CN106570915A - Method for constructing two-order geometric continuity completely convex closed curve - Google Patents

Abstract

The invention discloses a method for constructing a two-order geometric continuity completely convex closed curve. The method includes the following steps that: a convex hull point set P={pi|i= 0,1, ...,n-1} is constructed, when i<=0, or i>n, i indicates that i performs modulo operation on n; segmental cubic Bezier curves are adopted to construct a completely convex closed curve; an equation set is constructed and solved; and solution optimization and completely convex closed curve calculation are performed, so that a two-degree geometric continuity completely convex closed curve constructed by the segmental cubic Bezier curves is obtained. According to the method of the invention, one cubic Bezier curve is constructed between adjacent convex hull points, and the connection points of the curves satisfy two-order geometric continuity, so that the completely convex closed curve can be constructed. The method has the advantages of small computation amount, no need for solving a method group, simplicity and high practicability.

Description

A kind of construction method of the complete convex closed curve of second order geometry continuum

Technical field

The present invention relates to a kind of construction method of the complete convex closed curve of second order geometry continuum.

Background technology

Three Dimensional Ground laser scanner technique (Terrestrial Laser Scanning Technology, abbreviation TLS) is A kind of new surveying and mapping technology, results from the nineties in 20th century.TLS can fast and accurately obtain the point cloud number of target object surface It is believed that breath, such that it is able to the threedimensional model of fast constructing target object.Development over nearly more than 20 years, three-dimensional laser scanner Continuously rapidly to being observed object can carry out non-contact measurement, its pass through to obtain body surface to scanner away from From the three dimensional point cloud that voluminous object surface is obtained with emissive porwer.It is over nearly 10 years to extract forestry relevant parameter using TLS Study hotspot.

Curve interpolation is that the classics in applied mathematics, computer graphics and computer aided design and manufacture field are asked Topic.When given data are convex, the curve of structure is also convex, and such curve interpolation problem is referred to as curve and protects convex inserting Value.Existing curve convexity interpolation method pay attention to build one section of non-closed convex curve, more by subinterval increase node, Realized by the way of tension parameterses, Curve Subdivision.For given convex closure point, if there is the smooth complete convex of convex closure point Closed curve, and with the presence or absence of unique smooth complete convex closed curve for crossing convex closure point, await further research.

The content of the invention

In view of this, the purpose of the present invention is for the deficiencies in the prior art, there is provided a kind of second order geometry continuum it is complete convex The construction method of closed curve, to by building a three bezier curve between adjacent convex closure point, in curve tie point Place meets second order geometric continuity to build continuous complete convex closed curve.

To reach above-mentioned purpose, the present invention is employed the following technical solutions：

A kind of construction method of the complete convex closed curve of second order geometry continuum, comprises the steps：

Build convex closure point set P={ p_i| i=0,1 ..., n-1 }, and have when i≤0, or i>During n, i is expressed as i and n is taken Mould, such asAnd p₀,p₁,...,p_n-1It is the point set arranged according to counter-clockwise order；

Complete convex closed curve is built using segmentation three bezier curve；

Build and solving equation group；

The calculating of majorization of solutions and complete convex closed curve, the second order geometry for obtaining being made up of segmentation three bezier curve connects Continuous complete convex closed curve.

Preferably, it is described that complete convex closed curve is built using segmentation three bezier curve, including：

In adjacent convex closure point p_iWith p_i+1Between build a three bezier curve, with convex closure point p_iWith p_i+1As described three The 1st of secondary Bezier curve and the 4th control point, it is assumed that point q_2iWith q_2i+1Be the 2nd of the three bezier curve with 3rd control point；

Point p_iWith point q_2iThe vector of composition withWith point p_i-1With point p_i+1The vector of compositionIt is parallel, V_i It is vectorUnit vector；Point q_2i+1With point p_i+1The vector of composition withWith point p_iWith point p_i+2 The vector of compositionIt is parallel, V_i+1It is vectorUnit vector；Point q_2iWith point q_2i+1The vector of compositionWith point p_iWith point p_i+1The vector of compositionIt is parallel, L_iIt is vectorUnit vector；

According to the geometrical relationship for building, point q_2i+1With q_2i+2It is represented by：

q_2i+1=p_i+1-k_i+1V_i+1,k_i+1>0

q_2i+2=f_i+1V_i+1+p_i+1,f_i+1>0；

Build a three bezier curve between all adjacent convex closure points successively.

