CN100570641C - Plant leaf analogy method based on physics - Google Patents

Abstract

The invention provides a kind of method that plant leaf is simulated, mainly comprise the extraction of plant leaf profile, plant leaf vein structure, leaf surfaces model trigonometric ratio, structure leaf particle-spring bilayer model structure and carry out 5 steps of physical simulation computing based on physics.The present invention is based on botany and physical principle, set up particle-spring bilayer model and expressed the mechanical structure of leaf, reasonable setting to bilevel different parameters, show the different mechanical characteristics of mesophyll and vein well, can simulate the variation of variety classes plant leaf geometric shape in withered, ageing process very truly.Constitute and physical characteristics because plant tissue has similar biology, this method can expand to the moulded simulation of plant simultaneously, and the limb of plant is carried out simulation modelling based on physics.

Description

Plant leaf analogy method based on physics

Technical field

The invention belongs to computing machine photo realism graphic, virtual reality, geometric modeling, computer animation, Computerized three-dimensional modeling and simulative plant and learn the field that combines, be specifically related to a kind of by the method for physical simulation to the plant leaf moulding.

Background technology

In computer graphics, for the modeling of plant in the natural scene with to draw be emphasis in the rendering technique evolution always.Plant is carried out moulding, material expression and the sense of reality draw, be to be rich in challenging research work always.

As everyone knows, plant often is made up of the organ that much has different resemblances, as stem, leaf, flower, fruit etc.And the plant of occurring in nature, be with the difference of the maximum of most people's appearance body: artificial body is often according to people's aesthetic and application demand, and in manufacture process, its geometric configuration is to control, and is easy to be described and grasp; And for the plant of natural scene, the formation of its geometric configuration then is the various complicated internal and external factors of occurring in nature, as outside disease and pest invasion, climatic factor, man's activity etc., through interact for a long time, coefficient result.Therefore, as the plant of occurring in nature, have very special form usually.Especially the leaf of plant, along with the variation of season and weather, its metamorphosis is very remarkable, and this has also determined the plant external appearance characteristic to a great extent.And in Computer Aided Modeling in the past, be difficult to show truly the resemblance of leaf under varying environment and season with simple, fixing geometric figure.Simultaneously, because the restriction of prior art, in computer graphics sense of reality field of drawing, the scene that major part draws out is static scene, be that geometry of objects in the scene can not change over time, this not only is not inconsistent with natural truth, and the sense of reality of drafting is not strong, has greatly limited further developing of simulative plant technology yet.Therefore, need be at feature as the geometric shape of the plant leaf of one of main ingredient in the natural scene, and they change in time and situation about changing is analyzed, and the drawing result of leaf is got close to nature truly more.By these research, just can in the related application of virtual reality, make up scene more true to nature, also can allow the sense of reality of plant be plotted in fields such as recreation, video display, biology, environmental protection and further be used.

Simulation and drafting for natural forms outward appearance emulation plant in natural scene over nearly 40 years have obtained using widely.Research work about plant modeling aspect before this mainly comprises: Honda[1], Webber[2] etc. the parametric modeling method that proposes; Reeves[3] the emulation that proposes based on particIe system; Bloomenthal[4], Holton[5] based on the moulding of spline skeleton; Fournier[6], the modeling method that proposes of Viennot etc. [7] based on stochastic system; Lintermann and Deussen[8] the modeling that proposes based on graph structure; [9], Prusinkiewicz and Lindenmayer[10 such as De Reffye] system of rewriting (rewriting) rule that proposes; Lefebvre and Nyeret[11], Federl and Prusinkiewicz[12] the plant texture simulation that proposes based on physics.Wherein Lintermann and Deussen combine the positional information of plant in their the interactive plant model of Xfrog system, in axial direction the positional information of sampled point can influence the length of node and branch, the angle and the quantity of branch, and their feature.

Sung[16] proposed a kind ofly to make up the plant leaf surface by triangular mesh, and edit the method for plant leaf distortion by User Interface, the model result of its generation has the very strong sense of reality, but its method lacks good botany and physics foundation, and deformation result is by artificial setting.

It is at present also rare directly to carry out the work of configuration for the leaf form, Judd[14] etc. the people provided the expression of a description leaf shape, after this be widely used.And for the modeling process of plant leaf vein, Dengler and Kang[13] studies show that the model of vein and the shape of leaf have strong correlativity, therefore must consider the relation between vein and the Leaves'Shape.In the SIGGRAPH meeting in 2005, people such as Runions and Prusinkiewicz [15] have proposed a kind of more effectively vein building method, in order to generate the vein model relevant with the leaf profile.Based on the botany characteristic of leaf in the growth is observed, this method has been arranged some nutrition points equably on the mesophyll model surface.Then, the purpose of supposing the growth of vein is to arrive each nutrition point, and can thus be each cell delivery moisture and nutrition on the mesophyll, and then determines the mode of the growth of whole vein.Can obtain the very strong vein configuration of the sense of reality with this vein model generation method, but the weak point of Runions method is, the vein structure of its generation is only approaching with true vein on space distribution and growthform, but the result of its generation only is the plane effect of vein, promptly is a 2 d texture.

Therefore, in a lot of application scenarios of computer graphics, especially sense of reality field of drawing is badly in need of a kind of method efficient, true to nature and is generated the plant leaf geometric model with height sense of reality.

Summary of the invention

The objective of the invention is to use the computing machine photo realism graphic learn to draw and virtual reality technology, a kind of method that plant leaf is simulated be provided, promptly the plant leaf Various Seasonal and period dynamic modeling and the method for drafting.

