CN101029826A - Digital camera measurement collecting method for three-dimensional geologic structural surface information - Google Patents

Abstract

A digital video camera measuring method of 3-D geological structure surface information includes utilizing digital video stream as information carrier of plotting object, carrying out loading speed and frame position control on continuous and dynamic video stream parameter in computer stereo visual environment rebuilt on computer to realize 3-D space position calculation of object.

Description

The digital camera measurement of three-dimensional geologic structural surface information and acquisition method

Technical field

The invention belongs to the Surveying Science and Technology field.Relating to a kind of geologic section three-dimensional digital that with the digital camera is geologic structural surface information is gathered approach edits and records and information processing method.

Background technology

1. stereoscopic vision and computer stereo vision and photogrammetric stereoscopic vision are meant that the mankind might utilize two simple eye visually-perceptible to have the vision of the degree of depth, thereby locus, the shape of object are judged.Utilize this principle, Wheatstone invention stereoscope in 1838, make people can utilize two scenery pictures to observe view with degree of depth, to make film with the camera work gained merge as the media infiltration and with measuring technique become possibility, opened up since then one brand-new and extremely enliven the spatial vision research field all the time---photogrammetric.Nineteen fifty-nine, Random-dot Stereograms RDS (the Random-dot stereograms that Julesz utilizes computing machine to generate, RDS) confirmed that parallax is the adequate condition that produces stereoscopic vision, opened the biplate stereopsis model of being set up by to people's binocular stereoscopic visual function imitation, this is one of the argument basis and the practice the earliest of computer stereo vision.Thereafter in half a century, computer stereo vision technique is advanced by leaps and bounds along with the development of computing machine science and technology, and strong promotion the development of photogrammetric technology, particularly in World War II, what answer war need be important information acquisition means with boat sheet decipher enemy's situation, and exploitation has corresponding techniques: utilize two known (or resolve and know) to take the photograph space of points coordinate and cover photo---the volume coordinate of total point in two photos of stereogram decipher of same area; So far, technical development makes that the precision of decipher is more and more higher, and range of application is more and more wider.But existing photogrammetric technology all is the decipher basis with the stereogram, promptly does decipher work on individual photo, utilize shooting this have continuously, the digital stream medium of behavioral characteristics are as the underlying carrier of measurement decipher.

2. it is understanding, the element task of analyzing geologic body mechanics engineering characteristic that structural surface information during geologic section is edited and recorded and photography solution geologic section are edited and recorded, wherein to various geological interfaces, the mechanics plane of weakness of exposure on section---mapping, the statistics of the space spread information of structural plane are the important component parts of the work of editing and recording, and how very big the and confined condition of its workload is original, heavy " chicken ribs " in the Geological Engineering research work all the time.Current after in conjunction with photogrammetric technology, certain achievement in research is all arranged both at home and abroad.The continuously shot images that people such as Baratin use high gradient slope has been tested the dynamic monitoring of side slope, to compare Monitoring Data accurate with classic method, its ultimate principle is to use triangulation specified point is out of shape decipher, but must be prerequisite to cooperate high-acruracy survey to obtain the scalar quantity altimetric image also.Farmer has done research utilizing on the digital image decipher tectonic structure of beach, and he builds high tower on beach, overlook the shooting beach, with picture decipher is carried out in the position of macrotectonics exposure vestige.Lee winter field was in the construction of Guangzhou storage station the second stage of the project in 1994, use tunnel photography construction geology and edit and record method, and corresponding software, hardware have been developed, 1997 at Xiao Langdi row Sha Dongzhong, carry out using digital camera again and carried out the experimental study that tunnel photography construction geology is edited and recorded, its research purpose is that tunnel is edited and recorded, and must cooperate precision measurement decipher basic parameter, the limited application that limits its method of the storage capacity of digital camera in addition.Long committee can height, big, the long side slope of Xiong Youzhong in Three Gorges Projects edit and record and use number in the task and shoot with video-corder the auxiliary side slope of technology and edit and record, this method is to resolve the coordinate of all the other points on the image on the basis of 11 known point coordinates of control survey with direct linear equation, the side slope that its method is applied in the following height of 50m is successful, but the decipher of making a video recording is is all the time edited and recorded and will be leaned on experienced geological personnel to finish in the open air just as supplementary means.Gao Yonghai, the Zhai Liyue of the meeting of yellow committee ^[98]Also used the shooting decipher in the Field Geology Investigations in mine, principle is identical with the method for Xiong Youzhong, with the correspondence picture of 11 known points, article coordinate is found the solution other point with direct linear equation ground article coordinate.The photography solution of the open-air joint plane occurrence that Wang Shugen, Zhu Yixuan propose, accurately resolving on the control survey basis of camera station coordinate, shooting angle, with the three-dimensional imaging instrument corresponding image points on stereogram or two monolithics is measured, go out to represent the plane equation of this joint plane with iteration method with variable weights rough error The Fitting Calculation, separate the occurrence of obtaining the target joint plane according to certain mathematics formulas at last.Bandit newly-built (1999) has suffered the employing digital photogrammetry at the deformation monitoring of Shanghai City waste water control SB pumping plant large-scale well-sinking.His conceptual design is based on total station survey, resolves the coordinate of observation station how much according to the projection theory of light, and sets up the distortion model raising calculation accuracy of lens.Wu Zhiyong is in practical engineering application, adopted the distortion factor of finding the solution each elementary area according to the form general model subdivision, the method of in certain error allowed band, coming culture point coordinate in each unit of decipher, 2003 that in its PhD dissertation, propose again to simplify, be applicable to that the structural plane of adit hole wall section edits and records scheme.