Preferably, it is described to build and solving equation group, including：

According to point p_i、q_2i、q_2i+1With point p_i+1Between occluding relation, the expression formula of three bezier curve, three times The function expression and sectional curve of the single order second dervative of Bezier curve can be obtained in the condition of tie point second order geometry continuum To equation below group：

Whereinf_i、g_iWith k_iIt is the real number more than 0；

Solution of equations can be briefly described below：

Appoint to μ>0, select kth (0≤k in convex closure point set P<N) individual node is start node, makes real number α_iWith β_iDifference table Show as follows：

To each point p in convex closure point set P_iOne parameter value u more than 0 is set_i, start node p_kParameter value be u_k,

Order

Make e_iIt is equationPositive root, then have：

Then solution of equations is

Preferably, the calculating of the majorization of solutions and complete convex closed curve, obtains being made up of segmentation three bezier curve Second order geometry continuum complete convex closed curve, including：

Select ratio beta_k/α_kMinimum node μ_kAs start node, and set μ_k=μ；

(1) according to formulaCalculate each convex closure point corresponding α_i、β_iWithValue, and traversal obtainMinimum of a value

(2) for given μ parameter values, according to formula μ_k=μ,Calculate each The corresponding parameter value μ of convex closure point_i；

(3) according to formulaCalculate each convex closure The corresponding parameter value e of point_i；

(4) according to formula f_i=| | l_i-1+l_i||e_iWith formulaCalculate every The corresponding parameter value f of individual convex closure point_iWith k_i；

(5) according to parameter value f_i、k_i, formula q_2i+1=p_i+1-k_i+1V_i+1With formula q_2i+2=f_i+1V_i+1+p_i+1Calculate difference Obtain the 2nd and the 3rd control point q of every section of three bezier curve_2i+1With q_2i+2；

(6) successively respectively with point p_i、q_2i+1、q_2i+2With p_i+1For control point build three bezier curve obtain by point The complete convex closed curve of the second order geometry continuum that section three bezier curve is constituted.

Preferably, also include：Obtain convex closure point.

Preferably, the acquisition convex closure point, including：

Trunk point cloud is extracted in the tree point cloud obtained from Three Dimensional Ground laser scanner；

Calculate the anchor point in trunk trunk cross section at height h；

The minimum point in trunk point cloud is calculated, and the height of trunk is calculated based on the minimum point；

On the basis of minimum point, with vectorFor the normal vector of plane, preset with h+ at the top h of minimum point Two planes built respectively at distance；Trunk point cloud in the middle of two planes constitutes a trunk point cloud mass, will set Do and obtain a planar point in the plane that cloud mass point cloud projects at trunk height h and converge, Calculation Plane point converges composition The polygonal center of mass point of convex closure, the trunk at height h is cross-section with trunk for geometric center point that planar point converges for the center of mass point The anchor point in face；

Calculate the direction of growth of the trunk at height h and trunk cross section；

The direction of growth of the trunk at height h is the normal vector in trunk cross section of the trunk at height h；

The direction of growth of the trunk at height h is calculated using alternative manner；Kth time is iterated to calculate：Built anchor point And normal vector isA plane, plane on the basis of the plane；

Calculate the direction of growth of the trunk at height hWherein, the corresponding feature of the eigenvalue of maximum of covariance matrix Vector is the direction of growth of the trunk at height hPlanar process vector assignment isCarry out+1 iteration of kth；First iteration When normal vector beIteration termination condition is：Two trunk directions of growth that adjacent iteration twice is obtainedWith's Angle theta_kLess than 0.5 degree or θ_kWith θ_k+1Differential seat angle be less than 0.5 degree；The trunk direction of growth at the end of iterationAs trunk The direction of growth at height h；Normal vector with the direction of growth of the trunk at height h as plane, is built by anchor point and is set Do the trunk cross section at height h；

Obtain the convex closure point for calculating trunk diameter.

Preferably, trunk point cloud is extracted in the tree point cloud obtained from Three Dimensional Ground laser scanner, including：

The points cloud processing software being equipped with using Three Dimensional Ground laser scanner is swept to ground three-dimensional laser scanner in multistation The point cloud retouched carries out registration and obtains the cloud data of Dan Mu, removed Ground Point cloud, removes branch point cloud, removes discrete noise point After obtain trunk point cloud.

Preferably, traversal trunk point converges and obtains a minimum point of z coordinate value, and the point for obtaining is set to into trunk The minimum point of point cloud.

