CN111612892B - Point cloud coordinate construction method - Google Patents

Point cloud coordinate construction method Download PDF

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CN111612892B
CN111612892B CN202010446762.XA CN202010446762A CN111612892B CN 111612892 B CN111612892 B CN 111612892B CN 202010446762 A CN202010446762 A CN 202010446762A CN 111612892 B CN111612892 B CN 111612892B
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coordinate system
point cloud
coordinate
vector
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CN111612892A (en
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巴晓甫
侣胜武
程露
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Xian Aircraft Industry Group Co Ltd
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    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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Abstract

The invention discloses a coordinate structure of point cloudThe method comprises the steps of obtaining a point cloud relative to an equipment coordinate system R through coordinate measuring equipment, wherein the point cloud contains a large number of points Coordinate system To construct a point cloud relative to a point cloud coordinate system C Coordinate system Firstly, a point cloud is obtained by a coordinate measuring device relative to a device coordinate system R Coordinate system Then constructing a point cloud coordinate system C Coordinate system Origin C 0 In the device coordinate system R Coordinate system Then constructing a point cloud coordinate system C Coordinate system And then calibrating a point cloud coordinate system C Coordinate system X axis of (a) and then calibrating the point cloud coordinate system C Coordinate system Then calibrating the point cloud coordinate system C Coordinate system Then calibrating the point cloud coordinate system C Coordinate system Relative to a device coordinate system R Coordinate system Finally, constructing a point cloud relative to a point cloud coordinate system C Coordinate system The coordinate values of (2).

Description

Point cloud coordinate construction method
Technical Field
The application relates to the technical field of measurement, in particular to a coordinate construction method of point cloud.
Background
The manufacturing precision of the aerodynamic profile, the structural inner profile and the motion intersection point of the airplane is the most important control element for airplane manufacturing. According to the concept of finite dispersion, the intersection points of aerodynamic shape, structural shape and motion are dispersed into a large number of points, namely point clouds. Therefore, the coordinate precision of the point cloud becomes the basis for judging the manufacturing quality of the airplane.
The point cloud is a set of points with spatial position relationship, coordinates of the point cloud are obtained by a coordinate measuring device, but coordinates of the point cloud obtained by the coordinate measuring device are relative to a device coordinate system, the coordinate system changes along with the change of the device, and the point cloud coordinates also change, which is not beneficial to the use, transmission and management of data in the aircraft manufacturing and also affects the coordinate precision of the point cloud.
Disclosure of Invention
In order to solve the problems, the application discloses a method for determining a point cloud coordinate system and constructing a coordinate value of the point cloud under the point cloud coordinate system according to the point cloud, so that the point cloud and the point cloud coordinate system are solidified, the point cloud coordinate does not change along with the change of measuring equipment, and the coordinate construction precision of the point cloud is improved.
Of a kind of point cloudCoordinate construction method, wherein the point cloud contains a large number of points, and the coordinate measurement equipment is used for obtaining the point cloud relative to the equipment coordinate system R Coordinate system To construct a point cloud relative to a point cloud coordinate system C Coordinate system The method comprises the following steps:
(1) Obtaining a point cloud by a coordinate measurement device relative to a device coordinate system R Coordinate system Homogeneous coordinates of (a):
Figure BDA0002504278770000011
(2) Constructing a point cloud coordinate system C Coordinate system Origin C 0 In the device coordinate system R Coordinate system Homogeneous coordinates of (a):
Figure BDA0002504278770000021
(3) Constructing a point cloud coordinate system C Coordinate system Comprising the following steps:
(3-1) using a point cloud coordinate system C Coordinate system Origin C 0 As a starting point, using other points of the point cloud as directions to construct vectors of all points in the point cloud:
Figure BDA0002504278770000022
(3-2) calculating the modulus of the vector product between every two vectors:
Figure BDA0002504278770000023
(3-3) selecting a group with the maximum modulus, and assuming that two vectors of the group with the maximum modulus are respectively as follows:
Figure BDA0002504278770000024
and &>
Figure BDA0002504278770000025
Wherein i, j ∈ [1n ]](i≠j,i<j)；
(3-4) Point cloud coordinate System C Coordinate system From the origin C 0 Point i and point j.
(4) Comparing vectors
Figure BDA0002504278770000026
And &>
Figure BDA0002504278770000027
In a vector having a greater modulus (assumed @)>
Figure BDA0002504278770000028
) As a point cloud coordinate system C Coordinate system X-axis of (a) in the device coordinate system R Coordinate system The coordinate expression of the vector of (b) is:
Figure BDA0002504278770000029
(5) Will vector
Figure BDA00025042787700000210
And &>
Figure BDA00025042787700000211
And (3) performing vector product operation according to a right-hand rule: />
Figure BDA00025042787700000212
Pick up the vector>
Figure BDA00025042787700000213
Calibration as a point cloud coordinate system C Coordinate system Z-axis in the device coordinate system R Coordinate system The coordinate expression of the vector of (b) is:
Figure BDA00025042787700000214
(6) Will vector
Figure BDA00025042787700000215
And &>
Figure BDA00025042787700000216
And (3) performing vector product operation according to a right-hand rule: />
Figure BDA00025042787700000217
Combining vectors>
Figure BDA00025042787700000218
Calibration as point cloud coordinate system C Coordinate system Y-axis in the device coordinate system R Coordinate system The coordinate expression of the vector of (a) is:
Figure BDA0002504278770000031
(7) Point cloud coordinate system C Coordinate system Relative to a device coordinate system R Coordinate system Is calibrated by the following expression:
Figure BDA0002504278770000032
(8) Point cloud relative to point cloud coordinate system C Coordinate system The coordinate values of (c) are constructed by the following expressions:
Figure BDA0002504278770000033
device coordinate system R Coordinate system The coordinate system can be a rectangular coordinate system or an oblique coordinate system; point cloud coordinate system C Coordinate system Is a rectangular coordinate system.
The method for constructing the point cloud coordinates solves the following key problems:
(1) And (4) completely standing on the point cloud, and constructing a point cloud coordinate system.
(2) The point cloud and the point cloud coordinate system are in one-to-one correspondence, and the relationship between the point cloud and the point cloud coordinate system is solidified, namely, the point cloud can construct a unique point cloud coordinate system, and the point cloud coordinate system also uniquely determines the coordinates of the point cloud.
(3) The method is beneficial to the use, transmission and management of the point cloud and the coordinate data thereof.
(4) The coordinate construction precision of the point cloud is improved.
The present application is described in further detail below with reference to the accompanying drawings of embodiments:
drawings
FIG. 1 is a schematic diagram of a point cloud and a point cloud coordinate system
The numbering in the figures illustrates: 1 coordinate measuring device, 2 point cloud
Detailed Description
As shown in the figure, the point cloud 2 on the right is a measurement point on a rigid object, the object contour is hidden, and only all measurement points are displayed. On the left side is a coordinate measuring device 1, and the coordinate measuring device 1 is typically used as a laser tracker, a laser radar, or the like.
Firstly, stably placing a coordinate measuring device 1 on the ground or a platform, measuring each point in a point cloud 2 through the coordinate measuring device 1, and obtaining a coordinate system R of the point cloud 2 relative to a device Coordinate system To construct the point cloud 2 relative to the point cloud coordinate system C Coordinate system The method comprises the following steps:
(1) Acquisition of a point cloud 2 by a coordinate measuring device 1 relative to a device coordinate system R Coordinate system Homogeneous coordinates of (a):
Figure BDA0002504278770000041
(2) Constructing a point cloud coordinate system C Coordinate system Origin C 0 In the device coordinate system R Coordinate system Homogeneous coordinates of (a):
Figure BDA0002504278770000042
(3) Constructing a point cloud coordinate system C Coordinate system Comprising the following steps:
(3-1) in the form of a point cloudCoordinate system C Coordinate system Origin C 0 As a starting point, with other points of the point cloud 2 as a direction, constructing vectors of all points in the point cloud 2:
Figure BDA0002504278770000043
(3-2) calculating the modulus of the vector product between every two vectors:
Figure BDA0002504278770000044
/>
(3-3) selecting a group with the maximum modulus, and assuming that two vectors of the group with the maximum modulus are respectively as follows:
Figure BDA0002504278770000045
and &>
Figure BDA0002504278770000046
Wherein i, j ∈ [1n ]](i≠j,i<j)；
(3-4) Point cloud coordinate System C Coordinate system From the origin C 0 Point i and point j.
(4) Comparing vectors
Figure BDA0002504278770000051
And &>
Figure BDA0002504278770000052
In a vector with a greater modulus (assumed to be @)>
Figure BDA0002504278770000053
) As a point cloud coordinate system C Coordinate system X-axis in the device coordinate system R Coordinate system The coordinate expression of the vector of (a) is:
Figure BDA0002504278770000054
(5) Will vector
Figure BDA0002504278770000055
And &>
Figure BDA0002504278770000056
And (3) performing vector product operation according to a right-hand rule: />
Figure BDA0002504278770000057
Pick up the vector>
Figure BDA0002504278770000058
Calibration as point cloud coordinate system C Coordinate system Z-axis of (a) in the device coordinate system R Coordinate system The coordinate expression of the vector of (b) is:
Figure BDA0002504278770000059
(6) Will vector
Figure BDA00025042787700000510
And &>
Figure BDA00025042787700000511
And (3) performing vector product operation according to a right-hand rule: />
Figure BDA00025042787700000512
Pick up the vector>
Figure BDA00025042787700000513
Calibration as point cloud coordinate system C Coordinate system Y-axis in the device coordinate system R Coordinate system The coordinate expression of the vector of (b) is:
Figure BDA00025042787700000514
(7) Point cloud coordinate system C Coordinate system Relative to a device coordinate system R Coordinate system Is calibrated by the following expression:
Figure BDA00025042787700000515
(8) Point cloud relative to point cloud coordinate system C Coordinate system The coordinate values of (c) are constructed by the following expressions:
Figure BDA0002504278770000061
device coordinate system R Coordinate system The coordinate system can be a rectangular coordinate system or an oblique coordinate system; 2 point cloud coordinate system C Coordinate system Is a rectangular coordinate system.
The point cloud coordinate construction method solves the following key problems:
(1) The point cloud 2 itself is completely erected, and a point cloud coordinate system is constructed.
(2) The point cloud 2 and the point cloud coordinate system are in one-to-one correspondence, and the relationship between the point cloud 2 and the point cloud coordinate system is solidified, namely, the point cloud can construct a unique point cloud coordinate system, and the point cloud coordinate system also uniquely determines the coordinates of the point cloud.
(3) The use, transmission and management of the point cloud 2 and the coordinate data thereof are facilitated.
(4) The coordinate construction precision of the point cloud is improved.

Claims (3)

1. A coordinate construction method of point cloud is characterized in that the point cloud contains a large number of points, and coordinate measuring equipment is used for obtaining the point cloud relative to an equipment coordinate system R Coordinate system After the coordinates are obtained, a point cloud is constructed relative to a point cloud coordinate system C Coordinate system The method comprises the following steps:
step 1, obtaining a point cloud relative to a coordinate system R of equipment through coordinate measuring equipment Coordinate system Homogeneous coordinates of (a):
Figure FDA0002504278760000011
step 2, constructing a point cloud coordinate system C Coordinate system Origin C 0 In the device coordinate system R Coordinate system Homogeneous coordinates of (a):
Figure FDA0002504278760000012
step 3, constructing a point cloud coordinate system C Coordinate system Containing the following steps:
(3-1) using a point cloud coordinate system C Coordinate system Origin C 0 Taking other points of the point cloud as a starting point, constructing vectors of all the points in the point cloud:
Figure FDA0002504278760000013
(3-2) calculating the modulus of the vector product between every two vectors:
Figure FDA0002504278760000014
(3-3) selecting a group with the maximum modulus, and assuming that two vectors of the group with the maximum modulus are respectively as follows:
Figure FDA0002504278760000015
and &>
Figure FDA0002504278760000016
Wherein i, j ∈ [1n ]]，i≠j，i<j；
(3-4) Point cloud coordinate System C Coordinate system From the origin C 0 Point i and point j;
step 4 comparing vectors
Figure FDA0002504278760000017
And &>
Figure FDA0002504278760000018
Is based on the vector with the greater modulus, assumed to be @>
Figure FDA0002504278760000019
As a point cloud coordinate system C Coordinate system X-axis of (a) in the device coordinate system R Coordinate system The coordinate expression of the vector of (a) is:
Figure FDA0002504278760000021
step 5 vector quantity
Figure FDA0002504278760000022
And &>
Figure FDA0002504278760000023
And (3) performing vector product operation according to a right-hand rule: />
Figure FDA0002504278760000024
Combining vectors>
Figure FDA0002504278760000025
Calibration as a point cloud coordinate system C Coordinate system Z-axis in the device coordinate system R Coordinate system The coordinate expression of the vector of (b) is:
Figure FDA0002504278760000026
step 6 vector
Figure FDA0002504278760000027
And &>
Figure FDA0002504278760000028
And (3) performing vector product operation according to a right hand rule: />
Figure FDA0002504278760000029
Pick up the vector>
Figure FDA00025042787600000210
Calibration as point cloud coordinate system C Coordinate system Y-axis in the device coordinate system R Coordinate system The coordinate expression of the vector of (a) is:
Figure FDA00025042787600000211
step 7 point cloud coordinate system C Coordinate system Relative to a device coordinate system R Coordinate system The transformation relation T of (1) is calibrated by an expression:
Figure FDA00025042787600000212
step 8, point cloud coordinates system C relative to point cloud Coordinate system The coordinate values of (c) are constructed by the following expressions:
Figure FDA00025042787600000213
2. the method of claim 1, wherein the device coordinate system R is a point cloud coordinate system Coordinate system The coordinate system may be a rectangular coordinate system or an oblique coordinate system.
3. The method of claim 1, wherein the point cloud coordinate system C is a point cloud coordinate system Coordinate system Is a rectangular coordinate system.
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