A method and device for estimating the volume of construction waste dumping points

Abstract

The present invention relates to a method and device for estimating the volume of a construction waste stacking point. The method comprises the following steps: obtaining a discrete coordinate point set of a stacking body; determining convex hull points and generating convex hull polygons for the discrete coordinate point set; using the convex hull polygons to form an initial triangulated network; constructing a triangulated network model for the initial triangulated network, and using the triangulated network model to estimate the volume of the construction waste stacking point.

Description

Technical Field

[0001] The invention relates to the estimation of the volume of a stacking point, and in particular to the estimation of the volume of a stacking point for construction waste. Background Art

[0002] Construction and demolition waste (CDW) is a general term for engineering slag, engineering mud, engineering waste, demolition waste and decoration waste, including abandoned soil, abandoned materials and other wastes generated during the construction, expansion, reconstruction and demolition of various buildings, structures, pipe networks, etc., as well as the decoration and renovation of houses by residents. With the continuous development of urban renewal, large-scale construction activities generate a huge amount of construction waste, which aggravates a series of problems such as resource waste, environmental pollution and damage to the urban appearance. Effective treatment of construction waste can alleviate resource shortages, environmental pollution and damage to the urban appearance, and promote the sustainable development of the construction industry. In recent years, in order to estimate the volume of construction waste dumping sites, total stations, GNSS RTK receivers or laser radars have been used to obtain three-dimensional coordinate points of a certain density on the surface of the dump, or to obtain image data using drones, and then the volume is calculated using DTM method, grid method, contour line method, cross-section method and other methods, which have their own advantages in terms of applicability and accuracy indicators. However, the existing technology is still insufficient in how to achieve dynamic monitoring and management of the volume estimation of construction waste dumping sites while maintaining accuracy. Summary of the invention

[0003] In view of the problems in the prior art, the present invention is used to solve one or more problems in the prior art and at least provide a beneficial choice.

[0004] According to one aspect of the present invention, a method for estimating the volume of a construction waste dumping site is provided, comprising the following steps: obtaining a discrete coordinate point set of the dump; determining convex hull points for the discrete coordinate point set and generating convex hull polygons; using the convex hull polygons to form an initial triangulated network; constructing a triangulated network model for the initial triangulated network, and using the triangulated network model to estimate the volume of the construction waste dumping site.

[0005] According to another aspect of the present invention, a device for estimating the volume of a construction waste stacking point is provided, comprising: a discrete coordinate point acquisition unit, for obtaining a discrete coordinate point set of a stacking body; a convex hull polygon generation unit, for determining convex hull points and generating convex hull polygons for the discrete coordinate point set; a triangulated mesh generation unit, for forming an initial triangulated mesh using the convex hull polygons; a triangulated mesh model construction unit, for constructing a triangulated mesh model for the initial triangulated mesh; and a stacking point volume estimation unit, for estimating the volume of a construction waste stacking point using the triangulated mesh model.

[0006] According to another aspect of the present invention, an electronic device is provided, comprising: a processor; and a memory for storing instructions executable by the processor; wherein the processor is configured to execute the instructions to implement the method of the present invention.

[0007] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a device control program is stored. When the device control program is executed by a processor, the method of the present invention is implemented.

[0008] According to the implementation mode of the present invention, since the data collection means of discrete coordinate points are showing a diversified trend, for example, GNSS RTK can obtain discrete coordinate point data in real time, the present technical solution can be used to estimate the dynamic estimation results of the volume changes of construction waste storage points in real time, thereby realizing dynamic monitoring and management of construction waste while maintaining accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The present invention can be better understood with reference to the accompanying drawings, which are merely illustrative and are not intended to limit the scope of protection of the present invention.

[0010] Figure 1 It is a schematic flow chart showing a method for estimating the volume of a construction waste dumping site according to an embodiment of the present invention.

[0011] Figure 2 A schematic diagram of vertex search and deletion according to one embodiment is shown.

[0012] Figure 3 A schematic diagram of searching for convex hull points based on a recursive method is shown.

[0013] Figure 4 A schematic flow chart of generating an initial triangulated network according to an embodiment of the present invention is shown.

[0014] Figure 5 A schematic diagram of fill and cut is shown when the elevations of two vertices are both less than the base elevation and the elevation of one vertex is greater than the base elevation.

[0015] Figure 6 A schematic diagram of fill and cut is shown when the elevations of two vertices are both greater than the base elevation and the elevation of one vertex is less than the base elevation.