Preferably, the direction of growth for calculating trunk at height hIncluding：

Based on datum plane, 5 planes parallel with this are built respectively, wherein 3 planes are located on datum plane Side, 2 planes are located at datum plane lower section, and the distance between adjacent plane is 0.5 centimetre；

Obtain 5 trunk point cloud masses and 5 geometric center points；

The direction of growth of the trunk at height h is calculated using principal component analytical method to 5 geometric center points

Preferably, the convex closure point obtained for calculating trunk diameter, including：

The plane that an and distance parallel with trunk cross section is for 1 centimetre is built above trunk cross section, positioned at trunk Cross section is as used to calculate the trunk point cloud of trunk diameter with interplanar trunk point cloud, and this partial dot cloud is projected to trunk The planar point obtained on cross section on a three dimensions converges, using the rotation process in geometric transformation, by this planar point cloud The planar point that collection is rotated to be on a two-dimensional space with plane-parallel converges, and calculates this planar point according to algorithm of convex hull and converges Convex closure point set P.

The invention has the beneficial effects as follows：

The present invention provides a kind of construction method of the complete convex closed curve of second order geometry continuum, by between adjacent convex closure point A three bezier curve is built, it is bent to build continuous complete convex closure that second order geometric continuity is met at curve tie point Line, the method amount of calculation is little, simple and practical without the need for method for solving group, and the curve for building has the explanation on physics meaning.

Applied in Forestry Investigation using the method for the present invention, the accuracy that diameter is extracted from trunk point cloud is higher.

Other features and advantages of the present invention will be illustrated in the following description, also, the partly change from specification Obtain it is clear that or being understood by implementing the present invention.The purpose of the present invention and other advantages can be by the explanations write Specifically noted structure is realizing and obtain in book, claims and accompanying drawing.

Description of the drawings

The method flow diagram that Fig. 1 embodiment of the present invention 1 is provided；

The geometrical relationship figure that the segmentation three bezier curve that Fig. 2 present invention builds builds；

The exemplary plot of the lower complete convex closed curve for building of the identical convex closure point difference μ values of Fig. 3；

What Fig. 4 was simulated encloses chi examples of traces figure；

The method flow diagram that Fig. 5 embodiment of the present invention 2 is provided；

Fig. 6 is the schematic diagram for positioning trunk cross section；

Fig. 7 is to obtain the point cloud exemplary plot for calculating trunk diameter.

Specific embodiment

With reference to the accompanying drawings and examples the invention will be further described.

Embodiment 1：

As shown in figure 1, a kind of construction method of the complete convex closed curve of second order geometry continuum of the present embodiment offer, including Following steps：

Step S101, for given convex closure point set P={ p_i| i=0,1 ..., n-1 }, and have when i≤0, or i>During n, I is expressed as i to modulo n, such asAnd p₀,p₁,...,p_n-1It is the point arranged according to counter-clockwise order Collection；

Step S102, builds the geometrical relationship figure of complete convex closed curve, is built using segmentation three bezier curve complete convex Closed curve；

In adjacent convex closure point p_iWith p_i+1Between build a three bezier curve, with convex closure point p_iWith p_i+1As this three The 1st of secondary Bezier curve and the 4th control point, it is assumed that point q_2iWith q_2i+1Be the 2nd of this article of three bezier curve with 3rd control point, wherein, point p_iWith point q_2iThe vector of composition withWith point p_i-1With point p_i+1The vector of compositionParallel (wherein V_iIt is vectorUnit vector), point q_2i+1With point p_i+1The vector of composition withWith point p_iWith point p_i+2The vector of compositionParallel (wherein V_i+1It is vectorUnit to Amount), point q_2iWith point q_2i+1The vector of compositionWith point p_iWith point p_i+1The vector of compositionParallel (wherein L_i It is vectorUnit vector), thus, point q_2i+1With q_2i+2Can be expressed as follows：

q_2i+1=p_i+1-k_i+1V_i+1,k_i+1>0

q_2i+2=f_i+1V_i+1+p_i+1,f_i+1>0

Build a three bezier curve between all adjacent convex closure points successively, the structure schematic diagram of curve is as schemed Shown in 2, point p_i、q_2i、q_2i+1With p_i+1It is successively four control points of a three bezier curve, its midpoint p_iWith p_i+1It is phase Two adjacent convex closure points, point q_2iWith q_2i+1It is to need calculated control point；Point p_iWith point q_2iThe vector of composition withWith point p_i-1With point p_i+1The vector of compositionIt is parallel, V_iIt is vectorUnit vector；Point q_2i+1With Point p_i+1The vector of composition withWith point p_iWith point p_i+2The vector of compositionIt is parallel, V_i+1It is vectorUnit vector；Point q_2iWith point q_2i+1The vector of compositionWith point p_iWith point p_i+1The vector of composition It is parallel, L_iIt is vectorUnit vector；

