CN102609577A - Computer simulation method of paper marbling image - Google Patents

Abstract

The invention discloses a computer simulation method for stone paper dyeing graphics, which combines fluid mechanics to simulate the flow process of pigments, and the simulation is realized by giving a mathematical description to the fluid state at any given moment in the fluid flow process; and using The vector diagram technology realizes the output of stone pattern paper dyeing graphics, compared with existing methods, the computer simulation method of stone pattern paper dyeing graphics of the present invention can not only realize the computer simulation of stone pattern paper dyeing, but also the simulation results can maximize The graphic effect obtained by the actual stone pattern paper dyeing technique has a high degree of simulation.

Description

Computer Simulation Method of Stone Pattern Paper Dyeing Graphics

technical field

The invention relates to computer image simulation technology, in particular to a simulation technology realization method for drawing texture with artistic effect by using computer simulation fluid flow.

Background technique

Paper marbling is the earliest form of paper art invented in ancient Arab countries. It is a method of designing graphics on the surface of water. This paper art technology mainly operates on the surface of water or viscous liquid. Pigments can be used to form various styles, such as smooth and exquisite patterns similar to stone patterns, and the patterns can be transferred to the surface of paper or fabric. In recent years, people have used these stone papers to decorate books, picture backgrounds, stickers and more.

Because the traditional stone pattern paper dyeing technique requires no mistakes in the whole process of operation, once a mistake is made, not only has to start all over again, but also a lot of pigments will be wasted. Therefore, it is very meaningful to realize the simulation of paper art production effect by computer, so that not only the production cost can be reduced, but also the waste of resources and environmental pollution can be reduced.

In recent years, there has been some research on the use of computer simulation of fluid flow to paint textures with artistic effects.

There are three types of simulation methods at present: the simulation method based on the physical two-dimensional fluid model, the simulation method based on the vector diagram and the simulation method based on the graphics coordinate transformation function. Literature [1] uses the knowledge of fluid dynamics to simulate fluid motion to achieve the function of drawing messy graphics similar to stone patterns, but this method needs to initialize all motion paths before drawing, and it is difficult to achieve real-time drawing; Literature [2] ] proposed a real-time rendering technology based on GPU (Graphics Processing Unit), but the boundaries of the generated graphics are blurred. The methods of literature [3] and [4] can generate clear boundaries: Among them, literature [3] uses the B-spline curve interpolation method on the Euler grid to generate clear boundaries, while literature [4] uses vector graphics to draw the fluid, and control the boundary according to the curvature of the local boundary and the turbulence of the velocity, but these two methods can only produce unpredictable texture effects. Literature [5] extended literature [3], combined with CIP (Constrained Interpolation Profile) interpolation method and MacCormack method to solve the NS (Navier-Stokes) equation representing the velocity field and fluid density field, and obtained a clear fluid boundary. However, in When simulating the flow of multiple fluids, each fluid needs to build a grid, and when the fluid is continuously added, the amount of calculation will increase greatly. Literature [6] draws some graphics with specific characteristics through the mathematical representation method, that is, through the coordinate transformation function of some graphics. This method produces faster, but it does not reflect the flow characteristics of the pigment.

references:

[1] Mao X, Suzuki T, Imamiya A. Atelier M: a physically based interactive system for creating traditional marbling textures. In: Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia, 3.7 New York, 20 US 86.

[2] Jin X, Chen S, Mao X. Computer-generated marbling textures: a GPU-based design system. IEEE computer graphics and applications, 2007, 27(2): 78-84.

[3] Acar R, Boulanger P. Digital marbling: a multiscale fluid model. IEEE Transactions on Visualization and Computer Graphics, 2006, 12: 600-614.

[4] Ando R, Tsuruno R. Vector fluid: a vector graphics depiction of surface flow. In: Proceedings of the 8th International Symposium on Non-Photorealistic Animation and Rendering. New York, USA: 2010.129-135.

[5] Xu J, Mao X, Jin X. Non-dissipative marbling. IEEE Computer Graphics and Applications, 2008, 28(2): 35-43.

[6] Lu S, Jaffer, A., Jin X, Zhao H, Mao X. Mathematical Marbling. IEEE Computer Graphics and Applications, 2011, 99: 1-1.

Contents of the invention

Based on the problems existing in the above-mentioned prior art, the present invention proposes a computer simulation method for stone pattern paper dyeing graphics, which integrates fluid mechanics and vector diagram technology, and utilizes computer simulation to produce graphics with clear and complete contours and similar stone patterns. Pattern for artistic effect.

A computer simulation method for stone pattern paper dyeing graphics, combined with fluid mechanics to simulate the flow process of pigments, the simulation is realized by giving a mathematical description of the fluid state at any given moment in the fluid flow process; and using vector diagram technology to achieve The output of stone pattern paper dyeing figure, this method comprises the following steps:

Step 1: Construct the velocity field based on the theory of fluid mechanics:

$<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

$\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&dtri;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}$

Among them, u is the fluid velocity, ρ is the fluid density, p is the pressure term, f is the external force, and v is the viscosity coefficient.

Define the velocity field on an n×n uniform grid, and solve the equations (1) and (2) by central difference to obtain the change of the velocity field

Step 2, fluid boundary tracking and optimization: draw the fluid boundary with a vector diagram, and track the movement of the paint boundary as the velocity field changes after adding an external force: use bilinear interpolation to calculate the velocity at the boundary node i u(p _i ), and then calculate the new position p _i+1 of the boundary node i at the next moment

u(p _i )=t2(s2*u _{i, j} +s1*s1*u _{i, j+1} )+t1(s2*u _{i+1, j} +s1*u _{i+1, j+1} ) ( 4)

p _i+1 = p _i +u(p _i )·Δt (5)

Step 3, boundary filling and output: Based on OpenGL, the stencil test method using stencil cache is used to fill the fluid outline to obtain a solid fluid, and output graphics in SVG format;

Step 4, extension from single fluid to multiple fluids: extend single fluid simulation to multiple fluid simulations. , it is necessary to consider the viscosity characteristics of different fluids. When the user adds a new fluid, the initial boundary node of the fluid contour is added to the velocity v that diffuses to the outer periphery. The value of the velocity v is affected by the intrinsic viscosity coefficient value visc of the fluid ,Right now:

v(i)=(1-visc)*V (6)

Among them, v represents the velocity of the fluid boundary node i on the velocity grid, V represents the value of the viscosity coefficient, and the velocity when visc is 1.

In the process of fluid movement, the increase and decrease of boundary nodes is controlled by controlling the node distance threshold d to maintain the smoothness of the fluid boundary, and the distance threshold d is adjusted based on the curvature of the local boundary to ensure that the distance between two adjacent nodes The distance of is between d and d/2, that is, nodes are reduced where the contour is smooth, and nodes are added where the boundary is curved.

The calculation formula of the distance threshold d _i at the boundary node i is:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; curvature</span>}}$

为结点i处的曲率。Among them, d _max represents the maximum distance between adjacent nodes of the fluid boundary.

is the curvature at node i.

Compared with the existing methods, the computer simulation method of stone pattern paper dyeing graphics of the present invention can not only realize the computer simulation of stone pattern paper dyeing, but also the simulation result can be as close as possible to the actual stone pattern paper dyeing technique. Graphical effect, high degree of simulation.

Description of drawings

Fig. 1 is the overall flowchart of the computer simulation method of stone pattern paper dyeing figure;

Fig. 2 is a schematic diagram of a bilinear interpolation algorithm;

Fig. 3 is a schematic diagram of a disordered texture figure simulated by the simulation method of the present invention;

Fig. 4 is the schematic diagram of the flower texture figure simulated by the simulation method of the present invention;

Fig. 5 is a schematic diagram of flowing around through the fluid boundary of the present invention;

Figures 6(a) and 5(b) show the simulation results without viscous difference and with viscous difference, respectively.

Detailed ways

Below in conjunction with accompanying drawing, the concrete implementation of the present invention is described in detail:

As shown in Figure 1, it is the overall flowchart of computer simulation method of the present invention, and this method mainly comprises the following steps:

1. Construct the fluid velocity field.

In order to simulate the flow process of paint, there must be a mathematical description of the state of the fluid at any given moment in the simulation process, the most important part of which is the velocity field of the fluid. The velocity not only determines how the fluid itself moves, but also It also affects surrounding fluids. Most of the current research on simulating fluids is based on the NS equations, which describe the changes in the fluid's internal velocity and pressure and their relationship. Since the equation is nonlinear, the exact solution cannot be obtained, and the discretization method can only be used to approximate the solution. The present invention adopts the incompressible fluid equation, as follows:

$<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

$\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&dtri;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, u is the fluid velocity, ρ is the fluid density, p is the pressure term, f is the external force, and v is the viscosity coefficient.

The invention defines the velocity field on an n*n uniform grid, and obtains the change of the velocity field by solving equations (1) and (2) simultaneously.

2. Fluid boundary tracking and optimization

A vector diagram is a diagram described by a mathematical method, and the clarity of the diagram will not be affected when the graphics are arbitrarily enlarged or reduced. Therefore, the present invention adopts a method based on a vector diagram to represent the fluid boundary, and then fills the area represented by the boundary.

First, initialize the fluid contour boundaries. In the traditional stone paper dyeing technique, the pigment drops onto the liquid surface in a nearly circular shape, so some discrete points on the boundary of the initial solid circle area are selected as the initial boundary nodes of the fluid. When the external force is added, the motion of the paint boundary needs to be tracked as the velocity field changes continuously.

The present invention uses a bilinear interpolation method to calculate the velocity u(p _i ) at the boundary node i, specifically shown by formula (3). Then according to the formula (4), the new position p _i+1 of the boundary node i at the next moment is obtained.

u(p _i )=t2(s2*u _{i, j} +s1*s1*u _{i, j+1} )+t1(s2*u _{i+1, j} +s1*u _{i+1, j+1} ) ( 3)

p _i+1 = p _i +u(p _i )·Δt (4)

Pi is the coordinates (x, y) of the sampling point, s1, s2, t1, t2 are the proportional coefficients of bilinear interpolation, as shown in Figure 2, the schematic diagram of the linear interpolation algorithm.

Only tracing the initialized boundary nodes cannot describe the fluid contour very well, so it is necessary to add new boundary nodes appropriately to obtain a realistic fluid boundary. The present invention controls the increase and decrease of boundary nodes by controlling the node distance threshold d, and the basic principle followed is to ensure that the distance between two adjacent nodes is between d and d/2. In order to reduce the amount of calculation and obtain a smooth and realistic fluid boundary, the present invention adjusts the distance threshold d based on the degree of curvature of the local boundary, that is, to reduce some nodes in places where the contour is relatively smooth, and to increase some nodes in places where the boundary is relatively curved point.

The calculation formula of the distance threshold d _i at the boundary node i is:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; curvature</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

为结点i处的曲率。Among them, d _max represents the maximum distance between adjacent nodes of the fluid boundary.

is the curvature at node i.

3. Boundary fill and output

After obtaining the position information of the boundary nodes at any time, a polygon composed of boundary nodes can be easily generated, and then the polygon area needs to be filled. The invention fills the fluid outline based on OpenGL and adopts a template cache template testing method to obtain solid fluid. Based on the feature that no zoom-in or zoom-out of the vector graphics will affect the clarity of the graphics, according to the SVG open standard, the graphics are output in the SVG format, and the distortion is well avoided by using this method.

4. Expansion from a single fluid to multiple fluids

In order to obtain rich graphics like stone paper dyeing technology, it is not enough to only simulate the drawing of a single fluid, and we need to extend the method of the present invention to the simulation of multiple fluid flows. If the previously proposed method is used, then different fluids will have the same viscosity characteristics, which does not comply with the laws of pigment properties.

Therefore, when drawing a variety of fluids, it is necessary to consider the viscosity characteristics of different fluids. In order to visually let people feel the stone pattern paper dyeing technology, that is, different attributes between different pigment fluids can be observed. Viscosity coefficient. It is not difficult to find through observation that generally people can only observe the influence of the interaction between different fluids near the outline boundary in terms of visual effects. The speed v of the diffusion around the outside, as shown in Figure 2, the value of the speed v is affected by the intrinsic viscosity coefficient value visc of the fluid, namely:

v(i)=(1-visc)*V (6)

Among them, v represents the velocity of the fluid boundary node i on the velocity grid, V represents the value of the viscosity coefficient, and the velocity when visc is 1, in the system realized in this paper, V=1. Figures 3(a) and 3(b) show the simulation results without viscous difference and with viscous difference, respectively.

The present invention mainly realizes the fluid simulation of two kinds of texture effect graphics, one is a messy texture map (Fig. 4), and the other is a pattern with specific graphic effects such as flowers (Fig. 5).

Claims (2)

1. A computer simulation method for stone pattern paper dyeing graphics, combined with fluid mechanics to simulate the flow process of pigments, the simulation is realized by giving a mathematical description to the fluid state at any given moment in the fluid flow process; and using vector graphics The technology realizes the output of stone pattern paper dyeing figure, it is characterized in that, this method comprises the following steps: Step 1: Construct the velocity field based on the theory of fluid mechanics: $<span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ $\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; u</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&dtri;</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&dtri;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Among them, u is the fluid velocity, ρ is the fluid density, p is the pressure term, f is the external force, and v is the viscosity coefficient; The velocity field is defined on an n×n uniform grid, and the change of the velocity field is obtained by solving equations (1) and (2) simultaneously by central difference; Step 2, fluid boundary tracking and optimization: draw the fluid boundary with a vector diagram, and track the movement of the paint boundary as the velocity field changes after adding an external force: use bilinear interpolation to calculate the velocity at the boundary node i u(p _i ), and then calculate the new position p _i+1 of the boundary node i at the next moment u(p _i )=t2(s2*u _i,j +s1*s1*u _i,j+1 )+t1(s2*u _i+1,j +s1*u _i+1,j+1 ) p _i+1 = p _i +u(p _i )·Δt Wherein, p _i is the coordinates of the sampling point, p _i+1 is the coordinates s1, s2, t1, t2 of the sampling point at the next moment and is the proportional coefficient of bilinear interpolation; Step 3, boundary filling and output: Based on OpenGL, the stencil test method using stencil cache is used to fill the fluid outline to obtain a solid fluid, and output graphics in SVG format; Step 4, the extension of single fluid to multiple fluids: to extend the single fluid simulation to multiple fluid simulations, the viscosity characteristics of different fluids need to be considered. When the user adds a new fluid, the initial boundary node of the fluid contour is added to The speed v of the diffusion around the outside, the value of the speed v is affected by the intrinsic viscosity coefficient value visc of the fluid, that is: v(i)=(1-visc)*V Among them, v represents the velocity of the fluid boundary node i on the velocity grid, V represents the value of the viscosity coefficient, and the velocity when visc is 1. 2. the computer simulation method of stone grain paper dyeing figure as claimed in claim 1, it is characterized in that, described method also comprises a step: in fluid motion process, by controlling node distance threshold value d to control boundary node Increase or decrease, maintain the smoothness of the fluid boundary, adjust the distance threshold d based on the curvature of the local boundary, ensure that the distance between two adjacent nodes is between d and d/2, that is, reduce nodes where the contour is smooth, Add nodes where the boundary is curved, and the calculation formula of the distance threshold d _i at the boundary node i is: ${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; curvature</span>}}$ Among them, d _max represents the maximum distance between adjacent nodes of the fluid boundary,

is the curvature at node i.

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