3. remain breakthrough and improved problem in sum, the appliance computer stereovision technique solves section in the Geological Engineering research in conjunction with photogrammetric technology, and to edit and record element task still unfeasible, and be possible high-level efficiency solution route, integrate and remain to be broken through and improved aspect has:

1) because the nonuniformity of geologic body, even if (structured light illuminate condition under the precondition of the structural information of not considering light source, be the necessary condition of active vision), with the diffusion natural light irradiation, the reflected light signal of being shot with video-corder itself then is unordered, the information that is to say geologic body image that surface reflection becomes is formed the reflected light information that had both comprised its irregular complex material composition, the structural information that comprises the material of geologic body surface exposure again, for example, be in a certain pixel in the feature correspondence image of a certain spectral band of each object point on the same structural plane that is identified, the spectral signature of this point had not only reflected the reflectance spectrum of a unordered actual contents composition but also had contained the spatial positional information of this point that this was helpless to a judgement of place face.So computer image processing technology can only solve the problem that has stable apparent surface two dimension, three-dimensional identification as literal identification, chromosome pairing, anthraco-silicosis classification and some workpiece identification etc. at present.Current, can't carry out Computer Automatic Recognition and judgement for geologic body irregular visible surface, the complex material component.

2) current photogrammetric technology is based on traditional positive and negative film or electronic image, technological core is to utilize stereogram in groups to come the object point coordinate of decipher target, must survey and draw to resolve and demarcate the point coordinate of taking the photograph of every photo with image, this is that current this technology can not be widely used in the image decipher in a successive range---as the main cause of geologic section: first under little object distance condition, survey and draw and the staking-out work amount huge and loaded down with trivial details; Moreover under big object distance condition, the resolution of image, picture can not satisfy the accuracy requirement that geologic section is edited and recorded.

3) current photogrammetric GEOLOGICAL APPLICATION research, on information such as most spread positions, space that concentrate on the crack, length in the information acquisition of structural plane, and the occurrence of structural plane or manually measure or simulation calculates on certain statistical model setting up, promptly or guarantee the confidence level of data and increase labor workload or reduce the field work amount and reduce the confidence level of data.

4) current have the geologic section photogrammetric technology of practical engineering application value or rely on professional measurement camera, or use anaglyph spectacles, multiplex, equipment price costliness.

5) being used for photogrammetric camera set (photosensitizing type, electronic type) must demarcate one by one, and restricting condition for use is many.

6) modern study shows that there is individual difference in the stereoscopic vision acutance of human eye, and the stereogram of using in photogrammetric is to take the photograph point, parallax apart from fixing set of diagrams picture, and the decipher difficulty to the stereopsis thing also just varies with each individual so.

Summary of the invention

Edit and record under the prerequisite of desired data precision satisfying geologic section, do not use photogrammetric professional equipment, only adopt a Daepori to lead to Digital Video, do not need a large amount of surveying works and complicated shooting to demarcate, in videographic measurment, the decipher of finishing structural plane on the various geologic sections on the computing machine of a general configuration and edit and record work, be the soluble problem of the present invention.

