CN103017696A - Method for measuring single wood accumulating volume based on curve simulation - Google Patents

Abstract

The invention discloses a method for measuring single wood accumulating volume based on a curve simulation. The method comprises the following steps of: firstly, drilling three tree cores at 0.5 meter, 1.3 meters and 2.5 meters of a trunk along three directions (from north to south, from northeast to southwest, from northwest to southeast); then, measuring a width value from a tree core model value point to a heart centre, and determining the two-dimensional coordinate of the model value point; secondly substituting the coordinate of the model value point into a triple parameter splined curve equation to simulate a trunk cross section curve; then, utilizing a parabolic splined curve equation to simulate a trunk vertical section curve according to the cross section curves at three heights and tree height information to forming a three-dementional trunk shape; and finally, dividing the trunk into 9000 segments, and respectively calculating the volume of each segment and accumulating so as to obtain the single wood accumulating volume.

Description

A kind of method of measuring single timber accumulated amount based on curve simulation

Technical field

The present invention relates to a kind of new method of measuring individual plant trees volume, the Stem curve that the method is drawn up by computer mould carries out the calculating of trees volume.

Background technology

The measurement of the trees volume of timber has a wide range of applications at system for forestry, such as the calculating of calculating, log utilization rate and the volume recovery of forest land turnout, growth monitoring of standing tree etc.Traditional volume of timber measuring method mainly contains every wooden dipping, angle gauge survey, total powerstation assize etc., and these method hypothesis trunk transversal section are that rule is circular or oval, then calculate the volume of timber amount of trees by the measurement height of tree, the diameter of a cross-section of a tree trunk 1.3 meters above the ground.Yet in actual measurement, the trunk transversal section is not rule, so can have certain error between the volume of timber amount that obtains of traditional measurement method and the bigness scale amount, so that measurement result is not accurate enough.

Summary of the invention

Design of the present invention is divided into 3 parts, and concrete technical scheme is as follows:

First is the simulation of trunk transversal section curve:

At first, respectively drill through 3 tree cores on 0.5 meter on trunk, 1.3 meters, 2.5 meters 3 height, get access to the data point of 3 groups of 6 different azimuth, the distribution of data point on Stem curve as shown in Figure 1;

Then, select cubic parametric SPL equation to carry out the simulation of trunk transversal section curve, the curvilinear equation expression formula is $P_i\left(t\right)=P_i+P_i^{\′}t+[\frac{3(P_{i+1}-P_i)}{{t_{i+1}}^2}-\frac{2P_i^{\′}}{t_{i+1}}-\frac{{P_{i+1}}^{\′}}{t_{i+1}}]t^2+[\frac{2(P_i-P_{i+1})}{{t_{i+1}}^3}-\frac{P_i^{\′}}{{t_{i+1}}^2}-\frac{{P_{i+1}}^{\′}}{{t_{i+1}}^2}]t^3,$ P in the formula _iBe i data point; P _i' be the tangent vector at i data point place; T is the chord length that independent variable represents sectional curve, 0≤t≤t _I+1I=1,2 ..., n-1; t _I+1It is the chord length at i+1 data point place;

