CN106780748A - A kind of quaternary tree index point cloud sort method based on grid association - Google Patents
A kind of quaternary tree index point cloud sort method based on grid association Download PDFInfo
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Abstract
A kind of quaternary tree index point cloud sort method based on grid association, step is as follows：First, plane fitting is carried out to cloud data using least square method, the three-dimensional coordinate that will be put on projection plane is converted to two dimension；2nd, the convex closure of these two-dimensional points is asked for, and four straight lines is fitted according to these convex closure points；3rd, 2-D data point is ranked up initialization, draws the ranking results of two-dimensional points；4th, the anti-ranking results for releasing initial three-dimensional point of ordering scenario according to two-dimensional points；By above step, three-dimensional data points are associated through after two dimensionization with grid, it is ranked up according to the grid and data point after association, it is pushed into three-dimensional raw data points and reaches the effect that three-dimensional data points carried out with geometry sequence finally by a title is counter, the unordered practical problem of data point whole geometry in cloud data is solved, facility is provided subsequently to carry out data analysis.
Description
Technical field
The present invention provides a kind of quaternary tree index point cloud sort method based on grid association, belongs to Point Cloud Processing skill
Art field.
Background technology
Cloud data is the important component of the subjects such as optical measurement, reverse-engineering, geographical mapping, and normal conditions have
Following two features：Data volume is big, and data point whole geometry is unordered.These cloud datas relatively at random are in reverse-engineering
Curve reestablishing and curved surface signature analysis bring certain obstacle.Ground currently for a series of the of three-dimensional point data sorting at random
Study carefully and be concentrated mainly on cloud data denoising, cloud data simplification, the expression of point cloud parametrization, cloud data feature extraction, section line
The aspects such as cloud data sequence.Wherein, document " aircraft digital Fast Detection Technique research (the bright of Feng Zi based on threedimensional model
Aircraft digital Fast Detection Technique research [J] aero-manufacturing technologies based on threedimensional model, 2011 (21)) " describe base
In the digitalization test of threedimensional model, reverse-engineering treatment is carried out by a large amount of cloud datas, entered with initial three-dimensional digital-to-analogue
Row comparative analysis, realizes the comparison and quality analysis of measurement data and gross data.During reverse modeling, generally require
Treatment is ranked up to point cloud data.Document " the unorganized point-clouds sequencing problem research (Gai Shaoyan, up to winged roc, thunder in three-dimensionalreconstruction
Bright great waves, wait unorganized point-clouds sequencing problem research [J] the computers in three-dimensionalreconstructions and modernization, 2003 (10):33-35.)”
Then describe the sort method of section line scattered point cloud data.It with cross-section profile shape is according to carrying out that section line point cloud sequence is
Sequence, the method has carried out parallel cutting to cloud data, extracts indicatrix and only for point cloud at Partial key feature
Data are ranked up.
Sort method at feature applies more in reverse-engineering, but when significant surfaces feature is extracted, sometimes
Needs are analyzed to whole curved surface situation.For example, aircraft surfaces some special areas surface characteristics to the pneumatic of aircraft
Property with flying quality produce considerable influence, these surface characteristics are including flatness, surface waviness, surface profile etc..It is modern non-
When contact type measurement mode is measured above-mentioned surface characteristics, generally using the tested curved surface of cloud data description.In order to analyze correlation
Curved surface integral surface situation, demand is just no longer met just for the point cloud sequence method at key feature.
The content of the invention
The purpose of the present invention is the vacancy for making up prior art, there is provided a kind of quaternary tree index point cloud based on grid association
Sort method.
A kind of quaternary tree index point cloud sort method based on grid association of the present invention, it comprises the following steps：
Step one, plane fitting is carried out to cloud data using least square method, three-dimensional data spot projection is flat to being fitted
Face, and the three-dimensional coordinate that will be put on projection plane is to two dimension conversion；
Step 2, the convex closure for asking for these two-dimensional points, and fit four straight lines according to these convex closure points；Using this four
Lines enveloping whole two-dimensional points cloud sector domain；According to the required precision of retrieval, this four envelope sides are carried out into equal proportion division, obtained
Corresponding segmentation straight line and grid division；
Step 3,2-D data point is ranked up initialization, is entered data point with grid using quaternary tree indexing means
Row association；Data point is ranked up according to the grid after association, draws the ranking results of two-dimensional points；
Step 4, the anti-ranking results for releasing initial three-dimensional point of ordering scenario according to two-dimensional points.