Step S103, builds and solving equation group；

According to point p_i、q_2i、q_2i+1With point p_i+1Between occluding relation, the expression formula of three bezier curve, three times The function expression and sectional curve of the single order second dervative of Bezier curve can be obtained in the condition of tie point second order geometry continuum To equation below group：

Whereinf_i,g_i,k_i>0；

Solution of equations can be briefly described below：

Appoint to μ>0, select kth (0≤k in convex closure point set P<N) individual node is start node, is made：

To each point p in convex closure point set P_iOne parameter value u more than 0 is set_i, start node p_kParameter value be u_k,

Order

Make e_iIt is equationPositive root, then have：

Then solution of equations is

Step S104, the calculating of majorization of solutions and complete convex closed curve, obtains what is be made up of segmentation three bezier curve The complete convex closed curve of second order geometry continuum.

Can be seen that in the case where μ values determine according to the description of above-mentioned solution of equations, select different node p_k(0≤ k<N) as start node, parameter value u_iValue it is different, solution of equations is different, i.e., in the case where μ values determine, the shape of curve Shape is related to the selection of start node.For the correlation for avoiding curve shape from selecting with start node, present invention selection ratio beta_k/ α_kMinimum node μ_kAs start node, and set μ_k=μ so that the shape of curve is only related to parameter μ value.Experiment shows, For given convex closure point, μ values are bigger, and the length of curve between adjacent convex closure point is less, so as to the total length of closed curve is also got over Little, this is tighter equivalent to what curve stretched tight, as shown in figure 3, figure (a), (b), (c) represent respectively structure under identical convex closure point difference μ values The exemplary plot of the complete convex closed curve built, in figure (a), μ=1；In figure (b), μ=100；In figure (c), μ=10000.

Full the computational methods of convex closed curve are：

(1) according to formulaCalculate each convex closure point point corresponding α_i, β_iWithValue, and traversal obtainMinimum of a value

(2) for given μ parameter values, according to formula μ_k=μ,Calculate each convex The bag corresponding parameter value μ of point_i；

(3) according to formulaCalculate each convex closure point Corresponding parameter value e_i；

(4) according to formula f_i=| | l_i-1+l_i||e_iWith formulaCalculate every The corresponding parameter value f of individual convex closure point_iWith k_i；

(5) according to parameter value f_i、k_i, formula q_2i+1=p_i+1-k_i+1V_i+1With formula q_2i+2=f_i+1V_i+1+p_i+1Calculate difference Obtain the 2nd and the 3rd control point q of every section of three bezier curve_2i+1With q_2i+2；

(6) successively respectively with point p_i、q_2i+1、q_2i+2With p_i+1For control point build three bezier curve obtain by point The complete convex closed curve of the second order geometry continuum that section three bezier curve is constituted.

The correctness of solution：

For 4 given control point p₀、p₁、p₂With p₃, three bezier curve C (u) can be defined as follows：

C (u)=(1-u)³p₀+3u(1-u)²p₁+3u²(1-u)p₂+u³p₃,0u 1

First order parameter derivative of three bezier curve C (u) at parameter u is respectively with second order parameter derivative：

C ' (u)=3 (p₁-p₀)(1-u)²+6(p₂-p₁)(1-u)u+3(p₃-p₂)u²

C (u)=6 (p₂-2p₁+p₀)(1-u)+6(p₃-2p₂+p₁)u

Structure relation in the present invention, for by p_i、q_2i+1、q_2i+2With p_i+1For control point build one three times Bezier curve C_i, curve is in node p_iWith p_i+1The single order at place can be expressed as with second dervative：

C_i+1' (0)=3 (q_2i+2-p_i+1), C_i' (1)=3 (p_i+1-q_2i+1)

C_i+1(0)=6 (q_2i+3-2q_2i+2+p_i+1), C_i(1)=6 (p_i+1-2q_2i+1+q_2i)

Prove：

Closed：Curve C_n-1Cross point p_n, curve C₀Cross point p₀, because, so as to curve C_n-1With C₀In point p₀Point connects Connect.This also demonstrates two sections of curve C_iWith C_i+10 rank geometric continuity.

Single order geometric continuity：Had according to first derivative of the adjacent three bezier curve at tie point：

That is the Piecewise Bezier Curves of present invention construction have met single order geometric continuity at tie point.