Secondly, the condition of contact of setting curve is so that every sectional curve can join end to end, and the whole piece curve after guaranteeing to connect is smooth, the condition that the present invention sets be every section curve in end points junction Second Order Continuous, obtain following matrix equation: $\left(t_{i+2}2(t_{i+2}+t_{i+1})t_{i+1}\right)\left(\begin{array}{c}{P}_i^{\&prime;}\\ {P_{i+1}}^{\&prime;}\\ {P_{i+2}}^{\&prime;}\end{array}\right)=3[\frac{t_{i+1}}{t_{i+2}}(P_{i+2}-P_{i-1})+\frac{t_{i+2}}{t_{i+1}}(P_{i+1}-P_i)],$ Curve for being determined by n data point can obtain following system of equations, and n-2 equation has n unknown number (data point tangent vector) altogether $\left(\begin{array}{ccccccc}{t}_3& 2(t_3+t_2)& t_2& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ 0& t_4& 2(t_4+t_3)& t_3& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ 0& 0& {\mathrm{<figure-callout\; id="5"\; label="t"\; filenames="HSA00000577817300012.png"\; state="\{\{state\}\}">t</figure-callout>}}_5& 2({\mathrm{<figure-callout\; id="5"\; label="t"\; filenames="HSA00000577817300012.png"\; state="\{\{state\}\}">t</figure-callout>}}_5+t_4)& t_4& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& 0& 0& 0& t_n& 2(t_n+t_{n-1})& t_{n-1}\end{array}\right)\left(\begin{array}{c}{p}_1^{\&prime;}\\ p_2^{\&prime;}\\ p_3^{\&prime;}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ p_n^{\&prime;}\end{array}\right)=\left(\begin{array}{c}3[\frac{t_2}{t_3}(p_3-p_2)+\frac{t_3}{t_2}(p_2-p_1)]\\ 3[\frac{t_3}{t_4}(p_4-p_3)+\frac{t_4}{t_3}(p_3-p_2)]\\ 3[\frac{t_4}{t_5}(p_5-p_4)+\frac{t_5}{t_4}(p_4-p_3)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ 3[\frac{t_{n-1}}{t_n}(p_n-p_{n-1})+\frac{t_n}{t_{n-1}}(p_{n-1}-p_{n-2})]\end{array}\right)$ Can be in the hope of P by resolving above equation ₂', P ₃' ..., P _N+1' value;

Again, set end-point condition, namely the first and last end points second derivative of closed curve is identical, and the present invention supposes that this second derivative is 0, namely obtains following operational equation

With

Can be in the hope of P ₁', P _n', the tangent vector at n data point place all is calculated thus, and the curvilinear equation coefficient namely is determined;

At last, according to above method, utilize the data point digital simulation of 0.5 meter, 1.3 meters, 2.5 meters 3 height to go out the transversal section curve of 3 height of trunk, as shown in Figure 2.

Second portion is the simulation of trunk vertical curve:

At first, select parabola to carry out the simulation of trunk vertical curve, the curvilinear equation expression formula is: P (t)=A ₁+ A ₂T+A ₃t ², in the formula, A ₁, A ₂, A ₃Be respectively 3 undetermined coefficients of trunk solid curve section match, 0≤t≤1;

Then, set up 3 independent conditions of parabola: (1) is established para-curve and is crossed P _i, P _I+1, P _I+2Three points, P _iBe initial point, when parameter t=0, curve is crossed P _iThe point; (2) P _I+2Be terminal point, when parameter t=1, curve is crossed P _I+2The point; (3) when parameter t=0.5, curve is crossed P _I+1Point, and tangent vector is parallel to P _I+2-P _iThen have:

$S_i\left(t_i\right)=(2t_i^2-3t_i+1)P_i+(4t_i-4t_i^2)P_{i+1}+(2t_i^2-t_i)P_{i+2};$

Then, the segment of curve that draws by following formula is integrated between overlap between per two sections curves, article two, para-curve is can naturally not be overlapped into a curve, for two curves are connected with a smooth curve, need weighting synthetic, namely select two suitable weight functions, be respectively f (T)=1-T; G (T)=T (0≤T≤1), the curve after weighting is synthetic is: P _I+1(t)=f (T) S _i(t _i)+g (T) S _I+1(t _I+1).The span of establishing t in the simulation is: 0≤t≤0.5, then T=2t; t _i=0.5+t; t _I+1=t; Then resultant curve (two parabolical overlay segment) can be write as: P _I+1(t)=(4t ³+ 4t ²-t) P _i+ (12t ³-10t ²+ 1) P _I+1+ (12t ³+ 8t ²+ t) P _I+2+ (4t ³-2t ²) P _I+3

Secondly, set up end-point condition.N data point can only obtain n-3 section curve, but between n data point n-1 section should be arranged, and adds two end points P in the design ₀And P _N+1, and satisfy P ₀=P ₁P _N+1=P _nThe n-3 section curve of associating front just can obtain n-1 segment of curve.Utilize so above-mentioned parabolic batten equation to get final product the analog tree stem curve.