Wherein, " the carrying out plane fitting " described in step one refers to carry out plane fitting using least square method, profit
Projection plane is fitted with data point to be sorted, its fit procedure is as follows：If fit Plane is Sfitting：Ax+By-Cz+D=
0 (C ≠ 0),
It is also referred to as Sfitting：
NoteThen plane equation is：Z=a0x+a1y+a2.In formula, SfittingRepresent that fitting is flat
Face；A, B, C, D represent four unknown parameters in plane equation respectively；a0、a1、a2Be it is converted after three of plane equation
Unknown parameter.N data point is P in postulated point cloudi(xi,yi,zi), i=1,2,3...n, be using in these the Fitting Calculations
Plane equation is stated, is then madeIt is minimum.If making Δ minimum, should meetI.e.
Can be obtained according to above-mentioned equation：Solve a0,a1,
a2, obtain final product plane equation z=a0x+a1y+a2.In above-mentioned formula, Δ represents the fit object value tried to achieve by least square method；a0、
a1、a2It is three unknown parameters of plane equation；xi、yi、zi(i=1,2,3...n) point P is represented respectivelyi(xi,yi,zi) (i=1,
2,3...n X, Y, Z axis coordinate value).Described " projection to fit Plane " refers to state data spot projection to be sorted is supreme
In the fit Plane tried to achieve in step, its projection process is：If the equation of projection plane is z=a0x+a1y+a2, then point to be projected
Pi(xi,yi,zi), the projective transformation equation of i=1,2,3...n is：
In formula：The X, Y, Z axis coordinate value after projective transformation is represented respectively；xi、yi、zi(i
=1,2,3...n) initial X, Y, Z axis coordinate value is represented respectively；a0,a1,a2It is by three tried to achieve in projection plane equation
Number.
By above-mentioned coordinate transform will spot projection be sorted to fit Plane.Described " two dimension conversion " refers to throw
The position coordinates of the sequence point in shadow to fit Plane is converted into two-dimensional coordinate by three-dimensional coordinate.From projection relation, it is in
During multiple spot reprojection to another plane on same plane, if projection result is not straight line, the relative position between point is closed
It is constant.It is to simplify to calculate, can be with reprojection to XOY coordinate axial planes, i.e., during by data point two dimensionization on projection plane
Projective transformation formula in formula (1) is changed into：
Obtain the data point P` after two-dimensional transformi(x`i,y`i), i=1,2,3...n；
In formula：x`i、y`i(i=1,2,3...n) X, Y-axis coordinate value after projective transformation are represented respectively；xi、yi(i=1,
2,3...n initial X, Y-axis coordinate value) are represented respectively；a0,a1,a2By three coefficients tried to achieve in projection plane equation.
Wherein, " convex closure " described in step 2 is the concept in computational geometry (graphics), in a real number vector
In SPACE V, the convex closure of X is referred to as given set X, the common factor S of all convex sets comprising X.Two-dimensional points in this explanation are convex
Bag is exactly that outermost point is coupled together into the convex polygonal of composition.The step of it is asked for (Fig. 1 (a)-Fig. 1 (d) shown in) be：
(1) maximum and minimum point of a certain coordinate of cloud data are determined.Such as the point P of y-coordinate minimaxmax、Pmin,
Then point Pmax、PminIt must be the point on convex closure；
(2) initial convex closure triangle is formed.Cross point Pmax、PminStraight line be LPmaxPmin, found out apart from straight line in a cloud
LPmaxP minThe farthest point P in both sides0、P1, constitute initial convex closure triangle Δ P0PmaxPminWith Δ P1PmaxPmin。
(3) continue to generate convex closure triangle.Each triangle it is newly-generated while for new seek, continually look for newly-generated
The outermost points on side.
