CN115690316A - Aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelet - Google Patents
Aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelet Download PDFInfo
- Publication number
- CN115690316A CN115690316A CN202211358102.1A CN202211358102A CN115690316A CN 115690316 A CN115690316 A CN 115690316A CN 202211358102 A CN202211358102 A CN 202211358102A CN 115690316 A CN115690316 A CN 115690316A
- Authority
- CN
- China
- Prior art keywords
- spherical
- aggregate
- point cloud
- dimensional
- cloud data
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Landscapes
- Processing Or Creating Images (AREA)
Abstract
The invention discloses an aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelets, which comprises the following steps: 1, acquiring a three-dimensional point cloud coordinate of the surface of an aggregate by using a three-dimensional scanner; 2, simplifying the data of the original point cloud; 3, converting the simplified point cloud data from a Cartesian coordinate system to a spherical coordinate system; discretizing the position and the scale of the spherical DOG wavelet based on the spherical subdivision to construct a spherical DOG wavelet frame; 5, solving spherical DOG wavelet coefficients by adopting a regularization method; 6, obtaining an aggregate surface function by using a spherical DOG wavelet series; and 7, randomly changing the amplitude of the spherical DOG wavelet coefficient to randomly generate aggregate particles with different shapes. According to the invention, a large number of discrete coordinate points on the surface of the aggregate are converted into a small number of spherical DOG wavelet coefficients so as to reduce the storage space, and a continuous surface function of the aggregate can be obtained according to the spherical DOG wavelet coefficients, so that the calculation of three-dimensional morphology parameters of the aggregate and the interference judgment of putting into a geometric model are facilitated.
Description
Technical Field
The invention belongs to the technical field of aggregate three-dimensional shape reconstruction, and particularly relates to an aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelets.
Background
The aggregate accounts for 50-70% of the concrete, and has important influence on the rheological property, crack development, mechanical property and the like of the concrete. For a long time, researchers have paid more attention to the influence of aggregate particle size and gradation on concrete performance, and have paid less attention to the influence of particle shape on concrete performance. With the recent application of high-strength and high-performance concrete in a large quantity, the influence of the aggregate particle shape on various performances of the concrete is gradually paid attention by students.
Early researches on aggregate particle shapes are usually limited to a two-dimensional layer, a digital camera, a microscope and other means are adopted to shoot an aggregate projection drawing, indexes such as edge angles, roundness, roughness and the like of aggregates are calculated based on a digital image means and a Fourier reconstruction method, and the indexes are adopted to qualitatively explain the change of concrete performance. However, the two-dimensional profile of the aggregate depends on the shooting direction, so that the three-dimensional aggregate morphology can not be accurately represented due to high randomness. In recent years, with the development of CT technology and three-dimensional scanning technology, it has become possible to directly acquire point cloud coordinate information of a three-dimensional aggregate surface. In view of the fact that the original measurement data of the surface of the aggregate is huge and difficult to be directly used for calculating morphology parameters, the spherical harmonic basis function generated by expanding a Fourier function to a spherical surface is widely used for processing three-dimensional original measurement data of the aggregate, and results show that after reconstruction through a spherical harmonic reconstruction method, hundreds of spherical harmonic coefficients can be used for accurately reconstructing the original morphology of the aggregate, the error is not more than 1%, and the storage capacity compression ratio can reach 1%.
However, due to the global support of the spherical harmonic basis function, when a polygonal corner particle shape is reconstructed by using a finite term spherical harmonic series, a serious truncation error is introduced due to a ringing effect as the spherical harmonic reconstruction order increases. Therefore, in consideration of the current situation of wide application of the mechanism aggregate with more edges and sharp angles due to the shortage of natural aggregate in recent years, it is necessary to find a tightly supported basis function to realize the reconstruction of the multi-edge particle so as to avoid the existence of truncation errors. Until now, no method for reconstructing the shape of three-dimensional aggregate particles based on a tightly-supported wavelet function exists.
