surface splat.

Step 1: Calculate the vertices of the surface splat.

，此顶点表示它是第i_s层，第k_s条边上的顶点，此处的i_s、k_s是用户所设，一般i_s、k_s越大，表示曲面splat的复杂度越高，绘制效果越好。根据预处理时计算出的曲率c，局部坐标为，其中For a vertex of the surface splat

, this vertex indicates that it is the vertex on the i _s layer and the k _s edge, where i _s and k _s are set by the user, generally the larger the i _s and k _s , the higher the complexity of the surface splat , the better the drawing effect. According to the curvature c calculated during preprocessing, the local coordinates are ,in

表示第i_s层的半径， $\mathrm{\&phi;}\left({\mathrm{rs}}_{i_s}\right)=e^{-{\left(\frac{{\mathrm{rs}}_{\mathrm{is}}}{c}\right)}^2}$ n _s represents the total number of sides of the surface splat,

Indicates the radius of the i _s layer, $\mathrm{\&phi;}\left({\mathrm{rs}}_{i_{\mathrm{the\; s}}}\right)=e^{-{\left(\frac{{\mathrm{rs}}_{\mathrm{is}}}{c}\right)}^2}$

Step two: texture mapping.

的纹理坐标为

其中n_s代表曲面splat的总边数。vertex

The texture coordinates of

where n _s represents the total number of sides of the surface splat.

The second sub-stage: Surface Splatting (this method was proposed by Zwicker, which is a general term in this field and has no Chinese explanation) drawing. It includes four steps of determining the resampling kernel, Splatting, lighting calculation and normalization.

Step 1: Determine the resampling kernel.

The resampling kernel is the convolution of the reconstruction kernel projected onto the screen and the low-pass filter. Because the closure of the elliptic Gaussian function under affine transformation and convolution are both expressed, the resampling kernel can also be expressed in the form of an elliptic Gaussian function, and a better inversion can be achieved by selecting an appropriate variance matrix. Aliasing effect.

The expression of the elliptic Gaussian function is: $\mathrm{Gv}\left(x\right)=\frac{1}{2\mathrm{\&pi;}{\left|V\right|}^{\frac{1}{2}}}{e}^{-\frac{1}{2}{x}^T{V}^{-1}x}$

According to the properties of the elliptic Gaussian function, the expression of the resampling kernel is:

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{{\mathrm{<span\; class="notranslate">\; JVJ</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}}{<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; G</span>}}_{{\mathrm{<span\; class="notranslate">\; JVJ</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

In the above formula, J is the Jacobian matrix mapped from the object space to the screen space, and V is the covariance matrix at the sampling point, which is generally expressed as $V=\left(\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H200910243262XE00026.png"\; state="\{\{state\}\}">r</figure-callout>}}^2& 0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H200910243262XE00026.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\end{array}\right)$ , r is the radius of the sampling point, I is the identity matrix, x is the screen pixel covered by the splat, m(u) is the coordinate of the sampling point projected to the screen space, r' represents the spatial reconstruction kernel after the projection change, h Represents the low-pass filter function of the screen space, the elliptic Gaussian function is similar to a two-dimensional normal distribution, and is represented by r ² in all covariance matrices.

The second step: Splatting (the process of projecting spatial elements onto the screen to form a splat)

This step determines the visibility determination and fusion of each splat projected onto the screen pixels. The process is as follows:

分别为采样点P法向量的投影在屏幕空间x、y的轴的分量，在运行时计算这些值所属n1、n2、n3中的区间，以区间i、j、k为例，以i·n2·n3+j·n3+k+n1为索引查表即可得到此splat覆盖的像素点及权重法向量；n₁、n2、n3分别代表半径、采样点切平面与屏幕夹角θ，0≤θ＜90、椭圆与屏幕空间x轴的夹角ω0≤ω＜180)的区间数。n₁一般为用户设定，n2、n3通过用户设定的遍历步长deltang确定，n2＝90/deltang，n3＝180/deltang。(1) Selection of templates. It is not necessary to calculate the shape and size of the splat projected on the screen in real time, but to select the template generated by preprocessing: reconstruct the radius of the kernel according to the object space, the angle θ between the normal vector and the line of sight, and project the normal vector on the x and y axes the arctangent of the component $\mathrm{\&omega;}=\arctan \frac{{\stackrel{\&Right\; Arrow;}{\mathrm{no}}}_{\mathrm{p\&beta;x}}}{{\stackrel{\&Right\; Arrow;}{\mathrm{no}}}_{\mathrm{p\&beta;y}}}$ ,in