(4) all of convex closure point is found, i.e. there is no data point, convex closure point is stored in point set G in convex closure line outsideconvex。
" fitting four straight lines according to these convex closure points " described in step 2, refers to using above-mentioned convex closure point set
In data point four straight lines are gone out according to least square fitting, its specific steps (such as shown in Fig. 2 (a)-Fig. 2 (c)) are：According to
Ask for the maximum point and minimum point (i.e. P of a certain coordinate of determination in convex closure stepmax、Pmin) and apart from straight line LPmaxPminTwo
Side solstics (i.e. P0、P1) continue convex hull set GconvexIt is divided into four subsets.Postulated point P0X-axis coordinate be less than point P1's
X-axis coordinate, then can be divided into following four subsets, G by convex hull set1{(x,y)|xP0<x<xPmax,yP0<y<yPmax}、G2{(x,
y)|xPmax<x<xP1,yP1<y<yPmax}、G3{(x,y)|xPmin<x<xP1,yPmin<y<yP1}、G4{(x,y)|xP0<x<xPmin,yPmin<
y<yP0}。
In formula, G1、G2、G3、G4Four convex closure subsets are represented respectively；
xP0、yP0、xP1、yP1、xPmax、yPmax、xPmin、yPminPoint P is represented respectively0、P1、Pmax、PminX, Y-axis coordinate value.With G1For
Example, if Pi(xi,yi)∈G1(i=1,2 ..., N), if fit object straight line is y=a+bx, due to straight using least square fitting
Line, then should makeValue it is minimum.Local derviation is asked to obtain a, b in above formula respectively：
Solve the best estimate that above-mentioned equation group obtains a and b：
In formula：A, b represent two unknown numbers in fitting a straight line respectively；Represent that projection becomes respectively
Change X, the Y-axis coordinate value of rear data point；N is the total number of data point.
" utilizing this four lines enveloping whole two-dimensional points cloud sectors domain " described in step 2 refers to be tried to achieve above-mentioned
Four fitting a straight line is translated, and is enabled whole sequence point cloud envelope, and its step is：Try to achieve fitting a straight line y=a+
After bx (dotted line in Fig. 2 (c)), set G is found out1In the point P farthest from straight line y=a+bxfar, straight line y=a+bx is moved to a little
PfarPlace, obtains the envelope y`=a+bx` of two-dimensional points cloud, i.e. solid line in Fig. 2 (c).It is described that " four envelope sides carry out waiting ratio
Example division " refers to that the required precision respectively by four envelope sides as required wait than dividing, then straight by relative two
Along ent connection on line, obtains segmentation straight line and forms grid.
Wherein, " 2-D data point is ranked up initialization " described in step 3 refers to by each data point information
Add its envelope side information.Under most original state, the envelope side of all data points is the outermost bag generated in step 2
Network side, interpolation data point envelope while information be outermost envelope while, i.e. the initialization of data point.Described " data point and grid
It is associated " refer to be updated data point envelope side information, make the final envelope side of data point be Grid Edge.Assuming that initial
Envelope side is u0、v0、ui、vi, then it is as follows the step of grid is associated：
(1) index start when, be in a little in the envelope of above-mentioned four fitting a straight lines (in Fig. 3 (a)-Fig. 3 (d)
Dotted line is envelope side), i.e., initial envelope side a little be four fitting a straight lines, be designated as u0、v0、ui、vi, respectively represent u to
With v to envelope straight line.
(2) envelope side is updated, u is found respectively to, v to the grid straight line u in the middle of envelope sidemiddle、vmiddle.According to entering
The data point P` of line index is in umiddle、vmiddleThe location of, u is replaced to, v to envelope side, by data point envelope side scope
Reduce.
(3) until u is two adjacent straight lines to, v to envelope side, i.e., search complete.The data point that is retrieved is in quilt
Envelope side divide grid in, will the data point information be associated with the grid.
(4) grid after associating is ranked up according to the demand of sequence to the data point in grid, and then grid is carried out
Sequence, completes final sequence.
Wherein, " the anti-sequence knot for releasing initial three-dimensional point of ordering scenario according to two-dimensional points described in step 4
Really ", be ranked up for initial three-dimensional point by the 2-D data dot sequency after " counter to push away " refers to according to sequence；Due to two-dimensional points sequence
Point name information does not change afterwards, and three-dimensional initial data is ranked up according to these ranked good data point name orders,
The i.e. three-dimensional ranking results of the result for obtaining.
By above step, three-dimensional data points are associated through after two dimensionization with grid, according to grid and data point after association
It is ranked up, is pushed into three-dimensional raw data points and reaches the effect that three-dimensional data points carried out with geometry sequence finally by a title is counter
Really, the unordered practical problem of data point whole geometry in cloud data is solved, facility is provided subsequently to carry out data analysis.
The device have the advantages that:
1) overall sequence is carried out to point cloud data, meets the demand to overall data point arranged in sequence in surface analysis；
2) envelope side is solved using convex closure, except that all data point envelopes can be reflected into a cloud to a certain extent
Profile, is easy to subsequent meshes to divide；
3) indexing means associated with quaternary tree using grid, had both been avoided quaternary tree and had produced redundancy structure, were improve again
The index speed of simple grid.
Brief description of the drawings
Fig. 1 (a)-Fig. 1 (d) is to ask for schematic diagram according to the convex closure of embodiment of the present invention, wherein,
The extreme point of Fig. 1 (a) cloud datas.