Second order geometric continuity：

Had according to second dervative of the adjacent three bezier curve at tie point：

C_i+1(0)=6 (g_i+1L_i+1-f_i+1V_i+1), C_i(1)=6 (k_i+1V_i+1-g_i+1L_i+1)

According to the condition of second order geometric continuity, on the basis of 1 rank geometry continuum is met, if it is desired to two curves are even Junction reaches second order geometry continuum, then require that two curves have common curvature vector in junction point：

Above formula can abbreviation be：

Column is calculated, and above formula is rewritable to be：

Have

CauseHad according to determinant elementary transformation：

It is equivalent to the presence of λ_i+1So that：；

According toWithHave：

It is equivalent to

Because of l_iWith l_i+1Linear independence, therefore have

Full convexity：

Parameter curve C (u), if meeting when u is incremented by, curve is that counterclockwise then relative curvature is represented by：

If then when κ >=0, region is convex domain, if κ<0, region is Non-convex region.

Therefore, for the curve that the present invention builds, it is only necessary to prove κ >=0 at arbitrfary point.

According to the computing formula of relative curvature, because its denominator is permanent 0 is more than, therefore for one section of curve C_iIf, curve C_iMeet FormulaThen curve C_iIt is convex curve.

Have

Further abbreviation has：

Had according to formula

It is above-mentioned to have | l_i,l_i+1|>0, α_i/β_i>0, e_i>0 and there is a μ>0 and μ_i>0, therefore, above-mentioned 3 formulas are all higher than 0, therefore Have | C_i′(u),C_i(u) | >=0, i.e. curve C_iIt is convex curve, so as to closed curve is full convex curve.

Embodiment 2：

In Forestry Investigation, commonly used steel encloses the diameter that chi measures trunk, encloses chi ring in the presence of artificial pulling force Around trunk cross section one week, so as to read the diameter value of trunk.Steel encloses chi and has elasticity, in the presence of pulling force, encloses chi rail Mark is set up on the projection in trunk cross section, and it is a complete convex and continuous closed trajectory, and now, enclosing chi track can It is reduced to a smooth full convex curve.The construction method of the complete convex closed curve of the present invention is applied to from Three Dimensional Ground laser Trunk diameter is extracted in the trunk point cloud that scanner is obtained, 31 obtained during using field investigation trunk diameter data are used as true Value, by the lower μ for enclosing the diameter of chi trajectory extraction compared with measured diameter, drawing this field investigation optimum for building of different μ values It is worth for 0.3.Using fitting circle, convex closure broken line and the simulation in the present invention method extraction trunk diameter that chi calibrates is enclosed respectively again, Compared with the measured diameter of field investigation, the precision comparison of 3 kinds of method extraction trunk diameters is as shown in the table.

The distinct methods experimental result contrast ratio of table 1

The implication and computing formula of evaluation metricses are as follows in table：Mean absolute percentage error MAPE (mean absolute Percentage error), root-mean-square error RMSE (root mean square error) and coefficient of determination R²；Correspondence is calculated Formula is as follows：

N is sample unit, and D is the measured value of diameter, and its mean value is usedRepresent,Represent from the straight of trunk data reduction Footpath is worth.The MAPE and the smaller the better (R of RMSE in above-mentioned evaluation index²Then it is the bigger the better), this explanation is extracted straight from trunk point cloud The accuracy in footpath is higher.

When chi measurement diameter is enclosed, it is bigger to enclose chi stress, and it is tighter around trunk cross section to enclose chi, so as to trunk cross section week Length is less, and trunk diameter is also minimum.According to above-mentioned, μ values are bigger, and length of a curve is less, and the μ parameters for building curve reflect just The curve pulling force situation suffered when building.Thus, μ values are regarded as the tension coefficient of closed curve, can reflect that curve exists The tight degree of interpolation point stress and curve.

As shown in figure 5, a kind of construction method of the complete convex closed curve of second order geometry continuum in the present embodiment, including it is as follows Step：

Step S201, obtains convex closure point；

Step S202, builds convex closure point set P={ p_i| i=0,1 ..., n-1 }, and have when i≤0, or i>During n, i is represented It is i to modulo n, such asAnd p₀,p₁,...,p_n-1It is the point set arranged according to counter-clockwise order；

Step S203, using segmentation three bezier curve complete convex closed curve is built；

Step S204, builds and solving equation group；

Step S205, the calculating of majorization of solutions and complete convex closed curve, obtains what is be made up of segmentation three bezier curve The complete convex closed curve of second order geometry continuum.