They are the components of the projection of the normal vector of the sampling point P on the x and y axes of the screen space, and calculate the intervals in n1, n2, and n3 to which these values belong at runtime. Take the intervals i, j, and k as examples, and take i·n2 n3+j n3+k+n1 is the index lookup table to get the pixels covered by this splat and the weight normal vector; n ₁ , n2, n3 represent the radius, the angle θ between the sampling point tangent plane and the screen, 0≤ θ<90, the angle between the ellipse and the x-axis of the screen space ω0≤ω<180) interval number. _n1 is generally set by the user, n2 and n3 are determined by the traversal step deltang set by the user, n2=90/deltang, n3=180/deltang.

(2) Use the z-threshold method to determine visibility: Calculate the z-depth value of the covered pixel point along the line of sight when the splat is projected onto the screen. According to the perspective projection transformation model, the screen fragment can be back-projected to the sampling point Pk The point Qp is obtained on the space Surfel. The distance between Qp and viewpoint C is the desired depth value, as shown in Figure 8. If z and the depth value stored in this pixel are within a certain threshold range, then fusion will be performed. If it is less than the pixel depth, it can be regarded as occlusion, that is, use other The color and weight replace the current color and alpha value of the opacity of the pixel; otherwise, it is not processed, and the processing process of the visibility judgment is shown in Figure 9.

(3) Fusion. The texture, normal vector, and space coordinates of a pixel are all weighted averages of the corresponding information of each splat projected to a certain pixel.

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

ρ _k (x) is the resampling kernel, which represents the weight, and ω _k can be replaced by the texture color, normal vector, and space coordinates at the pixel point x.

The third step: lighting calculation.

According to the Phong lighting model, the light intensity on the pixel can be calculated by using the normal vector and space coordinates of the pixel obtained in Splatting. Replacing traditional per-splat lighting calculations with per-pixel lighting calculations can not only make the surface lighting of the model smoother and get better rendering effects, but also the delayed shading technology can avoid processing points on invisible splats and improve rendering efficiency .

According to the Phong lighting model I=I _a K _a +I _p K _d (L·N)+I _p K _s (R·V) ⁿ , where I _a K _a is ambient light, I _p K _d (L·N) is the scattered light, I _p K _s (R·V) ⁿ is the specular reflection light, and n is the reflection index (the value is generally 50-100). The larger the number, the smoother the surface of the object, which can be used to define the material of the object. Use the pixel normal vector obtained after filtering in the Splatting process to represent N, and use the filtered space coordinates to calculate V (respectively replace the formula (1) ω _k with the normal vectors and space coordinates of each overlapping splat to calculate the filtered normal vector and space coordinates), and then calculate the light intensity I on this pixel according to the Phong illumination model. Among them, the parameters I _a and I _p in the illumination model are ambient light intensity and incident light intensity respectively, and K _a , K _d , and K _s are ambient light reflection coefficient, scattered light reflection coefficient and specular reflection coefficient respectively. Simulation environment is set up (in this experiment of the present invention, K _a value 0.2, K _d and K _s value 0.5)

Replacing traditional per-splat lighting calculations with per-pixel lighting calculations can not only make the surface lighting of the model smoother and get better rendering effects, but also the delayed shading technology can avoid processing points on invisible splats and improve rendering efficiency .

Step 4: Normalize

为覆盖像素点x的各个splat的权重和。In order to eliminate the influence of Gaussian function interception and uneven distribution of sampling points on the image, it is necessary to perform normalization at the end of the algorithm. The final texture value of screen pixel point x $g\left(x\right)=\underset{k\&Element;N}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_k\frac{{\mathrm{\&rho;}}_k\left(x\right)}{{\mathrm{\&Sigma;}}_{j\&Element;N}{\mathrm{\&rho;}}_j\left(x\right)}$ , where ω _k is the texture information of pixel k, generally color, ρ _k (x) is the weight of pixel k at pixel x after the space splat of pixel k is projected to the screen,

is the weight sum of each splat covering pixel x.