The initial convex closure triangles of Fig. 1 (b).
Fig. 1 (c) finds convex closure point.
Fig. 1 (d) convex closures are asked for completing.
Fig. 2 (a)-Fig. 2 (c) is to ask for schematic diagram according to the envelope side of embodiment of the present invention, wherein,
Initial convex closure four angle points of triangle of Fig. 2 (a).
Fig. 2 (b) convex closure subsets G1Schematic diagram.
Fig. 2 (c) envelopes side generates.
Fig. 3 (a)-Fig. 3 (d) is the quadtree mesh association index method schematic diagram of foundation embodiment of the present invention, wherein,
Fig. 3 (a) original states.
Fig. 3 (b) envelopes side updates.
Fig. 3 (c) envelopes side updates.
The association of Fig. 3 (d) grids is completed.
Fig. 4 is example cloud data.
Fig. 5 is example point cloud envelope side.
Fig. 6 is the grade minute situation of example point cloud grid 20.
Fig. 7 (a)-Fig. 7 (d) is the sequence design sketch (20,50,100,150 decile) in the case of different accuracy decile, its
In,
Sequence effect under the deciles of Fig. 7 (a) 20.
Sequence effect under the deciles of Fig. 7 (b) 50.
Sequence effect under the deciles of Fig. 7 (c) 100.
Sequence effect under the deciles of Fig. 7 (d) 150.
Fig. 8 the method for the invention flow charts.
Sequence number, symbol, code name are described as follows in figure：
In Fig. 1 (a)-Fig. 1 (d), PmaxIt is the point that Y value in data point is maximum, PminIt is the point that Y value in data point is minimum.Ymax
It is expressed as Y value maximum, YminIt is expressed as Y value minimum.P0、P1It is range points PmaxPminTwo farthest points of line.P2、P3It is new life
Into convex closure triangle angle point.
In Fig. 2 (a)-Fig. 2 (c), Pmax、Pmin、P0、P1It is identical with implication in Fig. 1 (a)-Fig. 1 (d), Pmax、PminRepresent Y value
Two extreme points, P0、P1It is range points PmaxPminTwo farthest points of line.
In Fig. 3 (a)-Fig. 3 (d), u0、u1、u2、u3、u4、u5For u to six cut-off rules, v0、v1、v2、v3、v4For v to
Five cut-off rules.(1) (two) (three) (four) expression one, two, three, four-quadrant respectively.PiRepresent point to be associated.
Specific embodiment
The present invention sums up a kind of method that quaternary tree indexing means of utilization grid association sort to three-dimensional point cloud.It is this
Method is processed three dimensional point cloud two dimensionization through projecting by least square fitting projection plane.Asked using a cloud convex closure
Go out two-dimensional points cloud envelope side, and envelope area grid is divided.Finally number is completed using the quaternary tree indexing means of grid association
Sort at strong point.This method not only retains the sequence degree of accuracy to the full extent, and can be right using quaternary tree indexing means
Data point quicksort, meets the demand to overall data point arranged in sequence in surface analysis.
A kind of quaternary tree index point cloud sort method based on grid association of the present invention, as shown in figure 8, it includes following step
Suddenly：
1) plane fitting is carried out to cloud data using least square method, by three-dimensional data spot projection to fit Plane, and
And the three-dimensional coordinate that will be put on projection plane is converted to two dimension.
2) convex closure of these two-dimensional points is asked for, and four straight lines is fitted according to these convex closure points.Using this four straight lines
Envelope whole two-dimensional points cloud sector domain.According to the required precision of retrieval, this four envelope sides are carried out into equal proportion division, obtain corresponding
Segmentation straight line and grid division.
3) 2-D data point is ranked up initialization, data point is closed with grid using quaternary tree indexing means
Connection.Data point is ranked up according to the grid after association, draws the ranking results of two-dimensional points.
4) the anti-ranking results for releasing initial three-dimensional point of ordering scenario according to two-dimensional points.