1. the digital camera measurement videographic measurment that is applied to geologic section is based on the photogrammetric ultimate principle of resolving, and is improved making it to be fit to the geologic section application in conjunction with the characteristics of shooting.The area of taking under little object distance condition that single-frame images covered is little, but can obtain the section digital picture that sharpness meets the demands, so edit and record the application of aspect for geologic section:

1) use video camera uniform motion on trapped orbit to take, what need mapping only is camera motion initial space position, and required a certain two field picture takes the photograph a position and can be resolved by the video camera associ-ated motion parameters in other the decipher process.

x ₁＝x ₀+vt?sinθcosφ

y ₁＝y ₀+vt?cosθcosφ

z ₁＝z ₀+vt?sinφ

(x ₀, y ₀, z ₀) be video camera initial position volume coordinate; (x ₁, y ₁, z ₁) take the photograph space of points coordinate for waiting to ask; V is a camera motion speed; T is a run duration; θ is the track trend; The φ track angle of pitch.Coordinate system is earth coordinates, and the Y-axis positive dirction is a north orientation.

2) according to collinear relationship, from left to right arrange each two field picture by taking sequential, object point of the same name different time be about the volume coordinate of two two field pictures be:

$x=\frac{Y}{f}{x}_1=\frac{B}{P}{x}_1$

$y=\frac{B}{x_1-x_2}f=\frac{B}{P}f$ If: P=x ₁-x ₂

$z=\frac{Y}{f}{z}_1=\frac{B}{P}{z}_1$

B＝vΔt

(x, y is z) for waiting to ask the object point volume coordinate; x ₁, x ₂Be respectively about the X-axis coordinate of corresponding image points in two two field pictures; F is a focal length; B is the optical axis spacing of two two field pictures; V is a camera motion speed; Δ t is that two two field picture shooting times are poor.Coordinate system moves to taking the photograph a little of left two field picture by terrestrial coordinate, and around the Z axle θ that turns clockwise.With the oppositely translation rotation again of gained coordinate figure, be converted to the used terrestrial coordinate of geological system at last.

Use above-mentioned geologic section videographic measurment technology, can be under the condition of only surveying and drawing once, the locus of the unique point in kind (object point) that the decipher shooting is covered, because it is limited that geologic section is edited and recorded accuracy requirement, the derivation of above-mentioned formula has been ignored owing to not carrying out the error that the positive affine deformation of image causes.In the same way, this technology can be applied to the other industry use that similar geologic section is edited and recorded.

2. looking environment based on the Computerized 3 D of digital video, to build the computer stereo vision environment again be the necessary link of being reproduced the 3D vision model by two dimensional image, according to the principle of parallax of human-eye stereoscopic vision, two two dimensional images same object, that have the parallax distance are the sufficient and necessary conditions that forms stereoscopic vision.Use a video camera not only to reduce apparatus for making a video recording staking-out work amount, and the parallax distance of used arbitrary image is adjustable in the decipher process, has reduced the decipher difficulty.Use the OpenGL technology, set up two vision buffer areas on computers simultaneously, and load same video data, under the precondition that guarantees with two vision buffer areas of identical velocity process data, obtain two two field pictures by control loaded video data position, thereby can make the decipher personnel set up the solid image of two dimensional image within sweep of the eye by computer screen at it with variable parallax distance.Wherein, parallax amasss apart from being that video data alternate position spike (time difference) and loading velocity are, realize by digital camera just because of the vision carrier, promptly can obtain variable parallax distance by the continuous dynamic video, so greatly reduce of the requirement of decipher process, expanded the range of application of videographic measurment to decipher personnel stereopsis acutance.

3. man-machine interactive structural plane identification preamble is chatted and the current computer vision technique can't be discerned structural plane in the geologic body, but people's vision system is the light certain content in easy act recognition image then, in the computer stereo vision environment, isolate required information, this point is by the physiology in modern times, neural theories of vision confirms, so adopting utilizes the human visual system to isolate the image of structural plane from the geologic section image, the man-machine structural plane interactive identification method of recognition structure face unique point, each structural plane characteristic point coordinates of point-to-point collection in the stereopsis environment of Jian Liing on computers, the crack end points coordinate that comprises structural plane exposure on section, and characteristic point coordinates on the structural plane face.

4. the digital camera measurement of structural plane occurrence can calculate its occurrence behind the coordinate that obtains unique point (minimum 3 points) on the structural plane face.

If by n _a, n _b, n _cThree not the confirmable bikini plane equation of point of conllinear be:

$\left|\begin{array}{cccc}x& y& z& 1\\ x_a& y_a& z_b& 1\\ x_b& y_b& z_b& 1\\ x_c& y_{\mathrm{<figure-callout\; id="1"\; label="c\; z\; c"\; filenames="A20071000358900122.png"\; state="\{\{state\}\}">c</figure-callout>}}& z_c{}_{}& 1\end{array}\right|=0$

$\mathrm{\&gamma;}=\left|\mathrm{arttg}\left(\frac{\mathrm{<figure-callout\; id="2"\; label="m\; k"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">m</figure-callout>}\sqrt{k^{}}\sqrt{{}^2+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}}{\mathrm{kl}}\right)\right|$

${\mathrm{\&beta;}}^{\&prime;}=\arccos \left|\frac{\mathrm{<figure-callout\; id="2"\; label="l\; k"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">l</figure-callout>}}{\sqrt{k^{}}}\right|$

When k＞0, l＞0, m＞0 o'clock β=β '+ω

When k＞0, l＞0, m＜0 o'clock β=β '+ω+180 °

When k＞0, l＜0, m＞0 o'clock β=β '+ω+270 °

When k＞0, l＜0, m＜0 o'clock β=β '+ω+90 °

When k＜0, l＞0, m＞0 o'clock β=β '+ω+90 °

When k＜0, l＞0, m＜0 o'clock β=β '+ω+270 °

When k＜0, l＜0, m＞0 o'clock β=β '+ω+180 °

When k＜0, l＜0, m＜0 o'clock β=β '+ω

Wherein: k=(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Ya*Zb+Yb*Zc+Yc*Za-Ya*Zc-Yb*Za-Yc*Zb)

l＝-(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Xa*Zb+Xb*Zc+Xc*Za-Xa*Zc-Xb*Za-Xc*Zb)

m＝(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Xa*Yb+Xb*Yc+Xc*Ya-Xa*Yc-Xb*Ya-Xc*Yb)

γ is the structural plane inclination angle; β is the structural plane tendency; β ' calculates tendency for structural plane; ω section trend.When selected unique point number during, adopt least square method to select wherein to use the occurrence of above-mentioned formula computation structure face from hour the most definite 3 of sum apart from optimum identity distance more than 3.

Description of drawings

Fig. 1 is calculated the collinear relationship synoptic diagram of object point volume coordinate by parallax

Synoptic diagram is calculated in the occurrence of Fig. 2 structural plane

Fig. 3 structural surface information is gathered practical application and is showed

Specific implementation method

1. determine photographic schemes according to the section actual conditions, usually shooting is in proper order for from top to bottom, from left to right; After video camera, exclusive guideway are in place, perturbation mapping camera initial position coordinate, guide rail trend; Set camera motion speed; Take.

2. load the video file of taking on the videographic measurment special purpose computer stereoscopic vision platform of exploitation, recognition structure face, and the volume coordinate of point-to-point decipher structural plane unique point resolve the structural plane relevant information.Wherein:

1) position of taking the photograph arbitrarily that decipher is required is calculated by the formula pointwise:

x ₁＝x ₀+vt?sinθcosφ

y ₁＝y ₀+vt?cosθcosφ

z ₁＝z ₀+vt?sinφ

(x ₀, y ₀, z ₀) be video camera initial position volume coordinate; (x ₁, y ₁, z ₁) take the photograph space of points coordinate for waiting to ask; V is a camera motion speed; T is a run duration; θ is the track trend; The φ track angle of pitch.

2) look point-to-point the impact point volume coordinate of resolving in the environment at Computerized 3 D, formula is as follows:

$x=\frac{Y}{f}{x}_1=\frac{\mathrm{<figure-callout\; id="1"\; label="B\; P\; x"\; filenames="A20071000358900122.png"\; state="\{\{state\}\}">B</figure-callout>}}{P}{x}_{}{}_1$

$y=\frac{B}{x_1-x_2}f=\frac{B}{P}f$ If: P=x ₁-x ₂

$z=\frac{\mathrm{<figure-callout\; id="1"\; label="Y\; f\; z"\; filenames="A20071000358900122.png"\; state="\{\{state\}\}">Y</figure-callout>}}{f}{z}_{}{}_1=\frac{\mathrm{<figure-callout\; id="1"\; label="B\; P\; z"\; filenames="A20071000358900122.png"\; state="\{\{state\}\}">B</figure-callout>}}{P}{z}_{}{}_1$

B＝vΔt

(x, y is z) for waiting to ask the object point volume coordinate; x ₁, x ₂Be respectively about the X-axis coordinate of corresponding image points in two two field pictures; F is a focal length; B is the optical axis spacing of two two field pictures; V is a camera motion speed; Δ t is that two two field picture shooting times are poor.

3) by unique point---the end points volume coordinate can be calculated distance between end points; Can calculate its occurrence by the point on the structural plane:

If by n _a, n _b, n _cThree not the confirmable bikini plane equation of point of conllinear be:

$\left|\begin{array}{cccc}x& y& z& 1\\ x_a& y_a& z_b& 1\\ x_b& y_b& z_b& 1\\ x_c& y_{\mathrm{<figure-callout\; id="1"\; label="c\; z\; c"\; filenames="A20071000358900122.png"\; state="\{\{state\}\}">c</figure-callout>}}& z_c{}_{}& 1\end{array}\right|=0$

$\mathrm{\&gamma;}=\left|\mathrm{arttg}\left(\frac{m\sqrt{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}}{\mathrm{kl}}\right)\right|$

${\mathrm{\&beta;}}^{\&prime;}=\arccos \left|\frac{l}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071000358900123.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}}\right|$

When k＞0, l＞0, m＞0 o'clock β=β '+ω

When k＞0, l＞0, m＜0 o'clock β=β '+ω+180 °

When k＞0, l＜0, m＞0 o'clock β=β '+ω+270 °

When k＞0, l＜0, m＜0 o'clock β=β '+ω+90 °

When k＜0, l＞0, m＞0 o'clock β=β '+ω+90 °

When k＜0, l＞0, m＜0 o'clock β=β '+ω+270 °

When k＜0, l＜0, m＞0 o'clock β=β '+ω+180 °

When k＜0, l＜0, m＜0 o'clock β=β '+ω

Wherein: k=(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Ya*Zb+Yb*Zc+Yc*Za-Ya*Zc-Yb*Za-Yc*Zb)

l＝-(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Xa*Zb+Xb*Zc+Xc*Za-Xa*Zc-Xb*Za-Xc*Zb)

m＝(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Xa*Yb+Xb*Yc+Xc*Ya-Xa*Yc-Xb*Ya-Xc*Yb)

γ is the structural plane inclination angle; β is the structural plane tendency; β ' calculates tendency for structural plane; ω section trend.When selected unique point number during, adopt least square method to select wherein to use the occurrence of above-mentioned formula computation structure face from hour the most definite 3 of sum apart from optimum identity distance more than 3.

Claims (4)

1. be applied to the digital camera measurement method of geologic section

1) owing to adopted the information carrier of digital camera as the mapping object, abandon, reduced traditional photography and measured resolving of required interior outer orientation unit, by to continuously, dynamic video flowing parameter---thereby the control of loading velocity and frame position realizes that the three-dimensional space position of object point resolves, and this is the core of photographing measurement method.

2) use video camera uniform motion on trapped orbit to take, needing the instrument of mapping is camera motion initial space position, and a position of taking the photograph of required a certain two field picture is resolved by the video camera associ-ated motion parameters in other the decipher process.

x ₁＝x ₀+vtsinθcosφ

y ₁＝y ₀+vtcosθcosφ

z ₁＝z ₀+vtsinφ

(x ₀, y ₀, z ₀) be video camera initial position volume coordinate; (x ₁, y ₁, z ₁) take the photograph space of points coordinate for waiting to ask; V is a camera motion speed; T is a run duration; θ is the track trend; The φ track angle of pitch.Coordinate system is earth coordinates, and the Y-axis positive dirction is a north orientation.

3) according to collinear relationship, from left to right look each two field picture of loading in the environment by the priority of taking sequential at Computerized 3 D, the volume coordinate of object point of the same name two two field pictures about different time is:

$x=\frac{Y}{f}{x}_1=\frac{B}{P}{x}_1$

$y=\frac{B}{x_1-x_2}f=\frac{B}{P}f$ If: P=x ₁-x ₂

$z=\frac{Y}{f}{z}_1=\frac{B}{P}{z}_1$

B＝vΔt

(x, y is z) for waiting to ask the object point volume coordinate; x ₁, x ₂Be respectively about the X-axis coordinate of corresponding image points in two two field pictures; F is a focal length; B is the optical axis spacing of two two field pictures; V is a camera motion speed; Δ t is that two two field picture shooting times are poor.Coordinate system moves to taking the photograph a little of left two field picture by terrestrial coordinate, and around the Z axle θ that turns clockwise, promptly the X-axis positive dirction is the section trend.With oppositely translation, the rotation again of gained coordinate figure, be converted to the used terrestrial coordinate of geological system at last.

2. looking environment based on the Computerized 3 D of digital video builds again

Use the OpenGL technology, set up two vision buffer areas on computers simultaneously, and load same video data, when guaranteeing with two vision buffer areas of identical velocity process data, obtain two two field pictures by control loaded video data position, thereby can make the decipher personnel set up the solid image of two dimensional image within sweep of the eye by computer screen at it with variable parallax distance.Wherein, parallax amasss apart from being that video data alternate position spike (time difference) and loading velocity are, realize by digital camera just because of the vision carrier, promptly can obtain variable parallax distance by the continuous dynamic video, so greatly reduce of the requirement of decipher process, expanded the range of application of videographic measurment to decipher personnel stereopsis acutance.

3. man-machine interactive structural plane recognition methods

Utilize the human visual system from the geologic section image, to isolate the ability of structural plane image, recognition structure face unique point, each structural plane characteristic point coordinates of point-to-point collection in the stereopsis environment of Jian Liing on computers, the crack end points coordinate that comprises structural plane exposure on section, and characteristic point coordinates on the structural plane face.Not only obtained than the higher data precision of actual measurement, and objectively solved a current difficult problem that does not have the image segmentation algorithm of available irregular apparent surface, make the computer stereo vision range of application expand to the work that can't realize image segmentation such as geologic structural surface.

4. the digital camera measurement of structural plane occurrence

Behind the coordinate that obtains unique point (minimum 3 points) on the structural plane face, can calculate its occurrence.

If by n _a, n _b, n _cThree not the confirmable bikini plane equation of point of conllinear be:

$\left|\begin{array}{cccc}x& y& z& 1\\ x_a& y_a& z_b& 1\\ x_b& y_b& z_b& 1\\ x_c& y_c& z_c& 1\end{array}\right|=0$

$\mathrm{\&gamma;}=\left|\mathrm{arttg}\left(\frac{m\sqrt{k^2+l^2}}{\mathrm{kl}}\right)\right|$

${\mathrm{\&beta;}}^{\&prime;}=\arccos \left|\frac{l}{\sqrt{k^2+l^2}}\right|$

When k＞0, l＞0, m＞0 o'clock β=β '+ω

When k＞0, l＞0, m＜0 o'clock β=β '+ω+180 °

When k＞0, l＜0, m＞0 o'clock β=β '+ω+270 °

When k＞0, l＜0, m＜0 o'clock β=β '+ω+90 °

When k＜0, l＞0, m＞0 o'clock β=β '+ω+90 °

When k＜0, l＞0, m＜0 o'clock β=β '+ω+270 °

When k＜0, l＜0, m＞0 o'clock β=β '+ω+180 °

When k＜0, l＜0, m＜0 o'clock β=β '+ω

Wherein: k=(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Ya*Zb+Yb*Zc+Yc*Za-Ya*Zc-Yb*Za-Yc*Zb)

l＝-(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Xa*Zb+Xb*Zc+Xc*Za-Xa*Zc-Xb*Za-Xc*Zb)

m＝(Xa*Yb*Zc+Xb*Yc*Za+Xc*Ya*Zb-Xa*Yc*Zb-Xb*Ya*Zc-Xc*Yb*Za)/(Xa*Yb+Xb*Yc+Xc*Ya-Xa*Yc-Xb*Ya-Xc*Yb)

γ is the structural plane inclination angle; β is the structural plane tendency; β ' calculates tendency for structural plane; ω section trend.When selected unique point number during, adopt least square method to select wherein apart from optimum identity distance from using the occurrence of above-mentioned formula computation structure face with 3 of minimum more than 3.

Images