As previously mentioned, some present plant modeling major parts are based on semantic and fractal configuration and Modeling Technology, and their common feature realizes that exactly simply formation speed is fast.Other can generate the genuine plant geometric model of suitable plan based on the plant modeling technique of image.But, the common issue with of these existing methods be exactly can not fine simulating plant dynamic effect, be difficult to show the metamorphosis of plant under varying environment, the effect of flickering as wind moving the time, aging the curling of the plant leaf that arrives autumn waited variation effect.The present invention is by the research to the vegetable cell mechanical structure, established the analysis result that the base unit cell that constitutes plant is made up of harder cell membrane and softer inner structure, and by these analyses of forming for plant tissue, the mechanical model that has made up plant is simulated the form of plant, thereby, carried out good simulation to the form and the variation of plant under different tenses and season.

The method that the present invention simulates plant leaf mainly is divided into 5 steps: the extraction of plant leaf profile, plant leaf vein structure, leaf surfaces model trigonometric ratio, structure leaf particle-spring bilayer model structure, carry out the physical simulation computing.Below technical scheme of the present invention is described in detail:

1. the extraction of plant leaf profile

The 3-D geometric model of structure plant leaf at first will be sampled by the plant model from real world, obtains some actual data, so as to the simulation of plant leaf more near the situation in the real world.Leaching process to the plant leaf profile specifically comprises:

1.1 leaf image binaryzation

At first plant leaf is carried out image scanning, obtain the plane picture of leaf.Then image is carried out binaryzation, the value of all pixels is decided to be black or white on the leaf plane picture after just will scanning, and helps distinguishing which pixel like this and belongs to leaf inside, and which pixel does not belong to.After the image binaryzation, the leaf plane picture becomes a secondary black and white binary image.Bianry image can significantly reduce the operand when obtaining the leaf profile.By different separatrix values is set, can obtain different bianry images, as shown in Figure 1.

1.2 the stepping grid extraction method (Marching square) of leaf profile

The employed stepping square method of this method (Marching Square) is famous a kind of revise later the method for stepping cube algorithm (MarchingCube) [19] [20] under two-dimensional case.The stepping square method can be expressed as fundamental assumption by polygon with the leaf profile, supposes that also this polygon also is a closed curve simultaneously.The leaf bianry image is carried out the horizontal scanning of sweep trace mode with grid from order left to bottom right, enter the zone of leaf inside up to certain angle of grid, be that grid is through the leaf border, at this moment, grid stops the horizontal scanning of sweep trace mode, then beginning is moved with counter clockwise direction along the border of leaf.Because the sealing of the profile of leaf and hypothesis continuously, when the size to fit of grid, can access the polygonal profile that approaches very much leaf profile in the reality.

After having obtained the bianry image of leaf, just can bring into use stepping square method (MarchingSquare) to obtain the polygonal profile of leaf by the scanning leaf.In the stepping square method,, illustrate that then grid begins across leaf the zone between inside and outside in case the pixel of black is arranged in the pixel at four angles of grid.By four jiaos of color of pixel of grid, can differentiate which bar limit of grid is passed through by the leaf profile, as shown in Figure 2, just can obtain the trend and the position on leaf limit in the grid, thereby obtain a bit of of polygon leaf profile, the stepping square method is exactly the process that each segment of the profile line segment that will obtain finds and couples together.By of the scanning of stepping grid, just can obtain the polygonal profile of leaf to whole leaf image.The extracting mode synoptic diagram as shown in Figure 2, detailed process can list of references [16].

In the stepping square method (Marching Square) of binary map, because each pixel has two kinds of values of black and white, the situation that four jiaos of colors of grid may occur has 2 ⁴Totally 16 kinds, as shown in Figure 3,, just can judge that grid is positioned at the position of leaf profile, thereby profile is extracted by the situation of these 16 kinds of grids.The grid of different sizes can extract the polygon leaf profile of different details, as shown in Figure 4, the top of figure is the back side image of a slice maple leaf, the bottom of figure is that the part in the maple leaf square frame is extracted profile by the stepping square method, the result that the marquis obtained when the grid length of side was selected the difference size, from left to right the selected length of side of grid is 8 pixels, 5 pixels, 3 pixels, 2 pixels successively, and as can be seen, the more little profile that extracts of grid is meticulous more.

2. plant leaf vein is constructed

In real physical environment, the distortion of plant leaf can be subjected to the influence of diversified internal and external factor, studies for convenience and is without loss of generality, and the present invention considers wherein topmost influence factor---the moisture supply of leaf.Because in aging, the withered process of leaf, the model of vein has very important influence to the geometric configuration of leaf.And set up vein distribution true to nature is the basis of real simulation plant leaf distortion.

To this, Runions[15] a kind of method of effective generation vein had once been proposed, be commonly referred to as " based on the vein generation method of nutrition point ".This method is pursuant to some botany phenomenons that showed in the leaf growth, distributing equably on the surface of leaf, some represent " (or being called the growth vegetarian refreshments) selected in nutrition " of nutriment, and the target of supposing the growth of vein thus is exactly to arrive and connect each nutrition point on the leaf, thereby transports moisture and nutriment for each cell on the mesophyll in the growth.Like this, the profile of blade and the distribution of nutrition point have just determined the mode of vein growth, so just well the configuration of vein and the organic connections of leaf shape are got up.