Wherein, " the carrying out plane fitting " described in step one refers to carry out plane fitting using least square method, profit
Projection plane is fitted with data point to be sorted, its fit procedure is as follows：If fit Plane, i.e. also referred to as Sfitting：
NoteThen plane equation is：Z=a0x+a1y+a2.In formula, SfittingRepresent that fitting is flat
Face；A, B, C, D represent four unknown parameters in plane equation respectively；a0、a1、a2Be it is converted after three of plane equation
Unknown parameter.N data point is P in postulated point cloudi(xi,yi,zi), i=1,2,3...n, be using in these the Fitting Calculations
Plane equation is stated, is then madeIt is minimum.If making Δ minimum, should meetI.e.Can be obtained according to above-mentioned equation：
Solve a0,a1,a2, obtain final product plane equation z=a0x+a1y+a2.In above-mentioned formula, Δ represents the fitting tried to achieve by least square method
Desired value；a0、a1、a2It is three unknown parameters of plane equation；xi、yi、zi(i=1,2,3...n) point P is represented respectivelyi(xi,
yi,zi) (i=1,2,3...n) X, Y, Z axis coordinate value.Described " projection to fit Plane " refers to by data point to be sorted
Project in the fit Plane tried to achieve into above-mentioned steps, its projection process is：If the equation of projection plane is z=a0x+a1y+a2,
Then point P to be projectedi(xi,yi,zi), the projective transformation equation of i=1,2,3...n is：
In formula：x`i、y`i、z`i(i=1,2,3...n) the X, Y, Z axis coordinate value after projective transformation is represented respectively；xi、yi、
zi(i=1,2,3...n) initial X, Y, Z axis coordinate value is represented respectively；a0,a1,a2By tried to achieve in projection plane equation three
Individual coefficient.
By above-mentioned coordinate transform will spot projection be sorted to fit Plane.Described " two dimension conversion " refers to throw
The position coordinates of the sequence point in shadow to fit Plane is converted into two-dimensional coordinate by three-dimensional coordinate.From projection relation, it is in
During multiple spot reprojection to another plane on same plane, if projection result is not straight line, the relative position between point is closed
It is constant.It is to simplify to calculate, can be with reprojection to XOY coordinate axial planes, i.e., during by data point two dimensionization on projection plane
Projective transformation formula in formula (1) is changed into：
Obtain the data point P` after two-dimensional transformi(x`i,y`i), i=1,2,3...n.
In formula：x`i、y`i(i=1,2,3...n) X, Y-axis coordinate value after projective transformation are represented respectively；xi、yi(i=1,
2,3...n initial X, Y-axis coordinate value) are represented respectively；a0,a1,a2By three coefficients tried to achieve in projection plane equation.
Wherein, " convex closure " described in step 2 is the concept in computational geometry (graphics), in a real number vector
In SPACE V, the convex closure of X is referred to as given set X, the common factor S of all convex sets comprising X.Two-dimensional points in this explanation are convex
Bag is exactly that outermost point is coupled together into the convex polygonal of composition.The step of it is asked for (Fig. 1 (a)-Fig. 1 (d) shown in) be：
(1) maximum and minimum point of a certain coordinate of cloud data are determined.Such as the point P of y-coordinate minimaxmax、Pmin,
Then point Pmax、PminIt must be the point on convex closure；
(2) initial convex closure triangle is formed.Cross point Pmax、PminStraight line be LPmaxPmin, found out apart from straight line in a cloud
LPmaxPminThe farthest point P in both sides0、P1, constitute initial convex closure triangle Δ P0PmaxPminWith Δ P1PmaxPmin。
(3) continue to generate convex closure triangle.Each triangle it is newly-generated while for new seek, continually look for newly-generated
The outermost points on side.
(4) all of convex closure point is found, i.e. there is no data point, convex closure point is stored in point set G in convex closure line outsideconvex。
Described " four straight lines are fitted according to convex closure point " refer to the data point concentrated using above-mentioned convex closure point according to
Least square fitting goes out four straight lines, and its specific steps (such as shown in Fig. 2 (a)-Fig. 2 (c)) is：According in asking for convex closure step
The maximum point of a certain coordinate for determining and minimum point (i.e. Pmax、Pmin) and apart from straight line LPmaxPminBoth sides solstics (i.e. P0、
P1) continue convex hull set GconvexIt is divided into four subsets.Postulated point P0X-axis coordinate be less than point P1X-axis coordinate, then can be by
Convex hull set is divided into following four subsets, G1{(x,y)|xP0<x<xPmax,yP0<y<yPmax}、G2{(x,y)|xPmax<x<xP1,
yP1<y<yPmax}、G3{(x,y)|xPmin<x<xP1,yPmin<y<yP1}、G4{(x,y)|xP0<x<xPmin,yPmin<y<yP0}。
In formula, G1、G2、G3、G4Four convex closure subsets are represented respectively；
xP0、yP0、xP1、yP1、xPmax、yPmax、xPmin、yPminPoint P is represented respectively0、P1、Pmax、PminX, Y-axis coordinate value.With
G1As a example by, if Pi(xi,yi)∈G1(i=1,2 ..., N), if fit object straight line is y=a+bx, due to using least square method
Fitting a straight line, then should makeValue it is minimum.Local derviation is asked to obtain a, b in above formula respectively：Solve the best estimate that above-mentioned equation group obtains a and b：
In formula：A, b represent two unknown numbers in fitting a straight line respectively；xi、yi(i=1,2,3...n) projection is represented respectively
The X of data point, Y-axis coordinate value after conversion；N is the total number of data point.