[0016] Figure 7 It is a schematic block diagram showing a device for estimating the volume of a construction waste dumping site according to an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The specific embodiments of the present invention are described below in conjunction with the accompanying drawings. These descriptions are exemplary and are intended to enable those skilled in the art to implement the embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. The description does not describe any content that is indispensable for actual implementation but irrelevant to understanding the present invention.

[0018] Figure 1 FIG. 1 is a schematic flow chart showing a method for estimating the volume of a construction waste dumping site according to an embodiment of the present invention. Figure 1 As shown, according to one embodiment of the present invention, according to the method for estimating the volume of a construction waste dumping site of the present invention, first in step S100, a discrete coordinate point set P = {P1, P2, ..., Pn} of the dumping body is obtained. The discrete coordinate points of the construction waste dumping site can be acquired by one or any combination of a total station, a GNSS RTK receiver, a three-dimensional laser scanner, etc., so as to obtain a discrete coordinate point set. Assume that P (x, y, h) is any fragmented measurement point on the discrete coordinate point set P = {P1, P2, ..., Pn}. The shape of the construction waste dumping site is extremely irregular, and the fragmented measurement point is the point that needs to be measured, which is generally the turning point of the fluctuation of the construction waste dumping body.

[0019] Then, in step S200, the convex hull points are determined for the discrete coordinate point set, and a convex hull polygon is generated.

[0020] According to one embodiment, first search and delete four vertices in the discrete coordinate point set to form a new point set P'. According to one embodiment, first traverse the point set P, and search for the four vertices of up, down, left and right in P, where the minimum x is Pxmin, the maximum y is Pymax, the maximum x is Pxmax, and the minimum y is Pymin. Then, connect the four vertices of up, down, left and right in clockwise or counterclockwise direction to form four edges, namely Pxmin-Pymax, Pymax-Pxmax, Pxmax-Pymin and Pymin-Pxmin, and delete the four vertices of up, down, left and right from the origin set P to form a new point set P'. Figure 2 A schematic diagram showing vertex search and deletion according to the method is shown.

[0021] According to one implementation, the four vertices of the top, bottom, left and right are first connected in sequence to form four edges, and then the convex hull points are found using a recursive method. For example, assuming that Pymin-Pxmax is the first edge and Pymin is the starting point of the first edge, when searching for the convex hull point on the left side of the Pymin-Pxmax edge (an example of the outer side), all the fragmentary measurement points on the left side of the Pymin-Pxmax edge are found from the new point set P', deleted from the point set P' and included in the set LeftPoints (an example of the outer point set), and the set LeftPoints is judged as follows:

[0022] a. If the outer point set is a non-empty set, then search for the point FP farthest from the edge in the outer point set, determine the farthest point FP as a convex hull point, and include the convex hull point FP in the convex hull point set C, delete the convex hull point FP from the new point set, and form a new edge by the farthest point FP and a vertex in the counterclockwise direction of the first edge; recursively search for a new convex hull point FP' on the outside of the new edge, include the new convex hull point found in the convex hull point set C, and delete the new convex hull point from the new point set;

[0023] b. If the outer point set is an empty set, the vertices in the clockwise direction of the first edge are included in the convex hull point set C;

[0024] Then, for the remaining edges of the four edges, the remaining convex hull points are found using the method in the above steps, and the convex hull points are classified into set C, the determined convex hull points are deleted from the new point set, and finally adjacent convex hull points are connected to generate a convex hull polygon.

[0025] Next, in step S300, an initial triangulated network is formed using the convex hull polygon.

[0026] According to one implementation, a discrete coordinate point is arbitrarily selected from the new point set as a point to be inserted, taken out from the new point set, connected to each convex hull point of the convex hull polygon to generate multiple triangles, and the generated triangles are added to a triangle list set T. Using the triangle list set T, the selected point to be inserted is connected to all the convex hull points to form an initial triangulated network.

[0027] According to another embodiment, a point P to be inserted is randomly selected from the point set P', connected to each convex hull point of the convex hull polygon to generate multiple triangles, the generated triangles are added to the triangle list set T, and then the triangle list set T is used to form a triangulated network. Figure 4 FIG. 2 shows a schematic flow chart of generating a triangulated network according to an embodiment of the present invention. Figure 4 As shown, according to one embodiment, first, in step S310, the convex hull point set C = {C 1 , C 2 , …, C m}The plane geometric center coordinates of the plane formed by:

[0028]

[0029] In the formula, (x C ,y C ) is composed of the convex hull point set C = {C 1 , C 2 , …, Cm}The geometric center coordinates of the plane formed by are the plane coordinates of the i-th convex hull point in the convex hull point set C, where i = 1, 2, …, m.