Disclosure of Invention
In order to overcome the defects in the prior art, the aggregate three-dimensional reconstruction and random generation method based on the spherical DOG wavelet is provided, so that the multi-edge-angle aggregate particle three-dimensional morphology can be reconstructed more accurately by adopting fewer coefficients, and therefore, the morphology parameter calculation and the interference judgment of putting in a geometric model are carried out.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a method for reconstructing and randomly generating three-dimensional shape of aggregate based on spherical DOG wavelet, which is characterized by comprising the following steps:
step 1: acquiring original three-dimensional point cloud data of the surface of the aggregate by using a three-dimensional scanner;
step 2: simplifying the original three-dimensional point cloud data by taking the volume error VE and the surface area error SE as indexes to obtain simplified three-dimensional point cloud data;
and 3, step 3: converting the simplified three-dimensional point cloud data defined under the three-dimensional Cartesian coordinate system into a spherical coordinate system to obtain the simplified three-dimensional point cloud data defined under the spherical coordinate system;
and 4, step 4: discretizing the position and scale of a continuous spherical DOG wavelet function based on a spherical subdivision method of a regular icosahedron, and constructing a spherical DOG wavelet frame F;
and 5: decomposing the simplified three-dimensional point cloud data defined in a spherical coordinate system by adopting a frame function in a spherical DOG wavelet frame F, and solving a spherical DOG wavelet coefficient { a ] by utilizing a Tikhonov regularization method k I k =1,2, …, M }; wherein, a k Representing a kth spherical DOG wavelet expansion coefficient to be determined; m is the number of frame functions in the spherical DOG wavelet frame F;
step 6: according to spherical DOG wavelet coefficient { a k I k =1,2, …, M } and frame function
Obtaining approximate surface function of aggregate three-dimensional appearance
Approximating a surface function from the aggregate
Calculating the radius value of the aggregate along each angle to obtain coordinate data of a large number of points on the surface of the aggregate under a spherical coordinate system, converting the coordinate data into coordinate data under a three-dimensional Cartesian coordinate system, and further adopting a Delaunay triangulation method to realize visualization; wherein the content of the first and second substances,
representing the kth frame function in a spherical DOG wavelet frame F; theta represents a polar angle under the spherical coordinate system, represents an included angle between a connecting line of any surface point and an origin and the positive direction of the z axis,
the azimuth angle under the spherical coordinate system is represented, and the included angle between the connecting line of any surface point and the original point and the positive direction of the x axis is represented;
and 7: and randomly generating aggregate particles with different appearances according to the step 6 by randomly changing the amplitude of the partial spherical DOG wavelet coefficient.
The method for reconstructing and randomly generating the three-dimensional shape of the aggregate based on the spherical DOG wavelet is also characterized in that the step 2 specifically comprises the following steps:
step 2.1: based on a Delaunay triangulation principle, carrying out triangulation on original three-dimensional point cloud data so as to convert discrete point clouds in the original three-dimensional point cloud data into a triangular surface patch form, counting the sum of the areas of all triangular surface patches to be used as the real surface area of aggregate, respectively connecting three vertexes of all triangular surface patches with the center of the aggregate to form all tetrahedrons, and counting the sum of the volumes of all the tetrahedrons to be used as the real volume of the aggregate;
step 2.2: randomly deleting part of points in the original three-dimensional point cloud data according to a proportion, thereby simplifying the original three-dimensional point cloud data to obtain three-dimensional point cloud data under the current simplification degree;
step 2.3: performing Delaunay triangulation on the three-dimensional point cloud data under the current simplification, counting the sum of the areas of the triangular surface patches as the aggregate surface area under the current simplification degree, respectively connecting the three vertexes of the triangular surface patches and the aggregate center to form tetrahedrons, counting the sum of the volumes of all the tetrahedrons, and taking the sum as the aggregate volume under the current simplification degree;
step 2.4: respectively comparing the volume and the surface area of the aggregate under the current simplification degree with the real values obtained in the step 2.1 to obtain a volume error VE and a surface area error SE under the current simplification degree;
step 2.5: and if the volume error VE and the surface area error SE of the current aggregate meet the limit value requirement, increasing the proportion, returning to the step 2.2, and otherwise, taking the three-dimensional point cloud data obtained under the previous simplification degree as the finally simplified three-dimensional point cloud data.
The step 4 specifically includes:
step 4.1: after the center of the regular icosahedron is moved to the center of the unit sphere, each vertex { n ] of the regular icosahedron is moved j I j =1,2,3, …,12} is projected onto a unit sphere, and the resulting spherical grid is denoted as G 0 (ii) a Wherein n is j The jth vertex representing a regular icosahedron;
step 4.2: finding the middle point of each triangle side in the icosahedron, and connecting the sides of the triangleThe points thus divide a triangle into four small triangles, the vertices m of each small triangle c I c =1,2,3, …,40} is projected onto a unit sphere, and the resulting spherical grid is denoted as G 1 (ii) a Wherein m is c Representing the vertices of each small triangle;
step 4.3: according to the process of repeating the step 4.2, the spherical grids { G with different subdivision levels are obtained q | q =0,1,2, …, K }; wherein K is the maximum spherical subdivision number; g q Representing the spherical grid obtained under the q-th subdivision level;
step 4.4: respectively divide the spherical grids of different subdivision levels { G q Taking grid points in | q =0,1,2, …, K } as the central pole of the spherical DOG wavelet under the corresponding scale, and obtaining the spherical DOG wavelet with the central pole at X according to formula (1):
in the formula (1), the reaction mixture is,
is the central pole position of spherical DOG wavelet, where θ 0 The polar angle of the central pole is shown,
represents the azimuth of the central pole; gamma is the angle between the central pole and an arbitrary point X' on the sphere, wherein,
theta' represents the polar angle of any point on the sphere,