Described " utilizing this four lines enveloping whole two-dimensional points cloud sectors domain " refers to that above-mentioned four fittings tried to achieve are straight
Line is translated, and is enabled whole sequence point cloud envelope, and its step is：Fitting a straight line y=a+bx is tried to achieve (in Fig. 2 (c)
Dotted line) after, find out set G1In the point P farthest from straight line y=a+bxfar, straight line y=a+bx is moved into point PfarPlace, obtains
The envelope y`=a+bx` of two-dimensional points cloud, i.e. solid line in Fig. 2 (c).Described " four envelope sides carry out equal proportion division " refer to
Required precision by four envelope sides as required respectively wait than dividing, then by the Along ent on two relative straight lines
Connection, obtains segmentation straight line and forms grid.
Wherein, " 2-D data point is ranked up initialization " described in step 3 refers to by each data point information
Add its envelope side information.Under most original state, the envelope side of all data points is the outermost bag generated in step 2
Network side, interpolation data point envelope while information be outermost envelope while, i.e. the initialization of data point.Described " data point and grid
It is associated " refer to be updated data point envelope side information, make the final envelope side of data point be Grid Edge.Assuming that initial
Envelope side is u0、v0、ui、vi, then it is as follows the step of grid is associated：
(1) index start when, be in a little in the envelope of above-mentioned four fitting a straight lines (in Fig. 3 (a)-Fig. 3 (d)
Dotted line is envelope side), i.e., initial envelope side a little be four fitting a straight lines, be designated as u0、v0、ui、vi, respectively represent u to
With v to envelope straight line.
(2) envelope side is updated, u is found respectively to, v to the grid straight line u in the middle of envelope sidemiddle、vmiddle.According to entering
The data point P` of line index is in umiddle、vmiddleThe location of, u is replaced to, v to envelope side, by data point envelope side scope
Reduce.
(3) until u is two adjacent straight lines to, v to envelope side, i.e., search complete.The data point that is retrieved is in quilt
Envelope side divide grid in, will the data point information be associated with the grid.
(4) grid after associating is ranked up according to the demand of sequence to the data point in grid, and then grid is carried out
Sequence, completes final sequence.
Wherein, 2-D data dot sequency after " counter to push away " described in step 4 refers to according to sequence is by initial three-dimensional point
It is ranked up.Do not change due to putting name information after two-dimensional points sequence, according to these ranked good data point name orders
Three-dimensional initial data is ranked up, the i.e. three-dimensional ranking results of the result for obtaining.
Embodiment
1) cloud data is analyzed, it can be seen that Fig. 3 (a)-Fig. 3 (d) point cloud data is opposed flattened, does not have larger bending
Situation, splits without to cloud data；
2) data point now has a title, XYZ axial coordinate information comprising information.Least square method is used to cloud data point
Projection plane is fitted, by data spot projection to projection plane.Then data point three-dimensional coordinate is converted into two dimension, now data
Point information is point title, XY axial coordinate information；
3) two-dimensional points convex closure is asked for, and four straight lines is fitted according to these convex closure points.Then by this four rectilinear translations
At to corresponding outermost convex closure point, the lines enveloping whole two-dimensional points cloud sector domain after being translated using this four, such as Fig. 4.Point
Other 20 grades point that carried out to this four envelope sides are divided, and straight line and grid division are split accordingly, as shown in Figure 5.
4) 2-D data point is ranked up initialization, data point is closed with grid using quaternary tree indexing means
Connection.(Sort Direction is horizontal direction in Fig. 5), the row for drawing two-dimensional points are ranked up to data point according to the grid after association
Sequence result.Fig. 6 is 20 grades point sequence design sketch, and the data point in figure for same row is coupled together according to order.Fig. 7 (a)-figure
7 (d) is respectively 50,100,150 etc. points of sequence design sketch.
5) the anti-ranking results for releasing initial three-dimensional point of ordering scenario according to two-dimensional points.
Be can be seen that as mesh generation is more and more finer according to sequence effect, data point line bending situation is increasingly
It is small.In 100 grade timesharing, point line has not had larger bending, can meet ordering requirements.
