CN104615481B - A kind of wind based on cluster cluster has leaf tree to flicker analogy method - Google Patents

Abstract

The invention discloses a kind of winds based on cluster cluster to have leaf tree to flicker analogy method, is specifically implemented according to the following steps: step 1 divides and has leaf tree；The leaf for having leaf tree of each equal portions after dividing in step 1 is carried out Density Clustering by step 2, generates multiple leafages；Step 3, the sequencing for receiving wind-force effect according to the leafage in step 2 establish the topological structure of leafage；The wind-force size that leafage node and its connected branch and trunk in step 4, calculating step 3 in leafage topological structure are subject to, and Flexural cantilever model is combined to calculate deformation of the tree trunk part in wind, it is flickered simulation by the linkage that relative position be integrally formed leaf tree.A kind of wind based on cluster cluster of the present invention has leaf tree analogy method of flickering that can reconstruct the part of leaf tree and the movement flickered of generation that interacts occurs for wind.

Description

A kind of wind based on cluster cluster has leaf tree to flicker analogy method

Technical field

The invention belongs to the cross discipline technical fields that computer graphics is combined with mathematical modeling technology field, specifically Being related to a kind of wind based on cluster cluster has leaf tree to flicker analogy method.

Background technique

With the raising of computer performance and the development of computer graphics, the research of natural scene modeling is had been applied to Many fields, such as: game industry, video display special efficacy field.Tree as the important component in natural scene, force by form True simulation degree can effectively increase the vividness of scene.Traditional particIe system and texture mapping method, can simply simulate The natural phenomenas such as some wind, river, rain, snow, but there are also very big for the authenticity of its movement simulation and complexity and reality scene Distance.

With the development of computer simulation technique, the static simulation of tree has been unable to meet the requirement of practical application, for tree The simulation swung because nature external force influences becomes new research hotspot.Wind in an atmosphere plays to pass the movement of tree Important role, for wind as invisible fluid, complex shape is changeable, and constantly affects the environment of surrounding, for there is leaf tree Flicker for it is even more so.And the dynamic analog of tree is related to multiple subjects such as atmospheric dynamics, the mechanics of materials and physics, To realize that the real-time realistic simulation for having leaf tree to flicker under wind-force effect is a difficulty in computer graphics and mathematical modeling Topic.

The tree dynamic analog research of early stage is based on particIe system and texture mapping, and its implementation is simple but simulates effect Coarse, artificial trace is fairly obvious.In recent years, with the continuous development of computer graphics, domestic and foreign scholars are to tree dynamic analog Quasi- research work is more and more, and simulation effect is also more and more true to nature.Shinya utilizes mould by one RANDOM WIND FIELD of construction State analysis method analog tree is flickered wind.Wind field required for Hiromi is generated using Perlin noise function, using dividing shape Algorithm recurrence goes out the shape set, and the deformation of branch is calculated using spring-mass model.Stam simulates the branch of tree in turbulent flow Movement in wind field simulates the swing effect of the branch of tree.Grandson builds hair et al. and proposes during the recursive generation of three-dimensional tree Using Vector modulation principle, for spanning tree in the animation of movement in wind, this method can simply realize tree movement simulation, but simulate Effect is relatively rough.Hu Xiaoyi et al. proposes a kind of fortune of flickering based on the method analog tree of dynamics finite element in wind It is dynamic, the vortex theory of peripheral flow is applied to the calculating of Fluctuating Lift and resistance that branch is subject in wind, this method The fluid structurecoupling between tree and wind field is considered, the movement set under different wind scales can be simulated.

It is completely in and is simulated in the state of wind effect however, presently relevant research is all based on tree.But real feelings In condition, often the part of tree is by wind effect when setting by wind effect, rather than just entire tree.

Summary of the invention

The object of the present invention is to provide a kind of winds based on cluster cluster to have leaf tree to flicker analogy method, solves existing skill Art cannot reconstruct the part of leaf tree and wind occurs to interact to lead to the problem of to flicker to move.

The technical scheme adopted by the invention is that a kind of wind based on cluster cluster has leaf tree to flicker analogy method, specifically It follows the steps below to implement:

Step 1, division have leaf tree；

The leaf for having leaf tree of each equal portions after dividing in step 1 is carried out Density Clustering by step 2, generates multiple leaves Cluster；

Step 3, the sequencing for receiving wind-force effect according to the leafage in step 2 establish the topological structure of leafage；

The wind that leafage node and its connected branch and trunk in step 4, calculating step 3 in leafage topological structure are subject to Power size, and Flexural cantilever model is combined to calculate deformation of the tree trunk part in wind, it carries out being integrally formed leaf tree by relative position Linkage flicker simulation.

The features of the present invention also characterized in that

Step 1 has the division of leaf tree specifically:

Step 1.1, init state position sum=1, the wind speed that each equal portions nonleave tree is subject to are speed_i=0, and back up For copyspeed_i=0, to distinguish the wind speed that each equal portions are subject under different conditions；Wherein, sum is the sum times calculation of wind speed, I is the equal numbers that nonleave tree divides；

The distance of step 1.2, calculating trunk skeleton point to wind regime

It is assumed that wind and the angle of Z axis forward direction are zWind, look down from Z axis forward direction, the angle counterclockwise of wind and X-axis is XWind establishes the unit vector of wind according to spherical coordinate system:

Projection vector of the wind direction on the face XOY be

Distance of the trunk skeleton point to wind regime are as follows:

D=| cos (xWind) x₀+sin(xWind)·y₀+C|

It is minimized d_min, threshold value sheld=d_min/ 2, mode bit j=2, while backing up wind speed speed_iValue arrive copyspeed_iIn, wherein j indicates the jth equal portions of nonleave tree；