representing the azimuth of any point on the sphere; a =2 -q Q is a scale and is consistent with the spherical subdivision level; alpha is a constant value of the shape of the adjustment function, and alpha>1；λ a (γ) is a function related to γ and a and is derived from equation (2):
step 4.5: selecting the maximum spherical section level q for the reconstruction of the three-dimensional shape of the aggregate max And obtaining a spherical DOG wavelet frame F for reconstructing the three-dimensional shape of the aggregate by using the formula (3):
in the formula (3), X (q,j) Is a spherical grid G q The jth lattice point in (a); a =2 -q 。
The step 5 specifically includes:
step 5.1: the frame function in the spherical DOG frame F is rewritten in a certain order to the form of equation (4):
in the formula (4), M is the total number of functions in the spherical DOG wavelet frame F;
is the kth spherical DOG wavelet frame function;
step 5.2: converting the simplified three-dimensional point cloud data defined in the spherical coordinate system obtained in the step 3 into a linear combination of a frame function, thereby obtaining an observation equation shown as a formula (5):
in the formula (5), N is the number of points of the three-dimensional point cloud data after final simplification;
is the measured value at the nth point cloud data;
the calculated value of the kth frame function in the spherical DOG wavelet frame F at the nth point cloud data is obtained;
step 5.3: rewriting the observation equation of equation (5) into a matrix form as equation (6):
r＝Gm (6)
in the formula (6), G is a matrix of equation coefficients, and
r is the measured data matrix, and
m is a spherical DOG wavelet coefficient matrix, m = [ a = 1 ,a 2 ,…,a M ] T ；
Step 5.4: obtaining a coefficient matrix m consisting of spherical DOG wavelet coefficients by using the formula (7):
m＝(G T C D -1 G+ρ 2 R) -1 G T C D -1 r (7)
in the formula (7), C D The method is characterized in that the method is a covariance matrix of three-dimensional point cloud data after the aggregate surface is simplified; r is a regularization matrix with dimension M multiplied by M, and the element R of the k row and the k' column in R is obtained by formula (8) kk′ (ii) a Rho is a regularization parameter;
in the formula (8), S represents a spherical surface; Ω represents an integral infinitesimal.
The step 7 specifically includes:
step 7.1: randomly changing the amplitude of part of coefficients in the coefficient matrix m to obtain a randomly generated coefficient matrix m 1 ；
Step 7.2: according to a randomly generated coefficient matrix m 1 And calculating the corresponding approximate surface function, thereby obtaining the randomly generated aggregate according to the corresponding approximate surface function.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, a three-dimensional scanner is adopted to obtain original three-dimensional point cloud data of the aggregate surface, and the discrete three-dimensional point cloud data is reconstructed based on a DOG wavelet frame of a tightly-supported spherical surface, so that a continuous approximate surface function of the aggregate is obtained, the calculation of morphological parameters such as the volume, the surface area and the curvature of the aggregate is greatly facilitated, and the particle interference judgment during the construction of a concrete mesoscopic model is facilitated.
2. According to the invention, the storage mode of the original three-dimensional point cloud data is converted into the storage mode of the spherical DOG wavelet coefficient, and as the spherical DOG wavelet coefficient has the characteristic that the energy is concentrated to the low frequency, the main morphology information of the original aggregate can be reserved by adopting less wavelet coefficients, so that the internal memory occupation of the aggregate information is favorably reduced.
3. Compared with the existing spherical harmonic series reconstruction method, due to the tight support characteristic of the spherical DOG wavelet function, the method can effectively avoid truncation errors introduced when the spherical harmonic basis function of the global support is adopted to reconstruct the polygonal particles, can realize shape modeling with local variation, and can be used for random modeling of the shape of the recycled aggregate particles by considering the characteristic that residual mortar exists only in local positions of the recycled aggregate.
Drawings
FIG. 1 is a flow chart of an aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelets according to the present invention;
FIG. 2 is a schematic view of the three-dimensional scanner of the present invention acquiring an original surface of an aggregate;
FIG. 3 is a schematic illustration of the calculation of aggregate volume and surface area based on point cloud data in accordance with the present invention;
FIG. 4 is a schematic diagram of the surface of the aggregate when the point cloud data of the present invention are reduced to different amounts;
FIG. 5 is a schematic diagram of a spherical subdivision for discretizing spherical DOG wavelet dimensions and locations in accordance with the present invention;
FIG. 6 is a graph of OCV regularization parameter calculation results when solving spherical DOG wavelet expansion coefficients;
FIG. 7 is a schematic diagram of the machine-made sand aggregate of the present invention after reconstruction by different spherical DOG wavelet frames;
FIG. 8 is a schematic diagram of a randomly generated new aggregate surface with randomly varied spherical wavelet coefficients according to the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, a method for reconstructing and randomly generating a three-dimensional shape of an aggregate based on a spherical DOG wavelet is to convert a large number of discrete coordinate points on the surface of the aggregate into a small number of spherical DOG wavelet coefficients to reduce a storage space, and obtain a continuous surface function of the aggregate according to the spherical DOG wavelet coefficients, thereby facilitating calculation of three-dimensional shape parameters of the aggregate and interference determination of a put-in geometric model. Specifically, the method comprises the following steps:
step 1: acquiring original three-dimensional point cloud data of the surface of the aggregate by using a three-dimensional scanner;
step 2: simplifying the original three-dimensional point cloud data by taking the volume error VE and the surface area error SE as indexes to obtain simplified three-dimensional point cloud data;
step 2.1: based on a Delaunay triangulation principle, carrying out triangulation on original three-dimensional point cloud data so as to convert discrete point clouds in the original three-dimensional point cloud data into a triangular surface patch form, counting the sum of the areas of all triangular surface patches to be used as the real surface area of aggregate, respectively connecting three vertexes of all triangular surface patches with the center of the aggregate to form all tetrahedrons, and counting the sum of the volumes of all the tetrahedrons to be used as the real volume of the aggregate; wherein the aggregate surface area S is calculated based on three-dimensional point cloud data r And volume V r The methods (1) and (2) are shown in the following formula.