[0030] Then, in step S320, all discrete points in the new point set P' are traversed to calculate the distance from the plane geometric center (x C ,y C ) is the nearest point, which is the point to be inserted and is denoted by p x ,Right now:

[0031] p x =p′ i (2)

[0032] Where p′ i satisfy

[0033] Px is the point to be inserted each time selected from the P' point set, and i is the order of the point to be inserted.

[0034] Next, in step S330, p x The point to be inserted is taken from the point set P', connected to each convex hull point of the convex hull polygon, and multiple triangles are generated. The generated triangles are added to the triangle list set T.

[0035] Finally, in step S440, the above steps S320 and S330 are repeated, and then the triangle list set T is used to connect the selected points to be inserted with all the convex hull points to form a triangulated network.

[0036] According to yet another embodiment, the step of forming an initial triangulated network using convex hull polygons comprises:

[0037] The following formula is used to calculate the convex hull point set C = {C 1 , C 2 , …, C m}The three-dimensional geometric center coordinates of the space composed of:

[0038]

[0039] In the formula, (x C ,y C ,h C ) is composed of the convex hull point set C = {C 1 , C 2 , …, C m}The three-dimensional geometric center coordinates of the space composed of; is the three-dimensional coordinate of the i-th convex hull point in the convex hull point set C, where i = 1, 2, ..., m;

[0040] Traverse all discrete coordinate points in the new point set and calculate the distance from the three-dimensional geometric center (x C ,y C ,h C ) is the farthest point, which is the point to be inserted and is denoted by p x ,Right now:

[0041] p x =p′ i (4)

[0042] Where p′ i satisfy in, is a discrete coordinate point p′ in the new point set i The three-dimensional coordinates of p x The points to be inserted are taken from the new point set, connected to each convex hull point of the convex hull polygon, and multiple plane triangles are generated. The generated plane triangles are added to the triangle list set T, and the triangle list set T is used to form a triangulated network.

[0043] Then, in step S400, a triangulated network model is constructed for the initial triangulated network. According to one embodiment, the triangulated network model is constructed as follows:

[0044] a. Take a triangle ΔABC from the triangle list set T in order, and let its vertex be A(x 1 ,y 1 )、B(x 2 ,y 2 ) and C(x 3 ,y 3 ), and calculate the center O(x 0 ,y 0 ) and its radius r;

[0045] b. Determine the point to be inserted p x Is it inside the circumcircle of triangle ΔABC? If p x If the point is inside the circumcircle of triangle ΔABC, the triangle ΔABC is cut into the new triangle list T′;

[0046] c. Repeat step b until all triangles in the triangle list set T are traversed;

[0047] d. Find all common edges among the triangles in the new triangle list T′, delete these common edges, add the remaining edges to the edge list set S, and clear the new triangle list T′;

[0048] e. Align the endpoints of each edge in the edge list set S with the point to be inserted p xConnect the points to get multiple new triangles, add the new triangles to the new triangle list T′, and clear S.

[0049] f. Repeat the above steps until all points in the new point set P′ are traversed as points to be inserted, and the triangulated network model is formed by the new triangle list T′.

[0050] Next, in step S500, the volume of the stacking point is estimated.

[0051] According to one embodiment, the step of estimating the volume of the stacking point includes the step of calculating the equilibrium elevation, which can be determined as follows:

[0052] Assume that the triangle set K = {1, 2, ..., j, ..., m}, and triangle j is and The equilibrium height calculated based on the set K is:

[0053]

[0054] In the formula, h e is the equilibrium height; m is the number of triangles; is the average elevation of the three vertices of triangle j, s j is the plane area of ​​triangle j projected to the base, that is:

[0055]

[0056] According to one implementation, the volume estimation of the stacking point may be performed as follows:

[0057] Designed based on the benchmark elevation h 0 , the estimated volume of each triangle j is divided into the following cases:

[0058] (1) If the elevations of the three vertices are all less than h 0 , the volume estimation result for triangle j is in is the estimated value of the full fill volume; if the elevations of the three vertices are all greater than h 0 , the estimated volume of triangle j is in It is the estimated value of the total excavation volume;

[0059] (2) If the elevations of both vertices are less than h 0 The third vertex has a height greater than h 0 , and assume that L1 is the elevation of the edge AB equal to h 0 The critical point, L2 is the elevation on the AC side equal to h 0The critical points of L1 and L2 are obtained by linear interpolation.