The annulus center of circle where trunk skeleton point and branch of all distances to wind regime less than sheld is classified as by step 1.3 First equal portions, are denoted as unit₁；First equal portions the time it takes t is blowed air over according to the calculating of initial wind speed_sum, and will be after decaying Wind speed is stored in speed₁In, sum++；If unit at this time₁The wind speed copyspeed being subject to₁≠ 0, expression also needs to continue to divide, Go to step 1.4；If copyspeed₁=0, indicating to divide terminates, and goes to step 1.2；

Step 1.4, threshold value sheld=sheld+copyspeed_j-1·t_j, all distances to wind regime are less than sheld Trunk skeleton point and branch where the annulus center of circle be classified as jth equal portions, be denoted as unit_j；According to wind speed copyspeed_j-1Calculate wind Wind speed after blowing over jth equal portions, and it is stored in speed_jIn, j++；If unit at this time_jThe wind speed copyspeed being subject to_j≠ 0, table Showing also needs to continue to divide, and step 1.4 is repeated, until j > sum；If copyspeed_j=0, indicating to divide terminates, and goes to step Rapid 1.2.

Wind speed speed after blowing air over jth equal portions in step 1.4_jCalculation method are as follows:

Wherein, V_treeFor the volume of the tree of jth equal portions, V is the total volume of jth equal portions.

Have the Density Clustering of the leaf of leaf tree in step 2 specifically includes the following steps:

Step 2.1 takes first point of the petiole of each leaf to represent entire leaf, is deposited into array dataSets In, and its access state is set as false, affiliated cluster cluster is " 0 "；

Step 2.2 searches the point p that each of array dataSets access state is false₀Neighbor Points domain in Point p_i, such as fruit dot p₀With point p_iDistance no more than setting threshold tau, then will point p_iAddition point p₀Neighborhood in, and be stored in neighborhood List p₀.FieldId；If the distance of two o'clock, then will point p between (τ, 2 τ)_iIt is inserted into container VectPt, and records insertion Element number VectNum；

Step 2.3, such as fruit dot p₀Neighborhood in point number be not less than threshold value k, then set-point p₀For core point, point p is set₀ And the access state of the point in neighborhood is true, at this time with p₀Neighbor Points domain for core point is a cluster, cluster++； Such as fruit dot p₀It is not core point, then deletes VectNum element from container VectPt；

Step 2.4, successively the point p in container VectPt described in finding step 2.2_iNeighbor Points domain in point q, if Point p_iWith at a distance from point q no more than setting threshold tau, then by point q addition point p_iField in；Such as fruit dot p_iField in point Number is not less than threshold value k, point p_iFor core point, then point p is set_iAnd the access state of point q is true, and will point p_iAnd point q is added to p₀Then the cluster at place deletes point p from container VectPt_i；Such as fruit dot p_iIt is not core point, then it directly will point p_iFrom container It is deleted in VectPt；

Step 2.5 continues to execute from step 2.2, until having traversed all the points；

Threshold tau in step 2.6, amendment step 2.2, continue from step 2.2 execute, until all the points be included into it is poly- Class will have the leaf of leaf tree to cluster by different densities, generate multiple leafages.

The method for building up of the topological structure of leafage in step 3 are as follows:

Step 3.1, the tree structure treenode for establishing leafage, and initialize: read first in array dataSets A point p₀(x₀,y₀,z₀), it is denoted as root node root；It will point p₀In place cluster deposit treenode.clusterId, p₀Coordinate It is worth (x₀,y₀,z₀) be stored in treenode.Min and treenode.Max；Enable leaf number treenode.num=in node 1；

Step 3.2 enables treenode=root, reads the point p in array dataSets_i(x_i,y_i,z_i)；

Step 3.3, judgement point p_i(x_i,y_i,z_i) with node treenode whether be same class cluster: if belonging to same class Cluster then goes to step 3.4；If being not belonging to same class cluster, step 3.5 is gone to；

Step 3.4 is respectively compared x_iWith treenode.Min.x, y_iWith treenode.Min.y, z_iWith The value of treenode.Min.z, by it is lesser value respectively be stored in treenode.Min.x, treenode.Min.y, In treenode.Min.z；It is respectively compared x again_iWith treenode.Max.x, y_iWith treenode.Max.y, z_iWith The value of treenode.Max.z, by it is biggish value respectively be stored in treenode.Max.x, treenode.Max.y, In treenode.Max.z, and treenode.num++, it is continued to execute from step 3.2, until array dataSets is sky；

Step 3.5, such as fruit dot p_i(x_i,y_i,z_i) in the bounding box that treenode.Min and treenode.Max is formed Portion, node treenode is to point p_i(x_i,y_i,z_i) produce occlusion effect, then go to step 3.6；Such as fruit dot p_i(x_i,y_i,z_i) Outside the bounding box that treenode.Min and treenode.Max is formed, node treenode is to point p_i(x_i,y_i,z_i) do not produce Raw occlusion effect, then go to step 3.7；

Step 3.6, the left child nodes treenode.leftchild for searching treenode, if left child nodes Treenode.leftchild is sky, then will point p_i(x_i,y_i,z_i) it is denoted as its left child nodes, and enable treenode= Treenode.leftchild, point p_iIn place cluster deposit treenode.clusterId, p_iCoordinate value (x_i,y_i,z_i) It is stored in treenode.Min and treenode.Max, continues to execute from step 3.2, until array dataSets is sky；If left Child nodes treenode.leftchild is not sky, continues to execute from step 3.3；

Step 3.7, the right child nodes treenode.rightchild for searching treenode, if right child nodes Treenode.rightchild is sky, then will point p_i(x_i,y_i,z_i) it is denoted as its right child nodes, and enable treenode= Treenode.rightchild, point p_iIn place cluster deposit treenode.clusterId, p_iCoordinate value (x_i,y_i,z_i) It is stored in treenode.Min and treenode.Max, continues to execute from step 3.2, until array dataSets is sky；If right Child nodes treenode.rightchild is not sky, continues to execute from step 3.3.

