An algorithm for quickly and accurately calculating the similarity of sand and gravel spheres

Abstract

The present invention relates to an algorithm for quickly and accurately calculating the similarity of sand and gravel spheres. A three-dimensional scanned image of a single sand and gravel particle is obtained by scanning, and the volume of the sand and gravel particle is calculated. Any point in the three-dimensional scanned image is used as the initial center of the sphere, the maximum distance from the initial center of the sphere to the surface is used as the initial radius R0, and a circumscribed sphere with an initial radius of R0 is formed with the initial center of the sphere. The circumscribed sphere and the surface of the three-dimensional scanned image form a number of intersection points. The vectors from the initial center of the sphere to the intersection points of the circumscribed sphere and the surface are superimposed, and after normalization, a displacement vector is formed. The initial center of the sphere moves along the direction of the displacement vector to obtain a new center of the sphere to form a new circumscribed sphere, and the new circumscribed sphere and the surface form a number of intersection points. The iteration is repeated until the radius convergence speed of the new circumscribed sphere reaches a set value, and the sphere similarity of the sand and gravel particle is calculated with the current radius. The present invention can more accurately and quickly lock the radius of the minimum circumscribed sphere of the sand and gravel, and then more accurately calculate the sphericity of the sand and gravel particle.

Description

Technical Field

[0001] The present invention relates to the field of building materials, and particularly relates to an algorithm for quickly and accurately calculating the sphericity similarity of sand and gravel. Background Art

[0002] The particle shape of sand and gravel has a certain influence on the workability of concrete. Especially in view of the current shortage of natural sand and gravel resources and the large-scale application of manufactured sand and recycled aggregates, the particle shape of manufactured sand and recycled aggregates is more complex than that of natural sand and gravel. The evaluation of the particle shape of sand and gravel can be used as a basis for the selection of raw materials for high-performance concrete.

[0003] Sphericity similarity is one of the indicators used to measure the particle shape of sand and gravel. There are many definitions of sphericity similarity. One of them is defined according to the volume of sand and gravel and the volume of the minimum circumscribed sphere:

[0004] The existing method is to indirectly calculate the sphericity similarity by calculating the circularity using the maximum length of the projection as the diameter, which is a simplified calculation method based on this definition and has a large error, and the calculation result is not accurate enough. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides an algorithm for quickly and accurately calculating the sphericity similarity of sand and gravel, which calculates the sphericity similarity of sand and gravel particles by determining the radius of the minimum circumscribed sphere of the sand and gravel particles, and improves the calculation accuracy of the sphericity similarity.

[0006] The technical object of the present invention is achieved by the following technical solutions:

[0007] An algorithm for quickly and accurately calculating the sphericity similarity of sand and gravel, comprising the following steps:

[0008] S1. Scan the sand and gravel particles to obtain a three-dimensional scan image of a single sand and gravel particle. The three-dimensional scan image of the single sand and gravel particle is surrounded by a number of triangular elements;

[0009] S2. Calculate the volume G of the sand and gravel particles according to the three-dimensional coordinates of the triangular elements;

[0010] S3. Take any point in the three-dimensional scan image of the sand and gravel particles as the initial center of the sphere, and take the maximum distance from the initial center of the sphere to the surface of the three-dimensional scan image as the initial radius R 0 , and form a circumscribed sphere with the initial radius R 0 with the initial center of the sphere. The circumscribed sphere forms a number of intersection points with the surface of the three-dimensional scan image;

[0011] S4. The vectors from the initial center of the sphere to the intersection points of the circumscribed sphere and the surface of the three-dimensional scanned image are superimposed, and after normalization, a displacement vector is formed. The initial center of the sphere moves along the direction of the displacement vector to obtain a new center of the sphere, and the maximum distance from the new center of the sphere to the surface of the three-dimensional scanned image is used as the new radius R'. 0 , and a new circumscribed sphere with a radius of R' is formed with the new center of the sphere. 0 The new circumscribed sphere and the surface of the three-dimensional scanned image form several intersection points.

[0012] S5. Repeat step S4 for iteration until the convergence rate of the radius R' of the new circumscribed sphere 0 reaches the set value. When the convergence rate of the radius R' of the circumscribed sphere 0 reaches the set value, calculate the spherical similarity Y of the sand and gravel particles.

[0013] Furthermore, in step S3, the maximum distance from the three-dimensional coordinates of the initial center of the sphere to the surface of the three-dimensional scanned image is used as the initial radius R. 0 .

[0014] Furthermore, in step S3, when calculating the initial radius R 0 , calculate the average value of the extreme values of the coordinates of the surface of the three-dimensional scanned image as the coordinates of the initial center of the sphere.

[0015] Furthermore, step S1 also includes cleaning and drying the sand and gravel particles, and after cleaning and drying are completed, scan the sand and gravel particles to obtain the three-dimensional scanned image of a single sand and gravel particle.

[0016] Furthermore, in step S1, a three-dimensional laser scanner is used to scan the sand and gravel particles.

[0017] Furthermore, in step S4, the displacement vector where X 0 is the abscissa of the initial center of the sphere, Y 0 is the ordinate of the initial center of the sphere, Z 0 is the vertical coordinate of the initial center of the sphere, X i ' is the abscissa of the i-th intersection point of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image, Y i ' is the ordinate of the i-th intersection point of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image, Z i ' is the vertical coordinate of the i-th intersection point of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image, and k is the number of intersection points of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image.

[0018] Furthermore, the distance from the initial center of the sphere to the surface of the three-dimensional scanned image in the opposite direction of the displacement vector is L, and the initial center of the sphere moves a distance of d along the direction of the displacement vector. where the initial value of n is 1, and if R’ 0 compared with the previous R’ 0 increases, the value of n is incremented by 1, and the result of the previous iteration is maintained.

[0019] Furthermore, ∑d(A 0 A 1 A 2 A 3 ) represents the sum of the positive determinants taken from each triangle on each face of the three-dimensional scanned image.

[0020] Compared with the prior art, the beneficial effect of the present invention is that the algorithm for quickly and accurately calculating the sphericity similarity of sand and gravel has high accuracy and a fast convergence rate. It can relatively accurately and quickly lock and obtain the radius of the minimum circumscribed sphere of sand and gravel particles. By calculating the sphericity similarity of sand and gravel particles through this radius, a relatively accurate sphericity similarity of sand and gravel particles can be calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a three-dimensional image of the scanned sand and gravel particles in the present invention.

[0022] Figure 2 is a schematic diagram of the process of the circumscribed sphere radius R 0 of sand and gravel in the present invention converging with the number of iterations.

[0023] Figure 3 is a schematic diagram of the calculation result of the minimum circumscribed sphere of sand and gravel in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] The technical solution of the present invention will be further described below in conjunction with the specific embodiments:

[0025] An algorithm for quickly and accurately calculating the sphericity similarity of sand and gravel changes the original method of calculating the sphericity similarity using the maximum particle size length as the diameter, and relatively accurately locks the minimum circumscribed sphere closest to the sand and gravel, thereby obtaining the best calculation result of the sphericity similarity. This method can be used for calculating the sphericity similarity of natural sand and gravel, manufactured sand, and recycled aggregates. The method of the present invention includes the following steps:

[0026] S1. To reduce the impact on the calculation result, before scanning, the sand and gravel particles are cleaned and dried. After cleaning and drying, the sand and gravel particles are scanned by a three-dimensional laser scanner to obtain a three-dimensional scanned image of a single sand and gravel particle. The three-dimensional scanned image of a single sand and gravel particle is surrounded by a number of triangular units.

[0027] S2. Process the scanned 3D image through MATLAB programming. Call the MATLAB function stlRead to process the information data of the 3D image of sand and gravel particles to obtain (v, f, n); calculate the volume G of the sand and gravel particles according to the obtained (v, f, n).

[0028] ∑d(A 0 A 1 A 2 A 3 ) represents the sum of the positive determinants of each triangle element on each surface of the 3D scanned image. (The volume of a polyhedron in 3D space is equal to one-sixth of the sum of the positive determinants of each polygon on all its surfaces. "A Coordinate Calculation Algorithm for the Volume of Any Polyhedron in 3D Space", Wei Jin, Journal of Huzhou Teachers College (Natural Science), June 1997, Vol. 19, No. 5.)

[0029] S3. Take any point inside the 3D scanned image of the sand and gravel particles as the initial center of the sphere, and take the maximum distance from the 3D coordinates of the initial center of the sphere to the surface of the 3D scanned image as the initial radius R 0 , and the coordinates of the initial center of the sphere are represented as (X 0 , Y 0 , Z 0 ). Form a circumscribed sphere with the initial center of the sphere and an initial radius of R 0 . The circumscribed sphere forms k intersection points with the surface of the 3D scanned image, and the coordinates of the intersection points are represented as (X i ’, Y i ’, Z i ’), where i = 1, 2,... k.

[0030] As an optimal solution, when calculating the initial radius R 0 , calculate the initial radius R 0 with the average value of the extreme values of the coordinates of the surface of the 3D scanned image as the coordinates of the initial center of the sphere. For example, if the maximum value of the abscissa of the surface of the 3D scanned image is X max , the minimum value of the abscissa is X min , the maximum value of the ordinate is Y max , the minimum value of the ordinate is Y min , the maximum value of the vertical coordinate is Z max , and the minimum value of the vertical coordinate is Z min , where

[0031] S4. Superimpose the vectors from the initial center of the sphere to the intersection points of the circumscribed sphere and the surface of the 3D scanned image, and after unitization, form a displacement vector. The initial center of the sphere moves along the direction of the displacement vector to obtain a new center of the sphere.

[0032] Calculate the displacement vector

[0033] Among them, X 0 is the abscissa of the initial center of the sphere, Y 0 is the ordinate of the initial center of the sphere, Z 0 is the vertical coordinate of the initial center of the sphere, X i ’ is the abscissa of the i-th intersection point of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image, Y i ’ is the ordinate of the i-th intersection point of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image, Z i ’ is the vertical coordinate of the i-th intersection point of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image, and k is the number of intersection points of the circumscribed sphere formed by the initial center of the sphere and the surface of the three-dimensional scanned image.

[0034] The initial center of the sphere moves along the direction of the displacement vector to obtain a new center of the sphere, and the maximum distance from the new center of the sphere to the surface of the three-dimensional scanned image is used as the new radius R’ 0 , and a new circumscribed sphere with a radius of R’ 0 is formed with the new center of the sphere, and several intersection points are formed between the new circumscribed sphere and the surface of the three-dimensional scanned image. The distance from the initial center of the sphere to the surface of the three-dimensional scanned image in the opposite direction of the displacement vector is L, and the initial center of the sphere moves a distance of d along the direction of the displacement vector. Among them, the initial value of n is 1, and the value of n changes with the change of R’ 0 . If R’ 0 increases compared with the previous R’ 0 , the value of n is incremented by 1, that is, n = n + 1, and then the result of the previous iteration is selected for iterative calculation; if R’ 0 decreases or remains unchanged compared with the previous R’ 0 , then n remains unchanged, and the iterative calculation is continued with the current result.

[0035] S5. Repeat step S4 for iteration until the radius R’ 0 of the new circumscribed sphere converges to the set value. As Figure 2 shown, when the convergence speed reaches a certain value, the change of the circumscribed sphere radius tends to be stable. For example, when the change range of R’ 0 in the previous 10 iterations before the current iteration and R’ 0 in the current 100th iteration is less than 0.001% compared with each other, it can be considered that R’ 0 at this time is the circumscribed sphere radius closest to the actual value. As Figure 3 shown, the spherical similarity Y of the sand and gravel particles is calculated with R’ 0 as the circumscribed sphere radius closest to the actual value.

[0036] This embodiment is only a further explanation of the present invention and not a limitation thereof. After reading this specification, those skilled in the art may make non-creative modifications to this embodiment as needed, but as long as it is within the scope of the claims of the present invention, it is protected by the patent law.

Claims

1. An algorithm for quickly and accurately calculating the similarity of sand and gravel spheres, Characterized in that, It includes the following steps: S1. Scan the sand and gravel particles to obtain a three-dimensional scan image of a single sand and gravel particle. The three-dimensional scan image of a single sand and gravel particle is surrounded by several triangular units; S2. Calculate the volume G of the sand and gravel particle according to the three-dimensional coordinates of the triangular unit; S3. Take any point in the three-dimensional scanned image of the sand and gravel particles as the initial center of the sphere, and take the maximum distance from the initial center of the sphere to the surface of the three-dimensional scanned image as the initial radius R 0 , and form an circumscribed sphere with the initial center of the sphere and an initial radius of R 0 . The circumscribed sphere and the surface of the three-dimensional scanned image form a number of intersection points; S4. The vectors from the initial center of the sphere to the intersection points of the circumscribed sphere and the surface of the three-dimensional scanned image are superimposed. After normalization, a displacement vector is formed. The initial center of the sphere is moved along the direction of the displacement vector to obtain a new center of the sphere. The maximum distance from the new center of the sphere to the surface of the three-dimensional scanned image is used as the new radius R. , 0 , and a new circumscribed sphere with a radius of R is formed with the new center of the sphere. , 0 The new circumscribed sphere and the surface of the three-dimensional scanned image form several intersection points. S5. Repeat step S4 for iteration until the radius R of the new circumscribed sphere , 0 converges to the set value, and the radius R of the circumscribed sphere , 0 When the convergence rate reaches the set value, calculate the sphere similarity Y of the sand and gravel particles, 2. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 1, Characterized in that, In S3, the maximum distance from the three-dimensional coordinates of the initial center of the sphere to the surface of the three-dimensional scanned image is used as the initial radius R 0 .

3. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 2, Characterized in that, In the step S3, calculate the initial radius R 0 When calculating, the average value of the extreme values of the coordinates on the surface of the three-dimensional scanned image is used as the initial spherical center coordinates.

4. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 1, Characterized in that, In the step S1, it also includes cleaning and drying the sand and gravel particles, and after the cleaning and drying are completed, scanning the sand and gravel particles to obtain a three-dimensional scan image of a single sand and gravel particle.

5. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 1, Characterized in that, In the step S1, a three-dimensional laser scanner is used to scan the sand and gravel particles.

6. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 1, Characterized in that, In the said step S4, the displacement vector , where X 0 is the abscissa of the initial sphere center, Y 0 is the ordinate of the initial sphere center, Z 0 is the vertical coordinate of the initial sphere center, X i , is the abscissa of the i-th intersection point of the circumscribed sphere formed by the initial sphere center and the surface of the three-dimensional scanned image, Y i , is the ordinate of the i-th intersection point of the circumscribed sphere formed by the initial sphere center and the surface of the three-dimensional scanned image, Z i , is the vertical coordinate of the i-th intersection point of the circumscribed sphere formed by the initial sphere center and the surface of the three-dimensional scanned image, and k is the number of intersection points of the circumscribed sphere formed by the initial sphere center and the surface of the three-dimensional scanned image.

7. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 1, Characterized in that, The distance from the initial sphere center to the surface of the three-dimensional scanned image in the opposite direction of the displacement vector is L, and the initial sphere center moves a distance of d along the displacement vector direction. , where the initial value of n is 1. If R , 0 compared with the previous R , 0 increases, the value of n is incremented by 1, and the result of the previous iteration is maintained.

8. The algorithm for quickly and accurately calculating the similarity of sand and gravel spheres according to claim 1, Characterized in that, ∑d(A 0 A 1 A 2 A 3 ) represents the sum of the positive determinants taken for each triangle on each face of the three-dimensional scanned image.

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