Claims (5)
1. it is a kind of based on grid association quaternary tree index point cloud sort method, it is characterised in that：It comprises the following steps：
Step one, plane fitting is carried out to cloud data using least square method, by three-dimensional data spot projection to fit Plane, and
And the three-dimensional coordinate that will be put on projection plane is converted to two dimension；
Step 2, the convex closure for asking for these two-dimensional points, and fit four straight lines according to these convex closure points；Using this four straight lines
Envelope whole two-dimensional points cloud sector domain；According to the required precision of retrieval, this four envelope sides are carried out into equal proportion division, obtain corresponding
Segmentation straight line and grid division；
Step 3,2-D data point is ranked up initialization, data point is closed with grid using quaternary tree indexing means
Connection；Data point is ranked up according to the grid after association, draws the ranking results of two-dimensional points；
Step 4, the anti-ranking results for releasing initial three-dimensional point of ordering scenario according to two-dimensional points；
By above step, three-dimensional data points are associated through after two dimensionization with grid, are carried out according to the grid and data point after association
Sequence, is pushed into three-dimensional raw data points and reaches the effect that three-dimensional data points carried out with geometry sequence finally by a title is counter, solution
Determine the unordered practical problem of data point whole geometry in cloud data, facility is provided subsequently to carry out data analysis.
2. it is according to claim 1 it is a kind of based on grid association quaternary tree index point cloud sort method, it is characterised in that：
" carrying out plane fitting " described in step one refers to carry out plane fitting using least square method, using data to be sorted
Point fits projection plane, and its fit procedure is as follows：If fit Plane is Sfitting：Ax+By-Cz+D=0 (C ≠ 0),
It is expressed as Sfitting：NoteThen plane equation is：z
=a0x+a1y+a2；In formula, SfittingRepresent fit Plane；A, B, C, D represent four unknown parameters in plane equation respectively；
a0、a1、a2Be it is converted after plane equation three unknown parameters；N data point is P in postulated point cloudi(xi,yi,zi),i
=1,2,3...n, to utilize the above-mentioned plane equation of these the Fitting Calculations, then makeIt is minimum；
If making Δ minimum, should meetI.e.Root
Obtained according to above-mentioned equation：Solve a0,a1,a2,
Obtain final product plane equation z=a0x+a1y+a2；In above-mentioned formula, Δ represents the fit object value tried to achieve by least square method；a0、
a1、a2It is three unknown parameters of plane equation；xi、yi、zi(i=1,2,3...n) point P is represented respectivelyi(xi,yi,zi) (i=1,
2,3...n X, Y, Z axis coordinate value)；
Described " projection to fit Plane " refers to by the supreme fit Plane tried to achieve in step stated of data spot projection to be sorted
On, its projection process is：If the equation of projection plane is z=a0x+a1y+a2, then point P to be projectedi(xi,yi,zi), i=1,2,
3...n projective transformation equation is：
In formula：x`i、y`i、z`i(i=1,2,3...n) the X, Y, Z axis coordinate value after projective transformation is represented respectively；xi、yi、zi(i
=1,2,3...n) initial X, Y, Z axis coordinate value is represented respectively；a0,a1,a2It is by three tried to achieve in projection plane equation
Number；
By above-mentioned coordinate transform will spot projection be sorted to fit Plane；Described " two dimension conversion " refers to project extremely
The position coordinates of the sequence point in fit Plane is converted into two-dimensional coordinate by three-dimensional coordinate；Can be known by projection relation, in same
During multiple spot reprojection to another plane in plane, if projection result is not straight line, the relative position relation between point is not
Become；Calculated to simplify, by the data point two dimension Hua Shineng reprojections on projection plane to XOY coordinate axial planes, i.e. formula (1)
In projective transformation formula be changed into：
Obtain the data point P` after two-dimensional transformi(x`i,y`i), i=1,2,3...n；
In formula：x`i、y`i(i=1,2,3...n) X, Y-axis coordinate value after projective transformation are represented respectively；
xi、yi(i=1,2,3...n) initial X, Y-axis coordinate value are represented respectively；a0,a1,a2By being tried to achieve in projection plane equation
Three coefficients.