The bounding box that treenode.Min and treenode.Max are formed in step 3.5 be by point (treenode.Min.x, Treenode.Min.y, treenode.Min.z), point (treenode.Min.x, treenode.Min.y, Treenode.Max.z), point (treenode.Min.x, treenode.Max.y, treenode.Min.z), point (treenode.Min.x, treenode.Max.y, treenode.Max.z), point (treenode.Max.x, Treenode.Min.y, treenode.Min.z), point (treenode.Max.x, treenode.Min.y, Treenode.Max.z), point (treenode.Max.x, treenode.Max.y, treenode.Min.z), point The cube that (treenode.Max.x, treenode.Max.y, treenode.Max.z) eight points are formed.

The wind-force F that step 4 middle period cluster node and its connected branch and trunk receive are as follows:

F=F_l+F_d (1)

Wherein,For lift,For resistance caused by pressure, C_lTo rise Force coefficient, C_dFor resistance coefficient, S_FaceIndicate the contact area of object and wind, S_Face=2 π rL, ρ are atmospheric density, and V is wind speed, and L is The length of leaf；

Regard leaf as a square planar blade, the mass center of blade is its central point, blade under the action of the wind around Petiole rotation, rotary inertia I are as follows:

I=mr² (2)

Wherein, m be blade quality, r be blade mass center to petiole distance；

Using wind direction as referential, can be divided into two kinds of situations according to the relationship of wind direction and blade: wind direction and blade hang down Straight or parallel, wind direction and blade is at an acute angle or obtuse angle；

(1) wind direction and blade are perpendicular or parallel

When wind is to blade, using blade as referential, three kinds of feelings are segmented into according to the corner dimension of blade and wind direction Condition: wind vertically blows to blade, wind and blows to petiole side along tip-side to tip-side, wind along petiole is side-blown；

1. wind vertically blows to blade

Cantilever spring rotates angle under the action of the wind are as follows:

Formula (1), (2) are substituted into formula (3), are obtained:

Wherein E is the Young's modulus of leaf；

2. wind is side-blown to tip-side along petiole

According to the relationship of the three elements of power and power it is found that not all wind-force all produces influence to leaf, effect There was only Fsin θ in epiphyllous effective force, remaining power is gone out by coarse blade diffusing reflection, in the process, wind meeting Certain pressure is generated, leaf is pushed to move, the effective force that leaf is subject at this time should be F₁'=Fsin θ+F_press1,

Wherein,

F_press1=ξ₁·F(1-sinθ) (5)

ξ₁For diffusing reflection press factors, and 0 < ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf2Are as follows:

Wherein,

Angle of the θ between wind and tree trunk,For the unit direction vector of tree trunk,For the unit direction vector of wind direction；

3. wind blows to petiole side along tip-side

The effective force that leaf is subject at this time should be F₂'=Fsin θ+F_press2,

Wherein,

F_press2=ξ₂·F(1-sinθ) (7)

ξ₂For diffusing reflection press factors, and 0 < ξ₂< ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf3Are as follows:

(2) wind direction and blade is at an acute angle or obtuse angle

When wind is to blade, using blade as referential, three kinds of feelings are segmented into according to the corner dimension of blade and wind direction Condition: wind vertically blows to blade, wind and blows to petiole side along tip-side to tip-side, wind along petiole is side-blown；

1. wind vertically blows to blade

According to mechanics principle, wind perpendicular acting only has Fsin θ in epiphyllous effective force_plane, remaining power is by thick Rough blade diffusing reflection is gone out, and in the process, wind can generate certain pressure, push leaf move, at this time leaf by Effective force should be F₃'=Fsin θ_plane+F_press3,

Wherein,

F_press3=ξ F (1-sin θ_plane) (9)

ξ is diffusing reflection press factors, and 0 < ξ < 1,

Wherein,

θ_planeFor the angle of wind direction and blade,For the unit direction vector of blade,

Rotation angle, θ of the leaf under effective force effect_leaf4Are as follows:

2. wind is side-blown to tip-side along petiole

Wind along petiole it is side-blown to tip-side when, the effective force that leaf is subject at this time is F₄'=(Fsin θ_plane+ F_press4) sin θ,

Wherein,

F_press4=ξ₁·F(1-sinθ_plane) (11)

ξ₁For diffusing reflection press factors, and 0 < ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf5Are as follows:

3. wind blows to petiole side along tip-side

When wind blows to petiole side against tip-side, the effective force that leaf is subject at this time is F₅'=(Fsin θ_plane+ F_press5) sin θ,

Wherein,

F_press5=ξ₂·F(1-sinθ_plane) (13)

ξ₂For diffusing reflection press factors, and 0 < ξ₂< ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf6Are as follows:

The beneficial effects of the present invention are: a kind of wind based on cluster cluster of the present invention has leaf tree to flicker analogy method, pass through There to be the division of leaf tree, and the movement of the trunk and branch of each equal portions then be simulated respectively using Flexural cantilever model, finally according to wind To angles different with blade, giving leaf movement is the angle change model of wind and the dynamics changing pattern of wind leaf Type, and then realize the jitter simulation of leaf；There is leaf tree to flicker analogy method using a kind of wind based on cluster cluster of the present invention The part and wind that leaf tree can be reconstructed occur interaction and generate the movement flickered.

Detailed description of the invention

Fig. 1 is that wind of the present invention has leaf tree to flicker the relational graph of wind direction and blade in analogy method；

Fig. 2 is that wind of the present invention has leaf tree to flicker relational graph of the wind direction with blade when vertical in analogy method；

Fig. 3 is that wind of the present invention has leaf tree to flicker relational graph of the wind direction with blade when parallel in analogy method；

Fig. 4 is the relational graph that wind of the present invention has leaf tree to flicker when wind direction and blade are at an acute angle in analogy method；

Fig. 5 is the relational graph that wind of the present invention has leaf tree to flicker when wind direction and blade are at obtuse angle in analogy method；

Fig. 6 is that have leaf tree to flicker using wind of the present invention to have the deformation effects figure of leaf tree after analogy method.

Specific embodiment

The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.

A kind of wind based on cluster cluster of the present invention has leaf tree to flicker analogy method, is specifically implemented according to the following steps:

Step 1, division have leaf tree (will have leaf tree to be divided into 13 equal portions in the embodiment of the present invention):

Step 1.1, init state position sum=1, the wind speed that each equal portions nonleave tree is subject to are speed_i=0 (i=1, 2 ..., 13) it, and backs up as copyspeed_i=0 (i=1,2 ..., 13), to distinguish the wind that each equal portions are subject under different conditions Speed；Wherein, sum is the sum time calculation of wind speed, and i is the equal numbers of nonleave tree division (i value is 13 in the present embodiment)；

The distance of step 1.2, calculating trunk skeleton point to wind regime

It is assumed that wind and the angle of Z axis forward direction are zWind, look down from Z axis forward direction, the angle counterclockwise of wind and X-axis is XWind establishes the unit vector of wind according to spherical coordinate system:

Projection vector of the wind direction on the face XOY be

Distance of the trunk skeleton point to wind regime are as follows:

D=| cos (xWind) x₀+sin(xWind)·y₀+C|

It is minimized d_min, threshold value sheld=d_min/ 2, mode bit j=2, while backing up wind speed speed_iValue arrive copyspeed_iIn, wherein j indicates the jth equal portions of nonleave tree；The value of constant C is 0.1, and the value of distance d is smaller, illustrates the tree Dry section or branch are closer from wind regime, are influenced by wind-force more early；Conversely, then more late by the time of windage.

The annulus center of circle where trunk skeleton point and branch of all distances to wind regime less than sheld is classified as by step 1.3 First equal portions, are denoted as unit₁；First equal portions the time it takes t is blowed air over according to the calculating of initial wind speed_sum, and will be after decaying Wind speed is stored in speed₁In, sum++；If unit at this time₁The wind speed copyspeed being subject to₁≠ 0, expression also needs to continue to divide, Go to step 1.4；If copyspeed₁=0, indicating to divide terminates, and goes to step 1.2；

Step 1.4, threshold value sheld=sheld+copyspeed_j-1·t_j, all distances to wind regime are less than sheld Trunk skeleton point and branch where the annulus center of circle be classified as jth equal portions, be denoted as unit_j；According to wind speed copyspeed_j-1Calculate wind Wind speed after blowing over jth equal portions, and it is stored in speed_jIn, j++；If unit at this time_jThe wind speed copyspeed being subject to_j≠ 0, table Showing also needs to continue to divide, and step 1.4 is repeated, until j > sum；If copyspeed_j=0, indicating to divide terminates, and goes to step Rapid 1.2.

Wind speed speed after blowing air over jth equal portions in step 1.4_jCalculation method are as follows:

Wherein, V_treeFor the volume of the tree of jth equal portions, V is the total volume of jth equal portions.

Step 2 generates the cluster of the leaf of each equal portions of multiple leafages i.e. leaf:

Step 2.1 takes first point of the petiole of each leaf to represent entire leaf, is deposited into array dataSets In, and its access state is set as false, affiliated cluster cluster is " 0 "；

Step 2.2 searches the point p that each of array dataSets access state is false₀Neighbor Points domain in Point p_i, such as fruit dot p₀With point p_iDistance no more than setting threshold tau, then will point p_iAddition point p₀Neighborhood in, and be stored in neighborhood List p₀.FieldId；If the distance of two o'clock, then will point p between (τ, 2 τ)_iIt is inserted into container VectPt, and records insertion Element number VectNum；

Step 2.3, such as fruit dot p₀Neighborhood in point number be not less than threshold value k, then set-point p₀For core point, point p is set₀ And the access state of the point in neighborhood is true, at this time with p₀Neighbor Points domain for core point is a cluster, cluster++； Such as fruit dot p₀It is not core point, then deletes VectNum element from container VectPt；

Step 2.4, successively the point p in container VectPt described in finding step 2.2_iNeighbor Points domain in point q, if Point p_iWith at a distance from point q no more than setting threshold tau, then by point q addition point p_iField in；Such as fruit dot p_iField in point Number is not less than threshold value k, point p_iFor core point, then point p is set_iAnd the access state of point q is true, and will point p_iAnd point q is added to p₀Then the cluster at place deletes point p from container VectPt_i；Such as fruit dot p_iIt is not core point, then it directly will point p_iFrom container It is deleted in VectPt；

Step 2.5 continues to execute from step 2.2, until having traversed all the points；

Threshold tau in step 2.6, amendment step 2.2, continue from step 2.2 execute, until all the points be included into it is poly- Class will have the leaf of leaf tree to cluster by different densities, generate multiple leafages.

Step 3 establishes the topological structure of leafage:

Step 3.1, the tree structure treenode for establishing leafage, and initialize: read first in array dataSets A point p₀(x₀,y₀,z₀), it is denoted as root node root；It will point p₀In place cluster deposit treenode.clusterId, p₀Coordinate It is worth (x₀,y₀,z₀) be stored in treenode.Min and treenode.Max；Enable leaf number treenode.num=in node 1；

Step 3.2 enables treenode=root, reads the point p in array dataSets_i(x_i,y_i,z_i)；

Step 3.3, judgement point p_i(x_i,y_i,z_i) with node treenode whether be same class cluster: if belonging to same class Cluster then goes to step 3.4；If being not belonging to same class cluster, step 3.5 is gone to；

Step 3.4 is respectively compared x_iWith treenode.Min.x, y_iWith treenode.Min.y, z_iWith The value of treenode.Min.z, by it is lesser value respectively be stored in treenode.Min.x, treenode.Min.y, In treenode.Min.z；It is respectively compared x again_iWith treenode.Max.x, y_iWith treenode.Max.y, z_iWith The value of treenode.Max.z, by it is biggish value respectively be stored in treenode.Max.x, treenode.Max.y, In treenode.Max.z, and treenode.num++, it is continued to execute from step 3.2, until array dataSets is sky；

Step 3.5, such as fruit dot p_i(x_i,y_i,z_i) in the bounding box that treenode.Min and treenode.Max is formed Portion, node treenode is to point p_i(x_i,y_i,z_i) produce occlusion effect, then go to step 3.6；Such as fruit dot p_i(x_i,y_i,z_i) Outside the bounding box that treenode.Min and treenode.Max is formed, node treenode is to point p_i(x_i,y_i,z_i) do not produce Raw occlusion effect, then go to step 3.7；

The bounding box that wherein treenode.Min and treenode.Max are formed be by point (treenode.Min.x, Treenode.Min.y, treenode.Min.z), point (treenode.Min.x, treenode.Min.y, Treenode.Max.z), point (treenode.Min.x, treenode.Max.y, treenode.Min.z), point (treenode.Min.x, treenode.Max.y, treenode.Max.z), point (treenode.Max.x, Treenode.Min.y, treenode.Min.z), point (treenode.Max.x, treenode.Min.y, Treenode.Max.z), point (treenode.Max.x, treenode.Max.y, treenode.Min.z), point The cube that (treenode.Max.x, treenode.Max.y, treenode.Max.z) eight points are formed；

Step 3.6, the left child nodes treenode.leftchild for searching treenode, if left child nodes Treenode.leftchild is sky, then will point p_i(x_i,y_i,z_i) it is denoted as its left child nodes, and enable treenode= Treenode.leftchild, point p_iIn place cluster deposit treenode.clusterId, p_iCoordinate value (x_i,y_i,z_i) It is stored in treenode.Min and treenode.Max, continues to execute from step 3.2, until array dataSets is sky；If left Child nodes treenode.leftchild is not sky, continues to execute from step 3.3；

Step 3.7, the right child nodes treenode.rightchild for searching treenode, if right child nodes Treenode.rightchild is sky, then will point p_i(x_i,y_i,z_i) it is denoted as its right child nodes, and enable treenode= Treenode.rightchild, point p_iIn place cluster deposit treenode.clusterId, p_iCoordinate value (x_i,y_i,z_i) It is stored in treenode.Min and treenode.Max, continues to execute from step 3.2, until array dataSets is sky；If right Child nodes treenode.rightchild is not sky, continues to execute from step 3.3.

Step 4 has the skimulated motion of leaf tree:

The wind-force F that leafage node and its connected branch and trunk receive are as follows:

F=F_l+F_d (1)

Wherein,For lift,For resistance caused by pressure, C_lTo rise Force coefficient (C_l=0.013), C_dFor resistance coefficient (C_d=0.75), S_FaceIndicate the contact area of object and wind, S_Face=2 π rL, ρ are Atmospheric density (ρ=2.37 × 10^-3g/m³), V is wind speed, and L is the length of leaf；

The present invention simplifies leaf model, ignores the complicated factors such as its shape, is regarded as a square planar blade.Blade Mass center be its central point, blade under the action of the wind around petiole rotate, rotary inertia I are as follows:

I=mr² (2)

Wherein, m be blade quality, r be blade mass center to petiole distance；

Using wind direction as referential, can be divided into two kinds of situations according to the relationship of wind direction and blade: wind direction and blade hang down Straight or parallel, wind direction and blade is at an acute angle or obtuse angle；(as shown in Figure 1, due to calculating tree when wind direction and blade are perpendicular or parallel Rotation angle of the leaf under effective force effect is the same, thus by wind direction with blade is vertical and horizontal is classified as a kind of calculating, similarly, wind It is rotated as angle to blade at when obtuse angle or acute angle, so wind direction and blade are classified as a kind of calculating at obtuse angle and acute angle)

(1) wind direction and blade are perpendicular or parallel

When wind is to blade, using blade as referential, three kinds of feelings are segmented into according to the corner dimension of blade and wind direction Condition: wind vertically blows to blade, wind and blows to petiole side along tip-side to tip-side, wind along petiole is side-blown；

1. wind vertically blows to blade

Cantilever spring rotates angle under the action of the wind are as follows:

Formula (1), (2) are substituted into formula (3), obtain rotation angle, θ of the leaf under effective force effect_leaf1Are as follows:

It is 0.1GPa that wherein E, which is the Young's modulus value of leaf,；

2. wind is side-blown to tip-side along petiole

According to the relationship of the three elements of power and power it is found that not all wind-force all produces influence to leaf, effect There was only Fsin θ in epiphyllous effective force, remaining power is gone out by coarse blade diffusing reflection, in the process, wind meeting Certain pressure is generated, leaf is pushed to move, the effective force that leaf is subject at this time should be F₁'=Fsin θ+F_press1,

Wherein,

F_press1=ξ₁·F(1-sinθ) (5)

ξ₁For diffusing reflection press factors, and 0 < ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf2Are as follows:

Wherein,

Angle of the θ between wind and tree trunk,For the unit direction vector of tree trunk,For the unit direction vector of wind direction；

3. wind blows to petiole side along tip-side

Blow to along petiole that leaf is similar, and wind acts on epiphyllous effective force and there was only Fsin θ with wind.Remaining power is unrestrained It reflects away and generates certain pressure, push leaf movement.Unlike, this pressure mostly flows to petiole from blade tip.Leaf ratio Branch is relatively soft, and Young's modulus is smaller than branch, under irreflexive pressure leaf the degree of bending also will necessarily than wind along It is big when petiole is blown.

The effective force that leaf is subject at this time should be F₂'=Fsin θ+F_press2,

Wherein,

F_press2=ξ₂·F(1-sinθ) (7)

ξ₂For diffusing reflection press factors, and 0 < ξ₂< ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf3Are as follows:

(2) wind direction and blade is at an acute angle or obtuse angle

When wind is to blade, using blade as referential, three kinds of feelings are segmented into according to the corner dimension of blade and wind direction Condition: wind vertically blows to blade, wind and blows to petiole side along tip-side to tip-side, wind along petiole is side-blown；

1. wind vertically blows to blade

Wind direction and when blade is at an acute angle or obtuse angle, blade can not only bend movement under the action of the wind, can also overflow It reflects away and does jitter motion along width of blade direction under Action of Wind pressure.According to mechanics principle, wind perpendicular acting is on leaf Effective force there was only Fsin θ_plane, remaining power goes out by coarse blade diffusing reflection, and in the process, wind can generate one Fixed pressure, pushes leaf to move, and the effective force that leaf is subject at this time should be F₃'=Fsin θ_plane+F_press3,

Wherein,

F_press3=ξ F (1-sin θ_plane) (9)

ξ is diffusing reflection press factors, and 0 < ξ < 1,

Wherein,

θ_planeFor the angle of wind direction and blade,For the unit direction vector of blade,

Rotation angle, θ of the leaf under effective force effect_leaf4Are as follows:

2. wind is side-blown to tip-side along petiole

Wind along petiole it is side-blown to tip-side when, the effective force that leaf is subject at this time is F₄'=(Fsin θ_plane+ F_press4) sin θ,

Wherein,

F_press4=ξ₁·F(1-sinθ_plane) (11)

ξ₁For diffusing reflection press factors, and 0 < ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf5Are as follows:

3. wind blows to petiole side along tip-side

When wind blows to petiole side against tip-side, the effective force that leaf is subject at this time is F₅'=(Fsin θ_plane+ F_press5) sin θ,

Wherein,

F_press5=ξ₂·F(1-sinθ_plane) (13)

ξ₂For diffusing reflection press factors, and 0 < ξ₂< ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf6Are as follows:

It is rotation angle of counted leaf under the action of different effective forces, i.e. analog by above-mentioned different situations The jitter conditions of leaf leaf itself in real world are flickered mould by the linkage that relative position be integrally formed leaf tree It is quasi-.

Having leaf tree to flicker after analogy method using wind of the present invention has the deformation effects figure of leaf tree as shown in Figure 6.

Claims (5)

1. a kind of wind based on cluster cluster has leaf tree to flicker analogy method, which is characterized in that be specifically implemented according to the following steps:

Step 1, division have leaf tree；

The leaf for having leaf tree of each equal portions after dividing in step 1 is carried out Density Clustering by step 2, generates multiple leafages；

Step 3, the sequencing for receiving wind-force effect according to the leafage in step 2 establish the topological structure of leafage；

The wind-force that leafage node and its connected branch and trunk in step 4, calculating step 3 in leafage topological structure are subject to is big It is small, and Flexural cantilever model is combined to calculate deformation of the tree trunk part in wind, the connection for being integrally formed leaf tree is carried out by relative position Shake and drags simulation；

The step 1 has the division of leaf tree specifically:

Step 1.1, init state position sum=1, the wind speed that each equal portions have leaf tree to be subject to are speed_i=0, and back up and be copyspeed_i=0, to distinguish the wind speed that each equal portions are subject under different conditions；Wherein, sum is the sum times calculation of wind speed, i For the equal numbers for having leaf tree to divide, the value of i is 1,2 ..., 13；

The distance of step 1.2, calculating trunk skeleton point to wind regime

It is assumed that wind and the angle of Z axis forward direction are zWind, looking down from Z axis forward direction, the angle counterclockwise of wind and X-axis is xWind, The unit vector of wind is established according to spherical coordinate system:

Projection vector of the wind direction on the face XOY be

Distance of the trunk skeleton point to wind regime are as follows:

D=| cos (xWind) x₀+sin(xWind)·y₀+C|

It is minimized d_min, threshold value sheld=d_min/ 2, it is jth equal portions that setting mode bit j=2, which is used to record and currently be divided, The wind speed speed that each equal portions are subject to simultaneously_iBackup to copyspeed_i, in i=1,2 ..., 13, C is constant 0.1, (x₀, y₀,z₀) it is ring center where trunk skeleton point or branch, the value of distance d is smaller, illustrates that branch is closer from wind regime, by wind-force It influences more early；

Step 1.3, the trunk skeleton point by all distances to wind regime less than sheld and both points of the branch place annulus center of circle The first equal portions are classified as, unit is denoted as₁；First equal portions the time it takes t is blowed air over according to the calculating of initial wind speed_sum, and will decline Wind speed after subtracting is stored in speed₁In, enable sum=sum+1；If unit at this time₁The wind speed copyspeed being subject to₁≠ 0, it indicates It also needs to continue to divide, goes to step 1.4；If copyspeed₁=0, indicating to divide terminates；

Step 1.4, threshold value sheld=sheld+copyspeed_j-1·t_sum, all distances to wind regime are less than to the tree of sheld The annulus center of circle is classified as jth equal portions where dry skeletal point and branch, is denoted as unit_j；According to wind speed copyspeed_j-1Calculating blows air over Wind speed after jth equal portions, and it is stored in speed_jIn；If unit at this time_jThe wind speed copyspeed being subject to_j≠ 0, indicating need to also be after It is continuous to divide, j=j+1 is enabled, step 1.4 is repeated, when j > 13, if copyspeed_j=0, indicating to divide terminates, and goes to Step 1.2, the space set under new state is recalculated to divide；

Wind speed speed after blowing air over jth equal portions in step 1.4_jCalculation method are as follows:

Wherein, V_treeFor the volume of the tree of jth equal portions, V is the total volume of jth equal portions.