In the formula (1), S is the surface area of sand grains; s i Is the ith triangleArea of the dough sheet; p is a radical of 1 ，p 2 And p 3 Representing the three vertices of each triangular patch, respectively.
In the formula (2), V is the volume of the aggregate; v i Volume of the ith tetrahedron; o represents the center of the sand.
Step 2.2: randomly deleting part of points in the original three-dimensional point cloud data according to a proportion, thereby simplifying the original three-dimensional point cloud data to obtain three-dimensional point cloud data under the current simplification degree;
step 2.3: performing Delaunay triangulation on the three-dimensional point cloud data under the current simplification, counting the sum of the areas of the triangular surface patches as the aggregate surface area under the current simplification degree, respectively connecting the three vertexes of the triangular surface patches and the aggregate center to form tetrahedrons, counting the sum of the volumes of all the tetrahedrons, and taking the sum as the aggregate volume under the current simplification degree;
step 2.4: respectively comparing the volume and the surface area of the aggregate under the current simplification degree with the real values obtained in the step 2.1 to obtain a volume error VE and a surface area error SE under the current simplification degree;
step 2.5: if the volume error VE and the surface area error SE of the current aggregate meet the limit value requirement, the proportion is increased, the step 2.2 is returned, and otherwise, the three-dimensional point cloud data obtained under the previous simplification degree is used as the three-dimensional point cloud data after final simplification.
And step 3: converting the three-dimensional point cloud data defined under the three-dimensional Cartesian coordinate system after simplification into a spherical coordinate system according to the formula (3) to the formula (4), and obtaining the simplified three-dimensional point cloud data defined under the spherical coordinate system;
in the formula (3), x i ，y i And z i Representing three-dimensional point cloud data defined in a three-dimensional Cartesian coordinate system after the ith simplification; x is the number of c ，y c And z c Representing the coordinate of the central point of the aggregate in a three-dimensional Cartesian coordinate system, and solving according to the formula (4); theta i Is the included angle between the line connecting the ith point and the central point in the point cloud on the surface of the aggregate and the positive direction of the z axis, namely the zenith angle,
the included angle between the line connecting the ith point and the central point in the point cloud on the surface of the aggregate and the positive direction of the x axis, namely the azimuth angle, wherein the anticlockwise rotation is positive, the clockwise rotation is negative, and r is i The radial distance between the ith point and the central point in the point cloud on the surface of the aggregate.
In the formula (1), H is the total number of the point clouds on the surface of the aggregate.
And 4, step 4: considering that a continuous spherical DOG wavelet function is difficult to be applied, firstly discretizing the position and the scale of the continuous spherical DOG wavelet function based on a spherical subdivision method of a regular icosahedron, and constructing a spherical DOG wavelet frame F;
step 4.1: after the center of the regular icosahedron is moved to the center of the unit sphere, each vertex { n ] of the regular icosahedron is moved j I j =1,2,3, …,12} is projected onto a unit sphere, and the resulting spherical grid is denoted as G 0 (ii) a Wherein n is j Represents the jth vertex of a regular icosahedron;
step 4.2: finding the middle point of each triangle side in the icosahedron, and connecting the middle points of the triangle sides to divide a triangle into four small trianglesShape, the vertex { m ] of each small triangle c I c =1,2,3, …,40} is projected onto a unit sphere, and the resulting spherical grid is denoted as G 1 (ii) a Wherein m is c Representing the vertices of each small triangle;
step 4.3: obtaining the spherical grids of different subdivision levels according to the process of repeating the step 4.2 q | q =0,1,2, …, K }; wherein K is the maximum spherical subdivision number; g q Representing the spherical grid obtained under the qth subdivision level;
step 4.4: respectively divide the spherical grids of different subdivision levels { G q The grid point in | q =0,1,2, …, K } is used as the central pole of the spherical DOG wavelet under the corresponding scale, and the spherical DOG wavelet with the central pole at X is obtained according to equation (5):
in the formula (5), the reaction mixture is,
is the central pole position of spherical DOG wavelet, where θ 0 The polar angle of the central pole is shown,
representing the azimuth of the central pole; gamma is the angle between the central pole and the point X' on the sphere, where,
theta' represents the polar angle of any point on the sphere,
representing the azimuth angle of any point on the sphere; a =2 -q Q is a scale and is consistent with the spherical subdivision level; alpha is a constant value of the shape of the adjustment function, and alpha>1；λ a (γ) is a function related to γ and a, and is obtained from equation (6):
step 4.5: selecting the maximum spherical section level q for the reconstruction of the three-dimensional shape of the aggregate max And obtaining a spherical DOG wavelet frame F for reconstructing the three-dimensional shape of the aggregate by using the formula (3):
in the formula (7), X (q,j) Is a spherical grid G q The jth lattice point in (a); a =2 -q ；q max And the maximum spherical section level used for the reconstruction of the three-dimensional shape of the aggregate is shown.