Again, utilize the trunk transversal section curve of having simulated, measure the diameter of a cross-section of a tree trunk 1.3 meters above the ground of tree, calculate height of tree coordinate according to the height of tree-diameter of a cross-section of a tree trunk 1.3 meters above the ground relational expression, and from the trunk transversal section curve of 3 height, choose the data point of 3 correspondences, guarantee 3 data points on same trunk vertical curve, thereby form 4 data points of parabola, substitution parabola equation simulation trunk vertical curve;

At last, each transversal section curve is divided into 1000 parts by angle, according to the previous step method, forms 1000 trunk vertical curves, thereby simulate the three-dimensional shape of whole trunk, as shown in Figure 3.

Third part is the calculating of stem volume amount:

At first, along the trunk direction trunk is divided into 9000 sections, as shown in Figure 4;

Then, calculate the bottom surface area of each section of cutting apart.Because the trunk solid curve is to be made of 1000 trunk vertical curves, so each section of cutting apart reality also is divided into 1000 parts, calculates all areas of 1000 parts and cumulative, can obtain the bottom surface area, as shown in Figure 5;

At last, because complete trunk is slit into 9000 sections by average mark, can suppose when volume calculated that therefore every a bit of upper and lower base area is approximately equalised, it is exactly one of them floorage and high product that volume calculates.The floorage that calculates by step 2 and the height of the section of cutting apart can obtain the volume of each section of cutting apart, and 9000 segment bodies that add up amass the volume that can obtain whole trunk, i.e. stem volume amount.

Compared with prior art, the present invention has following advantage:

(1) the present invention will simulate the trunk true shape as main research object, so that measurement result is more accurate with respect to the trunk transversal section being approximately circle or oval-shaped classic method;

(2) the inventive method is take Computer Processing as main, and manual measurement is auxiliary, and is therefore more intelligent, greatly reduces people's labour intensity, improved task efficiency;

(3) the inventive method is in order to obtain trunk data point data, only is used in ad-hoc location and drills through trees tree core and get final product, and can not destroy the growth of standing tree alive;

(4) the present invention is suitable for the mensuration of many seeds of forest volume of timber amounts such as China fir, wet-land pine tree, masson pine, has very widely using value.

Description of drawings

Fig. 1 is data point orientation angles synoptic diagram;

Fig. 2 is the transversal section curve synoptic diagram at 0.5 meter, 1.3 meters and 2.5 meters 3 height;

Fig. 3 is the synoptic diagram by trunk vertical curve simulation trunk three-dimensional shape;

Fig. 4 is 9000 parts synoptic diagram for trunk is divided equally;

Fig. 5 is 10000 parts of synoptic diagram that calculate floorage for the trunk bottom surface is divided equally.

Embodiment

Embodiment 1: the extraction of Stem curve data point

At first, choose the forest sample prescription, and with lining rope it is impaled, carry out every wooden dipping, record seeds title and diameter of a cross-section of a tree trunk 1.3 meters above the ground value, and record simultaneously the information such as sample prescription title, date collected, the gradient, slope aspect, longitude and latitude, height above sea level.

Then, in sample prescription, choose typical trunk, set the core data acquisition.0.5 meter, 1.3 meters, 2.5 meters respectively drill through 3 root growths tree core on distance ground respectively, and every wood adopts identical Sampling Strategy to take a sample, namely in north and south, northeast to southwest, northwest to southeastern direction respectively get a core.After tree core collection is finished, with the branch bar will hole clog tight.

At last, pack into immediately the sample core in the paper suction pipe and on suction pipe, mark code with the oil pen, after sample core drying, with latex it is bonded on the sample trogue.For avoid that the distortion of sample core occurs in the latex dry run, with the fine rule rope it is pressed the binding of cross form and fix, after doing, latex can take out stitches.Then successively the sample core is polished with 120,320,600 purpose sand paper, until can clearly differentiate the size of cell at microscopically.Take near the part of bark as the sampling time, carried out fixed year from the periphery to medulla.With tree wheel width measuring instrument (LINTAB) trees sample core is carried out width measuring, measurement accuracy is 0.01mm.