2. a kind of wind based on cluster cluster according to claim 1 has leaf tree to flicker analogy method, which is characterized in that the step Have the Density Clustering of the leaf of leaf tree in rapid 2 specifically includes the following steps:

Step 2.1 takes first point of the petiole of each leaf to represent entire leaf, is deposited into array dataSets, and If its access state is false, affiliated cluster cluster is " 0 "；

Step 2.2 searches the point p that each of array dataSets access state is false₀Neighbor Points domain in point p_i, Such as fruit dot p₀With point p_iDistance no more than setting threshold tau, then will point p_iAddition point p₀Neighborhood in, and be stored in neighbor ist p₀.FieldId；If the distance of two o'clock, then will point p between (τ, 2 τ)_iIt is inserted into container VectPt, and records insertion element Number VectNum；

Step 2.3, such as fruit dot p₀Neighborhood in point number be not less than threshold value k, then set-point p₀For core point, point p is set₀And it is adjacent The access state of point in domain is true, at this time with p₀Neighbor Points domain for core point is a cluster, and enables cluster= cluster+1；Such as fruit dot p₀It is not core point, then successively deletes VectNum element from container VectPt, is i.e. deletion step All the points of the distance being inserted into 2.2 between (τ, 2 τ)；

Step 2.4, successively the point p in container VectPt described in finding step 2.2_iNeighbor Points domain in point q, such as fruit dot p_i With at a distance from point q no more than setting threshold tau, then by point q addition point p_iField in；Such as fruit dot p_iField in point number Not less than threshold value k, point p_iFor core point, then point p is set_iAnd the access state of point q is true, and will point p_iAnd point q is added to p₀Institute Cluster, then from container VectPt delete point p_i；Such as fruit dot p_iIt is not core point, then it directly will point p_iFrom container It is deleted in VectPt；

Step 2.5 continues to execute from step 2.2, until having traversed all the points；

Threshold tau in step 2.6, amendment step 2.2 continues to execute from step 2.2, until all the points are included into cluster, i.e., There to be the leaf of leaf tree to cluster by different densities, generates multiple leafages.

3. a kind of wind based on cluster cluster according to claim 2 has leaf tree to flicker analogy method, which is characterized in that the step The method for building up of the topological structure of leafage in rapid 3 are as follows:

Step 3.1, the tree structure treenode for establishing leafage, and initialize: read first point p in array dataSets₀ (x₀,y₀,z₀), it is denoted as root node root；It will point p₀In place cluster deposit treenode.clusterId, p₀Coordinate value (x₀, y₀,z₀) be stored in treenode.Min and treenode.Max, to initialize the smallest leaf of coordinate value in treenode With the maximum leaf of coordinate value；Enable leaf number treenode.num=1 in node；

Step 3.2 enables treenode=root, reads the point p in array dataSets_i(x_i,y_i,z_i)；

Step 3.3, judgement point p_i(x_i,y_i,z_i) with node treenode whether be same class cluster: if belonging to same class cluster, Go to step 3.4；If being not belonging to same class cluster, step 3.5 is gone to；

Step 3.4 is respectively compared x_iWith treenode.Min.x, y_iWith treenode.Min.y, z_iWith treenode.Min.z's Lesser value is stored in treenode.Min.x, treenode.Min.y, treenode.Min.z by value respectively；Compare respectively again Compared with x_iWith treenode.Max.x, y_iWith treenode.Max.y, z_iWith the value of treenode.Max.z, biggish value is distinguished It is stored in treenode.Max.x, treenode.Max.y, treenode.Max.z, and enables treenode.num= Treenode.num+1 is continued to execute from step 3.2, until array dataSets is sky；

Step 3.5, such as fruit dot p_i(x_i,y_i,z_i) inside the bounding box that treenode.Min and treenode.Max are formed, i.e. point p_i(x_i,y_i,z_i) be located inside using treenode.Min and treenode.Max as the cuboid on body diagonal vertex, node Treenode is to point p_i(x_i,y_i,z_i) produce occlusion effect, then go to step 3.6；Such as fruit dot p_i(x_i,y_i,z_i) Outside the cuboid that treenode.Min and treenode.Max is formed, node treenode is to point p_i(x_i,y_i,z_i) do not produce Raw occlusion effect, then go to step 3.7；

Step 3.6, the left child nodes treenode.leftchild for searching treenode, if left child nodes Treenode.leftchild is sky, then will point p_i(x_i,y_i,z_i) it is denoted as its left child nodes, point p_iPlace cluster deposit In treenode.clusterId, p_iCoordinate value (x_i,y_i,z_i) be stored in treenode.Min and treenode.Max, after It is continuous to be executed from step 3.2, until array dataSets is sky；If left child nodes treenode.leftchild is not empty, order Treenode=treenode.leftchild continues to execute from step 3.3；

Step 3.7, the right child nodes treenode.rightchild for searching treenode, if right child nodes Treenode.rightchild is sky, then will point p_i(x_i,y_i,z_i) it is denoted as its right child nodes, point p_iPlace cluster deposit In treenode.clusterId, p_iCoordinate value (x_i,y_i,z_i) be stored in treenode.Min and treenode.Max, Continue to execute from step 3.2, until array dataSets is sky；If right child nodes treenode.rightchild is not sky, Treenode=treenode.rightchild is then enabled, continues to execute from step 3.3.