[0060] The plane coordinates of L1 are calculated as follows:

[0061]

[0062] The plane coordinates of L2 are calculated as follows:

[0063]

[0064] And let the coordinates of L1 and L2 be expressed as (x L1 ,y L1 ,h 0 ) and (x L2 ,y L2 ,h 0 ), the estimated volume of triangle j is:

[0065]

[0066] On the contrary, if the elevations of both vertices are greater than h 0 The third vertex has a height less than h 0 , the estimated volume of triangle j is:

[0067]

[0068] Finally, the estimated volume values ​​of all triangles in set K are accumulated and summed to obtain the volume estimation result.

[0069] Figure 5 A schematic diagram of fill and cut is shown when the elevations of two vertices are both less than the base elevation and the elevation of one vertex is greater than the base elevation. Figure 6 A schematic diagram of fill and cut is shown when the elevations of two vertices are both greater than the base elevation and the elevation of one vertex is less than the base elevation.

[0070] According to formula (5) or formula (7), the cut or fill volume corresponding to all triangles in set T is calculated, and the total volume is obtained by accumulating.

[0071] Figure 7 It is a schematic block diagram showing a device for estimating the volume of a construction waste dumping site according to an embodiment of the present invention.

[0072] like Figure 7As shown, a device 10 for estimating the volume of a construction waste dumping site according to an embodiment of the present invention includes: a discrete coordinate point acquisition unit 100, for obtaining a discrete coordinate point set of a dumping body; a convex hull polygon generation unit 200, for determining convex hull points and generating convex hull polygons for the discrete coordinate point set; a triangulated mesh generation unit 300, for forming an initial triangulated mesh using the convex hull polygons; a triangulated mesh model construction unit 400, for constructing a triangulated mesh model for the initial triangulated mesh; and a stacking point volume estimation unit 500, for estimating the volume of the stacking point using the triangulated mesh model.

[0073] When each unit realizes its own function, the description of the method can be referred to above. For example, the triangulated network generation unit 300 uses the convex hull polygon to form an initial triangulated network using the steps and methods described above for step S300. The triangulated network model construction unit 400 uses the steps and methods described above for step S400 to construct a triangulated network model. The stacking point volume estimation unit 500 uses the methods and steps described above for step S500 to realize the stacking point volume estimation.

[0074] It is easy for a person skilled in the art to understand that the apparatus of the present invention can be understood by using the above description of the method.

[0075] Those skilled in the art will readily understand that the method of the present invention may also include other steps corresponding to the functions performed by the device of the present invention. The above steps may also be simplified.

[0076] The labels for units and steps in the present invention are only for convenience of explanation and do not represent the order of execution unless there is contrary description in the context.

[0077] Those skilled in the art should understand that the above-mentioned units can be implemented by software or special hardware, such as a field programmable gate array, a single-chip microcomputer, or a microchip, or can also be implemented by combining software with hardware.

[0078] The present invention also provides an electronic device, comprising: a processor; a memory for storing instructions executable by the processor; wherein the processor is configured to execute the instructions to implement the method of the present invention.

[0079] The present invention also relates to a computer software, which can implement the method of the present invention when executed by a computing device (such as a single chip microcomputer, a computer, a CPU, etc.).

[0080] The present invention also relates to a computer software storage device, such as a hard disk, a floppy disk, a flash memory, etc., wherein the computer software storage device stores the above-mentioned computer software.

[0081] The description of the method or step of the present invention can be used to understand the description of the unit or device, and the description of the unit or device can also be used to understand the method or step of the present invention. The above description is only illustrative and is not intended to limit the scope of protection of the present invention. Any changes and substitutions within the scope of the concept of the present invention are within the scope of protection of the present invention.