Embodiment 2: the simulation of trunk transversal section curve

At first, according to each data point P _iTo the width value of medulla and the deflection at data point place, calculate the data point two-dimensional coordinate value take medulla as true origin;

Sequence number	Tree core height (m)	The data point deflection (°)	To medulla width (cm)	The X coordinate	The Y coordinate
						1	0.5	-90	3.584	0	-3.584
2	0.5	-30	3.8905	3.369272	-1.94525
						3	0.5	30	3.4165	2.958776	1.70825
4	0.5	90	3.774	0	3.774
						5	0.5	150	3.462	-2.99818	1.731
6	0.5	-150	3.654	-3.16446	-1.827
						7	1.3	-90	3.0445	0	-3.0445
8	1.3	-30	2.838	2.45778	-1.419
						9	1.3	30	2.858	2.475101	1.429
10	1.3	90	2.913	0	2.913
						11	1.3	150	2.954	-2.55824	1.477
12	1.3	-150	3.024	-2.61886	-1.512
						13	2.5	-90	1.6635	0	-1.6635
14	2.5	-30	1.765	1.528535	-0.8825
						15	2.5	30	1.799	1.55798	0.8995
16	2.5	90	2.1515	0	2.1515
						17	2.5	150	1.6635	-1.44063	0.83175
18	2.5	-150	1.837	-1.59089	-0.9185

Then, set up the cubic parametric SPL equation of simulation trunk transversal section curve, the equation expression formula is $P_i\left(t\right)=P_i+P_i^{\&prime;}t+[\frac{3(P_{i+1}-P_i)}{{t_{i+1}}^2}-\frac{2P_i^{\&prime;}}{t_{i+1}}-\frac{{P_{i+1}}^{\&prime;}}{t_{i+1}}]t^2+[\frac{2(P_i-P_{i+1})}{{t_{i+1}}^3}-\frac{P_i^{\&prime;}}{{t_{i+1}}^2}-\frac{{P_{i+1}}^{\&prime;}}{{t_{i+1}}^2}]{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000577817300012.png"\; state="\{\{state\}\}">t</figure-callout>}}^3,$ 0≤t in the formula≤t _I+1I=1,2 ..., n-1; Get the chord length that t is sectional curve.

Secondly, for the curve that makes simulation can seamlessly transit, set corresponding end-point condition and condition of contact, obtain $\left(t_{i+2}2(t_{i+2}+t_{i+1})t_{i+1}\right)\left(\begin{array}{c}{P}_i^{\&prime;}\\ {P_{i+1}}^{\&prime;}\\ {P_{i+2}}^{\&prime;}\end{array}\right)=3[\frac{t_{i+1}}{t_{i+2}}(P_{i+2}-P_{i-1})+\frac{t_{i+2}}{t_{i+1}}(P_{i+1}-P_i)],$ $2P_1^{\&prime;}+P_2^{\&prime;}=\frac{3(P_2-P_1)}{t_2}$ With

System of equations, with the above system of equations of data point coordinate information substitution, obtain P ₁', P ₂', P ₃' ..., P _N+1', P _n' wait variable, thus solve the coefficient of cubic parametric SPL;

Again, for each cubic spline curve section, in program, set the chord length of each segment of curve is divided into 9000 parts, namely in every section curve, insert 8999 interpolation points, calculate the coordinate figure of each interpolation point according to the cubic parametric SPL equation that solves, then line is drawn, and draws out this section SPL;

At last, draw whole sectional curves, namely finished the simulation of a trees transversal section curve.Data point data according at 0.5 meter, 1.3 meters and 2.5 meters of setting simulate 3 trunk transversal section curves.

Example 3: the simulation of trunk vertical curve

At first, the transversal section curve on 3 differing heights is selected the data point of 3 correspondences, guarantees that these 3 points are on the same vertical section of trunk;

Then, according to the diameter of a cross-section of a tree trunk 1.3 meters above the ground value of data point DATA REASONING tree, calculate the height of trunk according to the height of tree-diameter of a cross-section of a tree trunk 1.3 meters above the ground relational expression;

Secondly, set up the parabola equation of simulation trunk vertical curve, its expression formula is $S_i\left(t_i\right)=(2t_i^2-3t_i+1)P_i+(4t_i-4t_i^2)P_{i+1}+(2t_i^2-t_i)P_{i+2}.$ For n data point connected with a smooth curve, the present invention selects a kind of weighting synthetic method, and curvilinear equation is transformed, and makes curvilinear equation become P _I+1(t)=(4t ³+ 4t ²-t) P _i+ (12t ³-10t ²+ 1) P _I+1+ (12t ³+ 8t ²+ t) P _I+2+ (4t ³-2t ²) P _I+3

Again, the data point that 3 data points that the first step is obtained and second step obtain forms 4 data points of parabola, and the 3rd step of the coordinate substitution equation with 4 points obtains the parabola equation

At last, 3 transversal section curves are divided into 1000 parts according to angle respectively, obtain 1000 data points on every transversal section curve, thereby forming in the vertical 1000 groups of parabolic batten offset point sets closes, simulate 1000 trunk vertical curves according to above operation steps, form the three-dimensional shape of trunk.

Claims (5)

1. measure the method for single timber accumulated amount based on curve simulation for one kind, may further comprise the steps:

The first step, the simulation of trunk transversal section curve:

At first, on 0.5 meter on trunk, 1.3 meters, 2.5 meters 3 height, respectively drill through 3 tree cores, get access to the data point of 3 groups of 6 different azimuth;

Then, select cubic parametric SPL equation to carry out the simulation of trunk transversal section curve, the curvilinear equation expression formula is $P_i\left(t\right)=P_i+P_i^{\&prime;}t+[\frac{3(P_{i+1}-P_i)}{{t_{i+1}}^2}-\frac{2P_i^{\&prime;}}{t_{i+1}}-\frac{{P_{i+1}}^{\&prime;}}{t_{i+1}}]t^2+[\frac{2(P_i-P_{i+1})}{{t_{i+1}}^3}-\frac{P_i^{\&prime;}}{{t_{i+1}}^2}-\frac{{P_{i+1}}^{\&prime;}}{{t_{i+1}}^2}]t^3,$ P in the formula _iBe i data point; P _i' be the tangent vector at i data point place; T is the chord length that independent variable represents sectional curve, 0≤t≤t _I+1I=1,2 ..., n-1; t _I+1It is the chord length at i+1 data point place;

Secondly, the condition of contact of setting curve is so that every sectional curve can join end to end, and the whole piece curve after guaranteeing to connect is smooth, the condition that the present invention sets be every section curve in end points junction Second Order Continuous, obtain following matrix equation: $\left(t_{i+2}2(t_{i+2}+t_{i+1})t_{i+1}\right)\left(\begin{array}{c}{P}_i^{\&prime;}\\ {P_{i+1}}^{\&prime;}\\ {P_{i+2}}^{\&prime;}\end{array}\right)=3[\frac{t_{i+1}}{t_{i+2}}(P_{i+2}-P_{i-1})+\frac{t_{i+2}}{t_{i+1}}(P_{i+1}-P_i)],$ Can be in the hope of P by resolving equation ₂', P ₃' ..., P _N+1' value;

Again, set end-point condition, namely the first and last end points second derivative of closed curve is identical, and the present invention supposes that this second derivative is 0, namely obtains following operational equation With Can be in the hope of P ₁', P _n', the tangent vector at each data point place is calculated thus, and the curvilinear equation coefficient namely is determined;

At last, according to above method, utilize the data point data substitution curvilinear equation of 0.5 meter, 1.3 meters, 2.5 meters 3 height to simulate the transversal section curve of 3 height of trunk;

Second step, the simulation of trunk vertical curve:

At first, select parabola to carry out the simulation of trunk vertical curve, the curvilinear equation expression formula is: P (t)=A ₁+ A ₂T+A ₃t ², in the formula, A ₁, A ₂, A ₃Be respectively 3 undetermined coefficients of trunk solid curve section match, 0≤t≤1;

Then, set up 3 independent conditions of parabola: (1) is established para-curve and is crossed P _i, P _I+1, P _I+2Three points, P _iBe initial point, when parameter t=0, curve is crossed P _iThe point; (2) P _I+2Be terminal point, when parameter t=1, curve is crossed P _I+2The point; (3) when parameter t=0.5, curve is crossed P _I+1Point, and tangent vector is parallel to P _I+2-P _i, then have:

$S_i\left(t_i\right)=(2t_i^2-3t_i+1)P_i+(4t_i-4t_i^2)P_{i+1}+(2t_i^2-t_i)P_{i+2};$