4. a kind of wind based on cluster cluster according to claim 3 has leaf tree to flicker analogy method, which is characterized in that the step The bounding box that treenode.Min and treenode.Max are formed in rapid 3.5 be by point (treenode.Min.x, Treenode.Min.y, treenode.Min.z), point (treenode.Min.x, treenode.Min.y, Treenode.Max.z), point (treenode.Min.x, treenode.Max.y, treenode.Min.z), point (treenode.Min.x, treenode.Max.y, treenode.Max.z), point (treenode.Max.x, Treenode.Min.y, treenode.Min.z), point (treenode.Max.x, treenode.Min.y, Treenode.Max.z), point (treenode.Max.x, treenode.Max.y, treenode.Min.z), point The cube that (treenode.Max.x, treenode.Max.y, treenode.Max.z) eight points are formed, midpoint (treenode.Min.x, treenode.Min.y, treenode.Min.z) and point (treenode.Max.x, Treenode.Max.y, treenode.Max.z) it is respectively two vertex on body diagonal.

5. a kind of wind based on cluster cluster according to claim 1 has leaf tree to flicker analogy method, which is characterized in that the step The wind-force F that rapid 4 middle period cluster node and its connected branch and trunk receive are as follows:

F=F_l+F_d (1)

Wherein,For lift,For resistance caused by pressure, C_lFor lift coefficient, C_dFor resistance coefficient, S_FaceIndicate the contact area of object and wind, S_Face=2 π rL, ρ are atmospheric density, and V is wind speed, and L is leaf Length；

Regard leaf as a square planar blade, the mass center of blade is its central point, and blade is under the action of the wind around petiole Rotation, rotary inertia I are as follows:

I=mr² (2)

Wherein, m be blade quality, r be blade mass center to petiole distance；

Using wind direction as referential, be divided into three kinds of situations according to wind direction and the relationship of blade: wind direction is vertical with blade, wind direction , wind direction parallel with blade and blade is at an acute angle or obtuse angle；

(1) wind direction is vertical with blade

Cantilever spring rotates angle under the action of the wind are as follows:

Formula (1), (2) are substituted into formula (3), are obtained:

Wherein E is the Young's modulus of leaf；

(2) wind direction is parallel with blade

When wind is to blade, using blade as referential, because blade has certain thickness, blowing over the wind come in parallel can act on surely The side of blade, is specifically segmented into three kinds of situations: wind vertically blow to blade, wind along petiole it is side-blown to tip-side, wind along Tip-side blows to petiole side；

1. wind vertically blows to blade

Such case is identical as (1), can find out rotation angle of the leaf in wind by formula (4)；

2. wind is side-blown to tip-side along petiole

According to the relationship of the three elements of power and power it is found that not all wind-force all produces influence to leaf, tree is acted on Effective force on leaf only has Fsin θ, and remaining power is gone out by coarse blade diffusing reflection, and in the process, wind can generate Certain pressure, pushes leaf to move, and the effective force that leaf is subject at this time should be F₁'=Fsin θ+F_press1,

Wherein,

F_press1=ξ₁·F(1-sinθ) (5)

ξ₁For diffusing reflection press factors, and 0 < ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf2Are as follows:

Wherein,

Angle of the θ between wind and tree trunk,For the unit direction vector of tree trunk,For the unit direction vector of wind direction；

3. wind blows to petiole side along tip-side

The effective force that leaf is subject at this time should be F₂'=Fsin θ+F_press2,

Wherein,

F_press2=ξ₂·F(1-sinθ) (7)

ξ₂For diffusing reflection press factors, and 0 < ξ₂< ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf3Are as follows:

(3) wind direction and blade is at an acute angle or obtuse angle

When wind is to blade, using blade as referential, three kinds of situations: wind are segmented into according to the corner dimension of blade and wind direction The other side, wind, which are blowed to, from blade side blows to petiole side along tip-side to tip-side, wind along petiole is side-blown；

1. wind blows to the other side from blade side

According to mechanics principle, wind perpendicular acting only has Fsin θ in epiphyllous effective force_plane, remaining power is by coarse Blade diffusing reflection is gone out, and in the process, wind can generate certain pressure, pushes leaf to move, what leaf was subject at this time has Effect should be F₃'=Fsin θ_plane+F_press3,

Wherein,

F_press3=ξ F (1-sin θ_plane) (9)

ξ is diffusing reflection press factors, and 0 < ξ < 1,

Wherein,

θ_planeFor the angle of wind direction and blade,For the unit direction vector of blade,

Rotation angle, θ of the leaf under effective force effect_leaf4Are as follows:

2. wind is side-blown to tip-side along petiole

Wind along petiole it is side-blown to tip-side when, the effective force that leaf is subject at this time is F₄'=(Fsin θ_plane+F_press4) sin θ,

Wherein,

F_press4=ξ₁·F(1-sinθ_plane) (11)

ξ₁For diffusing reflection press factors, and 0 < ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf5Are as follows:

3. wind blows to petiole side along tip-side

When wind blows to petiole side against tip-side, the effective force that leaf is subject at this time is F₅'=(Fsin θ_plane+F_press5) sin θ,

Wherein,

F_press5=ξ₂·F(1-sinθ_plane) (13)

ξ₂For diffusing reflection press factors, and 0 < ξ₂< ξ₁< 1,

Rotation angle, θ of the leaf under effective force effect_leaf6Are as follows: