TW202001615A - Method for using point cloud to determine rock discontinuity attitude which includes acquiring proper point cloud; and determining an attitude of rock discontinuity by using the point cloud according to geomagnetism and geographic directions - Google Patents

Method for using point cloud to determine rock discontinuity attitude which includes acquiring proper point cloud; and determining an attitude of rock discontinuity by using the point cloud according to geomagnetism and geographic directions Download PDF

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TW202001615A
TW202001615A TW107120439A TW107120439A TW202001615A TW 202001615 A TW202001615 A TW 202001615A TW 107120439 A TW107120439 A TW 107120439A TW 107120439 A TW107120439 A TW 107120439A TW 202001615 A TW202001615 A TW 202001615A
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王泰典
曹孟真
吳東洹
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國立臺北科技大學
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Abstract

The present invention relates to a method for using point cloud to determine rock discontinuity attitude, which includes acquiring proper point cloud; and determining an attitude of rock discontinuity by using the point cloud according to geomagnetism and geographic directions. The present invention is applicable to inspecting if the point cloud for describing an outcrop has sufficient degree of precision and selecting and acquiring analysis parameters required for rock discontinuity attitude, and reviewing and determining if the rock discontinuity and attitude so obtained meet specified significant standard requirement.

Description

一種利用點雲判斷岩石不連續面位態的方法A method for judging the discontinuity of rock by point cloud

本發明是關於量測岩石不連續面位態之結果的檢定方法，更特定而言是關於以點雲判釋岩石不連續面組位態所需的參數選定、最佳化以及判釋結果的檢核。The present invention relates to a verification method for measuring the results of rock discontinuity planes, more specifically, to the selection, optimization, and interpretation of parameters required to interpret the rock discontinuity planes by point clouds. Check.

不連續面影響岩體工程行為，為工程地質調查的重要項目。不連續面的空間姿態以位態稱之。位態相近的不連續面通常係在相似的地質環境及大地應力狀態下生成，具有類似的工程特性。國際岩石力學學會建議將位態相近的不連續面畫分為同一組，做為不連續面調查及評估的依據。不連續面的位態常以北方N、水平線H、不連續面與水平面交線10、不連續面最大傾斜線20、不連續面法向量

Figure 02_image001
、平面的走向α及傾角β，或是傾向γ表示(圖1)；不連續面組的代表位態，通常以人力手持地質羅盤測量岩石出露之不連續面1的位態，透過半球(立體)投影分析，觀察代表不連續面位態在赤道投影平面上的極點空間分佈特性，依據極點集中程度，區分調查場址岩石不連續面組0的數目，再依據費雪分佈的特性判讀各組不連續面集中程度最高的位態，做為不連續面組的代表位態。Discontinuities affect rock engineering behavior and are important items in engineering geological survey. The spatial attitude of the discontinuity is called the position. Discontinuities with similar positions are usually generated under similar geological conditions and geo-stress conditions, and have similar engineering characteristics. The International Society of Rock Mechanics recommends that the discontinuity paintings with similar positions be divided into the same group as the basis for the investigation and evaluation of the discontinuity. The position of the discontinuous surface is usually north N, horizontal line H, the line 10 of the intersection of the discontinuous surface and the horizontal plane, the maximum inclined line of the discontinuous surface 20, the normal vector of the discontinuous surface
Figure 02_image001
, The direction of the plane α and the inclination angle β, or the tendency of γ (Figure 1); the representative position of the discontinuous face group, usually a human hand holding a geological compass to measure the position of the discontinuous face 1 exposed by the rock, through the hemisphere ( (Stereoscopic) projection analysis, observe the spatial distribution characteristics of the poles on the equatorial projection plane representing the discontinuities, distinguish the number of rock discontinuities 0 on the survey site according to the degree of pole concentration, and then interpret each according to the characteristics of Fisher distribution The position with the highest concentration of discontinuous faces in the group is used as the representative position of the discontinuous face group.

地層岩石中的不連續面通常伴生出現，透過地質羅盤量測，配合半球投影分析，進而決定不連續面的組數及其代表位態的作業方法，常須於場址尋找岩石露頭，現地量測數十筆至數百筆不連續面的位態資料，始能提高分析結果的代表性及精度。透過航空攝影測量或是近景攝影測量產製的數值地表模型，雖然可以配合作圖法求得岩石不連續面的位態，但僅適用於平面特性延伸範圍較廣的不連續面，如顯著且規模較大的層面。對於平面出露範圍有限的不連續面如節理面、劈理、片理等葉理面，以及規模較小的層面，航空攝影測量產製的數值地表模型受限於解析度，常因難以取得同一不連續面上、三點以上不同位置的坐標值而無法應用；近景攝影產製的數值地表模型則因鏡頭扭曲、影像匹配誤差、解析度不一致等原因，導致作圖法判讀的不連續面位態常有明顯的變異、代表性及精度不足的疑慮。Discontinuities in formation rocks are usually associated with them. Through geological compass measurement and hemispheric projection analysis, the number of groups of discontinuities and their representative methods of operation are often determined. It is often necessary to look for rock outcrops at the site. Measuring the position data of dozens to hundreds of discontinuous surfaces can improve the representativeness and accuracy of the analysis results. The numerical surface model produced by aerial photogrammetry or close-range photogrammetry can be used to obtain the position of the rock discontinuity, but it is only applicable to the discontinuity with a wide range of planar characteristics. A larger scale. For discontinuous surfaces with limited plane exposure range, such as joint surfaces, cleavage surfaces, leaf surfaces, etc., and small-scale surfaces, the numerical surface model produced by aerial photogrammetry is limited by the resolution and is often difficult to obtain The coordinate values of different positions on the same discontinuous surface and more than three points cannot be applied; the numerical surface model produced by close-range photography is caused by lens distortion, image matching error, and inconsistent resolution. The position often has doubts about obvious variation, representativeness and insufficient precision.

三維雷射掃瞄可高密度、高精度地測繪物體表面的幾何形貌，應用於場址岩石露頭測量，可透過點雲形式精細描繪露頭坐標。雷射掃瞄必須通視無阻礙，因此測繪作業常自多個測站進行掃瞄，再將不同測站取得的點雲，透過測站位置坐標進行轉換，或是自點雲中辨識位置相同的共軛點，拼接以完整地描繪露頭幾何形貌。The three-dimensional laser scanning can measure the geometry of the surface of the object with high density and high precision. It is applied to the measurement of rock outcrop on the site, and the coordinates of the outcrop can be accurately depicted through the form of point cloud. Laser scanning must be clear and unobstructed, so surveying and mapping operations often scan from multiple stations, and then convert the point clouds obtained from different stations through the coordinates of the position of the station, or identify the same position from the point cloud The conjugate points are stitched together to completely depict the outcrop geometry.

精細描繪岩石露頭幾何的點雲具三維坐標值，可運用多種數學方法解算不連續面的位態，例如於點雲中隨機選擇4個初始點，利用最小二乘法迴歸求得平面方程式，再以該平面方程式為函數，逐一代入鄰近點雲的坐標值，當函數值小於設定的容許誤差值

Figure 02_image003
時，則視鄰近點雲與初始點共平面，否則視為非共平面點，並將其排除；與初始點共平面的點雲構成平面的面積大於設定的閾值
Figure 02_image005
，且外圍皆為非共平面點時，即完成一平面蒐尋，記錄該平面的形心、位態及面積後，排除描繪該平面的點雲。依序重覆前述步驟即可運算求得露頭上許多平面的位態，再配合半球投影分析即可求得不連續面的組數及各不連續面組的代表位態。又如選擇一構成叢集所需的最小點雲數
Figure 02_image007
，將描繪露頭的點雲依據
Figure 02_image007
數劃分成複數叢集，迴歸求得描述各叢集的平面方程式及形心位置；再考慮一法向量差值之閾值
Figure 02_image009
，相鄰叢集的迴歸平面法向量差值小於
Figure 02_image009
時，則視為落在同一平面上，可結合相鄰叢集進行擴展；最後選擇一描述同一平面所需的最低叢集數
Figure 02_image011
，若相鄰叢集可結合擴展為同一平面的數量大於
Figure 02_image011
，即視為描繪空間中面積足夠大的某一不連續面，可進一步計算該不連續面的位態及形心坐標，再配合半球投影分析即可求得不連續面的組數及代表位態。A point cloud that accurately describes the geometry of a rock outcrop has three-dimensional coordinate values. Various mathematical methods can be used to solve the discontinuity. For example, 4 initial points are randomly selected in the point cloud, and the least square method is used to obtain the plane equation. Using this plane equation as a function, the coordinate values of adjacent point clouds are entered one by one. When the function value is less than the set tolerance value
Figure 02_image003
When the adjacent point cloud is coplanar with the initial point, otherwise it is regarded as a non-coplanar point and excluded; the area of the plane formed by the point cloud coplanar with the initial point is greater than the set threshold
Figure 02_image005
, And when the periphery is all non-coplanar points, a plane search is completed, after recording the centroid, position and area of the plane, the point cloud depicting the plane is excluded. Repeat the above steps in sequence to calculate the positions of many planes on the outcrop, and then use hemispherical projection analysis to find the number of discontinuities and the representative positions of the discontinuities. Another example is to select a minimum number of point clouds required to form a cluster
Figure 02_image007
, The point cloud basis that will depict the outcrop
Figure 02_image007
The numbers are divided into complex clusters, and the plane equations and centroid positions describing each cluster are obtained by regression; then the threshold value of the difference of a normal vector is considered
Figure 02_image009
, The difference between the regression plane normal vectors of adjacent clusters is less than
Figure 02_image009
When it is considered to fall on the same plane, it can be expanded by combining adjacent clusters; finally, select the minimum number of clusters required to describe the same plane
Figure 02_image011
, If the number of adjacent clusters that can be combined to expand into the same plane is greater than
Figure 02_image011
, That is, to describe a discontinuous surface with a sufficiently large area in space, the position and centroid coordinates of the discontinuous surface can be further calculated, and then the number of groups and representative positions of the discontinuous surface can be obtained with hemispheric projection analysis state.

然而，三維雷射掃瞄因拼接過程測站坐標誤差、共軛點辨識誤差、掃瞄儀雷射遭遇水滴、粉塵引致程度不一的散射、或是雷射光軸與反射面夾角差異較大等因素，不同測站針對露頭同一表面取得掃瞄點雲拼接後常分佈在一帶狀範圍成薄膜狀。測量作業著重於較大範圍的表面幾何坐標描繪，通常採用平差方式提高測繪結果的精密度(precision)。對於範圍相對較小、通常由最小面積之閾值

Figure 02_image005
或是最低叢集數
Figure 02_image011
之閾值判釋是否為平面的岩石不連續面，平差方式嚴重影響了判釋參數的選擇，可能造成位態判釋的誤差，甚至導致不連續面的組數及代表位態錯誤的判釋結果。However, 3D laser scanning has errors due to station coordinate errors, conjugate point identification errors, laser scanner encounters water droplets, dust caused by varying degrees of scattering, or a large difference between the angle between the laser optical axis and the reflective surface. Due to different factors, the scanning point clouds obtained from different stations on the same surface of the outcrop are often distributed in a strip-shaped range into a thin film. The measurement operation focuses on the drawing of a large range of surface geometric coordinates, and usually the adjustment method is used to improve the precision of the surveying and mapping results. For a relatively small range, usually by the threshold of the smallest area
Figure 02_image005
Or the minimum number of clusters
Figure 02_image011
The threshold interpretation is whether it is a planar rock discontinuity. The adjustment method seriously affects the choice of interpretation parameters, which may cause errors in position interpretation, and even lead to the number of groups of discontinuities and the interpretation of the wrong position. result.

近景攝影或無人機空拍等攝影測量亦可描繪岩石露頭幾何形貌，然而攝影測量因鏡頭扭曲、採用的中央透視投影原理造成影像中不同位置的實體解析度不同、共軛點辨識誤差等因素，透過立體像對或共線方程式解析露頭幾何坐標時，亦造成程度不一的變異，限制了攝影測量測繪露頭點雲在判釋岩石不連續面的位態及其他描述項目的應用。Photogrammetry such as close-range photography or drone aerial photography can also depict the geometry of rock outcrops. However, due to lens distortion and the use of the central perspective projection principle, the physical resolution of different locations in the image is different, and the conjugate point identification error and other factors When analyzing the outcrop geometric coordinates through stereo pairs or collinear equations, it also causes varying degrees of variation, which limits the application of photogrammetric surveying and mapping outcrop point clouds in interpreting the discontinuities of rock discontinuities and other description items.

因此，需要發展一種精準、快速的檢定方法，檢核描繪露頭的點雲是否足以提供判釋岩石不連續面所需的精細程度，並消彌或抑低為完整描繪露頭幾何形貌而採用的測站位置坐標轉換，或是共軛點判釋以拼接點雲造成的誤差，並整合場址不同露頭、以及同一露頭不同位置利用點雲判釋岩石不連續面的組數及代表位態的結果，提供岩石不連續面其他項目調查及評估更充分的依據，以利更完整地描述及計量化場址的工程地質特性。Therefore, it is necessary to develop an accurate and rapid verification method to check whether the point cloud depicting the outcrop is sufficient to provide the fineness required to interpret the discontinuities of the rock, and to eliminate or suppress the use of the complete description of the outcrop geometry. Coordinate conversion of the station position, or conjugate point interpretation to the error caused by splicing point clouds, and integration of different outcrops on the site and different positions of the same outcrop to use point clouds to interpret the number of groups of rock discontinuities and the representative position As a result, it provides a more sufficient basis for the investigation and evaluation of other projects of rock discontinuities, so as to more fully describe and measure the engineering geological characteristics of the site.

本發明提供一種利用點雲判斷岩石不連續面位態的方法，係包括步驟： (S1) 得到適用的點雲；以及(S2) 基於地磁及地理方位而由該點雲得到岩石不連續面之位態。The invention provides a method for judging the position of a rock discontinuity using a point cloud. The method includes the steps of: (S1) obtaining a suitable point cloud; and (S2) obtaining the rock discontinuity from the point cloud based on geomagnetism and geographical orientation Posture.

本發明之一種利用點雲判斷岩石不連續面位態的方法，在步驟S2之後更包括(S3) 以參數最佳化檢查該岩石不連續面之位態。A method for judging the state of a rock discontinuity by using a point cloud of the present invention further includes (S3) checking the position of the rock discontinuity by parameter optimization after step S2.

本發明之一種利用點雲判斷岩石不連續面位態的方法，在步驟S2之後更包括(S4) 輸出該岩石不連續面之位態的報告，或者在步驟S3之後進行步驟S4。A method for judging the position of a rock discontinuity using a point cloud of the present invention further includes (S4) outputting a report of the position of the rock discontinuity after step S2, or performing step S4 after step S3.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，若檢定利用該點雲得到之岩石不連續面的位態之代表性為是，進行輸出該岩石不連續面之位態的報告，若檢定利用該點雲得到之岩石不連續面的位態之代表性為否，進行步驟(S3)以參數最佳化檢查該岩石不連續面之位態。A method for judging the state of a rock discontinuity by using a point cloud according to the present invention, wherein, if the representative state of the rock discontinuity obtained by using the point cloud is verified as being, the state of the rock discontinuity is output If it is verified that the representativeness of the discontinuity of the rock obtained by using the point cloud is not, proceed to step (S3) to check the location of the discontinuity of the rock with parameter optimization.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S20係以複數個框選之平面的量測走向與對應位置所描繪該點雲之擬合平面而計算走向差值之平均值。A method for judging the discontinuity of a rock by using a point cloud according to the present invention, wherein step S20 is to calculate the difference between the directions of the measured planes of a plurality of framed planes and the fitted planes of the point cloud described by the corresponding positions Of the average.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S21係自測繪露頭中框選擬判釋之該岩石不連續的面位態範圍之點雲，選擇構成叢集最小之點雲數、相鄰叢集迴歸平面法向量差值的閾值且描述同一平面最低叢集數等分析參數，以得到該岩石不連續面之位態。A method for judging the discontinuous surface state of a rock using a point cloud according to the present invention, wherein step S21 is to select a point cloud of the discontinuous surface state range of the rock that is to be interpreted from the outcrop in the survey and mapping, and select the one that constitutes the smallest cluster Analysis parameters such as the number of point clouds, the difference between the normal vectors of the regression planes of adjacent clusters, and the lowest cluster number in the same plane are described to obtain the discontinuity of the rock.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S22係將所得到該岩石不連續面之位態進行半球投影分析，決定該岩石不連續面之位態的組數，採用單位向量表示各該組的岩石不連續面之位態的平均值，透過所有各該組的岩石不連續面之位態至其對應平均值的向量差值的內積，求得各該組的岩石不連續面對應的純量型式變異數。A method for judging the position of a rock discontinuity using a point cloud according to the present invention, wherein step S22 is to perform hemispherical projection analysis on the obtained position of the rock discontinuity to determine the number of groups of the position of the rock discontinuity , The unit vector is used to represent the average value of the discontinuities of the rock discontinuities of each group, and the inner product of the vector differences of all the discontinuities of the rock discontinuities of the groups to their corresponding average values is used to obtain each The scalar variants corresponding to the rock discontinuities in the group.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S23係於測繪露頭框選之該點雲的位置附近，重覆量測該岩石不連續面之位態並進行半球投影分析，決定該岩石不連續面之位態的組數，並計算各該組的岩石不連續面的量測位態之平均值及變異數。A method for judging the position of a rock discontinuity using a point cloud in the present invention, wherein step S23 is to repeatedly measure the position of the rock discontinuity and hemisphere around the position of the point cloud selected by the mapping outcrop Projection analysis determines the number of groups of rock discontinuities, and calculates the average and variation of the measurement positions of each group of rock discontinuities.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S24係基於所得之該點雲與露頭之該岩石不連續面的量測位態之變異數，進行變異數檢定並計算合併變異數。A method for judging the discontinuity state of a rock using a point cloud according to the present invention, wherein step S24 is based on the obtained variation number of the measured dislocation state of the point cloud and the rock discontinuity surface of the outcrop to perform the variation number verification and Calculate the combined variance.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S25係考慮地磁北方與地理北方偏角而於露頭量測該岩石不連續面的位態之平均值，並視為地真值，在選定顯著水準下，檢定對應之利用該點雲得到之該岩石不連續面的位態之平均值是否與該地真值相符。A method for judging the position of a rock discontinuity using a point cloud according to the present invention, wherein step S25 is to measure the average value of the position of the rock discontinuity at the outcrop considering the declination of geomagnetic north and geographical north. The ground truth value, under the selected significance level, verifies whether the corresponding average value of the position of the rock discontinuity obtained by using the point cloud is consistent with the ground truth value.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，輸出該岩石不連續面之位態的報告包含該岩石不連續面的位態之平均值、變異數以及選定之顯著水準，供量化表示該岩石不連續面的位態之信賴區間，並完成該岩石不連續面的分析作業。A method for judging the state of rock discontinuities using a point cloud according to the present invention, wherein the report outputting the state of the rock discontinuities includes the average value of the state of the rock discontinuities, the number of variations and the selected significance level , For quantifying the confidence interval that represents the position of the rock discontinuity, and complete the analysis of the rock discontinuity.

本發明之一種利用點雲判斷岩石不連續面位態的方法，步驟S3包含以下步驟： (S30) 以分析參數重新得到該岩石不連續面的位態； (S31) 建立該岩石不連續面的位態之分析參數與該岩石不連續面之面積總和的迴歸方程式； (S32) 以最大之該面積總和的分析參數得到該岩石不連續面的位態；及(S33) 檢定利用該點雲得到之岩石不連續面的位態之代表性，若該代表性之檢定結果為可，則進行輸出該岩石不連續面之位態的報告。A method for judging the position of a rock discontinuity by using a point cloud according to the present invention, step S3 includes the following steps: (S30) Regain the position of the rock discontinuity by analyzing the parameters; (S31) Establish the rock discontinuity The regression equation of the analysis parameters of the position and the sum of the areas of the rock discontinuities; (S32) The analysis parameters of the largest sum of the areas are used to obtain the position of the rock discontinuities; and (S33) The verification is obtained by using the point cloud The representativeness of the discontinuity of the rock. If the representative test result is acceptable, a report to output the discontinuity of the rock is reported.

本發明之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S30係針對以分析參數重新得到該岩石不連續面的位態所需三分析參數，分別選擇三水準量值重新得到該岩石不連續面之位態，配合半球投影分析決定該岩石不連續面之組數後，計算該岩石不連續面的面積總和。A method for judging the position of a rock discontinuity using a point cloud according to the present invention, wherein step S30 is based on the analysis parameters to obtain the three analysis parameters required for retrieving the position of the rock discontinuity. After determining the number of groups of rock discontinuities by determining the number of groups of rock discontinuities with the hemispheric projection analysis, calculate the total area of the rock discontinuities.

相較於習知技術，本發明能藉由檢核描繪露頭的點雲而得到具足夠的精細程度之點雲，選擇得到岩石不連續面組位態所需分析參數，以及檢核判釋所得岩石不連續面位態是否符合指定顯著水準要求。Compared with the conventional technology, the present invention can obtain a point cloud with sufficient fineness by inspecting and delineating the outcrop point cloud, select the analysis parameters required to obtain the rock discontinuous surface group configuration, and check and interpret the results. Whether the discontinuity of the rock meets the specified significance level requirements.

為充分瞭解本發明之目的、特徵及功效，茲藉由下述具體之實施例，並配合所附之圖式，對本發明做一詳細說明，說明如後：In order to fully understand the purpose, features and effects of the present invention, the following specific examples and the accompanying drawings are used to make a detailed description of the present invention, as follows:

請參考圖2，係本發明利用點雲判斷岩石不連續面位態的方法之流程圖，其步驟包括步驟S1及步驟S2。步驟S1中，得到適用的點雲，且於步驟S2中，基於地磁及地理方位而由該點雲得到岩石不連續面之位態。在此態樣中，可直接利用所得到適用的點雲而基於地磁及地理方位以得到岩石不連續面之位態Please refer to FIG. 2, which is a flowchart of a method for judging the discontinuity of a rock using a point cloud according to the present invention. The steps include step S1 and step S2. In step S1, an applicable point cloud is obtained, and in step S2, the state of the rock discontinuity is obtained from the point cloud based on geomagnetism and geographical orientation. In this aspect, the applicable point cloud can be directly used to obtain the position of the rock discontinuity based on geomagnetism and geographical orientation

請參考圖3，係本發明利用點雲判斷岩石不連續面位態的方法之另一態樣的流程圖，其步驟更包括步驟S3，以參數最佳化檢查該岩石不連續面之位態，從而重新判釋與檢定該岩石不連續面之位態。Please refer to FIG. 3, which is a flow chart of another aspect of the method for judging the position of a rock discontinuity using a point cloud according to the present invention. The steps further include step S3 to check the position of the rock discontinuity with parameter optimization To reinterpret and verify the position of the rock discontinuity.

請參考圖4，係本發明利用點雲判斷岩石不連續面位態的方法之又一態樣的流程圖，其步驟更包括步驟S4。步驟S4中，輸出該岩石不連續面之位態的報告。值得注意的是，步驟S2後可進行步驟S4，或者在步驟S3之後可進行步驟S4。Please refer to FIG. 4, which is a flowchart of another aspect of the method for judging the discontinuity of a rock by using a point cloud according to the present invention. The steps further include step S4. In step S4, a report of the position of the rock discontinuity is output. It is worth noting that step S4 can be performed after step S2, or step S4 can be performed after step S3.

請參考圖5，係本發明之步驟S1之特定流程圖，其步驟包括步驟S10及步驟S11。步驟S10中，以複數個平面計算該點雲的擬合平面方程式之誤差量相對於該點雲的平均間距之比值而檢測該點雲之精細程度。特定而言，可自測繪所得點雲中框選複數平面，計算點雲密度、平均間距以及擬合平面方程式，並求得擬合平面方程式之誤差量相對於點雲平均間距之比值。詳細而言，可於測繪點雲中框選

Figure 02_image013
個複數平面(
Figure 02_image015
)範圍，即框選範圍之點雲的擬合平面101，並利用
Figure 02_image017
之等式而以最小二乘法迴歸求得第
Figure 02_image019
個擬合平面法向量
Figure 02_image021
及擬合誤差量
Figure 02_image023
(圖6)；依據各框選面積內點雲數量計算點雲密度及平均間距，以及擬合平面誤差量相對於點雲平均間距之比值。其中，
Figure 02_image017
之等號左側為第𝑖個框選範圍擬合平面函數，等號右側為擬合誤差量。Please refer to FIG. 5, which is a specific flowchart of step S1 of the present invention. The steps include step S10 and step S11. In step S10, the precision of the point cloud is detected by calculating the ratio of the error amount of the fitted plane equation of the point cloud with respect to the average distance of the point cloud using a plurality of planes. In particular, you can frame the complex planes from the point cloud obtained from surveying and mapping, calculate the point cloud density, average spacing, and fit plane equations, and find the ratio of the error amount of the fitted plane equations to the point cloud average spacing. In detail, it can be framed in the survey point cloud
Figure 02_image013
Complex planes (
Figure 02_image015
) Range, that is, the fitting plane 101 of the point cloud of the frame selection range, and use
Figure 02_image017
Equation to find the first
Figure 02_image019
Fitting plane normal vector
Figure 02_image021
And fitting error
Figure 02_image023
(Figure 6); Calculate the point cloud density and average spacing according to the number of point clouds in each framed area, and the ratio of the fitting plane error amount to the point cloud average spacing. among them,
Figure 02_image017
The left side of the equal sign is the fitting range function of the first frame selection range, and the right side of the equal sign is the fitting error.

詳細而言，框選範圍之點雲的擬合平面101之取得可例如於框選範圍之點雲中隨機選擇4個初始點，利用最小二乘法迴歸求得平面方程式，再以該平面方程式為函數，逐一代入鄰近點雲的坐標值，當函數值小於設定的容許誤差值時，則視鄰近點雲與初始點共平面，否則視為非共平面點，並將其排除；與初始點共平面的點雲構成平面的面積大於設定的閾值，且外圍皆為非共平面點時，即完成一平面蒐尋，記錄該平面的形心、位態及面積後，排除描繪該平面的點雲。In detail, the fitting plane 101 of the point cloud of the frame selection range can be obtained by randomly selecting 4 initial points in the point cloud of the frame selection range, using least squares regression to obtain the plane equation, and then using the plane equation as The function enters the coordinate values of neighboring point clouds one by one. When the function value is less than the set tolerance value, the neighboring point cloud is regarded as coplanar with the initial point, otherwise it is regarded as a non-coplanar point and excluded; it is shared with the initial point When the area of the plane formed by the point cloud of the plane is greater than the set threshold, and all the outer edges are non-coplanar points, a plane search is completed, and after recording the centroid, position and area of the plane, the point cloud depicting the plane is excluded.

步驟S11中，量測該些平面之法向量的差值，且以對應位置而描繪該點雲之擬合平面法向量的差值，進而得到適用之該點雲。特定而言，可依據框選複數平面量測法向量的差值，以及對應位置描繪點雲擬合平面法向量的差值，檢定利用點雲判釋岩石不連續面位態的適用性。詳細而言，可計算任意二組框選平面迴歸法向量差

Figure 02_image025
，於現地採用地質羅盤或其他適當方法量測對應的平面位
Figure 02_image027
，各重覆量
Figure 02_image029
次，採用單位向量表示平面位態並計算對應平面的量測位態平均
Figure 02_image031
、
Figure 02_image033
以及變異
Figure 02_image035
，再計算量測所得法向量差
Figure 02_image037
及其變異
Figure 02_image039
，計算點雲適用性檢定
Figure 02_image041
，比較適用性檢定量值與指定的顯著水
Figure 02_image043
的檢定量之閾
Figure 02_image045
，
Figure 02_image047
個框選平面中任意兩平面的適用性檢定量皆大於或等於閾值，
Figure 02_image049
，表示點雲精細度良好，適用於判釋岩石不連續面並進入步驟S2；反之，若有任意兩平面的適用性檢定量未達閾值，表示點雲不適用，必需重新測繪或尋求其他調查方法。In step S11, the difference between the normal vectors of the planes is measured, and the difference between the fitted plane normal vectors of the point cloud is plotted at the corresponding position, and then the point cloud is obtained. In particular, the difference between the measured normal vectors in the complex plane can be selected according to the frame selection, and the difference between the point cloud and the plane normal vector drawn at the corresponding position can be used to verify the applicability of the point cloud to interpret the discontinuity of the rock. In detail, it can calculate the normal vector difference of any two groups of frame selection plane regression
Figure 02_image025
, Use a geological compass or other appropriate method to measure the corresponding plane position
Figure 02_image027
, Each repeated amount
Figure 02_image029
Use unit vector to represent the plane position and calculate the average of the measurement position of the corresponding plane
Figure 02_image031
,
Figure 02_image033
And variation
Figure 02_image035
, And then calculate the measured normal vector difference
Figure 02_image037
And its variations
Figure 02_image039
, Verification of suitability for computing point clouds
Figure 02_image041
, Compare the applicability check value with the specified significant water
Figure 02_image043
Threshold
Figure 02_image045
,
Figure 02_image047
The applicability of any two planes in the frame selection plane is greater than or equal to the threshold,
Figure 02_image049
, Indicating that the fineness of the point cloud is good, which is suitable for interpreting the rock discontinuity and proceeding to step S2; otherwise, if the applicability of any two planes does not reach the threshold, it means that the point cloud is not suitable and must be re-mapped or seek other investigations method.

請參考圖7，係本發明之步驟S2之特定流程圖，其步驟包括步驟S20至步驟S25。步驟S20中，計算地磁北方與地理北方之偏角。特定而言，可以複數個框選之平面的量測走向與對應位置所描繪該點雲之擬合平面而計算走向差值之平均值。詳細而言，於描繪露頭之點雲適用於判釋露頭岩石不連續面時，地磁北方與地理北方偏角為框選平面量測走向與點雲判釋走向的差值，可自複數框選平面的差值求得平均值為代表，

Figure 02_image051
並取其於水平面投影與北方之夾角。Please refer to FIG. 7, which is a specific flowchart of step S2 of the present invention. The steps include steps S20 to S25. In step S20, the declination of geomagnetic north and geographical north is calculated. In particular, the average of the difference between the measured directions of a plurality of framed planes and the fitted plane of the point cloud depicted at the corresponding position can be calculated. In detail, when the point cloud depicting the outcrop is suitable for interpreting the discontinuous surface of the outcrop, the declination of the geomagnetic north and the geographic north is the difference between the measured direction of the frame selection plane and the point cloud interpretation direction. The average value of the difference between the planes is representative,
Figure 02_image051
And take its angle between the horizontal projection and the north.

步驟S21中，以該點雲得到該岩石不連續面之位態。特定而言，可框選點雲並判釋岩石不連續面位態，其係自測繪露頭中框選擬判釋岩石不連續面位態範圍之點雲，選擇構成叢集最小點雲數、相鄰叢集迴歸平面法向量差值之閾值、描述同一平面最低叢集數等分析參數，判釋岩石不連續面位態。詳細而言，可參考步驟S10求得的點雲密度，以及擬合平面方程式之誤差量相對於點雲平均間距之比值，選擇構成最小平面的點雲數

Figure 02_image007
、叢集平面結合擴展的法向量差值之閾值
Figure 02_image053
及描述同一平面所需的最低叢集數
Figure 02_image055
等分析參數，判釋岩石不連續面位態
Figure 02_image057
。In step S21, the position of the rock discontinuity is obtained with the point cloud. In particular, the point cloud can be framed and interpreted as the rock discontinuity plane state. It is a frame cloud that selects and interprets the point cloud of the rock discontinuity plane state range from the survey outcrop and selects the minimum point cloud number and phase that form the cluster. Threshold value of normal vector difference between adjacent cluster regression planes, description of the lowest cluster number in the same plane, and other analytical parameters to interpret the discontinuity of the rock. In detail, you can refer to the point cloud density obtained in step S10 and the ratio of the error amount of the fitted plane equation to the average spacing of the point clouds to select the number of point clouds that constitute the smallest plane
Figure 02_image007
, The threshold of the difference between the normal vectors of the cluster plane
Figure 02_image053
And the minimum number of clusters required to describe the same plane
Figure 02_image055
Equal analysis parameters to interpret the discontinuity of the rock
Figure 02_image057
.

步驟S22中，計算該岩石不連續面的位態平均值及變異數。特定而言，可將所得到該岩石不連續面之位態進行半球投影分析，決定該岩石不連續面之位態的組數，採用單位向量表示各該組的岩石不連續面之位態的平均值，透過所有各該組的岩石不連續面之位態至其對應平均值的向量差值的內積，求得各該組的岩石不連續面對應的純量型式變異數。詳細而言，可計算各不連續面組的判釋位態平均值及變異數(圖8及圖9)，其係將利用點雲判釋所得不連續面位態

Figure 02_image057
做為半球投影分析的輸入參數，觀察極點空間分佈特性，依據極點集中程度區分不連續面組數
Figure 02_image059
，並將判釋位態依各組加以分類，計算判釋所得各不連續面組位態的數量
Figure 02_image061
，(
Figure 02_image063
)，採用單位向量表示各不連續面組位態，並依據分類於各組的點雲判釋位態
Figure 02_image065
，計算各不連續面組的判釋位態平均值
Figure 02_image067
，以及判釋位態變異數
Figure 02_image069
。In step S22, the average value and the number of variations of the discontinuities of the rock are calculated. In particular, the position of the rock discontinuity can be analyzed by hemispherical projection to determine the number of groups of the rock discontinuity. The unit vector is used to represent the position of each group of rock discontinuities. The average value is obtained by the inner product of the vector difference between the position of all the rock discontinuities of each group and the corresponding average value, and the scalar type variation corresponding to the rock discontinuity of each group is obtained. In detail, the average and variance of the interpretation position of each discontinuous face group can be calculated (Figure 8 and Figure 9), which will be interpreted using the point cloud to interpret the discontinuous face position
Figure 02_image057
As an input parameter for hemispherical projection analysis, observe the spatial distribution characteristics of the poles, and distinguish the number of discontinuous surface groups according to the degree of pole concentration
Figure 02_image059
, And classify the interpretation position according to each group, and calculate the quantity of each discontinuous surface group position obtained by interpretation
Figure 02_image061
, (
Figure 02_image063
), the unit vector is used to represent the discontinuity of each quilt, and the position is interpreted according to the point clouds classified in each group
Figure 02_image065
, Calculate the average value of the interpretation of each discontinuous quilt
Figure 02_image067
, And the interpretation of positional variation
Figure 02_image069
.