And 5: decomposing the simplified three-dimensional point cloud data defined in the spherical coordinate system by adopting the first M frame functions in the spherical DOG wavelet frame F, and solving the spherical DOG wavelet coefficient { a ] by utilizing a Tikhonov regularization method k I k =1,2, …, M }; wherein, a k Representing a kth spherical DOG wavelet expansion coefficient to be determined; m is the number of frame functions in the spherical DOG wavelet frame F;
step 5.1: the frame function in the spherical DOG frame F is rewritten in a certain order to the form of equation (8):
in the formula (8), M is the total number of functions in the spherical DOG wavelet frame F;
is the kth spherical DOG wavelet frame function;
step 5.2: converting the simplified three-dimensional point cloud data defined in the spherical coordinate system obtained in the step 3 into a linear combination of a frame function, thereby obtaining an observation equation shown as a formula (9):
in the formula (9), N is the number of points of the three-dimensional point cloud data after final simplification;
is the measured value at the nth point cloud data;
the calculated value of the kth frame function in the spherical DOG wavelet frame F at the nth point cloud data is obtained;
step 5.3: the observation equation of equation (9) is rewritten as a matrix form as equation (10):
r＝Gm (10)
in equation (10), G is the equation coefficient matrix:
r is the measured data matrix:
m is a spherical DOG wavelet coefficient matrix, m = [ a = 1 ,a 2 ,…,a M ] T ；
Step 5.4: solving the spherical DOG wavelet coefficient a due to the fact that the spherical DOG wavelet obtained through position and scale discretization has larger redundancy k (k =1,2,3, …) may lead to non-unique solutions, i.e., ill-conditioned problems. Therefore, a Tikhonov regularization method is adopted, a regularization matrix and regularization parameters are introduced to constrain the solution, and a coefficient matrix m composed of spherical DOG wavelet coefficients is further obtained by using a formula (11):
m＝(G T C D -1 G+ρ 2 R) -1 G T C D -1 r (11)
in the formula (11), C D Is the surface of aggregateSimplifying a covariance matrix of the three-dimensional point cloud data; r is an M × M regularization matrix, and the element R of the k row and k' column in R is obtained from equation (12) kk′ (ii) a Rho is a regularization parameter and can be calculated by methods such as OCV and the like, and the basic idea is to remove a known surface point, calculate a parameter to be solved and then calculate the difference e between the actual value of the point and the estimated value of the model i Where H (ρ) in equation (13) is the minimum value, ρ corresponding to the minimum value is the selected optimal regularization parameter.
In formula (12), S represents a spherical surface; omega represents an integral infinitesimal;
step 6: according to spherical DOG wavelet coefficient { a k I k =1,2, …, M } and frame function
Obtaining approximate surface function of aggregate three-dimensional appearance
Performing visualization processing;
step 6.1: after obtaining the spherical DOG wavelet coefficient matrix m, the approximate surface function of the aggregate can be obtained by applying the spherical DOG wavelet series shown in the formula (14)
Step 6.2: according to aggregate surface approximation function
Calculating the radius value of the aggregate along each angle to obtain coordinate data of a large number of points on the surface of the aggregate under a spherical coordinate system, converting the coordinate data into coordinate data under a three-dimensional Cartesian coordinate system, and further adopting a Delaunay triangulation method to realize visualization:
and 7: and randomly generating the aggregate particles with different shapes according to the step 6 by randomly changing the amplitude of the partial spherical DOG wavelet coefficient.
Step 7.1: randomly changing the amplitude of part of coefficients in the coefficient matrix m to obtain a randomly generated coefficient matrix m 1 ；
Step 7.2: according to a randomly generated coefficient matrix m 1 And calculating the corresponding approximate surface function, thereby obtaining the randomly generated aggregate according to the corresponding approximate surface function.
The embodiment is as follows: with reference to fig. 1, a method for reconstructing and randomly generating a three-dimensional shape of an aggregate based on spherical DOG wavelets comprises the following steps:
step 1: acquiring surface data of aggregate particles by using a three-dimensional scanner:
selecting limestone machine-made sand particles with the particle size of 4.75mm-9.50mm, acquiring surface three-dimensional point cloud data of the limestone machine-made sand particles by adopting a high-precision three-dimensional scanner, wherein the surface three-dimensional point cloud data totally comprises 5.3 ten thousand surface points, and the schematic diagram of the original three-dimensional point cloud data after Delaunay triangulation is shown in figure 2;
step 2: simplifying original three-dimensional point cloud data:
performing Delaunay triangulation on the original three-dimensional point cloud data of the aggregate, and calculating the real volume V and the real surface area S (the calculation schematic diagram is shown in FIG. 3) of the machine-made sand aggregate, wherein the real volume V and the real surface area S are 177.09mm respectively 3 And 205.98mm 2 。
Simplifying the original three-dimensional point cloud data to different quantities according to different proportions (the result is shown in figure 4), taking the volume error and the surface area error of each reduced degree as indexes, and finally selecting the quantity of the reduced point cloud to be 6k.
And step 3: converting a coordinate system of the simplified point cloud data:
converting the three-dimensional point cloud data after the surface of the machine-made sand aggregate is simplified into a spherical coordinate system from a Cartesian coordinate system according to the formulas (3) to (4);
and 4, step 4: discretizing the position and the scale of the spherical DOG wavelet function, and establishing a spherical DOG wavelet frame:
selecting q separately max 1,2,3,4, where the spherical grid is schematically shown in fig. 5, four spherical DOG wavelet frames F are established.
And 5: solving spherical DOG wavelet coefficients by a Tikhonov regularization method:
further calculating a spherical DOG wavelet expansion coefficient matrix m of the aggregate under different spherical DOG wavelet frames according to the formula (10); FIG. 6 shows the equation when q is max The result of calculating the regularization parameter calculated using the OCV method is 4.
Step 6: reconstructing an aggregate surface function to realize visualization:
by using spherical DOG wavelet series, the surface function similar to the aggregate under different spherical DOG wavelet frames can be obtained
Computing spherical grids G 5 Further converting the coordinate value of each point under a spherical coordinate system into a coordinate under a three-dimensional Cartesian coordinate system by adopting a formula (15) according to the radius value of each grid point;
and connecting the reconstructed discrete points on the surface of the aggregate into a triangular surface patch by adopting Delaunay triangulation to realize visualization, and showing the three-dimensional shape of the machine-made sand aggregate after reconstruction by different spherical DOG wavelet frames in figure 7.
And 7: randomly changing the spherical DOG wavelet coefficient to randomly generate aggregate with any shape:
randomly changing the amplitude of 101-103 coefficients in a spherical DOG wavelet expansion coefficient matrix m to generate a new coefficient matrix m 1 ；
According to a randomly generated coefficient matrix m 1 ComputingAnd corresponding approximate surface functions to obtain randomly generated aggregates according to the corresponding approximate surface functions, as shown in fig. 8, wherein the difference of radius values of the aggregates at various angles before and after the coefficient change is represented by colors.
Claims (5)
1. A method for reconstructing and randomly generating an aggregate three-dimensional shape based on spherical DOG wavelets is characterized by comprising the following steps:
step 1: acquiring original three-dimensional point cloud data of the surface of the aggregate by using a three-dimensional scanner;
step 2: simplifying the original three-dimensional point cloud data by taking the volume error VE and the surface area error SE as indexes to obtain simplified three-dimensional point cloud data;
and 3, step 3: converting the simplified three-dimensional point cloud data defined under the three-dimensional Cartesian coordinate system into a spherical coordinate system to obtain the simplified three-dimensional point cloud data defined under the spherical coordinate system;
and 4, step 4: discretizing the position and scale of a continuous spherical DOG wavelet function based on a spherical subdivision method of a regular icosahedron, and constructing a spherical DOG wavelet frame F;
and 5: decomposing the simplified three-dimensional point cloud data defined in a spherical coordinate system by adopting a frame function in a spherical DOG wavelet frame F, and solving a spherical DOG wavelet coefficient { a ] by utilizing a Tikhonov regularization method k I k =1,2, …, M }; wherein, a k Representing a kth spherical DOG wavelet expansion coefficient to be determined; m is the number of frame functions in the spherical DOG wavelet frame F;
step 6: according to spherical DOG wavelet coefficient { a k I k =1,2, …, M } and frame function
Obtaining approximate surface function of aggregate three-dimensional appearance
Approximating a surface function from the aggregate
Calculating the radius value of the aggregate along each angle to obtain coordinate data of a large number of points on the surface of the aggregate under a spherical coordinate system, converting the coordinate data into coordinate data under a three-dimensional Cartesian coordinate system, and further adopting a Delaunay triangulation method to realize visualization; wherein the content of the first and second substances,
representing the kth frame function in a spherical DOG wavelet frame F; theta represents a polar angle under the spherical coordinate system, represents an included angle between a connecting line of any surface point and an origin and the positive direction of the z axis,
the azimuth angle under the spherical coordinate system is represented, and the included angle between the connecting line of any surface point and the original point and the positive direction of the x axis is represented;
and 7: and randomly generating the aggregate particles with different shapes according to the step 6 by randomly changing the amplitude of the partial spherical DOG wavelet coefficient.
2. The method for reconstructing and randomly generating the three-dimensional shape of the aggregate based on the spherical DOG wavelet according to claim 1, wherein the step 2 specifically comprises:
step 2.1: based on a Delaunay triangulation principle, carrying out triangulation on original three-dimensional point cloud data so as to convert discrete point clouds in the original three-dimensional point cloud data into a triangular surface patch form, counting the sum of the areas of all triangular surface patches to be used as the real surface area of aggregate, respectively connecting three vertexes of all triangular surface patches with the center of the aggregate to form all tetrahedrons, and counting the sum of the volumes of all the tetrahedrons to be used as the real volume of the aggregate;
step 2.2: randomly deleting part of points in the original three-dimensional point cloud data according to a proportion, thereby simplifying the original three-dimensional point cloud data to obtain three-dimensional point cloud data under the current simplification degree;
step 2.3: performing Delaunay triangulation on the three-dimensional point cloud data under the current simplification, counting the sum of the areas of the triangular surface patches as the aggregate surface area under the current simplification degree, respectively connecting the three vertexes of the triangular surface patches and the aggregate center to form tetrahedrons, counting the sum of the volumes of all the tetrahedrons, and taking the sum as the aggregate volume under the current simplification degree;
step 2.4: respectively comparing the volume and the surface area of the aggregate under the current simplification degree with the real values obtained in the step 2.1 to obtain a volume error VE and a surface area error SE under the current simplification degree;
step 2.5: and if the volume error VE and the surface area error SE of the current aggregate meet the limit value requirement, increasing the proportion, returning to the step 2.2, and otherwise, taking the three-dimensional point cloud data obtained under the previous simplification degree as the finally simplified three-dimensional point cloud data.
3. The method for reconstructing and randomly generating the three-dimensional shape of the aggregate based on the spherical DOG wavelet according to claim 1, wherein the step 4 specifically comprises:
step 4.1: after the center of the regular icosahedron is moved to the center of the unit sphere, each vertex { n ] of the regular icosahedron is moved j I j =1,2,3, …,12} is projected onto a unit sphere, and the resulting spherical grid is denoted as G 0 (ii) a Wherein n is j Represents the jth vertex of a regular icosahedron;
step 4.2: finding the middle point of each triangle side in the icosahedron, connecting the middle points of the triangle sides to divide one triangle into four small triangles, and dividing the vertexes { m ] of the small triangles c I c =1,2,3, …,40} is projected onto a unit sphere, and the resulting spherical grid is denoted G 1 (ii) a Wherein m is c Representing the vertices of each small triangle;
step 4.3: according to the process of repeating the step 4.2, the spherical grids { G with different subdivision levels are obtained q | q =0,1,2, …, K }; wherein K is the maximum spherical subdivision number; g q Representing the spherical grid obtained under the q-th subdivision level;
step 4.4: respectively divide the spherical grids of different subdivision levels { G q Grid points in | q =0,1,2, …, K }For the central pole of the spherical DOG wavelet at the corresponding scale, the spherical DOG wavelet at the X position of the central pole is obtained according to equation (1):
in the formula (1), the acid-base catalyst,
is the central pole position of spherical DOG wavelet, where θ 0 The polar angle of the central pole is shown,
representing the azimuth of the central pole; gamma is the angle between the central pole and an arbitrary point X' on the sphere, wherein,
theta' represents the polar angle of any point on the sphere,
representing the azimuth angle of any point on the sphere; a =2 -q Q is a scale and is consistent with the spherical subdivision level; alpha is a constant value of the shape of the adjustment function, and alpha>1；λ a (γ) is a function related to γ and a, and is obtained by equation (2):
step 4.5: selecting the maximum spherical section level q for the reconstruction of the three-dimensional shape of the aggregate max And thus obtaining a spherical DOG wavelet frame F for reconstructing the three-dimensional shape of the aggregate by using the formula (3):
in the formula (3), X (q,j) Is a spherical grid G q The jth lattice point in (a); a =2 -q 。
4. The method for reconstructing and randomly generating the three-dimensional morphology of the aggregate based on the spherical DOG wavelet as claimed in claim 3, wherein the step 5 specifically comprises:
step 5.1: the frame function in the spherical DOG frame F is rewritten in a certain order to the form of equation (4):
in the formula (4), M is the total number of functions in the spherical DOG wavelet frame F;
is the kth spherical DOG wavelet frame function;
step 5.2: converting the simplified three-dimensional point cloud data defined in the spherical coordinate system obtained in the step 3 into a linear combination of a frame function, thereby obtaining an observation equation shown as a formula (5):
in the formula (5), N is the number of points of the three-dimensional point cloud data after final simplification;
is the measured value at the nth point cloud data;
the calculated value of the kth frame function in the spherical DOG wavelet frame F at the nth point cloud data is obtained;
step 5.3: rewriting the observation equation of equation (5) into a matrix form as equation (6):
r＝Gm (6)
in the formula (6), G is a matrix of equation coefficients, and
r is the measured data matrix, and
m is a spherical DOG wavelet coefficient matrix, m = [ a = 1 ,a 2 ,…,a M ] T ；
Step 5.4: obtaining a coefficient matrix m consisting of spherical DOG wavelet coefficients by using the formula (7):
m＝(G T C D -1 G+ρ 2 R) -1 G T C D -1 r (7)
in the formula (7), C D The method is characterized in that the method is a covariance matrix of three-dimensional point cloud data after the aggregate surface is simplified; r is a regularization matrix with dimension M multiplied by M, and the element R of the k row and the k' column in R is obtained by formula (8) kk′ (ii) a Rho is a regularization parameter;
in the formula (8), S represents a spherical surface; Ω represents an integral infinitesimal.