3. it is according to claim 1 it is a kind of based on grid association quaternary tree index point cloud sort method, it is characterised in that：
" convex closure " described in step 2 is the concept in computational geometry i.e. graphics, right in a real number vector space V
In given set X, the common factor S of all convex sets comprising X is referred to as the convex closure of X；Described two-dimensional points convex closure is exactly by outermost layer
Point couple together the convex polygonal of composition；The step of it is asked for be：
(1) maximum and minimum point of the coordinate of cloud data one are determined；Such as the point P of y-coordinate minimaxmax、Pmin, then point
Pmax、PminIt must be the point on convex closure；
(2) initial convex closure triangle is formed；Cross point Pmax、PminStraight line be LPmaxPmin, found out apart from straight line in a cloud
LPmaxPminThe farthest point P in both sides0、P1, constitute initial convex closure triangle Δ P0PmaxPminWith Δ P1PmaxPmin；
(3) continue to generate convex closure triangle；Each triangle it is newly-generated while for new seek, continually look for newly-generated side
Outermost points；
(4) all of convex closure point is found, i.e. there is no data point, convex closure point is stored in point set G in convex closure line outsideconvex；
" fitting four straight lines according to these convex closure points " described in step 2, refers to be concentrated using above-mentioned convex closure point
Data point goes out four straight lines according to least square fitting, and it is concretely comprised the following steps：According to the seat for asking for determining in convex closure step
Target maximum point and minimum point are Pmax、PminWith apart from straight line LPmaxPminBoth sides solstics is P0、P1Continue convex closure collection
Close GconvexIt is divided into four subsets；Postulated point P0X-axis coordinate be less than point P1X-axis coordinate, then by convex hull set be divided into as
Lower four subsets,
G1{(x,y)|xP0<x<xPmax,yP0<y<yPmax}、G2{(x,y)|xPmax<x<xP1,yP1<y<yPmax}、G3{(x,y)|xPmin<x
<xP1,yPmin<y<yP1}、G4{(x,y)|xP0<x<xPmin,yPmin<y<yP0}；
In formula, G1、G2、G3、G4Four convex closure subsets are represented respectively；xP0、yP0、xP1、yP1、xPmax、yPmax、xPmin、yPminDifference table
Show point P0、P1、Pmax、PminX, Y-axis coordinate value；
" utilizing this four lines enveloping whole two-dimensional points cloud sectors domain " described in step 2 refers to by above-mentioned four for trying to achieve
Fitting a straight line is translated, and is enabled whole sequence point cloud envelope, and its step is：After fitting a straight line y=a+bx is tried to achieve,
Find out set G1In the point P farthest from straight line y=a+bxfar, straight line y=a+bx is moved into point PfarPlace, obtains two-dimensional points cloud
Envelope y`=a+bx`；Described " four envelopes are carrying out equal proportion division " refer to respectively by four envelopes while according to need
The required precision wanted wait than dividing, and then connects the Along ent on two relative straight lines, obtains segmentation straight line and shape
Into grid.
4. it is according to claim 1 it is a kind of based on grid association quaternary tree index point cloud sort method, it is characterised in that：
" 2-D data point is ranked up initialization " described in step 3 refers to that its bag will be added in each data point information
Network side information；Under most original state, the envelope of all data points is added in the outermost envelope generated in being step 2
Data point envelope while information be outermost envelope while, i.e. the initialization of data point；Described " data point is associated with grid "
Refer to be updated data point envelope side information, make the final envelope side of data point be Grid Edge；Assuming that initial envelope side is
u0、v0、ui、vi, then it is as follows the step of grid is associated：
(1) index start when, be in a little in the envelope of above-mentioned four fitting a straight lines, i.e., initial envelope side a little
Four fitting a straight lines are, u is designated as0、v0、ui、vi, respectively represent u to v to envelope straight line；
(2) envelope side is updated, u is found respectively to, v to the grid straight line u in the middle of envelope sidemiddle、vmiddle；According to carrying out rope
The data point P` for drawing is in umiddle、vmiddleThe location of, u is replaced to, v to envelope side, by data point envelope side range shorter；
(3) until u is two adjacent straight lines to, v to envelope side, i.e., search complete；The data point that is retrieved is in by envelope
Side divide grid in, will the data point information be associated with the grid；
(4) grid after associating is ranked up according to the demand of sequence to the data point in grid, and then grid is ranked up,
Complete final sequence.
5. it is according to claim 1 it is a kind of based on grid association quaternary tree index point cloud sort method, it is characterised in that：
" the anti-ranking results for releasing initial three-dimensional point of ordering scenario according to two-dimensional points " described in step 4, being somebody's turn to do " counter to push away " refers to
Initial three-dimensional point is ranked up according to the 2-D data dot sequency after sequence；Do not have due to putting name information after two-dimensional points sequence
Change, three-dimensional initial data is ranked up according to these ranked good data point name orders, the result for obtaining i.e. three-dimensional
Ranking results.
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