步驟S23中，計算該岩石不連續面的量測位態平均值及變異數。特定而言，可計算各不連續面組的量測位態平均值及變異數，係於步驟S21測繪露頭點雲框選判釋位置附近，採用地質羅盤或其他適當方法，現地重覆量測不連續面位態，並進行半球投影分析，取得各不連續面組的量測位態平均值及變異數。詳細而言，可計算各不連續面組的量測位態平均值及變異數，其係於步驟S21測繪露頭框選點雲附近，採用地質羅盤、電子陀螺儀或其他適當方法，重覆量測不連續面位態，將量測位態

Figure 02_image071
做為半球投影分析的輸入參數，區分不連續面組數
Figure 02_image073
，再將量測位態依各組加以分類，計算各不連續面組位態的量測數量
Figure 02_image075
，再計算各不連續面組的量測位態平均值
Figure 02_image077
，(
Figure 02_image079
)，以及量測位態變異數
Figure 02_image081
。In step S23, the measurement position average and variation of the rock discontinuity are calculated. Specifically, the average and variability of the measurement positions of each discontinuous quilt can be calculated. It is located near the location of the interpretation of the point cloud frame of the outcrop point in step S21, using a geological compass or other appropriate method to repeat the measurement in situ The discontinuous surface configuration and hemispherical projection analysis are used to obtain the average and variation of the measured configuration of each discontinuous surface group. In detail, the measurement position average and variance of each discontinuous quilt can be calculated, which is near the point cloud of the outcrop frame selection in step S21, using a geological compass, electronic gyroscope or other suitable method to repeat the amount Measure the position of the discontinuous surface and measure the position
Figure 02_image071
As an input parameter for hemispherical projection analysis, distinguish the number of discontinuous quilts
Figure 02_image073
, And then classify the measurement position according to each group, and calculate the number of measurements of each discontinuous surface group position
Figure 02_image075
, And then calculate the average measurement position of each discontinuous quilt
Figure 02_image077
, (
Figure 02_image079
), and measuring the number of positional variations
Figure 02_image081
.

步驟S24中，計算該岩石不連續面的位態合併變異數。特定而言，可基於所得之該點雲與露頭之該岩石不連續面的量測位態之變異數，進行變異數檢定並計算合併變異數，即計算各不連續面組的位態合併變異數，其可比較利用點雲判釋與應對露頭量測的各不連續面組位態的變異數是否相近，統計檢定量

Figure 02_image083
，依據選定顯著水準
Figure 02_image085
對應的型 I 錯誤機率
Figure 02_image087
的臨界門檻值
Figure 02_image089
，若
Figure 02_image091
，表示點雲判釋與露頭量測岩石不連續面組的位態變異數無異，第
Figure 02_image093
組不連續面位態的變異數可透過點雲判釋與露頭量測結果合併估計，
Figure 02_image095
；反之，若
Figure 02_image097
，表示點雲判釋與露頭量測岩石不連續面組的位態變異數不同，則第
Figure 02_image099
組不連續面組的位態合併變異數
Figure 02_image101
。In step S24, the positional combined variance of the rock discontinuity is calculated. In particular, based on the measured positional variation of the point cloud and the rock discontinuity of the outcrop, the number of variations can be verified and the combined variation can be calculated, that is, the positional combined variation of each discontinuous surface group can be calculated Number, which can be compared with the point cloud to determine whether the number of variances of each discontinuous face group measured for outcrop measurements is similar, and statistical check
Figure 02_image083
, Based on the selected significance level
Figure 02_image085
Corresponding type I error probability
Figure 02_image087
Critical threshold
Figure 02_image089
If
Figure 02_image091
, Indicating that the point cloud interpretation is no different from that of outcrop measurement of the discontinuity of the rock discontinuous surface group.
Figure 02_image093
The number of variations of the group of discontinuities can be estimated by combining point cloud interpretation and outcrop measurement results.
Figure 02_image095
; Conversely, if
Figure 02_image097
, Indicating that the point cloud interpretation is different from the outlier measurement of the discontinuity of the rock discontinuous surface group, then the first
Figure 02_image099
Group discontinuous quilt's combined morphology
Figure 02_image101
.

步驟S25中，檢定利用該點雲得到之岩石不連續面的位態之代表性。特定而言，可檢定利用點雲判釋與露頭量測岩石不連續面位態的代表性，係依據地磁北方與地理北方偏角，修正地質羅盤量測各不連續面組的位態平均值後，視為地真值，在選定顯著水準下，檢定對應的利用點雲判釋各不連續面組的位態平均值是否與地真值無異。若檢定利用該點雲得到之岩石不連續面的位態之代表性為是，則進入步驟S4；若檢定利用該點雲得到之岩石不連續面的位態之代表性為否或需最佳化分析參數進行判釋作業，則進入步驟S3。詳細而言，檢定利用點雲判釋岩石不連續面組位態的代表性(圖10)，其係考慮步驟S21地磁北方與地理北方偏角，修正步驟S23地質羅盤量測各不連續面組的位態平均值後，視為地真值，在選定顯著水準下，檢定利用點雲判釋的各不連續面組位態是否具代表性。對於步驟S24點雲判釋與露頭量測岩石不連續面組位態變異數相等情況，統計檢定量

Figure 02_image103
，若
Figure 02_image105
小於或等於選定顯著水準
Figure 02_image107
對應的型 I 錯誤機率
Figure 02_image109
的臨界閾值
Figure 02_image111
，表示利用點雲判釋所得第
Figure 02_image093
組不連續面位態與地真值無異，可進入步驟S4；反之，若
Figure 02_image113
，表示點雲判釋所得第
Figure 02_image093
組不連續面位態不同於地真值，或需最佳化分析參數進行判釋作業，則進入步驟S3。對於步驟S24點雲判釋與露頭量測岩石不連續面位態變異數不相等情況，統計檢定量
Figure 02_image115
，此時
Figure 02_image117
，
Figure 02_image119
的數值非整數時，捨去至最接近整數值，若
Figure 02_image121
小於或等於選定顯著水準對應的臨界閾值
Figure 02_image123
，表示利用點雲判釋所得第
Figure 02_image093
組不連續面位態與地真值無異，可進入步驟S4；反之，若
Figure 02_image125
，表示點雲判釋所得第
Figure 02_image093
組不連續面位態不同於地真值，或需最佳化分析參數進行判釋作業，則進入步驟S3。In step S25, the representativeness of the discontinuity of the rock obtained by using the point cloud is verified. In particular, it is possible to verify the representativeness of the discontinuity of the rock by point cloud interpretation and outcrop measurement, based on the declination of the geomagnetic north and the geographic north, and correct the geological compass to measure the average value of the discontinuities After that, it is regarded as the ground truth value. Under the selected significance level, the corresponding point cloud is used to determine whether the average value of the discontinuity of each discontinuous surface group is the same as the ground truth value. If it is verified that the representativeness of the discontinuity of the rock obtained by using the point cloud is yes, then go to step S4; if it is verified that the representativeness of the discontinuity of the rock obtained by using the point cloud is no or best To analyze the parameters to perform the interpretation operation, proceed to step S3. In detail, the point cloud is used to interpret the representativeness of the discontinuity of the rock group (Figure 10). It considers the declination of the geomagnetic north and the geographic north in step S21, and corrects the discontinuity in the geological compass in step S23. After the average value of the posture is regarded as the true value of the ground, under the selected significance level, it is verified whether the posture of each discontinuous quilt interpreted by the point cloud is representative. For the case where the point cloud interpretation in step S24 is equal to the number of outliers measured in the discontinuities of rock discontinuities, statistical verification
Figure 02_image103
If
Figure 02_image105
Less than or equal to the selected significance level
Figure 02_image107
Corresponding type I error probability
Figure 02_image109
Critical threshold
Figure 02_image111
, Indicating the first
Figure 02_image093
The group discontinuous plane position is the same as the ground truth value, you can go to step S4; otherwise, if
Figure 02_image113
, Indicating the point obtained from the point cloud interpretation
Figure 02_image093
If the group discontinuity plane is different from the ground truth value, or the analysis parameters need to be optimized for interpretation, then step S3 is entered. For the case where the point cloud interpretation in step S24 is not equal to the number of outliers measured in the discontinuous surface, the statistical verification
Figure 02_image115
,at this time
Figure 02_image117
,
Figure 02_image119
When the value of is not an integer, round down to the nearest integer value, if
Figure 02_image121
Less than or equal to the critical threshold corresponding to the selected significance level
Figure 02_image123
, Indicating the first
Figure 02_image093
The group discontinuous plane position is the same as the ground truth value, you can go to step S4; otherwise, if
Figure 02_image125
, Indicating the point obtained from the point cloud interpretation
Figure 02_image093
If the group discontinuity plane is different from the ground truth value, or the analysis parameters need to be optimized for interpretation, then step S3 is entered.