Claims

1. A method for estimating the volume of a construction waste dumping site, characterized in that: The following steps are involved: Obtain a discrete coordinate point set of the heap; For the discrete coordinate point set, determining the convex hull points and generating a convex hull polygon; Using the convex hull polygon, forming an initial triangulated network; For the initial triangulated network, build a triangulated network model, and The triangulated network model is used to estimate the volume of construction waste dumping points. The method is characterized in that the step of estimating the volume of the stacking point comprises: (1) Based on the design of the reference elevation as h0, for the volume estimation of each triangle j, if the elevations of the three vertices are all less than h0, the volume estimation result of triangle j is If the elevations of the three vertices are all greater than h0, the estimated volume of triangle j is Among them, triangle j is composed of and It consists of three vertices. is the estimated value of the full fill volume, is the estimated value of the total excavation volume, s j is the plane area of ​​triangle j projected onto the base, is the average elevation of the three vertices of triangle j, (2) If the elevations of two vertices are less than h0 and the elevation of the third vertex is greater than h0, and assuming that L1 is the critical point on the AB edge with an elevation equal to h0, and L2 is the critical point on the AC edge with an elevation equal to h0, the plane coordinates of L1 and L2 are obtained by linear interpolation. The plane coordinates of L1 are calculated as follows: The plane coordinates of L2 are calculated as follows: And let the coordinates of L1 and L2 be expressed as (x L1 ,y L1 ,h0) and (x L2 ,y L2 ,h0), the estimated volume of triangle j is: On the contrary, if the elevations of two vertices are greater than h0 and the elevation of the third vertex is less than h0, the estimated volume of triangle j is: Finally, all the estimated values ​​of the triangle volumes are accumulated to obtain the estimated volume of the construction waste dumping point.

2. The method for estimating the volume of a construction waste dump site according to claim 1, characterized in that: The discrete coordinate point set can be obtained by measuring with a total station, a GNSS RTK receiver, a three-dimensional laser scanner, etc., or any combination thereof.

3. The method for estimating the volume of construction waste dumping sites according to claim 1, characterized in that: The steps of determining the convex hull points and generating the convex hull polygon include: Step 1, searching and deleting the four upper, lower, left and right vertices in the discrete coordinate point set, thereby forming a new point set; Step 2, connecting the four vertices of top, bottom, left and right in clockwise or counterclockwise direction to form four edges; Step 3, finding the convex hull points outside the first edge, including finding all discrete coordinate points outside the edge from the new point set, copying them from the new point set and classifying them into the outer point set, and making the following judgment on the outer point set: a. If the outer point set is a non-empty set, then search for the point FP farthest from the edge in the outer point set, determine the farthest point FP as a convex hull point, and include the convex hull point FP in the convex hull point set C, delete the convex hull point FP from the new point set, and form a new edge by the farthest point FP and a vertex in the counterclockwise direction of the first edge; recursively search for a new convex hull point FP' on the outside of the new edge, include the new convex hull point found in the convex hull point set C, and delete the new convex hull point from the new point set; b. If the outer point set is an empty set, the vertices in the clockwise direction of the first edge are included in the convex hull point set C; Step 4: For the remaining edges of the four edges, use the method in step 3 to find the remaining convex hull points, and classify the convex hull points into set C, delete the determined convex hull points from the new point set, and finally connect adjacent convex hull points to generate a convex hull polygon.

4. The method for estimating the volume of a construction waste dump site according to claim 3, characterized in that: The steps of forming an initial triangulated network using the convex hull polygon include: A discrete coordinate point is randomly selected from the new point set as a point to be inserted, and is taken out from the new point set, connected to each convex hull point of the convex hull polygon to generate multiple triangles, and the generated triangles are added to the triangle list set T, and the triangle list set T is used to form an initial triangulated network.

5. The method for estimating the volume of construction waste dumping sites according to claim 3 is characterized in that: The steps of forming an initial triangulated network using the convex hull polygon include: The following formula is used to calculate the convex hull point set C = {C1, C2, ..., C m }The plane geometric center coordinates of the plane formed by: In the formula, (x C ,y C ) is composed of the convex hull point set C = {C1, C2, ..., C m } plane geometric center coordinates of the plane formed by (x Ci ,y Ci ) is the plane coordinate of the i-th convex hull point in the convex hull point set C, where i = 1, 2, …, m; Traverse all discrete coordinate points in the new point set and calculate the distance from the plane geometric center (x C ,y C ) is the nearest point, which is the point to be inserted and is denoted by p x ,Right now: p x =p i ' (2) Where p' i satisfy in, is a discrete coordinate point p' in the new point set i The plane coordinates of Next, p x The points to be inserted are taken from the new point set, connected to each convex hull point of the convex hull polygon, to generate multiple triangles, and the generated triangles are added to the triangle list set T, and the triangle list set T is used to form an initial triangulated network.

6. The method for estimating the volume of construction waste dumping sites according to claim 3, characterized in that: The steps of forming an initial triangulated network using the convex hull polygon include: The following formula is used to calculate the convex hull point set C = {C1, C2, ..., C m }The three-dimensional geometric center coordinates of the space composed of: In the formula, (x C ,y C ,h C ) is composed of the convex hull point set C = {C1, C2, ..., C m }The three-dimensional geometric center coordinates of the space composed of; is the three-dimensional coordinate of the i-th convex hull point in the convex hull point set C, where i = 1, 2, …, m; Traverse all discrete coordinate points in the new point set and calculate the distance from the three-dimensional geometric center (x C ,y C ,h C ) is the farthest point, which is the point to be inserted and is denoted by p x ,Right now: p x =p i ' (4) Where p' i satisfy in, is a discrete coordinate point p' in the new point set i The three-dimensional coordinates of p x The points to be inserted are taken from the new point set, connected to each convex hull point of the convex hull polygon, and multiple plane triangles are generated. The generated plane triangles are added to the triangle list set T, and the triangle list set T is used to form a triangulated network.

7. The method for estimating the volume of a construction waste dumping site according to any one of claims 4 to 6, characterized in that: The triangulated network model is constructed as follows: a. Take a triangle △ABC from the triangle list set T in order, set its vertices to A(x1,y1), B(x2,y2) and C(x3,y3), and calculate the center O(x0,y0) and radius r of the circumscribed circle of triangle △ABC; b. Determine the point to be inserted p x Is it inside the circumcircle of triangle △ABC? If p x If the point is inside the circumcircle of triangle △ABC, the triangle △ABC is cut into the new triangle list T'; c. Repeat step b until all triangles in the triangle list set T are traversed; d. Find all common edges in the triangles of the new triangle list T', delete these common edges, add the remaining edges to the edge list set S, and clear the new triangle list T'; e. Align the endpoints of each edge in the edge list set S with the point to be inserted p x Connect the points to get multiple new triangles, add the new triangles to the new triangle list T', and clear S; f. Repeat the above steps until all points in the new point set P' are traversed as points to be inserted, and the triangulated network model is formed by the new triangle list T'.

8. The method for estimating the volume of a construction waste dump site according to claim 1, characterized in that: The steps for estimating the volume of the stacking point include calculating the equilibrium elevation, The equilibrium height is determined as follows: Assume that the triangle set K = {1,2,…,j,…,m}, and the equilibrium elevation calculated based on the set K is: In the formula, h e is the equilibrium height; m is the number of triangles; Right now:

9. A device for estimating the volume of a construction waste dumping site, characterized in that: include: A discrete coordinate point acquisition unit, used to obtain a discrete coordinate point set of a pile body; A convex hull polygon generating unit, for the discrete coordinate point set, determines the convex hull points and generates a convex hull polygon; A triangulated network generation unit, using the convex hull polygon to form an initial triangulated network; A triangulated network model building unit builds a triangulated network model for the initial triangulated network; as well as The stacking point volume estimation unit uses the triangulated network model to estimate the volume of the construction waste stacking point. It is characterized in that the stacking point volume estimation unit performs the stacking point volume estimation as follows: (1) Based on the design of the reference elevation as h0, for the volume estimation of each triangle j, if the elevations of the three vertices are all less than h0, the volume estimation result of triangle j is in is the estimated value of the full fill volume; if the elevations of the three vertices are all greater than h0, the estimated value of the volume of triangle j is Among them, triangle j is composed of and It consists of three vertices. is the estimated value of the total excavation volume, s j is the plane area of ​​triangle j projected onto the base, is the average elevation of the three vertices of triangle j, (2) If the elevations of two vertices are less than h0 and the elevation of the third vertex is greater than h0, and assuming that L1 is the critical point on the AB edge with an elevation equal to h0, and L2 is the critical point on the AC edge with an elevation equal to h0, the plane coordinates of L1 and L2 are obtained by linear interpolation. The plane coordinates of L1 are calculated as follows: The plane coordinates of L2 are calculated as follows: And let the coordinates of L1 and L2 be expressed as (x L1 ,y L1 ,h0) and (x L2 ,y L2 ,h0), the estimated volume of triangle j is: On the contrary, if the elevations of two vertices are greater than h0 and the elevation of the third vertex is less than h0, the estimated volume of triangle j is: Finally, all the estimated values ​​of the triangle volumes are accumulated to obtain the estimated volume of the construction waste dumping point.

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