Concrete steps are (black circle is represented the nutrition point among Fig. 5, the node on the ring-type point expression vein) as shown in Figure 5:

1. scatter the nutrition point in the internal random of existing leaf profile;

2. seek nearest vein node for each nutrition point;

3. seeking becomes these nodes that nearest vein node is put in nutrition, and writes down it;

4. be that each such " node recently " calculates direction of growth, direction by to the nutrition point of its generation effect to the weighted mean of its influence with calculate;

According to the direction that calculates to limit the vein node that the spacing growth makes new advances;

6. according to certain given radius, calculate nutrition point and whether reached by vein;

7. delete the nutrition point that has reached;

8. profile adjustment;

9. the nutrition point that random scatter is new;

10. near and the new nutrition point near excessively apart from the vein node were put in the existing nutrition of deletion distance;

11. get back to step 1, recomputate in the next process vein and should how to grow.

Through too much repeating query ring processing, the vein that is generated is actually by the line segment that connects each vein node to be formed.This existing technology can be used for generating the vein structure that the many types leaf is had truly, comprises the leaf of shapes such as yulan leaf, cherry leaf, maple leaf and phoenix tree leaf.Though L-system[10] also can generate similar vein structure, often lack the theoretical foundation on the botany.

In botany, the leaf of most dicotyledons, at the initial stage of growth, the middle arteries and veins that connects blade root portion and leaf top in the leaf just forms, and branch's vein of rib shape all is that therefrom the arteries and veins differential growth comes out, and the physical strength of therefore middle arteries and veins and geometric diameter are all much larger than other branch's veins.Equally, in toe shape leaf growth course, each toe structure can form self a middle arteries and veins, and grows the branch's vein structure based on arteries and veins in this gradually.Utilize this influence, the present invention has improved existing vein generation method, particular content is promptly in the process that vein generates, the intensity and the speed of growth of master pulse and middle arteries and veins in the raising simulation process, because the main lobe arteries and veins of true leaf can reach and the essentially identical speed of growth of leaf profile, and than the fast growth of secondary vein, the speed of growth of generally setting master pulse and middle arteries and veins be secondary vein 1.5-4 doubly, be preferably 2 times.Like this, just can guarantee that the vein structure that is generated can have more real vein structure physical strength.In addition, very fast middle arteries and veins of the speed of growth and the master pulse growth pattern that can influence secondary vein by their space distribution.By adjusting and test, the present invention can obtain vein structure and distribution of shapes effect more true to nature.As shown in Figure 6, the vein of the leftmost side for using former method to generate, the centre is the vein that method of the present invention generates, and the rightmost side is real leaf image, and the vein of this method generation is more near truth as can be seen.

In the physical simulation process of back, be abstracted into the result who directly affects the physical simulation distortion for the hardness of every section vein of line segment.And the main nervate thickness of the intensity of vein (being diameter) decision, the present invention is according to Murray[17] the Murray law that proposes comes the diameter of vein in the structure is provided with:

$d_{\mathrm{parent}}^n=d_{\mathrm{child}1}^n+d_{\mathrm{child}2}^n$

Here d represents the diameter of vein section, the width of vein just, d _Parent, d _Child1And d _Child2Represent the diameter of two vein sections forming behind the diameter of the vein section before the vein bifurcation branch and the branch respectively, n is a constant.Runions[15] in his work, try to achieve the drafting that the vein width carries out leaf with n=3.And in the present invention, the setting of vein section diameter is not in order to draw out the vein section of one section width in this step, but prepare for the setting of vein intensity in the follow-up physical simulation process, because in the process of physical simulation, the diameter d of supposing every section vein is a constant constant, and initial vein hardness is the cross-sectional area π (d/2) of vein in proportion to ², therefore, find that n=1 or n=2 are accurate more in the present invention, more near true through experiment.Like this, every section final vein diameter d of vein will directly be presented as the hardness of vein, goes and participate in the physical simulation computing of back.

3. leaf surfaces model trigonometric ratio

The vein and the profile that only have leaf also are not enough to make up the physical arrangement of leaf, and leaf is carried out physical simulation.Therefore the three-dimensional physical model that needs the whole leaf of structure.

As a kind of organ of plant, the surface of leaf is made up of a lot of cells.And be divided into the structure on the vertical directions such as epicuticle, palisade tissue, spongy tissue, lower epidermis.But in the physical simulation of leaf being carried out macroscopic view, very the little because thickness of leaf seems relatively, be far smaller than leaf yardstick in the horizontal direction, therefore can with leaf surfaces structure abstract simplification on macroscopic view become a two dimensional surface.And for annexation and interaction between the various piece that can better express leaf on this two dimensional surface, the present invention uses triangular mesh to make up the structure on leaf mesophyll surface.

The trigonometric ratio method that the present invention uses is a Delaunay trigonometric ratio method [21] [22] [23].Owing to had basis and the restriction of vein and leaf profile as triangular mesh, here select the Delaunay trigonometric ratio method (Constrained Delauany Triangulation) under restricted to come model of the present invention is carried out triangle gridding, be constraint promptly, carry out the process of trigonometric ratio with existing vein line segment and profile line segment.Leaf surfaces is being carried out in the process of trigonometric ratio, the present invention has used the CGAL program of increasing income to assist, and make that by angle and the minimum area that limits each leg-of-mutton minimum angle the leaf surfaces triangle gridding behind the trigonometric ratio is more even, thereby be beneficial to the structure of cyto-mechanics model in the following step, can be good at supporting ensuing physical simulation process.The Exact_predicates_inexact_constructions_kernel class that concrete steps in the trigonometric ratio process are to use the CGAL storehouse to provide, the Delaunay_mesher_2 class, the Delaunay_mesh_face_base_2 class, these 4 kinds of data structures of Constrained_Delaunay_triangulation_2 class are organized with leaf profile and vein line segment and the point data as restriction, and use the refine_Delaunay_mesh_2 function to carry out restricted Delaunay trigonometric ratio, data structure Criteria carries out triangle minimum angles and minimum area control, generally choose parameters C riteria (0.005,0.5), the length of side of at this time representing the triangle minimum edge can not be less than 0.005, the angle at minimum angle can not be less than 0.5 radian, thereby makes the triangular mesh that generates be suitable for the process of physical simulation more.Part trigonometric ratio result as shown in Figure 7.

4. construct leaf particle-spring bilayer model structure

After profile that has plant leaf and vein, just can consider the physical arrangement of tissue construction leaf.

What the leaf of plant showed in different seasons is different forms, and when summer, sunlight and moisture were very sufficient, leaf can trail, and presents the form that upper surface protrudes.And autumn then, the leaf of a lot of broad leaved plants can be because the loss of the decline of temperature and moisture and inwardly curling, and the variation of the variation of moisture and some other condition all can make leaf that variation clocklike takes place on geometric configuration in the variation of humidity in the air, the plant.

The cell of plant can be owing to the variation of external environment be out of shape, and the distortion of the plant leaf result that numerous cells are out of shape jointly on the leaf just.By the observation to plant leaf, the present invention finds, on micro-scale, the leaf of most plants mainly is made up of the vein that the mesophyll and the major part of upper surface is positioned at the tree structure of leaf lower surface.Mesophyll mainly is made up of epicuticle, palisade tissue, spongy tissue and lower epidermis, and vein mainly is made up of numerous vascular bundles.

Vascular bundle has very different hardness and physical arrangement with mesophyll cell.Mesophyll cell has volumetric contraction clearly in water loss, and under same case, fascicular volume change is but much smaller relatively.This mainly is owing to contain a lot of wooden and fibers between the fascicular cell.

When change season, as autumn, along with scattering and disappearing of leaves of plants moisture, vein that physical arrangement is different and mesophyll will produce distortion in various degree: because vein has much along vein vascular bundle radially, the fibre structure that contains substantial radial in these vascular bundles radially, will cause in the water loss process, the contraction ratio of vein is also little; And mesophyll is made up of a large amount of mesophyll cells that is full of moisture, not having strong fibre structure between cell and the cell keeps form constant, therefore along with moisture loss in the fall, the cell of mesophyll part significantly shrinks at the tangential direction area along the mesophyll plane.

This unequal shrinkage rates is all taking place in each micro-structure of leaf, comprises each position that vein arrives.Finally it can cause this part of leaf to leaf upper surface direction bending self, the i.e. variation of geometric shape in the three dimensions.The result of final distortion also is the stressed coefficient result in back of leaf all sites distortion.

4.1 cyto-mechanics model

The present invention proposes to adopt the Elasticity model to simplify the physics stressing conditions of simulation mesophyll cell.Suppose that a cell on the leaf mainly is subjected to two kinds of power, a kind of is the bulging force f of the cell interior that produced by tenuigenin _In, another is the tension force f by the outside of cell membrane generation _Out, as shown in Figure 8, wherein the A figure of the leftmost side is to the stressed analysis of individual cells, and middle B figure is a plurality of cell force analysis and spring analog case, and the C figure of the rightmost side is the synoptic diagram of abstract particle spring network analog cell physical arrangement of coming out.

In order to describe these suffered two kinds of physical force of leaf cells more accurately, make up the bulging force that contraction spring is represented cell, in like manner, the employing extension spring is represented the tension force between the cell.Hence one can see that, and it is these two kinds of mutual balances of power that a cell is in the condition of stablizing geometric shape, and available following equation is expressed:

f _in＝-f _out＝-k(s-s ₀) (1)

Wherein, s and s ₀Represent static length of spring and the spring length of cell after dehydration is shunk under the full state of cell respectively, and the length s after shrinking ₀Also exactly determine the size of cell; What k represented is the elasticity coefficient of spring.Find that by actual observation intracellular vacuole can must arrive along with autumn, significantly dwindle, just caused cell interior bulging force f thus owing to water loss _InMinimizing, the static length s of cell spring also reduces thereupon.That is to say, along with this process of cell water loss, the variation that the inside of cell is formed has caused the variation of its physics and mechanical characteristic, therefore it can be regarded as the inherent mechanical property of spring of analog cell and the process that parameter changes, and this process also can be regarded the process that spring changes as.After mesophyll cell dried out, the process of its contraction just showed as the process that the static length s of spring reduces in analogy method of the present invention.

According to top simplified model, the mesophyll cell tissue can be simulated by the particle shown in the C figure-spring reticulate texture among Fig. 8.Observe based on botany as above, the present invention proposes a kind of distortion of simulating leaf based on the double-deck mechanical model DLM (doublelayered model) of physical simulation.The basic thought that makes up bilayer model comes from a brass tacks in the nature: most veins are to be positioned at the leaf back side, and especially for some broad leaved plants, and vein also protrudes from leaf surfaces.And in bilayer model, the present invention adopts the cell on the very high mesophyll of upper strata grid representation shrinkage factor, and understructure then is used for representing the cell on the vein of stone and difficult contraction.Simultaneously such double-layer structure model is also by being connected to each other the stability that guarantees on the mechanics, the structure that on behalf of mesophyll, the spring structure of connection link to each other with the vein cell.

4.2 last layer model

For tectonic model particle-spring network at the middle and upper levels, by obtaining the leaf profile in the above-mentioned steps, and to leaf surfaces generation vein, carry out the Delaunay trigonometric ratio with vein and profile as obligatory point then, thereby obtain a Zhang San angle network, the vertex representation cell of grid is as particle, and the spring of adjacent particle is represented to connect in the limit in the grid, in order to the mechanical structure of express cell.Can make up such particle-spring network thus, spring wherein is the foundation structure that guarantees blade shape.

In model, any two adjacent, and, use s by particle i and particle j that spring is connected _IjRepresent to connect one section spring, wherein p of particle i and particle j _iAnd p _jThe position of corresponding expression particle i and these two particles of particle j.By for particle i force analysis, spring s _IjEffect f thereon _IjCan obtain by Hooke's law:

$f_{\mathrm{ij}}=-[h_{\mathrm{ij}}\left(\right|l_{\mathrm{ij}}|-r_{\mathrm{ij}})+d_{\mathrm{ij}}\frac{\stackrel{\·}{l_{\mathrm{ij}}}\·l_{\mathrm{ij}}}{\left|l_{\mathrm{ij}}\right|}]\frac{l_{\mathrm{ij}}}{\left|l_{\mathrm{ij}}\right|}---\left(2\right)$

L wherein _IjExpression is from p _iTo p _jVector, h _IjExpression spring s _IjElasticity coefficient, d _IjExpression spring s _IjRatio of damping, r _IjExpression spring s _IjStatic length.The static length r here _IjIt in model one group of time dependent parameter.

The speed of related movement of expression particle i and j, i.e. l _IjDerivative to the time.Here can also know $\stackrel{\·}{l_{\mathrm{ij}}}=v_i-v_j,$ v _iAnd v _jThe speed of representing particle i and j respectively.

In equation (2), poor in two particle physical lengths and static length of being in proportion of spring force, damping force is the relative velocity of two particle i and j in proportion to.Like this, two particles that spring connected, it is identical to be subjected to size, the power that direction is opposite.On two particles that the damping action of spring acts on spring symmetrically and connected, do not influence the motion of two common barycenter of particle.

Particle i links to each other with adjacent some particle j, and the power on the particle i of acting on is making a concerted effort by these particles that are connected by spring with i respectively $f_i=\underset{p_j\∈S_i}{\mathrm{\Σ}}{f}_{\mathrm{ij}}$ Decision, S here _iWhat represent is the set of all springs that link to each other with particle i, p _jThe position of expression particle j.Like this, the present invention has set up a static length r _IjBy variable s decision in the equation (1), and elasticity coefficient h _IjParticle-spring the network system of t variation in time.The final simulation equation of going up layer model can be described as:

$f_i\left(t\right)=-\underset{p_j\∈S_i}{\mathrm{\Σ}}\left\{h_{\mathrm{ij}}\left(t\right)\right[\left|l_{\mathrm{ij}}\right|-r_{\mathrm{ij}}\left(t\right)]+d_{\mathrm{ij}}\frac{\stackrel{\·}{l_{\mathrm{ij}}}\·l_{\mathrm{ij}}}{\left|l_{\mathrm{ij}}\right|}\}\frac{l_{\mathrm{ij}}}{\left|l_{\mathrm{ij}}\right|}---\left(3\right)$

In the equation (3), j represents particle adjacent with i and that be connected with i by spring, s _IjExpression connects one section spring of particle i and particle j, p _iAnd p _jThe position of corresponding expression particle i and particle j, S _iRepresent the set of the spring that all link to each other with particle i, l _IjExpression is from p _iTo position p _jVector, h _Ij(t) expression spring s _IjElasticity coefficient, d _IjExpression spring s _IjRatio of damping, r _Ij(t) expression spring s _IjStatic length,

The speed of related movement of expression particle i and j, i.e. l _IjDerivative to the time.In the last surface analysis, i, j represent any two particles adjacent and that be connected by spring among the particle set M.

The dynamic acceleration a of particle i _iCan be expressed as $a_i=\frac{f_i\left(t\right)}{m_i},$ Here m _iIt is the quality of particle i.The static length r of the spring here _IjBe a variable that changes with space distribution in time, the spring of simulation vein is owing to having more fiber in the vascular bundle in the vein, and is harder relatively, so the static length of these springs is shorter, and spring hardness is harder relatively; The spring of simulation mesophyll cell is then softer relatively, and static length is longer relatively at the beginning.

4.3 following layer model

The tree structure of lower floor's model representation leaf vein, and the structure of vein also determines most important link in the whole simulation process just.With the lower floor particle of vein node as expression vein cell, per two adjacent lower floor's particles and two upper strata particles directly over it constitute a rectangle on the same vein, these four particles link to each other in twos by spring each other, so just provided lower floor's particle-spring model of band criss-cross construction in a kind of rectangle, as shown in Figure 9, each decussate texture all has 6 springs to constitute, and following layer model just mainly is made up of these interconnective decussate textures.In Fig. 9, v1, v2 and v3 are the upper strata particles of expression mesophyll cell; B1, b2 and b3 are lower floor's particles of expression vein cell; Spring s _B1v2, s _B2v1, s _B2v3And s _B3v2These 4 intersect the cross spring of forming " X " shape, and s _B1b2And s _B2b3These two control lower floor veins are along the springs of vein direction link, are used for representing that the harder spring structure of lower floor represents vein, and the structure of control lower floor vein; Simultaneously, spring s _B1v1, s _B2v2And s _B3v3The spring that connects vein and mesophyll on these three vertical directions up and down is connected the levels structure, is used for controlling relative position and direction relations between mesophyll and the vein, guarantee between the vein of same position and the mesophyll structure can be strictly adjacency up and down.

Because all springs are all observed Hooke's law in the model, therefore available equation (3) carries out deformation simulative.Because in the real world, vein can cause the variation of its physical characteristics in the variation of Various Seasonal along with moisture, as the variation of hardness, extension power, volume etc.Therefore in lower floor's vein model, theoretically, along with the time changes, and space distribution is also different than the elasticity coefficient of hard spring and ratio of damping, that is to say be in time-spatial variations, this situation with last layer model is identical.But, because water loss is so obvious unlike the influence for mesophyll cell for the hardness influence of vein, therefore, in order to simplify the parameter setting in the total system, suppose that the spring of expression vein and the deformation coefficient of the spring that is connected the levels model can not change, so the deformation coefficient of these springs (comprises elasticity coefficient h in the following layer model _Ij, ratio of damping d _IjStatic length r with spring _Ij) be simplified and be set to not change in time.In a series of tests of being undertaken by the present invention, this simplification can be well near legitimate reading.

The upper right portion of Fig. 9 has represented, and when upper strata mesophyll structure was shunk, how whole vein structure was bent upwards.Fig. 9 the latter half has been showed the simulating shape that upsweeps along the vein profile.

4.4 the combination of levels model

In concrete simulation process, adopt particle-spring system to realize the simulation of this bilayer model, wherein represent the last layer model of mesophyll cell to interconnect by the softer spring of one deck, form network, this spring net of representing mesophyll cell is exactly the triangle gridding on the mesophyll surface that obtained by before trigonometric ratio.And the following layer model of representing the vein cell is by comprising being formed than hard spring of decussate texture.As shown in Figure 9, position in each vein fragment, the abstract soft spring wire (this line is a part in the mesophyll spring network) that becomes of mesophyll with the vein top, become a spring wire of rigidity relatively more and the vein of lower floor is abstract, middlely be connected with the vein part particle of lower floor by the mesophyll part particle of one group of decussate texture spring with the upper strata.

Like this, double-layer structure is vertically linked to each other by spring again, finally constitutes the whole mechanical structure of leaf, as shown in figure 10, superstructure is the particle-spring network on a plane, and following layer model is by each vein place, represents the particle-spring structure of the harder spring fragment composition of vein.

5. physical simulation computing

Above-mentioned particle-spring layer aggregated(particle) structure that can real simulation leaf physical arrangement has been arranged, just can begin the geometric modeling of leaf is carried out physical simulation, promptly after particle spring model structure construction of the present invention is good, change according to the time by Visual C++ written program, carry out simulation progressively, along with the contraction of spring, every through a time period, the configuration of leaf begins to begin to change under the control of structure, and the form that simulates plant leaf under the state of nature progressively.

In the concrete physical simulation program, written program of the present invention has used the method for Euler's iteration that the metamorphosis and the motion of whole particle-spring model are simulated, and concrete grammar will be set forth below, and principle can be referring to document [24].Original state has the particle that is generated by each step of previous methods and gathers the model that M and this particle of spring S set and spring constitute, and their relevant parameters.Generally, the width of least significant end vein section is made as 1, this is a standard 1 with regard to the hardness of representing least significant end vein spring also, the upper strata spring hardness of also representing mesophyll in leaf particle-spring bilayer model is set to standard 1, the biology implication here be exactly least significant end vein consistency and elasticity contraction coefficient with mesophyll cell similar, but along with the overstriking of vein and the increase of vascular bundle and proportion of fibers, the hardness of those senior, thicker veins increases, volume change can be littler.As previously mentioned, according to formula $d_{\mathrm{parent}}^n=d_{\mathrm{child}1}^n+d_{\mathrm{child}2}^n$ Extrapolate the width of vein sections at different levels in the whole vein structure, width defines the hardness of other vein of upper level more and even trunk vein spring thus, and generally its hardness is between 1～50.The parameter of concrete manifestation spring hardness is exactly h in the physical simulation process _Ij, therefore,, carry out the parameter setting by elasticity coefficient to whole particle-spring model of comprising mesophyll, vein and levels syndeton according to above rule.Simultaneously, in order to simplify the parameter setting in the total system, set the spring of expression vein and the deformation coefficient of the spring that is connected the levels model and do not change in time, the elasticity coefficient h of the spring of expression mesophyll _IjWith ratio of damping d _IjDo not change in time yet, have only the static length r of the spring of expression mesophyll _Ij(t) change in time.

Concrete physical simulation step is as follows, supposes that simulation process since the time 0, simulated time t:

1. according to by spring s _IjParticle i that is connected and the positional information of j calculate spring s _IjStressing conditions f _Ij(t), this process will be calculated all springs in the spring S set.

2. will be by s _IjThe spring force that calculates is applied on coupled two particle i and the j, promptly for any particle i, $f_i=\underset{p_j\∈S_i}{\mathrm{\Σ}}{f}_{\mathrm{ij}},$ This step is come out the Force Calculation of all springs, is applied on the particle.

3. for each particle in the particle set, particle i for example,, quality stressed by it are according to the Newtonian mechanics formula $a_i\left(t\right)=\frac{f_i\left(t\right)}{m_i}$ Calculate it at this moment acceleration a _i(t).

4. for each particle in the particle set, particle i for example, the movement velocity v that it is initial _i(0)=0, at t constantly by its acceleration a _i(t) and speed v _i(t), according to the kinematics formula, calculate the position p that next this particle constantly should be in _i(t+1) and new speed v _i(t+1).

5. upgrade speed, acceleration and the positional information of all particles and calculate (t+1) constantly, and upgrade the deformation coefficient of the spring of expression mesophyll, promptly by reducing the static length r of mesophyll spring to next _Ij(t) embody the contraction of mesophyll.

6. repeating step 1.

Constantly repeat top process, the position of each particle and speed are also just along with this physical simulation process changing slowly, in the simulation process, the variation of model geometric shape, the variation of the leaf geometric shape that just simulated, the final net result that can obtain simulating, thereby the aging final form of leaf just.

The present invention is by finding for the analysis of plant cell biology and mechanical structure, in the leaf blastment, mesophyll with vein since different separately institutional frameworks caused the shrinkage rates difference, thereby the form of leaf changed.In physical simulation,, be used for the metamorphosis of simulating plant under particular case and environment at first with particle-spring model introduced plant simulation field.By setting up double-deck particle-spring model, and, the different mechanical characteristics of mesophyll and vein have been showed well to the reasonable setting of bilevel different parameters about leaf basic structure.The interaction of bilayer model has determined the mode and the effect of the final distortion of leaf, can simulate the variation of variety classes plant leaf geometric shape in withered, ageing process thus very truly.

Plant leaf analogy method provided by the present invention gets close to nature truly the drawing result of leaf more.Constitute and the material resources characteristic because plant tissue has similar biology, this method while can expand to the moulded simulation of plant, and the limb of plant is carried out simulation modelling based on physics.Can in the related application of virtual reality, make up plant scene more true to nature by method of the present invention, also can allow the sense of reality of plant be plotted in fields such as recreation, video display, biology, environmental protection and further be used.

Description of drawings

Fig. 1 is that the scan image to plant leaf is provided with the different bianry image that obtains after the different separatrix values.

Fig. 2 is the stepping square method extracting mode synoptic diagram of leaf profile.

16 kinds of situation synoptic diagram that four jiaos of colors of grid may occur when Fig. 3 was stepping square method extraction bianry image.

Fig. 4 is in the stepping square method, the detailed schematic of the leaf profile that grid extracted of different sizes.

Fig. 5 is the step synoptic diagram based on nutrition point methods generation vein of Runions.

Fig. 6 is the vein of existing method and the inventive method generation and the comparative effectiveness figure of true leaf image.

Fig. 7 has behind vein and the leaf profile leaf is carried out result schematic diagram after the triangle gridding.

Fig. 8 is cell mechanical model and force analysis synoptic diagram under the microcosmic situation, wherein: A is the synoptic diagram to the individual cells force analysis, B is a plurality of cell force analysis and spring analog case synoptic diagram, and C is the synoptic diagram of abstract particle spring network analog cell physical arrangement of coming out.

Fig. 9 is the synoptic diagram that is used to make up the decussate texture of layer model under the leaf.

Figure 10 is the whole mechanics structural representation of leaf that makes up with double-deck particle of the present invention-spring model.

Figure 11 is the drawing result with the distortion of the Boston ivy leaf of method simulation of the present invention.

Figure 12 is with the Chinese toon leaf of method simulation of the present invention and the deformation result of Chinese parasol tree leaf.

Figure 13 is the result who draws by the photon tracking with the leaf of method simulation distortion of the present invention.

Figure 14 is the result who draws in the woods with the multi-disc Chinese toon leaf of method simulation of the present invention.

Embodiment

Below by embodiment, further specify the present invention in conjunction with the accompanying drawings, but the scope that does not limit the present invention in any way.

According to the analogue system based on biological and physics of the present invention, the various forms of different types of leaf in Various Seasonal have been constructed.Figure 11 be to the Boston ivy leaf under different external conditions and parameter, to its configuration physics Simulation result.Figure 12 has showed three experiment scenes wherein: be the distortion sequence of Boston ivy leaf, the sequence of Chinese toon leaf distortion and the sequence of Chinese parasol tree leaf distortion from top to bottom successively.Figure 13 and Figure 14 carry out the result that global illumination is drawn with the leaf model result of distortion.Simultaneously the leaf texture of Various Seasonal is applied in the specific implementation process on the model after the distortion.Wherein, Ailanthus altissima and Boston ivy leaf have all been showed the deformation effect that front and back is observed.Because shape, size and the texture of various leaves is different, the imaging resolution of drawing result is decided to be 800 * 600.All experimental results on the common PC of 1GB internal memory and Nvidia 7300 video cards, and adopt the Ray-tracing algorithm to draw all at 1.6GHz Athlon CPU.

The particle spring model of most of leaf structure is made of 1500 to 5000 particles, because the particle spring model is in the process of simulation, by damped vibration, steady state (SS) to the end gradually, therefore its computation process needs the long period, concrete simulated time such as following table usually:

	The particle number	The spring number	Shrink the simulation step number	Physical simulation is always consuming time
					Boston ivy	3247	4184	50	3h 21min 52s
Ailanthus altissima	1412	2574	50	1h 15min 17s
					Oriental plane tree	5024	7314	100	6h 23min 22s
Maple leaf	1973	3695	100	4h 50min 33s

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Claims (6)

1. the analogy method of a plant leaf comprises the following steps:

1) the plant leaf profile extracts: plant leaf is carried out image scanning, obtain the plane picture of leaf, then this image is carried out binaryzation, obtain bianry image, extract the leaf profile with the stepping square method at last;

2) plant leaf vein structure: utilization generates vein based on the vein generation method of nutrition point, and the vein that is generated is made up of the line segment that connects each vein node, and the speed of growth of setting master pulse and middle arteries and veins in the process that generates vein is 1.5-4 a times of secondary vein; Simultaneously, be provided with according to the diameter of Murray law every section vein: $d_{\mathrm{parent}}^n=d_{\mathrm{child}1}^n+d_{\mathrm{child}2}^n,$ D wherein _Parent, d _Child1And d _Child2The diameter of representing two vein sections forming behind the diameter of the vein section before the vein bifurcation branch and the branch respectively, n=1 or 2;

3) leaf surfaces model trigonometric ratio: with vein and leaf profile is constraint, and leaf surfaces is carried out restricted Delaunay trigonometric ratio, constructs the triangle gridding structure of leaf surfaces;

4) structure leaf particle-spring bilayer model: according to the triangle gridding structure of step 3) structure, with the summit of triangle gridding particle as the expression mesophyll cell, the spring of adjacent particle is represented to connect in limit in the triangle gridding, constructs the upper strata particle-spring network model of expression mesophyll tissue; According to step 2) structure vein, with the lower floor particle of vein node as expression vein cell, per two adjacent lower floor's particles and two upper strata particles directly over it constitute a rectangle on the same vein, these four particles link to each other in twos by spring each other, construct lower floor's particle-spring model of band criss-cross construction in the rectangle, and couple together, thereby form the particle-spring bilayer model that to express the leaf mechanical structure with upper strata particle-spring network model; In this bilayer model, with i, j represent among the particle set M any two adjacent and by the particle that spring is connected, use s _IjExpression connects the spring of particle i and particle j, p _iAnd p _jThe position of representing particle i and particle j respectively, S _iRepresent the set of the spring that all link to each other with particle i, the power that then acts on the particle i is:

$f_i\left(t\right)=-\underset{p_j\∈S_i}{\mathrm{\Σ}}\left\{h_{\mathrm{ij}}\left(t\right)\right[\left|l_{\mathrm{ij}}\right|-r_{\mathrm{ij}}\left(t\right)]+d_{\mathrm{ij}}\frac{\stackrel{\·}{l_{\mathrm{ij}}}\·l_{\mathrm{ij}}}{\left|l_{\mathrm{ij}}\right|}\}\frac{l_{\mathrm{ij}}}{\left|l_{\mathrm{ij}}\right|}$

Wherein, l _IjExpression is from p _iTo position p _jVector; h _Ij(t) expression spring s _IjElasticity coefficient; d _IjExpression spring s _IjRatio of damping; r _Ij(t) expression spring s _IjStatic length;

The speed of related movement of expression particle i and j, i.e. l _IjDerivative to the time;

5) carry out the physical simulation computing: according to the leaf particle-spring bilayer model coding of step 4) structure, change the form progressively simulate plant leaf under the state of nature according to the time, detailed process is: at first set the spring of expression vein and the elasticity coefficient h of the spring that is connected the levels model _Ij, ratio of damping d _IjWith static length r _IjDo not change the elasticity coefficient h of the spring of expression mesophyll in time _IjWith ratio of damping d _IjDo not change in time yet; After the initial parameter of setting leaf particle-spring bilayer model, begin to repeat successively following step a～e then from t=0:

A. for each spring s _Ij, according to by spring s _IjParticle i that is connected and the positional information of j calculate at moment t spring s _IjStressing conditions f _Ij(t);

B. will be by s _IjThe spring force that calculates is applied on coupled two particle i and the j, promptly for any particle i,

$f_i=\underset{p_j\∈S_i}{\mathrm{\Σ}}{f}_{\mathrm{ij}};$

C. for each particle i, by its stressed f at moment t _i(t) and quality m _i, according to the Newtonian mechanics formula $a_i\left(t\right)=\frac{f_i\left(t\right)}{m_i}$ Calculate it at this acceleration a constantly _i(t);

D. for each particle i, the movement velocity v that it is initial _i(0)=0, at t constantly by its acceleration a _i(t) and speed v _i(t), according to the kinematics formula, the position p that this particle should be in when calculating next one moment t+1 _i(t+1) and new speed v _i(t+1);

E. upgrade speed, acceleration and the positional information of all particles and calculate (t+1) constantly, and upgrade the static length r of the spring of expression mesophyll to next _Ij(t).

2. the analogy method of plant leaf as claimed in claim 1, it is characterized in that: the concrete grammar of stepping square method extraction leaf profile is in the described step 1): the profile of supposing leaf is sealing and continuous, the leaf bianry image is carried out the horizontal scanning of sweep trace mode with grid from order left to bottom right, enter the zone of leaf inside up to certain angle of grid, grid stops the horizontal scanning of sweep trace mode then, then begin to move with counter clockwise direction along the border of leaf, up to the polygonal profile that obtains whole leaf.

3. the analogy method of plant leaf as claimed in claim 1 is characterized in that: the speed of growth of setting master pulse and middle arteries and veins described step 2) is 2 times of secondary vein.

4. the analogy method of plant leaf as claimed in claim 1, it is characterized in that: the Exact_predicates_inexact_constructions_kernel class that described step 3) uses the CGAL storehouse to provide, the Delaunay_mesher_2 class, the Delaunay_mesh_face_base_2 class, these 4 kinds of data structures of Constrained_Delaunay_triangulation_2 class are organized with leaf profile and vein line segment and the point data as restriction, and use the refine_Delaunay_mesh_2 function to carry out restricted Delaunay trigonometric ratio, carry out triangle minimum angles and minimum area control with data structure Criteria.

5. the analogy method of plant leaf as claimed in claim 4 is characterized in that: choose parameters C riteria (0.005,0.5) in the described step 3), the length of side of expression triangle minimum edge can not be less than 0.005, and the angle at minimum angle can not be less than 0.5 radian.

6. the analogy method of plant leaf as claimed in claim 1 is characterized in that: in step 2) in the diameter of least significant end vein section is made as 1, according to formula $d_{\mathrm{parent}}^n=d_{\mathrm{child}1}^n+d_{\mathrm{child}2}^n$ Calculate the diameter of other vein sections at different levels, in step 5), characterize the hardness of vein spring with the diameter of vein section, the hardness of least significant end vein spring is standard 1, the hardness that to represent the upper strata particle-spring network model medi-spring of mesophyll tissue simultaneously also is set to standard 1, and the hardness of spring is embodied as elasticity coefficient h _IjSize, thus the elasticity coefficient of the spring in whole particle-spring bilayer model is carried out the parameter setting.

Images