In one embodiment, step S201, obtains convex closure point, comprises the following steps：

Step 1, extracts trunk point cloud in the tree point cloud obtained from Three Dimensional Ground laser scanner；

The points cloud processing software being equipped with using Three Dimensional Ground laser scanner is swept to ground three-dimensional laser scanner in multistation The point cloud retouched carries out registration and obtains the cloud data of Dan Mu, removed Ground Point cloud, removes branch point cloud, removes discrete noise point After obtain trunk point cloud.

Step 2, calculates the anchor point in trunk trunk cross section at height h.

According to the coordinate value of z-axis, calculate the minimum point in trunk point cloud, and by this put based on calculate the height of trunk； On the basis of minimum point, with vectorFor the normal vector of plane, punish with h+0.5 centimetre at the top h of minimum point Two planes not built, the plane at trunk height h is as shown in Figure 6.In Fig. 6, dotted line 2 is lower flat during anchor point to calculate Face, point 1 is anchor point, and dotted line 3 is cross section of the trunk at height h, and arrow direction is the normal direction in trunk cross section Amount.Fig. 7 is to obtain the point cloud exemplary plot for calculating trunk diameter.In Fig. 7, dotted line 2 is the cross section of trunk, dotted line 1 be with Dotted line 2 is parallel and trunk point to the plane that the place plan range of dotted line 2 is 1 centimetre, in the middle of dotted line 1 and dotted line 2 Cloud is as calculating the point cloud of trunk diameter.Trunk point cloud in two planes constitutes a trunk point cloud mass, A planar point is obtained in the plane for projecting at trunk height h by this partial dot cloud to converge, calculate this planar point and converge composition The polygonal center of mass point of convex closure, center of mass point is the geometric center point that this planar point converges, while being also trunk at height h The anchor point in trunk cross section.

Step 3, calculates the direction of growth of the trunk at height h and trunk cross section.

The direction of growth of the trunk at height h is the normal vector in trunk cross section of the trunk at height h.Using iteration Method calculates the direction of growth of the trunk at height h, and kth time iterative calculation is：Built anchor point and normal vector wasOne Individual plane, claims plane on the basis of this plane.

Based on datum plane, 5 planes parallel with this are built respectively, wherein 3 planes are located on datum plane Side, 2 planes are located at datum plane lower section, and the distance between adjacent plane is 0.5 centimetre；Thus 5 trunk point cloud masses are obtained With 5 geometric center points, the direction of growth of the trunk at height h is calculated using principal component analytical method to 5 geometric center pointsWherein, the corresponding characteristic vector of the eigenvalue of maximum of covariance matrix is the direction of growth of the trunk at height hIt is flat Face normal vector is entered asCarry out+1 iteration of kth；Normal vector is during first iterationIteration termination condition is：Phase Adjacent two trunk directions of growth that twice iteration is obtainedWithAngle theta_kLess than 0.5 degree or θ_kWith θ_k+1Differential seat angle it is little In 0.5 degree；The trunk direction of growth at the end of iterationThe as direction of growth of the trunk at height h；With trunk at height h The direction of growth be the normal vector of plane, cross anchor point and build trunk cross section of the trunk at height h.

Step 4, obtains the convex closure point for calculating trunk diameter.

On the basis of trunk cross section of the trunk at height h is obtained, above this trunk cross section build one with Trunk cross section it is parallel and distance for 1 centimetre (enclosing the width of chi) plane, positioned at trunk cross section and interplanar trunk point Cloud is as used to calculate the trunk point cloud of trunk diameter, this partial dot cloud is projected to trunk cross section and obtains a three-dimensional space Between on planar point converge, using the rotation process in geometric transformation, this planar point is converged and is rotated to be and plane-parallel Planar point on one two-dimensional space converges, and according to algorithm of convex hull the convex closure point set P that this planar point converges is calculated.

It should be noted that above example is only to illustrate technical scheme and unrestricted, this area is common Other modifications or equivalent that technical staff is made to technical scheme, without departing from technical solution of the present invention Spirit and scope, all should cover in the middle of scope of the presently claimed invention.

Claims (10)

1. a kind of construction method of the complete convex closed curve of second order geometry continuum, it is characterised in that：Comprise the steps：

Build convex closure point set P={ p_i| i=0,1 ..., n-1 }, and have when i≤0, or i>During n, i is expressed as i to modulo n；

Complete convex closed curve is built using segmentation three bezier curve；

Build and solving equation group；

The calculating of majorization of solutions and complete convex closed curve, the second order geometry continuum for obtaining being made up of segmentation three bezier curve Complete convex closed curve.

2. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 1, it is characterised in that： It is described that complete convex closed curve is built using segmentation three bezier curve, including：

In adjacent convex closure point p_iWith p_i+1Between build a three bezier curve, with convex closure point p_iWith p_i+1As described three times The 1st of Bezier curve and the 4th control point, it is assumed that point q_2iWith q_2i+1It is the 2nd and the 3rd of the three bezier curve Individual control point；

Point p_iWith point q_2iThe vector of composition withWith point p_i-1With point p_i+1The vector of compositionIt is parallel, V_iIt is vectorUnit vector；Point q_2i+1With point p_i+1The vector of composition withWith point p_iWith point p_i+2Constitute VectorIt is parallel, V_i+1It is vectorUnit vector；Point q_2iWith point q_2i+1The vector of compositionWith point p_iWith point p_i+1The vector of compositionIt is parallel, L_iIt is vectorUnit vector；

According to the geometrical relationship for building, point q_2i+1With q_2i+2It is represented by：

q_2i+1=p_i+1-k_i+1V_i+1,k_i+1>0

q_2i+2=f_i+1V_i+1+p_i+1,f_i+1>0；

Build a three bezier curve between all adjacent convex closure points successively.

3. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 2, it is characterised in that： It is described to build and solving equation group, including：

According to point p_i、q_2i、q_2i+1With point p_i+1Between occluding relation, the expression formula of three bezier curve, cubic Bezier it is bent The function expression and sectional curve of the single order second dervative of line is available such as lower section in the condition of tie point second order geometry continuum Journey group：

$\left\{\begin{array}{c}{f}_i{V}_i+g_i{L}_i+k_{i+1}{V}_{i+1}=l_i\\ \frac{f_{i+1}^2{g}_i}{\left|\right|l_i\left|\right|}=\frac{k_{i+1}^2{g}_{i+1}}{\left|\right|l_{i+1}\left|\right|}\end{array}\right.$

Whereinf_i、g_iWith k_iIt is the real number more than 0；

Solution of equations can be described as follows：

Appoint to μ>0, select kth (0≤k in convex closure point set P<N) individual node is start node, and real number α of the real number more than 0 is made respectively_i With β_iFor,

${\mathrm{\&alpha;}}_i=\frac{|l_{i-1},l_{i+1}|}{|l_i,l_{i+1}|},{\mathrm{\&beta;}}_i=\frac{|l_{i-1},l_{i+1}|}{|l_{i-1},l_i|},\frac{{\mathrm{\&alpha;}}_i}{{\mathrm{\&beta;}}_i}=\frac{|l_{i-1},l_i|}{|l_i,l_{i+1}|}$

To each point p in convex closure point set P_iOne parameter value u more than 0 is set_i, start node p_kParameter value be u_k,

Order

Make e_iIt is equationPositive root, then have：

Then solution of equations is

$\left\{\begin{array}{c}{f}_i=\left|\right|l_{i-1}+l_i\left|\right|e_i\\ k_{i+1}=\frac{{\mathrm{\&alpha;}}_i\left|\right|l_i+l_{i+1}\left|\right|}{{\mathrm{\&beta;}}_i\left|\right|l_{i-1}+l_i\left|\right|}{f}_i=\frac{{\mathrm{\&alpha;}}_i}{{\mathrm{\&beta;}}_i}\left|\right|l_i+l_{i+1}\left|\right|e_i\\ g_i=\left|\right|l_i\left|\right|-\frac{\left({\mathrm{\&alpha;}}_i/{\mathrm{\&beta;}}_i+{\mathrm{\&alpha;}}_i+1\right)\left|\right|l_i\left|\right|}{\left|\right|l_{i-1}+l_i\left|\right|}{f}_i=\left|\right|l_i\left|\right|\left(1-e_i\left({\mathrm{\&alpha;}}_i/{\mathrm{\&beta;}}_i+{\mathrm{\&alpha;}}_i+1\right)\right)\end{array}\right..$

4. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 3, it is characterised in that： The calculating of the majorization of solutions and complete convex closed curve, the second order geometry continuum for obtaining being made up of segmentation three bezier curve Complete convex closed curve, including：

Select ratio beta_k/α_kMinimum node μ_kAs start node, and set μ_k=μ；

(1) according to formulaCalculate the corresponding α of each convex closure point_i、β_i WithValue, and traversal obtainMinimum of a value

(2) for given μ parameter values, according to formulaCalculate each convex closure The corresponding parameter value μ of point_i；