請參考圖11，係本發明之步驟S3之特定流程圖，其步驟包括步驟S30至及步驟S33。步驟S30中，以分析參數重新得到該岩石不連續面的位態。特定而言，可重新選擇不同分析參數量值判釋不連續面位態，係針對利用點雲判釋岩石不連續面位態所需的三個參數，考慮三水準量值重新判釋後，進行半球投影分析，決定不連續面組數，並計算判釋所得各不連續面組的面積總和。詳細而言，依據實驗設計法，針對利用點雲判釋岩石不連續面位態所需的三個分析參數

Figure 02_image007
、
Figure 02_image009
及
Figure 02_image011
等，皆考慮三水準量值重新分析，判釋岩石不連續面位態
Figure 02_image057
，計算判釋所得各不連續面的面積，並採用半球投影分析分類判釋不連續面組別，並計算判釋所得各不連續面組的面積總和。Please refer to FIG. 11, which is a specific flowchart of step S3 of the present invention. The steps include steps S30 to S33. In step S30, the position of the rock discontinuity is retrieved based on the analysis parameters. In particular, different analysis parameter values can be re-selected to interpret the discontinuous surface state. For the three parameters required to interpret the rock discontinuous surface state using point clouds, after considering the three-level value to reinterpret, Perform hemispheric projection analysis to determine the number of discontinuous quilts, and calculate the sum of the areas of the discontinuous quilts obtained by interpretation. In detail, according to the experimental design method, the three analysis parameters required to use the point cloud to interpret the discontinuity of the rock
Figure 02_image007
,
Figure 02_image009
and
Figure 02_image011
Etc., all of which are considered to be re-analyzed by three-level measurements to interpret the discontinuity of the rock
Figure 02_image057
, Calculate the area of each discontinuous surface obtained by interpretation, and classify and interpret the discontinuous surface group by hemispheric projection analysis, and calculate the total area of each discontinuous surface group obtained by interpretation.

步驟S31中，建立該岩石不連續面的位態之分析參數與該岩石不連續面之面積總和的迴歸方程式。特定而言，可建立點雲判釋位態分析參數與判釋所得各不連續面組面積總和之迴歸方程式。詳細而言，可建立點雲判釋位態分析參數與判釋所得各不連續面組面積總和之迴歸方程式，係以

Figure 02_image007
、
Figure 02_image009
及
Figure 02_image011
為自變數，判釋所得各不連續面組的面積總和為應變數，進行統計複迴歸分析，建立迴歸方程式。In step S31, a regression equation of the sum of the analysis parameters of the position of the rock discontinuity and the area of the rock discontinuity is established. In particular, a regression equation can be established for the sum of the point cloud interpretation status analysis parameters and the total area of each discontinuous quilt obtained by interpretation. In detail, a regression equation can be established for the sum of the point cloud interpretation state analysis parameters and the total area of the discontinuous quilts obtained by the interpretation.
Figure 02_image007
,
Figure 02_image009
and
Figure 02_image011
For the independent variables, the sum of the areas of the discontinuous quilts obtained from the interpretation is the strain number. Statistical multiple regression analysis is performed to establish the regression equation.

步驟S32中，以最大之該面積總和的分析參數得到該岩石不連續面的位態。特定而言，可選擇判釋所得各不連續面組面積總和最大的分析參數，重新判釋不連續面位態，係依據步驟S31求得的迴歸方程式，依據各不連續面組面積總和最大的

Figure 02_image007
、
Figure 02_image009
及
Figure 02_image011
等分析參數，重新判釋岩石不連續面位態，重覆步驟S22，並依據步驟S23結果重新執行步驟S24。詳細而言，可選擇判釋所得各不連續面組面積總和最大的分析參數，重新判釋不連續面位態，共係依據步驟S31求得的迴歸方程式，依據各不連續面組面積總和最大的
Figure 02_image007
、
Figure 02_image009
及
Figure 02_image011
等分析參數，重新判釋岩石不連續面位態，重覆步驟S22，並依據步驟S23結果重新執行步驟S24。In step S32, the position of the rock discontinuity is obtained with the analysis parameter of the largest sum of the areas. In particular, the analysis parameter with the largest sum of the areas of the discontinuous quilts obtained by interpretation can be selected to reinterpret the discontinuous face posture, which is based on the regression equation obtained in step S31 and the maximum sum of the area of the discontinuous quilts.
Figure 02_image007
,
Figure 02_image009
and
Figure 02_image011
After analyzing the parameters, re-interpret the rock discontinuous plane state, repeat step S22, and re-execute step S24 according to the result of step S23. In detail, the analysis parameter with the largest sum of the areas of the discontinuous quilts obtained by interpretation can be selected to reinterpret the discontinuous face posture. The regression equation obtained according to step S31 is based on the maximum sum of the areas of the discontinuous quilts. of
Figure 02_image007
,
Figure 02_image009
and
Figure 02_image011
After analyzing the parameters, re-interpret the rock discontinuous plane state, repeat step S22, and re-execute step S24 according to the result of step S23.

步驟S33中，檢定利用該點雲得到之岩石不連續面的位態之代表性，若該代表性之檢定結果為可，則進行輸出該岩石不連續面之位態的報告。特定而言，可重新檢定點雲判釋與露頭量測各組岩石不連續面位態代表性，係依據重新計算所得各不連續面組的平均位態及變異數，執行步驟S25的檢定步驟，若檢定通過則輸出點雲判釋成果報告，完成判釋分析作業；否則即表示該描繪露頭之點雲無法滿足在選定顯著水準下，岩石不連續面的位態判釋要求，必須重新測繪。詳細而言，可重新檢定利用點雲判釋各岩石不連續面組位態的代表性，係依據重新計算所得的

Figure 02_image127
及
Figure 02_image129
，重新執行步驟S25的檢定步驟，若檢定通過，則進入步驟S4；若不通過，則表示相較於該露頭量測的地真值，利用點雲判釋岩石不連續面組的位態，無法滿足選定顯著水準的要求，必須重新測繪或尋求其他方法調查岩石不連續面位態。In step S33, the representativeness of the state of the rock discontinuity obtained by using the point cloud is verified, and if the representative verification result is acceptable, a report is output of the state of the rocky discontinuity. In particular, the point cloud interpretation and outcrop measurement can be re-verified to measure the representativeness of each group of rock discontinuities. Based on the recalculated average position and variation of each group of discontinuities, the verification step of step S25 is performed. If the verification is passed, a point cloud interpretation result report will be output to complete the interpretation analysis operation; otherwise, it means that the point cloud depicting the outcrop cannot meet the requirements for the position interpretation of the rock discontinuity at the selected significant level, and must be re-mapped . In detail, the point cloud can be used to re-examine the representativeness of the discontinuity of each rock group, based on the recalculation
Figure 02_image127
and
Figure 02_image129
, Re-execute the verification step of step S25, if the verification is passed, then go to step S4; if not, it means that compared with the measured ground truth value of the outcrop, the point cloud is used to interpret the position of the rock discontinuous quilt, Unable to meet the requirements of the selected significant level, you must re-map or seek other methods to investigate the discontinuity of the rock.

如上所述之步驟S4中，特定而言，可輸出描繪露頭的點雲密度及平均間距，利用點雲判釋岩石各不連續面位態所需的構成叢集最小點雲數、相鄰叢集迴歸平面法向量差值之閾值、描述同一平面最低叢集數等參數，以及判釋所得岩石各不連續面組的位態平均值、變異數以及選定之顯著水準。In step S4 as described above, specifically, the density and average spacing of the point clouds depicting the outcrop can be output, and the point cloud can be used to interpret the discontinuities of the rock. Thresholds for the difference of plane normal vectors, the parameters describing the lowest cluster number in the same plane, and the average value of the discontinuities of the discontinuous quilts, the number of variances and the selected significance level.

綜上所述，本發明能檢核描繪露頭的點雲是否足以提供判釋岩石不連續面所需的精細程度，並消彌或抑低為完整描繪露頭幾何形貌而採用的測站位置坐標轉換，或是共軛點判釋以拼接點雲造成的誤差，並整合場址不同露頭、以及同一露頭不同位置利用點雲判釋岩石不連續面的組數及代表位態的結果，提供岩石不連續面其他項目調查及評估更充分的依據，以利更完整地描述及計量化場址的工程地質特性。In summary, the present invention can check whether the point cloud depicting the outcrop is sufficient to provide the fineness required to interpret the discontinuities of the rock, and eliminate or suppress the coordinates of the station position used for the complete depiction of the geometric shape of the outcrop Conversion, or conjugate point interpretation to the error caused by splicing point clouds, and integration of different outcrops on the site and different locations of the same outcrop to use point clouds to interpret the number of rock discontinuities and the results of representative positions to provide rock The discontinuity is a more sufficient basis for the investigation and evaluation of other projects in order to more fully describe and measure the engineering geological characteristics of the site.

本發明在上文中已以較佳實施例揭露，然熟習本項技術者應理解的是，該實施例僅用於描繪本發明，而不應解讀為限制本發明之範圍。應注意的是，舉凡與該實施例等效之變化與置換，均應設為涵蓋於本發明之範疇內。因此，本發明之保護範圍當以申請專利範圍所界定者為準。The present invention has been disclosed in the above with preferred embodiments, but those skilled in the art should understand that this embodiment is only used to depict the present invention and should not be interpreted as limiting the scope of the present invention. It should be noted that all changes and substitutions equivalent to this embodiment should be included within the scope of the present invention. Therefore, the scope of protection of the present invention shall be subject to those defined in the scope of patent application.

N‧‧‧北方 H‧‧‧水平線 0‧‧‧不連續面組 1‧‧‧出露之不連續面 10‧‧‧不連續面與水平面交線 20‧‧‧不連續面最大傾斜線 α‧‧‧走向 β‧‧‧傾角 γ‧‧‧傾向

Figure 107120439-A0304-12-0014-1
‧‧‧不連續面法向量
Figure 107120439-A0304-12-0014-2
‧‧‧第i個框選範圍擬合平面法向量 f(x,y,z)‧‧‧第i個框選範圍擬合平面函數 efni‧‧‧第i個框選範圍擬合平面方程式之誤差量
Figure 107120439-A0304-12-0014-3
‧‧‧第i個點雲判釋第J組不連續面位態
Figure 107120439-A0304-12-0014-4
‧‧‧點雲判釋第J組不連續面位態平均值
Figure 107120439-A0304-12-0014-5
‧‧‧點雲判釋第J組不連續面位態變異數
Figure 107120439-A0304-12-0014-6
‧‧‧羅盤量測第I個框選平面位態平均值
Figure 107120439-A0304-12-0014-7
‧‧‧羅盤量測第J組不連續面位態平均值
Figure 107120439-A0304-12-0014-8
‧‧‧地磁北方與地理北方偏角 3‧‧‧對應於利用點雲判釋第J組不連續面位態平均值之地真值 101‧‧‧框選範圍之點雲的擬合平面 S1、S10、S11、S2、S20、S21、S22、S23、S24、S25、S3、S30、S31、S32、S33、S4‧‧‧步驟N‧‧‧North H‧‧‧horizontal line 0‧‧‧discontinuous surface group 1‧‧‧discontinuous surface 10‧‧‧discontinuity surface and horizontal plane intersection line 20‧‧‧discontinuous surface maximum inclined line α ‧‧‧ toward β‧‧‧tilt angle
Figure 107120439-A0304-12-0014-1
‧‧‧ Discontinuity normal vector
Figure 107120439-A0304-12-0014-2
‧‧‧I frame selection range fitting plane normal vector f(x,y,z) ‧‧‧I frame selection range fitting plane function e fni ‧‧‧I frame selection range fitting plane equation Error
Figure 107120439-A0304-12-0014-3
‧‧‧ The i-th point cloud interprets the discontinuity of group J
Figure 107120439-A0304-12-0014-4
‧‧‧ point cloud interpretation of the average value of the group J discontinuous surface configuration
Figure 107120439-A0304-12-0014-5
‧‧‧ point cloud interpretation of the group J discontinuous surface configuration variation
Figure 107120439-A0304-12-0014-6
‧‧‧ Compass to measure the average value of the first framed plane configuration
Figure 107120439-A0304-12-0014-7
‧‧‧Compass measurement average of group J discontinuous surface configuration
Figure 107120439-A0304-12-0014-8
‧‧‧ Geomagnetic North and Geographic North declination 3 ‧‧‧ corresponds to the ground truth value 101 of the point cloud to interpret the average value of the group J discontinuous surface states 101 , S10, S11, S2, S20, S21, S22, S23, S24, S25, S3, S30, S31, S32, S33, S4‧‧‧

圖1係不連續面的位態常以平面的走向及傾角，或是傾向及傾角的示意圖。 圖2係本發明利用點雲判斷岩石不連續面位態的方法之流程圖。 圖3係本發明利用點雲判斷岩石不連續面位態的方法之另一態樣的流程圖。 圖4係本發明利用點雲判斷岩石不連續面位態的方法之又一態樣的流程圖。 圖5係本發明之步驟S1之特定流程圖。 圖6係本發明之步驟S10之示意圖。 圖7係本發明之步驟S2之特定流程圖。 圖8係本發明第i 個點雲判釋第J 組不連續面位態之示意圖。 圖9係本發明計算各不連續面組的判釋位態平均值及變異數之示意圖。 圖10係本發明檢定利用點雲判釋岩石不連續面組位態的代表性之示意圖。 圖11係本發明之步驟S3之特定流程圖。Figure 1 is a schematic diagram of the discontinuous plane's position, usually with the direction and inclination of the plane, or the tendency and inclination. FIG. 2 is a flow chart of the method for judging the discontinuity of the rock by using point clouds in the present invention. FIG. 3 is a flowchart of another aspect of the method for judging the discontinuity of the rock by using point clouds in the present invention. 4 is a flow chart of another aspect of the method for judging the discontinuity of a rock by using point clouds in the present invention. FIG. 5 is a specific flowchart of step S1 of the present invention. FIG. 6 is a schematic diagram of step S10 of the present invention. 7 is a specific flowchart of step S2 of the present invention. FIG. 8 is a schematic diagram of the i- th point cloud of the present invention for interpreting the discontinuity of group J. FIG. 9 is a schematic diagram of calculating the average value and variation of the interpretation status of each discontinuous quilt according to the present invention. FIG. 10 is a representative schematic diagram of the verification of the present invention using a point cloud to interpret the discontinuity of the rock group. FIG. 11 is a specific flowchart of step S3 of the present invention.

S1、S2‧‧‧步驟 S1, S2‧‧‧Step

Claims (17)

本發明之一種利用點雲判斷岩石不連續面位態的方法，步驟S1包含以下步驟： (S10) 以複數個平面計算該點雲的擬合平面方程式之誤差量相對於該點雲的平均間距之比值而檢測該點雲之精細程度；及(S11) 量測該些平面之法向量的差值，且以對應位置而描繪該點雲之擬合平面法向量的差值，進而得到適用之該點雲。A method for judging the discontinuity of a rock using a point cloud according to the present invention, step S1 includes the following steps: (S10) Calculate the error amount of the fitted plane equation of the point cloud with a plurality of planes relative to the average distance of the point cloud Ratio to detect the fineness of the point cloud; and (S11) measure the difference of the normal vectors of the planes, and plot the difference of the fitted plane normal vectors of the point cloud with the corresponding positions, and then obtain the applicable The point cloud. 本發明之一種利用點雲判斷岩石不連續面位態的方法，步驟S2包含以下步驟： (S20) 計算地磁北方與地理北方之偏角； (S21) 以該點雲得到該岩石不連續面之位態； (S22) 計算該岩石不連續面的位態平均值及變異數；(S23) 計算該岩石不連續面的量測位態平均值及變異數；(S24) 計算該岩石不連續面的位態合併變異數；及(S25) 檢定利用該點雲得到之岩石不連續面的位態之代表性。A method for judging the state of a rock discontinuity using a point cloud of the present invention, step S2 includes the following steps: (S20) Calculate the declination of geomagnetic north and geographical north; (S21) Use the point cloud to obtain the rock discontinuity Position; (S22) Calculate the mean value and variation of the discontinuity of the rock; (S23) Calculate the mean value and variation of the measured discontinuity of the rock; (S24) Calculate the discontinuity of the rock The combined variability of the morphology of the; and (S25) verify the representativeness of the morphology of the discontinuous surface of the rock obtained from the point cloud. 一種利用點雲判斷岩石不連續面位態的方法，係包括步驟： (S1) 得到適用的點雲；以及 (S2) 基於地磁及地理方位而由該點雲得到岩石不連續面之位態。A method for judging the position of a rock discontinuity using a point cloud includes the steps of: (S1) obtaining a suitable point cloud; and (S2) obtaining the position of the rock discontinuity from the point cloud based on geomagnetism and geographic orientation. 如申請專利範圍第1項所述之一種利用點雲判斷岩石不連續面位態的方法，在步驟S2之後更包括(S3) 以參數最佳化檢查該岩石不連續面之位態。As described in item 1 of the scope of the patent application, a method for judging the position of the rock discontinuity using a point cloud, after step S2, further includes (S3) checking the position of the rock discontinuity with parameter optimization. 如申請專利範圍第1或2項所述之一種利用點雲判斷岩石不連續面位態的方法，在步驟S2之後更包括(S4) 輸出該岩石不連續面之位態的報告，或者在步驟S3之後進行步驟S4。As described in item 1 or 2 of the scope of the patent application, a method for judging the state of the rock discontinuity using a point cloud, after step S2, it further includes (S4) outputting a report of the state of the rock discontinuity, or in the step After S3, step S4 is performed. 如申請專利範圍第1項所述之一種利用點雲判斷岩石不連續面位態的方法，步驟S1包含以下步驟： (S10) 以複數個平面計算該點雲的擬合平面方程式之誤差量相對於該點雲的平均間距之比值而檢測該點雲之精細程度；及 (S11) 量測該些平面之法向量的差值，且以對應位置而描繪該點雲之擬合平面法向量的差值，進而得到適用之該點雲。As described in item 1 of the scope of the patent application, a method for judging the discontinuity of a rock by using a point cloud, step S1 includes the following steps: (S10) Calculate the fitting error of the fitted plane equation of the point cloud using multiple planes. Detecting the fineness of the point cloud based on the ratio of the average spacing of the point cloud; and (S11) measuring the difference between the normal vectors of the planes, and plotting the fitting plane normal vector of the point cloud with the corresponding positions The difference value is used to obtain the applicable point cloud. 如申請專利範圍第1項所述之一種利用點雲判斷岩石不連續面位態的方法，步驟S2包含以下步驟： (S20) 計算地磁北方與地理北方之偏角； (S21) 以該點雲得到該岩石不連續面之位態； (S22) 計算該岩石不連續面的位態平均值及變異數； (S23) 計算該岩石不連續面的量測位態平均值及變異數； (S24) 計算該岩石不連續面的位態合併變異數；及 (S25) 檢定利用該點雲得到之岩石不連續面的位態之代表性。As described in item 1 of the scope of the patent application, a method for judging the discontinuity of a rock using a point cloud, step S2 includes the following steps: (S20) Calculate the declination of geomagnetic north and geographical north; (S21) use the point cloud Obtain the position of the rock discontinuity; (S22) Calculate the mean value and variation of the rock discontinuity; (S23) Calculate the mean value and variation of the measurement discontinuity of the rock; (S24 ) Calculate the combined variability of the discontinuity of the rock discontinuity; and (S25) verify the representativeness of the discontinuity of the rock by using the point cloud. 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，若檢定利用該點雲得到之岩石不連續面的位態之代表性為是，進行輸出該岩石不連續面之位態的報告，若檢定利用該點雲得到之岩石不連續面的位態之代表性為否，進行步驟(S3)以參數最佳化檢查該岩石不連續面之位態。As described in item 5 of the scope of the patent application, a method for judging the state of rock discontinuity using a point cloud, wherein if the representativeness of the state of the rock discontinuity obtained by using the point cloud is yes, output Report on the position of the rock discontinuity. If the representativeness of the position of the rock discontinuity obtained from the point cloud is verified, proceed to step (S3) to check the position of the rock discontinuity by parameter optimization . 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S20係以複數個框選之平面的量測走向與對應位置所描繪該點雲之擬合平面而計算走向差值之平均值。As described in item 5 of the patent application, a method for judging the discontinuity of a rock using a point cloud, wherein step S20 is based on the measurement trend of a plurality of framed planes and the corresponding position Calculate the average value of the difference in the direction of movement. 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S21係自測繪露頭中框選擬判釋之該岩石不連續的面位態範圍之點雲，選擇構成叢集最小之點雲數、相鄰叢集迴歸平面法向量差值的閾值且描述同一平面最低叢集數等分析參數，以得到該岩石不連續面之位態。As described in item 5 of the patent application scope, a method for judging the discontinuity of the rock's discontinuity using a point cloud, wherein step S21 selects the point of the discontinuity of the discontinuity of the rock from the surveying and mapping outcrop Clouds, select the minimum number of point clouds that constitute the cluster, the threshold value of the difference between the normal vectors of the regression planes of adjacent clusters, and describe the analysis parameters such as the lowest cluster number in the same plane to obtain the position of the discontinuous surface of the rock. 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S22係將所得到該岩石不連續面之位態進行半球投影分析，決定該岩石不連續面之位態的組數，採用單位向量表示各該組的岩石不連續面之位態的平均值，透過所有各該組的岩石不連續面之位態至其對應平均值的向量差值的內積，求得各該組的岩石不連續面對應的純量型式變異數。As described in item 5 of the patent application, a method for judging the discontinuity of a rock using a point cloud, wherein in step S22, the obtained discontinuity of the rock is subjected to hemispherical projection analysis to determine the discontinuity of the rock The number of groups of face positions, the unit vector is used to represent the average value of the discontinuities of each group of rock discontinuities, through the vector difference of all the positions of the rock discontinuities of each group to their corresponding average Inner product, find the scalar type variation corresponding to each group of rock discontinuities. 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S23係於測繪露頭框選之該點雲的位置附近，重覆量測該岩石不連續面之位態並進行半球投影分析，決定該岩石不連續面之位態的組數，並計算各該組的岩石不連續面的量測位態之平均值及變異數。As described in item 5 of the patent application, a method for judging the discontinuity of a rock using a point cloud, wherein step S23 is to repeatedly measure the rock discontinuity near the position of the point cloud framed by the mapping outcrop Perform the hemispherical projection analysis on the face position to determine the number of groups of rock discontinuities, and calculate the average and variation of the measured position of each group of rock discontinuities. 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S24係基於所得之該點雲與露頭之該岩石不連續面的量測位態之變異數，進行變異數檢定並計算合併變異數。As described in item 5 of the patent application, a method for judging the discontinuity of rock discontinuities using a point cloud, wherein step S24 is based on the measurement of the variation of the discontinuities of the discontinuity of the rock from the point cloud and the outcrop The number of mutations is checked and the number of combined mutations is calculated. 如申請專利範圍第5項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S25係考慮地磁北方與地理北方偏角而於露頭量測該岩石不連續面的位態之平均值，並視為地真值，在選定顯著水準下，檢定對應之利用該點雲得到之該岩石不連續面的位態之平均值是否與該地真值相符。As described in item 5 of the patent application, a method for judging the position of a rock discontinuity using a point cloud, wherein step S25 is to measure the position of the rock discontinuity at the outcrop considering the declination of geomagnetic north and geographical north The average value is regarded as the ground truth value. Under the selected significance level, it is checked whether the corresponding average value of the position of the rock discontinuity obtained by using the point cloud is consistent with the ground truth value. 如申請專利範圍第6項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，輸出該岩石不連續面之位態的報告包含該岩石不連續面的位態之平均值、變異數以及選定之顯著水準，供量化表示該岩石不連續面的位態之信賴區間，並完成該岩石不連續面的分析作業。As described in item 6 of the patent application scope, a method for judging the state of rock discontinuity using a point cloud, wherein the report outputting the state of the rock discontinuity includes the average value of the state of the rock discontinuity, The number of variations and the selected significant level are used to quantify the confidence interval that represents the position of the rock discontinuity and complete the analysis of the rock discontinuity. 如申請專利範圍第6項所述之一種利用點雲判斷岩石不連續面位態的方法，步驟S3包含以下步驟： (S30) 以分析參數重新得到該岩石不連續面的位態； (S31) 建立該岩石不連續面的位態之分析參數與該岩石不連續面之面積總和的迴歸方程式； (S32) 以最大之該面積總和的分析參數得到該岩石不連續面的位態；及 (S33) 檢定利用該點雲得到之岩石不連續面的位態之代表性，若該代表性之檢定結果為可則進行輸出該岩石不連續面之位態的報告。As described in Item 6 of the patent application scope, a method for judging the position of a rock discontinuity using a point cloud, step S3 includes the following steps: (S30) Regain the position of the rock discontinuity by analyzing the parameters; (S31) Establish a regression equation for the analysis parameters of the position of the rock discontinuity and the total area of the rock discontinuity; (S32) obtain the position of the rock discontinuity with the largest analysis parameter of the total area; and (S33 ) Verify the representativeness of the discontinuity of the rock obtained by using the point cloud. If the representative verification result is available, report the position of the discontinuity of the rock. 如申請專利範圍第14項所述之一種利用點雲判斷岩石不連續面位態的方法，其中，步驟S30係針對以分析參數重新得到該岩石不連續面的位態所需三分析參數，分別選擇三水準量值重新得到該岩石不連續面之位態，配合半球投影分析決定該岩石不連續面之組數後，計算該岩石不連續面的面積總和。As described in item 14 of the scope of the patent application, a method for judging the position of a rock discontinuity using a point cloud, wherein step S30 is for the three analysis parameters required to obtain the position of the rock discontinuity using the analysis parameters, respectively Select the three-level magnitude to get the position of the rock discontinuity again. After determining the number of groups of the rock discontinuity in conjunction with hemispheric projection analysis, calculate the total area of the rock discontinuity.
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CN111581583A (en) * 2020-05-09 2020-08-25 陕西宝成航空仪表有限责任公司 Geomagnetic map suitability comprehensive evaluation method based on improved projection pursuit
CN115546116A (en) * 2022-09-15 2022-12-30 山东大学 Method and system for extracting and calculating spacing of discontinuous surface of fully-covered rock mass

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CN111461981A (en) * 2020-03-30 2020-07-28 北京百度网讯科技有限公司 Error estimation method and device for point cloud splicing algorithm
CN111461981B (en) * 2020-03-30 2023-09-01 北京百度网讯科技有限公司 Error estimation method and device for point cloud stitching algorithm
CN111581583A (en) * 2020-05-09 2020-08-25 陕西宝成航空仪表有限责任公司 Geomagnetic map suitability comprehensive evaluation method based on improved projection pursuit
CN111581583B (en) * 2020-05-09 2024-02-06 陕西宝成航空仪表有限责任公司 Geomagnetic chart suitability comprehensive evaluation method based on improved projection pursuit
CN115546116A (en) * 2022-09-15 2022-12-30 山东大学 Method and system for extracting and calculating spacing of discontinuous surface of fully-covered rock mass

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