Aiming at the problem of aliasing and drawing efficiency in traditional point drawing, the present invention provides a real-time surface that enhances the model outline by combining Surface Splatting with high-quality drawing effect and surface splat that is closer to the local area than surfel Point drawing method. By generating templates in preprocessing, drawing surface sampling points at runtime by Surface Splatting, and drawing contour sampling points by surface splatting, a continuous surface that retains high-frequency signals at the edge of the model can be reconstructed, and at the same time, it can better meet the requirements of real-time rendering.

In Fig. 4, a is the traditional algorithm without calculating illumination, and Fig. b is the method of the present invention. From the comparison of the above figure, it can be seen that for a colorless model, the traditional algorithm that does not calculate the illumination only draws a single-color area, while the method of the present invention can well represent the illumination and light and shade changes on the surface of the model, increasing the Realistic and detailed features of surfaces.

In Fig. 5, a is the drawn model, the circled area is the comparison part between the traditional algorithm and the method of the present invention, and b is the traditional algorithm. It can be seen from the comparison that the present invention utilizes the advantages of the curved surface splat to better eliminate the jagged phenomenon and enhance the profile features of the model.

The contents and contents not elaborated in the present invention are common knowledge of those skilled in the art.

The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (7)

1. surface point method for drafting that strengthens model silhouette is characterized in that: be divided into pretreatment stage and operation phase, wherein:

Step in pretreatment stage is:

(1) at first reads also volume coordinate, normal vector, radius and the colouring information of store sample point;

(2) generate the projection of bin at screen space, i.e. splat template according to given hierachy number;

(3) according to user's specified threshold value the rectangular parallelepiped bounding box that the volume coordinate of sampled point forms is carried out spatial division again;

(4) the cube grid that obtains according to spatial division solves k neighbour of each sampled point;

(5) utilize the k neighbour, solve each sampled point, comprise the curvature of configuration sampling point and non-configuration sampling point by coordinate transformation method;

Step in the operation phase is:

(1) when viewpoint changes, judges according to sampled point normal vector and sight line angle whether this sampled point is point, if then carry out the step (2) of operation phase, otherwise carry out the step (3) of operation phase;

(2) combine the curvature of certain configuration sampling point that pretreatment stage obtains, calculating a series of compositions is the apex coordinate of the curved surface splat at center with this sampled point;

(3) utilize Surface Splatting algorithm to draw: the Jacobi matrix of finding the solution the 2D spatial mappings of sample point; Again each splat that projects to screen is carried out observability and judge, (1) step obtained during for pre-service color, normal vector, volume coordinate merge; Utilize illumination model and light and shade to handle the spatial light intensity that calculates the screen pixel, carry out normalization at last.

2. a kind of surface point method for drafting that strengthens model silhouette according to claim 1 is characterized in that: the process according to given hierachy number generation splat template in the step of said pretreatment stage (2) is following:

A. according to the radius information in the step (1) of pretreatment stage, the hierachy number n given by the user is divided into n1 interval with radius, and sampled point section and screen angle are θ; 0≤θ＜90; θ is divided into n2 interval, and oval angle with screen space x axle is ω, 0≤ω＜180; ω is divided into n3 interval, then can generates n1n2n3 splat template;

I among the b.n1 is interval, and the j among the n2 is interval, and the k among the n3 is interval, and the generative process of its splat template is following: by the projection theory of object space to screen, long axis of ellipse is the radius r of space splat _i, sampled point section and screen angle are θ _j, oval angle with screen space x axle is ω _k

C. be respectively (r for lower left corner coordinate and upper right corner coordinate _i,-r _i), (r _i, r _i) matrix in a certain pixel (x, y), if it satisfies (xcos ω _k-ysin ω _k) ²/ (r _iCos θ _j) ²+ (ycos ω _k+ xsin ω _k) ²/ r _i ²≤1 this pixel is capped, and all pixels in the Ergodic Matrices promptly calculate this oval shape;

D. for other intervals, the splat template also generates according to the method.

3. a kind of surface point method for drafting that strengthens model silhouette according to claim 1 is characterized in that: following to the process that sampled point carries out spatial division according to user's specified threshold value in the step of said pretreatment stage (3):

A. obtain the rectangular parallelepiped bounding box of sampled point by the volume coordinate that reads;

B. according to the length of side a of user's appointment, this bounding box is divided into mnl small cubes, m, n, l are respectively the number of small cubes on x, y, the z axle;

C. store the point in each small cubes with the Hash table HashList [mnl] that adopts chain address method to handle conflict, finding the solution each sampled point is n at the index of x, y, z direction _x, n _y, n _z, store into

Chained list in, so far the sampled point in each small cubes all is stored in the corresponding chained list, has promptly accomplished spatial division.

4. a kind of surface point method for drafting that strengthens model silhouette according to claim 1 is characterized in that: it is following to solve the process of curvature of certain sampled point by coordinate transformation method in the step of said pretreatment stage (5):

A. k neighbor point projected on the sampled point section; Choose sampled point to the vector of unit length of subpoint direction farthest as the u coordinate axis; Through u vector and normal vector multiplication cross compute vector v as the v coordinate axis; Thereby calculate the component of neighbor point on u, v coordinate axis, i.e. u, v coordinate figure and at the coordinate figure h of normal vector direction;

U, v and the h coordinate figure of k the neighbor point that b. obtains above the basis utilize least square method to carry out parabolic match;

C. the parabola that simulates is in the i.e. sampled point curvature for this reason of the mean curvature of initial point, and sampled point curvature is similar obtains for other.

5. a kind of surface point method for drafting that strengthens model silhouette according to claim 2 is characterized in that: the process of apex coordinate of curved surface splat that calculates a series of compositions in the step of said operation phase (2) and with the sampled point be the center is following:

A. for certain summit P of curved surface splat _Ik, the i layer, k bar limit, according to the curvature c that pretreatment stage calculates, local coordinate is (rs _iCos (2k π/n _s), rs _iSin (2k π/n _s), φ (rs _i)), n wherein _sRepresent total limit number of curved surface splat, rs _iThe radius of representing the i layer,

B. summit P _IkTexture coordinate do

N wherein _sRepresent total limit number of curved surface splat.

6. a kind of surface point method for drafting that strengthens model silhouette according to claim 1 is characterized in that: the process of observability judgement and fusion is in the step of said operation phase (3):

A. the splat template that the step (2) of claim 1 pretreatment stage is generated is chosen: the arc-tangent value

that is projected in x, y axle component according to radius, normal vector and sight line angle theta, the normal vector of object space reconstruct nuclear wherein

be respectively sampled point P normal vector be projected in screen space x, y spool component; When operation, calculate the affiliated n1 of these values, n2, n3; N1 representes the interval number of sampled point radius; N2 representes that sampled point represents the interval number of section and screen angle; N3 representes the interval in the interval number at oval and screen space x axle clamp angle, and tabling look-up to obtain this splat covered pixels point and weight;

B. utilizing the z-threshold method to carry out observability judges: calculate splat and project to screen; The pixel that covers along the z depth value of direction of visual lines; If z pixel depth value therewith then merges in certain threshold range; If then replace color of pixel and opacity, i.e. alpha value with its color and weight less than pixel depth; Otherwise do not handle;

C. merge: the color of pixel, normal vector, volume coordinate are the weighted mean that projects to each splat corresponding information of certain pixel, and wherein the color of each splat, normal vector, volume coordinate are obtained in the step (1) of claim 1 pretreatment stage.

7. a kind of surface point method for drafting that strengthens model silhouette according to claim 1; It is characterized in that: the process of utilizing illumination model and light and shade to handle the spatial light intensity that calculates the screen pixel in the said operation phase step (3) is: screen pixel back projection is p to the spatial point on the splat; Promptly calculate the light intensity that p is ordered, according to Phong illumination model I=I _aK _a+ I _pK _d(LN)+I _pK _s(RV) ⁿ, I wherein _aK _aBe surround lighting, I _pK _d(LN) be scattered light, L representes that the p point points to the vector of light source, and N representes the normal vector that p is ordered, and utilizes the filtering in the Splatting process to calculate; I _pK _s(RV) ⁿBe specular light, R representes the vector of the reflection ray that light is ordered at p, and V representes that the p point points to the vector of viewpoint, utilizes filtered spatial coordinates calculation, and n is a reflection index, and the big more expression body surfaces of this number are smooth more, can be used to define the material of object, I _a, I _pBe respectively environmental light intensity and incident intensity, K _a, K _d, K _sBe respectively reflection of ambient light coefficient, scattered light reflection coefficient, specularity factor; At last can calculate the light intensity I on this pixel according to the Phong illumination model.

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