(3) according to formulaCalculate each convex closure point pair The parameter value e for answering_i；

(4) according to formula f_i=| | l_i-1+l_i||e_iWith formulaCalculate each convex The bag corresponding parameter value f of point_iWith k_i；

(5) according to parameter value f_i、k_i, formula q_2i+1=p_i+1-k_i+1V_i+1With formula q_2i+2=f_i+1V_i+1+p_i+1Calculating is respectively obtained often The 2nd of section three bezier curve and the 3rd control point q_2i+1With q_2i+2；

(6) successively respectively with point p_i、q_2i+1、q_2i+2With p_i+1A three bezier curve is built for control point to obtain by segmentation three The complete convex closed curve of the second order geometry continuum that secondary Bezier curve is constituted.

5. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 1, it is characterised in that： Also include：Obtain convex closure point.

6. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 5, it is characterised in that： The acquisition convex closure point, including：

Trunk point cloud is extracted in the tree point cloud obtained from Three Dimensional Ground laser scanner；

Calculate the anchor point in trunk trunk cross section at height h；

The minimum point in trunk point cloud is calculated, and the height of trunk is calculated based on the minimum point；

On the basis of minimum point, with vectorFor the normal vector of plane, with h+ predeterminable ranges at the top h of minimum point Two planes that place builds respectively；Trunk point cloud in the middle of two planes constitutes a trunk point cloud mass, by trunk point A planar point is obtained in the plane that cloud mass point cloud projects at trunk height h to converge, Calculation Plane point converges the convex closure of composition Polygonal center of mass point, geometric center point and trunk trunk cross section at height h that the center of mass point is converged for planar point Anchor point；

Calculate the direction of growth of the trunk at height h and trunk cross section；

The direction of growth of the trunk at height h is the normal vector in trunk cross section of the trunk at height h；Using alternative manner Calculate the direction of growth of the trunk at height h；Kth time is iterated to calculate：Built anchor point and normal vector wasOne put down Face, plane on the basis of the plane；

Calculate the direction of growth of the trunk at height hWherein, the corresponding characteristic vector of the eigenvalue of maximum of covariance matrix For the direction of growth of the trunk at height hPlanar process vector assignment isCarry out+1 iteration of kth；Method during first iteration Vector isIteration termination condition is：Two trunk directions of growth that adjacent iteration twice is obtainedWithAngle θ_kLess than 0.5 degree or θ_kWith θ_k+1Differential seat angle be less than 0.5 degree；The trunk direction of growth at the end of iterationAs trunk is in height The direction of growth at degree h；Normal vector with the direction of growth of the trunk at height h as plane, builds trunk and exists by anchor point Trunk cross section at height h；

Obtain the convex closure point for calculating trunk diameter.

7. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 6, it is characterised in that： Trunk point cloud is extracted in the tree point cloud obtained from Three Dimensional Ground laser scanner, including：

What the points cloud processing software being equipped with using Three Dimensional Ground laser scanner was scanned to ground three-dimensional laser scanner in multistation Point cloud carries out registration and obtains the cloud data of Dan Mu, removed Ground Point cloud, removes branch point cloud, removes after discrete noise point To trunk point cloud.

8. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 6, it is characterised in that： Traversal trunk point converges and obtains a minimum point of z coordinate value, and the point for obtaining is set to into the minimum point of trunk point cloud.

9. the construction method of the complete convex closed curve of a kind of second order geometry continuum according to claim 6, it is characterised in that： The direction of growth that trunk is calculated at height hIncluding：

Based on datum plane, 5 planes parallel with this are built respectively, wherein 3 planes are located above datum plane, 2 Individual plane is located at datum plane lower section, and the distance between adjacent plane is 0.5 centimetre；

Obtain 5 trunk point cloud masses and 5 geometric center points；

The direction of growth of the trunk at height h is calculated using principal component analytical method to 5 geometric center points

10. a kind of construction method of the complete convex closed curve of second order geometry continuum according to claim 6, its feature exists In：The convex closure point obtained for calculating trunk diameter, including：

The plane that an and distance parallel with trunk cross section is for 1 centimetre is built above trunk cross section, it is cross-section positioned at trunk Face is as used to calculate the trunk point cloud of trunk diameter with interplanar trunk point cloud, this partial dot cloud is projected cross-section to trunk The planar point obtained on face on a three dimensions converges, and using the rotation process in geometric transformation, this planar point is converged into rotation The planar point switched on a two-dimensional space with plane-parallel converges, according to algorithm of convex hull calculate that this planar point converges it is convex Bag point set P.