Then, the segment of curve that draws by following formula is integrated between overlap between per two sections curves, article two, para-curve is can naturally not be overlapped into a curve, for two curves are connected with a smooth curve, need weighting synthetic, namely select two suitable weight functions, be respectively f (T)=1-T; G (T)=T (0≤T≤1), the curve after weighting is synthetic is: P _I+1(t)=f (T) S _i(t _i)+g (T) S _I+1(t _I+1), the span of establishing t in the simulation is: 0≤t≤0.5, then T=2t; t _i=0.5+t; t _I+1=t; Then resultant curve (two parabolical overlay segment) can be write as: P _I+1(t)=(4t ³+ 4t ²-t) P _i+ (12t ³-10t ²+ 1) P _I+1+ (12t ³+ 8t ²+ t) P _I+2+ (4t ³-2t ²) P _I+3

Secondly, set up end-point condition, n data point can only obtain n-3 section curve, but between n data point n-1 section should be arranged, and adds two end points P in the research ₀And P _N+1, and satisfy P ₀=P ₁P _N+1=P _n, the n-3 section curve of associating front just can obtain n-1 segment of curve, utilizes so above-mentioned parabolic batten equation to get final product the analog tree stem curve;

Again, utilize the trunk transversal section curve of having simulated, measure the diameter of a cross-section of a tree trunk 1.3 meters above the ground of tree, calculate height of tree coordinate according to the height of tree-diameter of a cross-section of a tree trunk 1.3 meters above the ground relational expression, and from the trunk transversal section curve of 3 height, choose the data point of 3 correspondences, altogether form 4 data points of parabola, substitution parabola equation simulation trunk vertical curve;

At last, each transversal section curve is divided into 1000 parts by angle, according to the previous step method, forms 1000 trunk vertical curves, thereby simulate the three-dimensional shape of whole trunk;

The 3rd step, the calculating of stem volume amount:

At first, along the trunk direction trunk is divided into 9000 sections;

Then, calculate the bottom surface area of each section of cutting apart, because the trunk solid curve is to be made of 1000 trunk vertical curves, so each section of cutting apart reality also is divided into 1000 parts, calculate all areas of 1000 parts and cumulative, can obtain the bottom surface area;

At last, because complete trunk is slit into 9000 sections by average mark, therefore can suppose when volume calculated that every a bit of upper and lower base area is approximately equalised, it is exactly one of them floorage and high product that volume calculates, the floorage that calculates by step 2 and the height of the section of cutting apart can obtain the volume of each section of cutting apart, the long-pending volume that can obtain whole trunk of cumulative 9000 segment bodies, i.e. stem volume amount.

2. single timber as claimed in claim 1 amasss measuring method, it is characterized in that: the long-pending measurement of described single timber comprises trunk transversal section curve simulation, the simulation of trunk vertical curve and trunk cubing.

3. such as right 2 described trunk transversal section curve simulation methods, it is characterized in that: described trunk transversal section curve simulation, at first, drill through 3 tree cores from trunk, calculate the data point two-dimensional coordinate according to tree core data, then with the segment of curve between the adjacent data point of two-dimensional coordinate substitution cubic parametric SPL equation simulation, secondly by setting end-point condition and condition of contact each independent segment of curve is smoothly connected processing, forms trunk transversal section curve.

4. such as right 2 described trunk vertical curve analogy methods, it is characterized in that: described trunk vertical curve simulation, at first at 0.5 meter on trunk, 1.3 meters and 2.5 meters 3 altitude simulation trunk transversal section curves, then choose respectively the data point of 3 correspondences from 3 curves, and obtain height of tree information by searching the diameter of a cross-section of a tree trunk 1.3 meters above the ground-height of tree monobasic table, with the segment of curve between data point and the adjacent data point of height of tree information substitution parabola equation simulation, be smoothly connected processing by the synthetic independently segment of curve of weighting at last, form the trunk vertical curve.

5. such as right 2 described trunk volume measuring methods, it is characterized in that: described trunk cubing, at first trunk is divided into 9000 parts, then the up and down floorage of supposing every a trunk is approximately equal, obtain the volume of every a trunk by floorage and height product, obtain whole trunk volume by cumulative 9000 parts of trunk volumes at last.

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