5. The method for reconstructing and randomly generating the three-dimensional morphology of the aggregate based on the spherical DOG wavelet as claimed in claim 4, wherein the step 7 specifically comprises:
step 7.1: randomly changing the amplitude of part of coefficients in the coefficient matrix m to obtain a randomly generated coefficient matrix m 1 ；
Step 7.2: according to random generationCoefficient matrix m 1 And calculating the corresponding approximate surface function, thereby obtaining the randomly generated aggregate according to the corresponding approximate surface function.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211358102.1A CN115690316A (en) | 2022-11-01 | 2022-11-01 | Aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelet |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211358102.1A CN115690316A (en) | 2022-11-01 | 2022-11-01 | Aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelet |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115690316A true CN115690316A (en) | 2023-02-03 |
Family
ID=85048075
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211358102.1A Pending CN115690316A (en) | 2022-11-01 | 2022-11-01 | Aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelet |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115690316A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116385642A (en) * | 2023-03-31 | 2023-07-04 | 浙江大学 | Three-dimensional scalar information compression reconstruction method based on spherical Shearlet |
| CN116663378A (en) * | 2023-05-23 | 2023-08-29 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
| CN116663378B (en) * | 2023-05-23 | 2024-06-04 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
-
2022
- 2022-11-01 CN CN202211358102.1A patent/CN115690316A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116385642A (en) * | 2023-03-31 | 2023-07-04 | 浙江大学 | Three-dimensional scalar information compression reconstruction method based on spherical Shearlet |
| CN116385642B (en) * | 2023-03-31 | 2023-09-12 | 浙江大学 | Three-dimensional scalar information compression reconstruction method based on spherical Shearlet |
| CN116663378A (en) * | 2023-05-23 | 2023-08-29 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
| CN116663378B (en) * | 2023-05-23 | 2024-06-04 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110097624B (en) | Method and device for generating three-dimensional data LOD simplified model | |
| CN110866531A (en) | Building feature extraction method and system based on three-dimensional modeling and storage medium | |
| CN108180918B (en) | Point cloud geodesic path forward tracking generation method and device | |
| CN115690316A (en) | Aggregate three-dimensional reconstruction and random generation method based on spherical DOG wavelet | |
| CN116071519B (en) | Image processing method and device for generating grid model based on harmonic mapping | |
| Peyré et al. | Geodesic computations for fast and accurate surface remeshing and parameterization | |
| CN106600551A (en) | High-precision geometry geometric correction method for large-scene spaceborne SAR image | |
| CN108986218A (en) | A kind of building point off density cloud fast reconstructing method based on PMVS | |
| CN114494641B (en) | Three-dimensional model light weight method and device | |
| CN112711888A (en) | Combined scattering joint calculation method for bidirectional reflection distribution function and scattering center | |
| Pfeifer | A subdivision algorithm for smooth 3D terrain models | |
| CN116992513B (en) | Simulation software body-attached particle generation method adapting to complex geometry | |
| WO2022104251A1 (en) | Image analysis for aerial images | |
| CN104318619B (en) | The method for reconstructing perceived towards the self-adapting compressing of Non-Destructive Testing | |
| CN109241212A (en) | Based on mesoscale numerical value atmospheric model and high-resolution history rainfall inversion method | |
| Maurya et al. | Performance of greedy triangulation algorithm on reconstruction of coastal dune surface | |
| CN111968237A (en) | Visual feature-maintained three-dimensional model simplification method | |
| CN114332440B (en) | Method for generating target SAR image by adopting stl format 3D model inversion | |
| CN115236759B (en) | Hexagonal grid subdivision method for determining earth gravity field | |
| CN115760954A (en) | Method for rapidly calculating surface area of complex surface based on point cloud data | |
| CN115564820A (en) | Volume determination method, system, device and medium based on greedy projection triangularization | |
| CN115631317A (en) | Tunnel lining ortho-image generation method and device, storage medium and terminal | |
| CN108957454B (en) | Interference phase simulation method of airborne interference synthetic aperture radar | |
| Rydesäter et al. | Investigation of smooth basis functions and an approximated projection algorithm for faster tomography | |
| Fu et al. | Reconstruct 3D geometry of target using differentiable SAR renderer |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |