CN113255027A - Efficient concrete three-dimensional aggregate generation and feeding method-three-dimensional residual space method - Google Patents

Efficient concrete three-dimensional aggregate generation and feeding method-three-dimensional residual space method Download PDF

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CN113255027A
CN113255027A CN202110242982.5A CN202110242982A CN113255027A CN 113255027 A CN113255027 A CN 113255027A CN 202110242982 A CN202110242982 A CN 202110242982A CN 113255027 A CN113255027 A CN 113255027A
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应敬伟
简榆峻
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Abstract

本发明公开了一种高效的混凝土三维骨料生成与投放方法——三维剩余空间法，将三维矩阵运算和灰度图像处理技术结合，通过三维矩阵元素值判断骨料重叠或超出边界，给出适用于各种三维骨料模型的生成算法。提出一种由真实的宏观实验通过切片扫描重构三维骨料，并对其中的骨料进行分离、拟合成理想形状并提取其参数，基于提取到的三维参数建立了不同尺寸、不同取代率下的三维混凝土细观模型。提出一种用聚类算法改进剩余空间法的三维剩余空间法，将三维像素模型切片，通过形态学细化操作获取三个方向所有切片的骨架分支点，使用聚类算法优化分支点取点流程，进而提高整个模型生成的效率。

Figure 202110242982

The invention discloses an efficient concrete three-dimensional aggregate generation and delivery method, the three-dimensional residual space method, which combines three-dimensional matrix operation and grayscale image processing technology, judges that the aggregate overlaps or exceeds the boundary by the three-dimensional matrix element value, and gives Generating algorithms for various 3D aggregate models. A method of reconstructing three-dimensional aggregates by slice scanning from real macroscopic experiments is proposed, and the aggregates are separated, fitted into ideal shapes, and their parameters are extracted. Based on the extracted three-dimensional parameters, different sizes and different substitution rates are established. 3D concrete mesomodel below. This paper proposes a 3D residual space method which improves the residual space method with clustering algorithm. The three-dimensional pixel model is sliced, and the skeleton branch points of all slices in three directions are obtained through the morphological refinement operation, and the clustering algorithm is used to optimize the branch point selection process. , thereby improving the efficiency of the entire model generation.

Figure 202110242982

Description

Efficient concrete three-dimensional aggregate generation and feeding method-three-dimensional residual space method
Technical Field
The invention relates to the field of concrete mesoscopic numerical modeling, in particular to a high-efficiency concrete three-dimensional aggregate generating and feeding method, namely a three-dimensional residual space method.
Background
Concrete is a heterogeneous and uniform entity, is limited by manpower, financial resources and material resources only through macroscopic research, and is difficult to analyze the mechanical behavior of each part in concrete components, aggregate, mortar and an Interface Transition Zone (ITZ) between the aggregate and the mortar in what way to participate in the whole concrete. Therefore, research needs to be carried out on concrete from a mesoscopic level, for example, how to establish a concrete mesoscopic model closer to a real situation, so that various concrete mesoscopic simulations have higher reliability; how to explore a concrete mesoscopic model modeling method with higher efficiency and wider application range is suitable for common concrete, recycled concrete, dam concrete and the like, even composite materials composed of different phases.
At present, with the maturity of the mesoscopic technology, generation and feeding methods of various forms of aggregates are considered to be based on a random aggregate method, and the bottleneck problem of later-stage feeding efficiency is improved through an additional means, but the methods have to be further researched on the universality of two-dimensional models, three-dimensional models and various aggregate types. The skeleton theory is used for obtaining branch points through the generation and reutilization of the two-dimensional pixels to put the aggregates, although a general generation algorithm for various two-dimensional aggregates and the putting efficiency acceleration can be provided, the two-dimensional aggregates have different mechanical properties compared with the three-dimensional aggregates; the framework theory is directly applied to a three-dimensional space, the number of the obtained three-dimensional framework branch points is always in the order of magnitude of 10^4, if each branch point is put, the aggregate putting efficiency is low, and the density of the branch points in the middle of the framework is higher than that of the branch points outside the model.
Disclosure of Invention
The invention provides a high-efficiency concrete three-dimensional aggregate generating and feeding method, namely a three-dimensional residual space method, which combines three-dimensional matrix operation and gray level image processing technologies, specifically utilizes a three-dimensional pixel sampling point to perform matrix operation to position aggregates, utilizes pixel points to generate a three-dimensional pixel model, judges whether the aggregates are overlapped or exceed a boundary according to a three-dimensional matrix element value, and provides a generating algorithm suitable for various three-dimensional aggregate models.
And providing an algorithm for selecting a proper aggregate shape according to the actual condition of the real test piece. The method comprises the steps of reconstructing three-dimensional aggregate through slice scanning by a real macroscopic experiment, separating and fitting the aggregate into an ideal shape, extracting parameters such as a length representative value and concave-convex degree of the aggregate, and establishing three-dimensional concrete mesoscopic models with different sizes and different substitution rates based on the extracted three-dimensional parameters. In the model generation process, the real aggregate can be generated only by reading the coordinate data of a certain aggregate in the aggregate library and assigning the elements at the corresponding positions in the matrix for putting.
The three-dimensional residual space method for improving the residual space method by using the clustering algorithm is provided, a three-dimensional pixel model is sliced, skeleton branch points of all slices in three directions are obtained through morphological thinning operation, a branch point taking process is optimized by using a convex hull algorithm and an Euclidean point cloud clustering algorithm, the success rate of aggregate putting is improved, and the efficiency of generating the whole model is further improved; the three-dimensional residual space method flow is shown in the attached figure 1.
Step 1, establishing a three-dimensional pixel model and a three-dimensional pixel sampling point
Determining the size x of an aggregate feeding area according to the size of the modelmax×ymax×zmaxSelecting a scale B to establish a three-dimensional matrix X with all element values of 0.5max×Ymax×Zmax＝(B×xmax)×(B×ymax)×(B×zmax) The three-dimensional pixel model is used for putting aggregates, element positions and element center point coordinates of a matrix are recorded, elements in the three-dimensional matrix are cube units in the three-dimensional pixel model, and different element values correspond to different pixel colors;
if the aggregate is not allowed to exceed the boundary, the three-dimensional matrix is expanded to Xmax×Ymax×Zmax＝ (B×xmax+2)×(B×ymax+2)×(B×zmax+2), the extension area element is set to 1; recording element positions and element center point coordinates of the matrix;
establishing three-dimensional pixel sampling points o, p and q for controlling the directions of x, y and z;
o is used to locate the X-axis, whose element along the X-axis is i, (i ═ 1, 2, 3 … … Xmax) In total of XmaxSlice layer, when x is i, YZ slice size is Ymax×ZmaxAll the element values are i;
p is used to locate the Y-axis, whose element in the Y-axis direction is j, (j ═ 1, 2, 3 … … Ymax) In total of YmaxSlice of Z size when y is imax×XmaxAll the element values are j;
q is used to locate the Z-axis, whose element along the Z-axis is k, (k ═ 1, 2, 3 … … Zmax) In total of ZmaxSlice-by-slice, when z is k, XY-slice size is Xmax×YmaxAll the element values are k;
step 2, determining the total volume ratio p of the aggregate and the maximum particle size dmaxThe particle size range and the cumulative volume percentage of each grade of aggregate are calculated;
step 3, establishing an aggregate library based on shape modeling
(3.1) building a ball aggregate:
the spherical radius is the radius of each grade of aggregate; substituting the central point, the radius and the three-dimensional pixel sampling point of the aggregate to be put into a ball formula to obtain a logic matrix, wherein the logic matrix and the three-dimensional matrix have the same scale, recording element positions meeting conditions and mapping the element positions to the three-dimensional matrix, and adding 0.5 to the element values of the corresponding positions in the three-dimensional matrix to become 1, namely changing the material of the corresponding pixels in the three-dimensional pixel model from mortar to aggregate;
the multiplication and division operation among the three-dimensional pixel sampling points is matrix point multiplication and point division, namely element multiplication and division of each same position of a matrix;
(3.2) building an ellipsoid or ovoid aggregate:
determining the slenderness ratio, taking the radius of each level of aggregate to be matched by the equivalent radius, and calculating the long radius, the short radius, the symmetrical radius and the extreme radius;
randomly rotating an ellipsoid or an egg sphere by three Euler angles alpha, beta and gamma by taking a central point to be put into the aggregate as a rotation point, wherein the range of beta is a uniform distribution function of [0, pi ], and alpha and gamma are uniform distribution functions of [0,2 pi ];
substituting the central point, various radii and the three-dimensional pixel sampling point to be added with the aggregate into the rotated shape formula to obtain a logic matrix, wherein the logic matrix and the three-dimensional matrix have the same scale, recording element positions meeting conditions and mapping the element positions to the three-dimensional matrix, and adding 0.5 to the element values of corresponding positions in the three-dimensional matrix to change the element values into 1, namely changing the material of the corresponding pixels in the three-dimensional pixel model from mortar to aggregate;
the equivalent radius is the radius of the aggregate equivalent to a sphere by an isometric method; the equivalent radius of the sphere is the radius of the sphere;
(3.3) building convex polyhedral aggregate:
determining the slenderness ratio, taking the radius of each level of aggregate according to the equivalent radius, and calculating the long radius, the short radius, the symmetric radius and the extreme radius of the external egg ball; generating an egg ball at an original point, taking the egg ball as a polyhedral aggregate center, dividing the egg ball equally in three axes of x, y and z by taking 6 end points of the egg ball as fixed vertexes of a convex polyhedron in order to ensure that the generated convex polyhedral aggregate and the egg ball have the same slenderness ratio, substituting a plane equation into an egg ball equation to solve to obtain a supplementary point on the egg ball, and taking the supplementary point as a supplementary vertex of the polyhedral aggregate;
adopting a Convex hull enclosure to construct an outer enclosure surface of a Convex enclosure body and obtain information of each surface, judging whether a central point of each element is in the polyhedron according to coordinates of the central point of the element, if the central point of the element is in the polyhedron and does not comprise elements with central points on the surface and the edge in the three-dimensional pixel model, adding 0.5 to a matrix element value of a corresponding position to change the matrix element value into 1, and changing a material of the pixel at the position from mortar to aggregate; rotating the aggregate by taking the original point as a rotation point according to the method in the step (3.2) and performing three-dimensional translation to the feeding central point to generate the aggregate;
(3.4) establishing a concave polyhedral aggregate:
the operation step (3.3) generates a Convex polyhedron which is not rotated and does three-dimensional translation, the Convex hull bounding volume is adopted to construct the outer bounding volume of the Convex bounding volume and obtain the information of each surface, three angular points of any surface are selected, and the midpoint (X) of the surface is calculatedc,Yc,Zc) And is connected with the origin as a line segment lcAt lcUpper fetching point (X)ao,Yao,Zao) As pits of a polyhedron; the coordinates of the newly generated pits are expressed by the following formula:
Xao＝δXc,Yao＝δYc,Zao＝δZc,δ∈(0,1) (2)
where δ is the distance/l from the pit to the origincThe length of (2) is randomly selected on (0,1), which represents the degree of concave points newly generated on the edge, the more delta is close to 1, the less the concave height of the edge is, the more mu is close to 0, the higher the concave height of the edge is;
selecting three angular points of the surface and newly generated concave points, constructing a Convex trihedron by using the Convex hull enclosure in the step (3.3), and subtracting the trihedron from the original Convex polyhedron to obtain concave polyhedron aggregate, namely subtracting 0.5 from the element value of the corresponding position of the trihedron to obtain 0.5, and changing the material of the pixel from the aggregate into mortar; rotating the aggregate by taking the original point as a rotation point according to the method in the step (3.2) and performing three-dimensional translation to the feeding central point to generate the aggregate;
(3.5) recycled aggregate:
determining the substitution rate v, successfully generating the aggregate in the step (3.1), (3.2), (3.3) or (3.4) through the step 5, or changing the aggregate element from 1 to 0.8 every time the aggregate is successfully generated in the step 8, and changing the material of the corresponding pixel into old mortar;
one side is a generation mode of old mortar, the other side is old aggregate, a plane or a curved surface is generated through an aggregate feeding center, and three euler angles alpha ', beta' and gamma 'are randomly rotated, wherein the range of beta' is a uniform distribution function of [0, pi ], and alpha 'and gamma' are uniform distribution functions of [0,2 pi ]; selecting pixels of which the central points simultaneously meet the requirements of being in aggregate and being on one side of a generating surface in the three-dimensional pixel model, and changing the element values of the corresponding positions in the three-dimensional matrix to 1, namely changing the materials of the pixels into old aggregate;
selecting one aggregate with the equivalent radius smaller than that of the old mortar from the steps (3.1), (3.2), (3.3) or (3.4) at the aggregate putting center of the old mortar; changing the element value which simultaneously satisfies 'in old mortar' and 'in aggregate' in the matrix into 1, namely changing the material of the pixel into old aggregate;
step 4, establishing an aggregate library based on real aggregates
(4.1) pretreatment for extraction
Iron oxide (Fe) of the iron green S5605 type was used2O3) And iron red S190 type iron oxide (Fe)2O3) Dyeing the components in the test block; after pouring and maintenance, polishing the color concrete test block layer by using a water mill, scanning the polished and leveled test piece by using a scanner, and polishing the next time after scanning is finished; the grinding depth is 1mm each time; the pigment is not limited to the above pigments, and pigments capable of forming distinct red and green colors can be used for dyeing concrete;
(4.2) reconstructing a real three-dimensional model:
reconstructing the slice images with the scanned and identified components into a three-dimensional model, and generating a matrix with the size consistent with the actual size by using the actual size of 1mm to correspond to the matrix scale of 1 pixel;
(4.3) reconstructing a real three-dimensional coarse aggregate:
extracting all real aggregates from the three-dimensional model to serve as a three-dimensional aggregate library for parameter extraction and aggregate putting; in a three-dimensional space, if a certain voxel is connected with other voxels in a neighborhood, the two voxels are in the same connected domain; extracting different aggregates by a method of extracting different connected domains, and independently extracting voxels belonging to the aggregates into a new matrix;
storing aggregate in a matrix in a coordinate mode, wherein each new matrix is consistent with the actual size;
the equivalent radius of the reconstructed three-dimensional real aggregate is the radius of a sphere with the same voxel;
(4.4) pretreatment of fitting of single coarse aggregate:
calculating the coordinate of the center point of the aggregate, namely the total sum of the coordinate values and the coordinate number of each direction; constructing a polyhedron comprising all the coordinate points of the aggregate by using a convex hull algorithm, finally obtaining the coordinates of all outward convex vertexes of the aggregate, calculating a connecting line of the two vertexes with the longest distance in the aggregate, and recording the connecting line as the longest axis; performing three-dimensional translation and rotation on the whole aggregate to enable the center point of the aggregate to coincide with the origin of coordinates, and enabling the longest axis to coincide with the x axis;
(4.5) selecting convex vertexes of the convex surface of the coarse aggregate to perform fitting:
translating a single aggregate along the x axis for one time, translating the aggregate by +/-0.01-0.02 times of the longest axis every time, autorotating the aggregate around the x axis for m times, rotating the aggregate for 360 DEG/k every time, and then symmetrical 1 time about a yz plane to obtain (1+ l + m) groups of aggregates at different positions; fitting the outward convex vertexes of the aggregates at all the groups of positions to a standard sphere equation, an ellipsoid equation and an egg-ball equation respectively by using an iterative reweighted least square method; taking Mean Square Error (MSE) as the fitting error reference value; the polyhedron skips fitting treatment, and an aggregate coordinate with the minimum fitting error is stored in each type of aggregate form;
(4.6) generating an aggregate library:
after obtaining each aggregate, counting the equivalent particle size of each aggregate, wherein the aggregates with the equivalent particle size of more than or equal to 5mm are classified into four types of aggregate forms according to the grading of the sieve so as to count the parameters of the aggregates with different grades; the aggregate with the equivalent grain diameter of less than 5mm is counted into the mortar part;
setting the center of the aggregate as an origin, randomly rotating for t (t is more than or equal to 50) times around x, y and z axes, wherein 360 DEG/t is used for each time, more than 62500 groups of rotation forms are shared, and all the rotation forms of the aggregate are stored;
(4.7) generating the aggregate by using a real aggregate warehouse:
b is made to be 1, the shape of the aggregate is selected, the equivalent radius is the radius of each level of aggregate, the first rotation form of the aggregate in the radius range is randomly selected, the aggregate is mapped to the three-dimensional pixel model and three-dimensionally translated to the aggregate feeding center, the aggregate center is superposed with the feeding center, the element value of the corresponding coordinate in the three-dimensional matrix is added by 0.5 to become 1, namely the material of the corresponding pixel in the three-dimensional pixel model is changed from mortar to aggregate;
step 5, manually putting the front n aggregates
If the lengths of the three boundaries of the real model size are not less than 5dmaxIf n is 9, putting aggregates at the center point of the three-dimensional pixel model and 8 points which are at the boundary length from 1/4-1/3 of the three-dimensional pixel model;
if the boundary length of the real model size in a certain direction is less than 5dmaxThen n is 5, at the center of the voxel modelThe aggregate is put at 4 points which are half the length of the boundary in the direction and are apart from the boundary lengths 1/4-1/3 of the boundary surfaces in other directions;
if the boundary lengths of the real model size in two directions are both less than 5dmaxIf n is 3, putting aggregates at the center point of the three-dimensional pixel model and at 2 points which are half of the boundary length and are at the boundary length from boundary surfaces 1/4-1/3 in other directions;
if the lengths of the three boundaries of the real model size are all less than 5dmaxIf n is 1, putting aggregate at the central point of the three-dimensional pixel model;
step 6, selecting three-dimensional residual space to generate skeleton
Obtaining Z perpendicular to Z-direction in three-dimensional matrixmaxSlicing the layers, wherein the acquisition method comprises the steps of slicing one layer of each pixel, and each layer of slice has only one unit length in the z direction; selecting a space without the aggregate, namely a three-dimensional residual space, on each layer of slices, and obtaining a skeleton through a skeleton algorithm, namely a set of circle centers of maximum inscribed circles of the target contour; in the sliced skeleton pixel points, if the pixels at adjacent positions of a certain pixel point along positive x, positive y, negative x and negative y directions are all skeleton pixel points, the pixel point is a branch point of a skeleton, and the position and the coordinates of a central point are recorded; combining each layer of slices to a three-dimensional pixel model according to the original position;
using the same method as the above to obtain the frame branch point of the slice vertical to the x and y directions, and recording the position and the center point coordinate;
step 7, clustering branch points of the skeleton
(7.1) combining the skeleton branch points of the slices vertical to the x, y and z directions to the three-dimensional pixel model according to the original positions; deleting repeated branch points;
(7.2) adopting a convex hull algorithm for branch points of aggregate corners, namely generating an outer-wrapped polyhedron containing all branch points, deleting repeated faces, taking the vertex of the outer-wrapped polyhedron as a clustering point, and deleting the vertex positioned on the boundary;
(7.3) adopting a point cloud clustering algorithm based on Euclidean at branch points in the middle part of the skeleton:
substituting all branch points into an Euclidean point cloud clustering algorithm, wherein 1/10 of aggregate particle size is taken as a distance parameter, if the distance parameter is smaller than 1mm, 1mm is taken, the branch points of all clusters are obtained as clustering points, and if the number of the branch points in a certain cluster is larger than or equal to 3, the mean value of the coordinates of the center points of all the branch points in the cluster is taken as the clustering points;
(7.4) branching points of skeleton edges:
acquiring all framework branch points closest to the boundary surface, adopting a point cloud clustering algorithm based on Euclidean, taking 1mm as a distance parameter, and taking the mean value of the coordinates of the center points of all branch points in various clusters as a clustering point;
(7.5) recording the coordinates of all the clustering points;
step 8, starting to put aggregate
(8.1) sequentially selecting coordinates of the clustering points, and putting the aggregates generated in the step 3 or the step 4:
(8.2) whether boundary exceeded or overlap
If the element value of not less than 1.5 exists in the three-dimensional matrix, the aggregate exceeds the boundary or is overlapped with the thrown aggregate, and the thrown aggregate is deleted, namely the element value of the corresponding position of the thrown aggregate is reduced by 0.5 in the three-dimensional matrix;
otherwise, the putting is successful, and the current volume rate L is calculated;
(8.3) after all the clustering points are selected, finishing the round of putting; in the round of putting, if the current volume rate does not meet the requirement of putting content and the aggregate is successfully put in the round of putting, the generation process of the model is not finished, and then the three-dimensional residual space after the round of putting is selected to carry out the operations of the steps 6, 7 and 8;
(8.4) if all the clustering points in the round can not be successfully put in the aggregate or the L meets the content requirement, stopping putting, and storing the final three-dimensional pixel model.
When the three-dimensional aggregate is generated, respectively taking an equivalent radius in each particle size range, taking the maximum radius as the equivalent radius of the three-dimensional aggregate, and multiplying all types of radii by B to be used as the radius for programming; in the step 8, the three-dimensional aggregate is successfully put in each time, if L does not meet the requirement of putting content and is larger than the cumulative volume percentage of the particle size range, the equivalent radius is changed into the equivalent radius of the next particle size range, and the three-dimensional aggregate parameters are recalculated; if the recycled concrete is recycled concrete, firstly feeding recycled aggregate, when the volume ratio of the recycled aggregate meets v multiplied by p, feeding the natural aggregate next time, when the volume ratio of the natural aggregate meets (1-v) multiplied by p, feeding the recycled aggregate next time, and if the volume ratio of the natural aggregate meets the requirement of feeding the recycled aggregate next time.
If a reinforced concrete model is to be generated, the positions of the steel bars are recorded in advance in the step 1, the element value of the matrix of the corresponding positions is set to be 1, and the aggregate is not manually put in the step 5; and after the three-dimensional aggregate is put into the container, changing the element value of the position of the corresponding pixel of the reinforcing steel bar into 2, namely changing the material of the corresponding pixel into the reinforcing steel bar.
If concrete with other cross section needs to be generated, and the cross section needs to be in xmax×ymax×zmaxIn the range of (1), two matrixes are selected from o, p and q according to the surface of the section and substituted into a shape formula, and in the mapping to the three-dimensional pixel model, the element value of the corresponding three-dimensional matrix is changed to 0.5, and the element values of other positions are changed to 1 to be used as a three-dimensional matrix expansion area.
When the model is stored, the model which is allowed to exceed the boundary can be directly stored, and the model which is not allowed to exceed the boundary needs to perform the following processing on the three-dimensional matrix after the release is finished:
and deleting elements in the three-dimensional matrix expanded area to make the three-dimensional pixel model consistent with the real three-dimensional aggregate model.
The invention has the following beneficial effects:
firstly, three-dimensional matrix operation and gray level image processing technology are combined for the first time, a three-dimensional pixel model is generated by utilizing three-dimensional pixel points, aggregate overlapping or exceeding of a boundary can be judged simultaneously through three-dimensional matrix element values, programming is simple, efficiency is high, and the algorithm is suitable for various programming software, common concrete with various sections, recycled concrete, dam concrete and the like, and even composite materials composed of different phases.
Secondly, a three-dimensional recycled aggregate generation algorithm realizes the mesoscopic modeling of the recycled aggregate under the three-dimensional complex aggregate form, and can further form each interface transition area in the recycled concrete through the scaling of the aggregate boundary so as to analyze the aspects of mechanics or chloride ions and the like;
thirdly, reconstructing a real three-dimensional aggregate by using the pixel points for the first time, obtaining various parameters of the aggregate through fitting, generating the real aggregate by only reading coordinate data of a certain aggregate in an aggregate library and assigning the elements at corresponding positions in a matrix for putting, and establishing an aggregate model which is closer to the real aggregate than the aggregate model based on shape equation modeling, wherein the generation efficiency of the three-dimensional model can be accelerated due to the fact that the steps of aggregate modeling are saved, and particularly when the volume fraction of the aggregate is more than 40%, the generation efficiency is greatly improved compared with the aggregate generation method based on shape modeling.
And fourthly, the framework theory is used for three-dimensional aggregate feeding for the first time, the residual space method is improved, the branch points are obtained by utilizing the slices, the branch points are clustered through a convex hull algorithm and a clustering algorithm, and the aggregates are fed at the clustering points, so that the aggregate feeding success rate can be improved, and the generation efficiency of the whole model can be improved. The algorithm is suitable for the release of aggregates with three dimensions and different shapes, is also suitable for the modeling of standard cube test blocks, non-standard cube test blocks, cylinder test blocks and reinforced concrete beam models, and has strong universality; can meet the requirement of the volume ratio of common concrete, and the spatial distribution of the aggregate is close to a real model.
Drawings
FIG. 1 is a flow chart of aggregate feeding by a three-dimensional residual space method according to the invention;
FIG. 2 is a diagram of a three-dimensional pixel model according to the present invention; (a) the three-dimensional pixel model is a schematic diagram of 7 multiplied by 7, and a small black point is a pixel central point; (b) a slice when the 7 × 7 × 7 voxel model z is 3;
FIG. 3 is a diagram of the process of forming a three-dimensional aggregate according to the present invention; (a) the slice element value when z is 3 in the 7 × 7 × 7 three-dimensional matrix D in example one; (b) a round aggregate of 3 slices for the 7 × 7 × 7 voxel model in example one; (c) a three-dimensional sphere aggregate which is a 7 × 7 × 7 three-dimensional pixel model in example one, wherein a black pixel with an element value of 1 represents the aggregate, and a light blue pixel with an element value of 0.5 represents mortar;
FIG. 4 is a diagram illustrating a skeleton generation process by a three-dimensional residual space method according to an embodiment of the present invention; (a) the first 9 aggregates to be manually thrown in; (b) the skeleton is sliced in the xy direction of the center of the three-dimensional pixel model, white pixels represent ball aggregate, white thin lines represent the skeleton, and gray pixels represent the residual space; (c) a three-dimensional skeleton diagram which is formed by superposing all xy-direction slices to the original position; (d) a three-dimensional skeleton diagram which is formed by overlaying slices in all directions to the original position;
FIG. 5 is a diagram illustrating a first round of three-dimensional skeleton branch point clustering process according to an embodiment of the present invention; (a) schematic diagram of all branch points; (b) convex hull maps for all branch points; (c) a clustering point diagram is obtained after the branch points are clustered;
FIG. 6 is a three-dimensional skeleton diagram of a ball aggregate model according to an embodiment of the present invention; (a) is a three-dimensional skeleton schematic diagram of the model; (b) is a slice image in the xz direction passing through the center of the model; (c) a yz direction slice image passing through the center of the model; (d) a slice image in the xy direction passing through the center of the model; (b) white pixels in the (c) and (d) represent ball aggregate, white thin lines represent a framework, and black pixels represent residual space;
FIG. 7 is a schematic representation of a final spherical aggregate produced in accordance with an embodiment of the present invention; (a) is a three-dimensional schematic diagram of the model; (b) is an xz direction slice image; (c) is a yz direction slice image; (d) slicing in the xy direction; (b) white pixels in the (c), (d) and (e) represent ball aggregate, and the white pixels represent mortar; (e) the positions of the slices (b), (c) and (d);
FIG. 8 is a diagram illustrating a process of forming a three-dimensional concave polyhedral aggregate according to a second embodiment of the present invention; (a) selecting a vertex schematic for the polyhedron; (b) is a Convex trihedron diagram of the Convex hull bounding volume structure; (c) generating a single convex polyhedral aggregate graph; (d) generating a single concave polyhedral aggregate graph;
FIG. 9 is a diagram showing the process of producing recycled aggregate of three-dimensional concave polyhedron according to the second embodiment of the present invention; (a) the aggregate regeneration schematic diagram is a three-dimensional matrix slice, wherein a pixel with an element value of 0.5 represents new mortar, a pixel with an outermost element value of 1 represents a boundary, a pixel with an element value of 0.8 represents old mortar, and a pixel with an element value of 1 represents old aggregate; (b) is a three-dimensional concave polyhedron recycled aggregate model diagram; (c) slicing in the xy direction; (d) is a yz direction slice image; (e) is an xz direction slice image; (c) in the steps (d) and (e), the green pixel represents old aggregate, the yellow pixel represents old mortar, and the red pixel represents new mortar;
FIG. 10 is a diagram of a three-dimensional reconstruction of a single real aggregate in example three of the present invention; (a) is a three-dimensional real aggregate model diagram; (b) slicing in the xy direction; (c) is a yz direction slice image; (d) is an xz direction slice image; (e) extracting single three-dimensional aggregate; (f) a polyhedral external packing diagram of a single aggregate; (g) the (h) and the (i) are respectively fitting graphs of a single aggregate to a spherical formula, an elliptical formula and an oval formula;
FIG. 11 is a diagram of a final model based on real aggregate according to example three of the present invention; (a) is a three-dimensional model diagram based on real aggregate; (b) is an xz direction slice image; (c) is a yz direction slice image; (d) slicing in the xy direction; (b) black pixels in the (c), (d) and (e) represent aggregates, and white pixels represent mortar; (e) the positions of the slices (b), (c) and (d);
Detailed Description
To further illustrate the beneficial effects of the present invention, the following detailed description of the three-dimensional aggregate mesoscopic modeling algorithm provided by the present invention is provided by way of example;
example one:
the purpose of this example is to illustrate the optimization of the branch point placement aggregate flow by using the pixel generation ball aggregate and the three-dimensional residual space method, and the high efficiency of the three-dimensional residual space method;
step 1, establishing a three-dimensional pixel model and a three-dimensional pixel sampling point
Determining the size x of an aggregate feeding area according to the size of the modelmax×ymax×zmax100mm X100 mm, a three-dimensional matrix X with all 0.5 elements is created with a scale B1 selectedmax×Ymax×Zmax＝(B×xmax)×(B×ymax)×(B×zmax) The three-dimensional pixel model for putting aggregate is 100mm × 100mm × 100mm, and the element position and the element center point coordinates of the matrix are recorded, for example, the three-dimensional pixel model of 7 × 7 × 7 is shown in fig. 2;
establishing three-dimensional pixel sampling points o, p and q for controlling the directions of x, y and z;
o is used to locate the x-axis, whose elements along the x-axis are i, (i ═ 1, 2, 3 … … 100), for a total of 100 slices, and when x ═ i, YZ slice size is 100 × 100, the element values are all i;
p is used to locate the y-axis, whose elements along the y-axis are j, (j ═ 1, 2, 3 … … 100), for a total of 100 slices, and when y ═ i, ZX slice size is 100 × 100, the element values are all j;
q is used to locate the z-axis, whose elements along the z-axis are k, (k is 1, 2, 3 … … 100), there are 100 slices, and when z is k, the XY slice size is 100 × 100, the element values are all k;
step 2, determining the aggregate total volume p as 50 percent and the maximum grain diameter dmax20mm, the particle size range of each grade of aggregate is 20-16 mm, 16-10 mm, 10-5 mm and the cumulative volume ratio percentage is (12.55 XP/50)%, (32.7 XP/50)%, p;
establishing a ball aggregate library through step 3
(3.1) building a ball aggregate:
the radius r of each grade of aggregate is 8.75, 6.25 and 3; central point (x) to be charged with aggregate0，y0) Substituting radius and three-dimensional pixel sampling points o, p and q into a sphere formula o2+p2+q2≤r2The matrix on the left side of the equation is denoted as D, for example: a slice with z being 3 in a 7 × 7 × 7 three-dimensional matrix D is shown in fig. 3 (a); recording the elements of the football formula filled with the elements in the D to obtain a logic matrix, wherein the logic matrix and the three-dimensional matrix have the same scale, and recording the element positions meeting the conditions and mapping the element positions to the three-dimensional matrix; adding 0.5 to the element value of the corresponding position in the three-dimensional matrix to change the element value into 1, namely changing the material of the corresponding pixel in the three-dimensional pixel model from mortar to aggregate; example (c): the ball aggregate in the 7 × 7 × 7 three-dimensional pixel model is shown in FIGS. 3(b) and (c);
starting to put aggregates;
step 5, manually putting the front n aggregates
The lengths of the three boundaries are not less than 5d max100, n 9, maximum radius 8.75The aggregate is put at the center point of the three-dimensional pixel model and 8 points which are at the boundary length from 1/4-1/3 of the boundary surface of the three-dimensional pixel model, as shown in the figure 4 (a);
step 6, selecting three-dimensional residual space to generate skeleton
Obtaining Z perpendicular to Z-direction in three-dimensional matrixmaxSlicing the layers, wherein the acquisition method comprises the steps of slicing one layer of each pixel, and each layer of slice has only one unit length in the z direction; selecting a space without the aggregate, namely a three-dimensional residual space, on each layer of slices, and obtaining a skeleton through a skeleton algorithm, namely a set of circle centers of maximum inscribed circles of the target contour; in the sliced skeleton pixel points, if the pixels at adjacent positions of a certain pixel point along positive x, positive y, negative x and negative y directions are all skeleton pixel points, the pixel point is a branch point of a skeleton, and the position and the coordinates of a central point are recorded; combining each layer of slices to the three-dimensional pixel model in situ, as shown in fig. 4(b) and (c);
using the same method as the above to obtain the frame branch point of the slice vertical to the x and y directions, and recording the position and the center point coordinate; the skeleton of the final three-dimensional pixel model is shown in FIG. 4(d)
Step 7, clustering branch points of the skeleton
(7.1) combining the skeleton branch points of the slices vertical to the x, y and z directions to the three-dimensional pixel model according to the original positions; deleting repeated branch points, as shown in FIG. 5 (a);
(7.2) adopting a convex hull algorithm for branch points of the aggregate corners, namely generating an outer-wrapped polyhedron containing all branch points, as shown in the figure 5(b), deleting repeated faces, taking the vertex of the outer-wrapped polyhedron as a clustering point, and deleting the vertex which is positioned at the boundary;
(7.3) adopting a point cloud clustering algorithm based on Euclidean at branch points in the middle part of the skeleton:
substituting all branch points into an Euclidean point cloud clustering algorithm, wherein 1/10 of aggregate particle size is taken as a distance parameter, if the distance parameter is smaller than 1mm, 1mm is taken, the branch points of all clusters are obtained as clustering points, and if the number of the branch points in a certain cluster is larger than or equal to 3, the mean value of the coordinates of the center points of all the branch points in the cluster is taken as the clustering points;
(7.4) branching points of skeleton edges:
acquiring all framework branch points closest to the boundary surface, adopting a point cloud clustering algorithm based on Euclidean, taking 1mm as a distance parameter, and taking the mean value of the coordinates of the center points of all branch points in various clusters as a clustering point;
(7.5) recording the coordinates of all the clustering points as shown in the figure 5 (c);
step 8, starting to put aggregate
(8.1) sequentially selecting coordinates of the clustering points, and putting the aggregates generated in the step 3 by using the maximum radius of 8.75:
(8.2) whether boundary exceeded or overlap
If the element value of not less than 1.5 exists in the three-dimensional matrix, the aggregate exceeds the boundary or is overlapped with the thrown aggregate, and the thrown aggregate is deleted, namely the element value of the corresponding position of the thrown aggregate is reduced by 0.5 in the three-dimensional matrix;
otherwise, the putting is successful, and the current volume rate L is calculated;
(8.3) after all the clustering points are selected, finishing the round of putting; in the round of putting, if the current volume rate does not meet the requirement of putting content and the putting of the aggregate is successful in the round of putting, the generation process of the model is not finished, and if L meets the accumulative volume percentage of the particle size range, the equivalent radius is changed into the equivalent radius of the next particle size range; for example: l > 12.55%, then r ═ 6.25; then, selecting the three-dimensional residual space after the round of putting is finished to perform the operations of the steps 6, 7 and 8, and referring to the attached figure 6, wherein the three-dimensional residual space is a framework of the round of three-dimensional residual space;
(8.4) if all the clustering points in the round can not be successfully put with the aggregates or the L reaches the putting content, stopping putting, and storing the final three-dimensional pixel model, as shown in the attached figure 7.
Respectively modeling p as 30%, 40% and 50% by using a three-dimensional residual space method and a traditional random aggregate;
TABLE 1 comparison of time generated by three-dimensional residual space method and conventional random aggregate method
Figure RE-RE-GDA0003147984670000111
The two methods can meet the requirements of general concrete gradation and aggregate content, but the larger the volume ratio is, the faster the three-dimensional residual space method is compared with the traditional random aggregate modeling method; the "model time consumption" in all examples refers to the average of the time consumed to generate 10 models on a workstation with 8 cores, 16 threads, 3.7GHz dominant frequency Intel Xeon W-2145 processor, 32.0GB memory.
Example two:
the purpose of this example is to illustrate the method of producing a concave polyhedral recycled concrete cylinder;
step 1, establishing a three-dimensional pixel model and a three-dimensional pixel sampling point
Determining the size x of an aggregate feeding area according to the size of the modelmax×ymax×zmaxThe operation is the same as that of the first example except that the thickness of the film is 100mm multiplied by 50 mm; and substituting o and p into o2+p2≤502Obtaining element coordinates meeting the formula, mapping the element coordinates to a three-dimensional pixel model, and only keeping the three-dimensional pixels of corresponding coordinates to obtain a cylinder;
step 2, determining the aggregate total volume ratio p to 40 percent and the maximum particle size dmaxThe aggregate grain size ranges of 20-16 mm, 16-10 mm, 10-5 mm and the cumulative volume percentage of 10.04%, 26.16% and 40%;
establishing a concave aggregate warehouse through step 3
(3.3) building convex polyhedral aggregate:
determining the slenderness ratio, wherein the equivalent radius is the radius r of each grade of aggregate, namely 8.75, 6.25 and 3.75, the long radius a of the corresponding circumscribed egg ball is 15.85, 9.26 and 6.26, the short radius b is 12.967, 7.55 and 4.94, the symmetrical radius c is 11.05, 6.36 and 4.00, and the polar radius d is 8.70, 5.12 and 3.14; the origin serves as the polyhedral aggregate center to generate an egg-ball equation:
Figure RE-RE-GDA0003147984670000121
dividing the ovum ball equally in three axes of x, y and z by using 6 endpoints of the ovum ball as fixed vertices of the convex polyhedron, substituting the plane equation into the ovum ball equation to solve to obtain supplementary points on the ovum ball as supplementary vertices of the polyhedron aggregate as shown in figure 8 (a);
adopting a Convex hull enclosure to construct an outer enclosure surface of a Convex enclosure body and acquiring information of each surface, as shown in figure 8(b), judging whether a central point of each element is in the polyhedron through coordinates of the central point of the element, if the central point of the element is in the polyhedron, adding 0.5 to a matrix element value of a corresponding position to become 1, and changing a material of a pixel at the position from mortar to aggregate as shown in figure 8 (c);
(3.4) establishing a concave polyhedral aggregate:
selecting three angular points of any surface, calculating the midpoint (X) of the surfacec,Yc,Zc) And is connected with the origin as a line segment lcAt lcUpper fetching point (X)ao,Yao,Zao) As pits of a polyhedron; the coordinates of the newly generated pits are expressed by the following formula:
Xao＝δXc,Yao＝δYc,Zao＝δZc,δ∈(0,1) (4)
where δ is the distance/l from the pit to the origincThe length of (c) is randomly selected from (0, 1);
selecting three angular points of the surface and newly generated concave points, constructing a Convex trihedron by using the Convex hull bounding body in the step (3.3), subtracting the trihedron from the original Convex polyhedron to obtain concave polyhedral aggregate, namely subtracting 0.5 from the element value of the corresponding position of the trihedron to obtain 0.5, and changing the material of the pixel from the aggregate into mortar as shown in the attached figure 8 (d); randomly rotating the concave aggregate by three Euler angles alpha, beta and gamma by taking the original point as a rotation point, wherein the range of beta is a uniform distribution function of [0, pi ], and alpha and gamma are uniform distribution functions of [0,2 pi ]; example (c): substituting coordinate points of all points of the aggregate into a rotation equation:
Figure RE-RE-GDA0003147984670000131
in the formula, x ', y ' and z ' are coordinates after rotation;
(3.5) recycled aggregate:
determining that the substitution rate v is 50%, successfully generating the aggregate in the step (3.3) and the step (3.4) through the step 5, or changing the aggregate element from 1 to 0.8 every time the aggregate is successfully generated in the step 8, and changing the material of the corresponding pixel into old mortar;
selecting one aggregate with the equivalent radius smaller than that of the old mortar from the steps (3.1), (3.2), (3.3) or (3.4) at the aggregate putting center of the old mortar; changing the element value of the matrix which simultaneously satisfies 'in old mortar' and 'in aggregate' to 1, namely, the material of the pixel is changed into old aggregate, as shown in figure 9 (a);
step 5, step 6, step 7 and step 8, the same operation as the first example is carried out, firstly, the recycled aggregate is put in, after the three-dimensional aggregate is successfully generated in step 8 each time, the natural aggregate is put in next time if the volume ratio of the recycled aggregate meets v x p, the recycled aggregate is put in next time if the volume ratio of the natural aggregate meets (1-v) x p, and the recycled aggregate is put in next time if the volume ratio of the natural aggregate meets the next time;
finally, the cylindrical volume rate of the recycled concrete with 50 percent of substitution rate reaches 41.93 percent; generating a three-dimensional concave polyhedron recycled concrete cylinder as shown in the attached figures 9(b) (c) (d) (e); if an interface transition area needs to be established, selecting the thickness of the interface, and establishing an interface with the same rotation angle as that of the old mortar and the old aggregate as the interface transition area;
example three
The purpose of this example is to illustrate the three-dimensional reconstruction flow, fitting, and no-over-boundary dropping of real aggregates;
step 1 is the same as the example one, and the three-dimensional matrix is expanded to Xmax×Ymax×Zmax102 × 102 × 102, the extension area element is set to 1; recording element positions and element center point coordinates of the matrix;
step 2, determining that the total volume of the aggregate p is 30%, and performing other operations in the same way as the first example;
step 4, establishing an aggregate library based on real aggregates
(4.1) pretreatment for extraction
Staining the components in the test block with iron green type S5605 iron oxide (Fe2O3) and iron red type S190 iron oxide (Fe2O 3); after pouring and maintenance, polishing the color concrete test block layer by using a water mill, scanning the polished and leveled test piece by using a scanner, and polishing the next time after scanning is finished; the grinding depth is 1mm each time;
(4.2) reconstructing a real three-dimensional model:
reconstructing the slice images with the scanned and identified components into a three-dimensional model, and generating a matrix with the actual size of 100mm multiplied by 80mm by the matrix scale of 1 pixel corresponding to the actual size of 1mm, as shown in the attached figures 10(a), (b), (c) and (d);
(4.3) reconstructing a real three-dimensional coarse aggregate:
extracting all real aggregates from the three-dimensional model to serve as a three-dimensional aggregate library for parameter extraction and aggregate putting; in a three-dimensional space, if a certain voxel is connected with other voxels in a neighborhood, the two voxels are in the same connected domain; extracting different aggregates by extracting different connected domains, and individually extracting voxels belonging to the aggregates into a new matrix, as shown in fig. 10 (e);
the aggregate is stored in the form of coordinates in the matrix, such as the form shown in the figure 2 (b); each new matrix is consistent with the actual size;
(4.4) pretreatment of fitting of single coarse aggregate:
calculating the coordinate of the center point of the aggregate, namely the total sum of the coordinate values and the coordinate number of each direction; constructing a polyhedron comprising all the coordinate points of the aggregate by using a convex hull algorithm, finally obtaining the coordinates of all outward convex vertexes of the aggregate, calculating a connecting line of the two vertexes with the longest distance in the aggregate, and recording the connecting line as the longest axis; performing three-dimensional translation and rotation on the whole aggregate to enable the center point of the aggregate to coincide with the origin of coordinates, and enabling the longest axis to coincide with the x axis;
(4.5) selecting convex vertexes of the convex surface of the coarse aggregate to perform fitting:
translating a single aggregate along the x axis for one time, translating the aggregate by +/-0.01-0.02 times of the longest axis every time, autorotating the aggregate around the x axis for m times, rotating the aggregate for 360 DEG/k every time, and then symmetrical 1 time about a yz plane to obtain (1+ l + m) groups of aggregates at different positions; fitting the outward convex vertexes of the aggregates at all the groups of positions to a standard sphere equation, an ellipsoid equation and an egg-ball equation respectively by using an iterative reweighted least square method; taking Mean Square Error (MSE) as the fitting error reference value; skipping fitting treatment of the polyhedron, and storing an aggregate coordinate with the minimum fitting error in each type of aggregate form, as shown in the attached drawing 10(f) (g) (h) (i);
(4.6) generating an aggregate library:
after obtaining each aggregate, counting the equivalent particle size of each aggregate, wherein the aggregates with the equivalent particle size of more than or equal to 5mm are classified into four types of aggregate forms according to the grading of the sieve so as to count the parameters of the aggregates with different grades; the aggregate with the equivalent grain diameter of less than 5mm is counted into the mortar part;
setting the center of the aggregate as an origin, randomly rotating for t (t is more than or equal to 50) times around x, y and z axes, wherein 360 DEG/t is used for each time, more than 62500 groups of rotation forms are shared, and all the rotation forms of the aggregate are stored;
(4.7) generating the aggregate by using a real aggregate warehouse:
b is made to be 1, the shape of the aggregate is selected, the equivalent radius is the radius of each level of aggregate, the first rotation form of the aggregate in the radius range is randomly selected, the aggregate is mapped to the three-dimensional pixel model and three-dimensionally translated to the aggregate feeding center, the aggregate center is superposed with the feeding center, the element value of the corresponding coordinate in the three-dimensional matrix is added by 0.5 to become 1, namely the material of the corresponding pixel in the three-dimensional pixel model is changed from mortar to aggregate;
steps 5, 6, 7 and 8 are the same as the example I;
deleting elements in the three-dimensional matrix expanded area to finally obtain the oval aggregate concrete with the volume rate of 30.0 percent based on the real aggregate; the time is 69.3s, and the three-dimensional real aggregate concrete is generated as shown in the attached figure 11.

Claims (5)

1.一种高效的混凝土三维骨料生成与投放方法——三维剩余空间法，其特征在于，包括以下步骤：1. an efficient concrete three-dimensional aggregate generation and throwing method---three-dimensional residual space method, is characterized in that, comprises the following steps: 步骤1、建立三维像素模型和三维像素采样点Step 1. Establish a three-dimensional pixel model and three-dimensional pixel sampling points 根据模型的尺寸确定骨料投放区域大小xmax×ymax×zmax，选定比例尺B建立元素值全为0.5的三维矩阵Xmax×Ymax×Zmax＝(B×xmax)×(B×ymax)×(B×zmax)，作为投放骨料的三维像素模型并记录矩阵的元素位置和元素中心点坐标，三维矩阵中的元素即为三维像素模型中的正方体单元，不同的元素值对应不同的像素颜色；Determine the size of the aggregate placement area x max ×y max ×z max according to the size of the model, and select the scale B to establish a three-dimensional matrix X max ×Y max ×Z max =(B×x max )×(B ×y max )×(B×z max ), as the three-dimensional pixel model for placing aggregates and record the element position of the matrix and the coordinates of the element center point. The elements in the three-dimensional matrix are the cube units in the three-dimensional pixel model. Different elements Values correspond to different pixel colors; 若不允许骨料超出边界，则将三维矩阵扩展到Xmax×Ymax×Zmax＝(B×xmax+2)×(B×ymax+2)×(B×zmax+2)，扩展区域元素设为1；并记录矩阵的元素位置和元素中心点坐标；If the aggregate is not allowed to exceed the boundary, the three-dimensional matrix is extended to X max ×Y max ×Z max =(B×x max +2)×(B×y max +2)×(B×z max +2), The element of the extended area is set to 1; and the element position of the matrix and the coordinates of the center point of the element are recorded; 建立控制x、y、z方向的三维像素采样点o、p、q；Establish three-dimensional pixel sampling points o, p, q that control the x, y, and z directions; o用于定位x轴，它沿x轴方向的元素为i，(i＝1，2，3……Xmax)，共有Xmax层切片，当x＝i，YZ切片大小为Ymax×Zmax，元素值全为i；o is used to locate the x-axis, and its elements along the x-axis are i, (i=1, 2, 3...X max ), there are X max slices in total, when x=i, the size of the YZ slice is Y max ×Z max , the element value is all i; p用于定位y轴，它沿y轴方向的元素为j，(j＝1，2，3……Ymax)，共有Ymax层切片，当y＝i，ZX切片大小为Zmax×Xmax，元素值全为j；p is used to locate the y-axis, and its elements along the y- axis are j , ( j =1, 2, 3... max , the element values are all j; q用于定位z轴，它沿z轴方向的元素为k，(k＝1，2，3……Zmax)，共有Zmax层切片，当z＝k，XY切片大小为Xmax×Ymax，元素值全为k；q is used to locate the z-axis, and its elements along the z-axis are k, (k=1, 2, 3... Z max ), there are Z max slices in total, when z=k, the XY slice size is X max ×Y max , the element value is all k; 步骤2、确定骨料总体积占比p、最大粒径dmax、各级配骨料粒径范围和累计体积占比百分数；Step 2. Determine the aggregate volume percentage p, the maximum particle size d max , the particle size range of the aggregates at all levels and the cumulative volume percentage; 步骤3、建立基于形状建模的骨料库Step 3. Build an aggregate library based on shape modeling (3.1)建立球骨料：(3.1) Establish ball aggregate: 球半径取各级配骨料的半径；将即将投放骨料的中心点、半径和三维像素采样点代入球公式，得到一个逻辑矩阵，记录满足条件的元素位置并映射到三维矩阵，将三维矩阵内对应位置的元素值加0.5变为1，即在三维像素模型内对应像素的所属材料从砂浆改变成骨料；The radius of the ball is the radius of the aggregates at all levels; the center point, radius and three-dimensional pixel sampling point of the aggregate to be put into the ball formula, get a logical matrix, record the positions of the elements that meet the conditions and map them to the three-dimensional matrix, and the three-dimensional matrix The element value of the corresponding position in the interior is increased by 0.5 to become 1, that is, the material of the corresponding pixel in the three-dimensional pixel model is changed from mortar to aggregate; 所述三维像素采样点之间的乘除运算为矩阵点乘和点除，即矩阵各个相同位置的元素相乘和相除；The multiplication and division operations between the three-dimensional pixel sampling points are matrix dot multiplication and dot division, that is, multiplication and division of elements in the same positions of the matrix; (3.2)建立椭球或卵球骨料：(3.2) Establish ellipsoid or egg ball aggregates: 确定长细比，等效半径取各级配骨料的半径，计算长半径、短半径、对称半径和极半径；Determine the slenderness ratio, the equivalent radius is the radius of the aggregates at all levels, and calculate the long radius, short radius, symmetrical radius and polar radius; 以即将投放骨料的中心点为旋转点将椭球或卵球随机旋转三个欧拉角α、β、γ，其中，β的范围是[0，π]均布函数，α和y是范围为[0，2π]的均布函数；Rotate the ellipsoid or egg ball randomly with three Euler angles α, β, γ taking the center point of the aggregate to be placed as the rotation point, where the range of β is the uniform distribution function of [0, π], and α and y are the range is a uniform distribution function of [0, 2π]; 将即将投放骨料的中心点、各类半径和三维像素采样点代入旋转后的形状公式，得到一个逻辑矩阵，记录满足条件的元素位置并映射到三维矩阵，将三维矩阵内对应位置的元素值加0.5变为1，即在三维像素模型内对应像素的所属材料从砂浆改变成骨料；Substitute the center point, various radii and three-dimensional pixel sampling points of the aggregate to be put into the rotated shape formula to obtain a logical matrix, record the element positions that meet the conditions and map them to the three-dimensional matrix, and convert the element values of the corresponding positions in the three-dimensional matrix. Add 0.5 to 1, that is, the material of the corresponding pixel in the three-dimensional pixel model is changed from mortar to aggregate; (3.3)建立凸多面体骨料：(3.3) Establish convex polyhedron aggregates: 确定长细比，等效半径取各级配骨料的半径，计算外接卵球的长半径、短半径、对称半径和极半径；在原点生成卵球，作为多面体骨料中心，以卵球的6个端点作为凸多面体的固定顶点，将卵球在x、y、z三轴平分，将平面方程代入卵球方程求解得到在卵球上的补充点，作为多面体骨料的补充顶点；Determine the slenderness ratio, the equivalent radius is the radius of the aggregates at all levels, and calculate the long radius, short radius, symmetrical radius and polar radius of the circumscribed egg sphere; The 6 endpoints are used as the fixed vertices of the convex polyhedron, and the egg ball is bisected on the three axes of x, y, and z, and the plane equation is substituted into the egg ball equation to solve the supplementary point on the egg ball, which is used as the supplementary vertex of the polyhedron aggregate; 采用Convex hull包围体构造凸包围体的外包面并获取各面信息，通过元素中心点坐标判断各元素中心点是否在该多面体内，三维像素模型中若元素中心点在多面体内，不包括中心点在面和边上的元素，则对应位置的矩阵元素值加0.5变为1，该位置像素所属材料从砂浆变为骨料；再以原点为旋转点按步骤(3.2)的方法旋转骨料并三维平移到投放中心点生成骨料；Convex hull bounding volume is used to construct the outer surface of the convex bounding volume and obtain the information of each surface, and judge whether the center point of each element is within the polyhedron by the coordinates of the element center point. For elements on faces and edges, the matrix element value of the corresponding position is increased by 0.5 to become 1, and the material to which the pixel belongs is changed from mortar to aggregate; then rotate the aggregate according to the method of step (3.2) with the origin as the rotation point and Three-dimensional translation to the delivery center point to generate aggregate; (3.4)建立凹多面体骨料：(3.4) Establish concave polyhedron aggregates: 运行步骤(3.3)生成进行未旋转和三维平移的凸多面体，采用Convex hull包围体构造凸包围体的外包面并获取各面信息，选取任意面的三个角点，计算出该面中点(Xc，Yc，Zc)并与原点相连记为线段lc，在lc上取点(Xao，Yao，Zao)作为多面体的凹点；新生成凹点的坐标以下式表示：Run step (3.3) to generate an unrotated and three-dimensionally translated convex polyhedron, use the Convex hull bounding volume to construct the outer surface of the convex bounding volume and obtain the information of each surface, select the three corner points of any surface, and calculate the midpoint of the surface ( X c , Y c , Z c ) and connected to the origin, denoted as line segment l c , take the point (X ao , Y ao , Z ao ) on l c as the concave point of the polyhedron; the coordinates of the newly generated concave point are expressed by the following formula : Xao＝δXc，Yao＝δYc，Zao＝δZc，δ∈(0，1) (1)X ao =δX c , Y ao =δY c , Z ao =δZ c , δ∈(0,1) (1) 式中，δ＝该凹点到原点的距离/lc的长度，在(0，1)上随机取值，表示这条边新生成的凹点向内凹的程度，δ越接近1，该边凹陷高度较小，μ越接近0，该边凹陷高度较高；In the formula, δ = the distance from the concave point to the origin / the length of l c , which is randomly selected on (0, 1), indicating the degree of concave inward of the newly generated concave point on this edge. The closer δ is to 1, the more The side concave height is smaller, the closer μ is to 0, the higher the side concave height; 选取该面的三个角点和新生成的凹点，用步骤(3.3)的Convex hull包围体构造凸三面体，用原凸多面体减去该三面体得到凹多面体骨料，即在三面体对应位置的元素值减0.5变为0.5，像素所属材料从骨料改为砂浆；再以原点为旋转点按步骤(3.2)的方法旋转骨料并三维平移到投放中心点生成骨料；Select the three corner points of the surface and the newly generated concave point, use the Convex hull bounding volume of step (3.3) to construct a convex trihedron, and subtract the trihedron from the original convex polyhedron to obtain the concave polyhedron aggregate, that is, the corresponding trihedron The element value of the position is reduced by 0.5 to 0.5, and the material to which the pixel belongs is changed from aggregate to mortar; then, using the origin as the rotation point, rotate the aggregate according to the method of step (3.2) and translate it three-dimensionally to the delivery center point to generate aggregate; (3.5)再生骨料：(3.5) Regenerated aggregate: 确定取代率v，在步骤(3.1)、(3.2)、(3.3)或(3.4)经过步骤5成功生成骨料，或在步骤8中每成功生成一次骨料，将骨料元素由1改为0.8，对应像素的所属材料变为老砂浆；Determine the substitution rate v, in step (3.1), (3.2), (3.3) or (3.4) to successfully generate aggregate after step 5, or in step 8 every time the aggregate is successfully generated, change the aggregate element from 1 to 0.8, the material of the corresponding pixel becomes the old mortar; 一侧为老砂浆另一侧为老骨料的生成方式，过骨料投放中心生成一个平面或曲面，随机旋转三个欧拉角α’、β’、y’，其中，β’的范围是[0，π]均布函数，α’和y’是范围为[0，2π]的均布函数；在三维像素模型中选定中心点同时满足“在骨料内”和“在生成面一侧”的像素，将三维矩阵中对应位置的元素值改为1，即像素所属材料变为老骨料；One side is the old mortar and the other side is the generation method of the old aggregate. A plane or curved surface is generated through the aggregate delivery center, and the three Euler angles α', β', and y' are randomly rotated, where the range of β' is [0, π] uniform distribution function, α' and y' are uniform distribution functions in the range [0, 2π]; in the three-dimensional pixel model, the center point is selected to satisfy both "in the aggregate" and "in the generation surface one" Change the element value of the corresponding position in the three-dimensional matrix to 1, that is, the material to which the pixel belongs becomes the old aggregate; 老砂浆完全包围或部分包围老骨料的生成方式，在老砂浆的骨料投放中心，在步骤(3.1)、(3.2)、(3.3)或(3.4)中选取一种建立等效半径小于老砂浆等效半径的骨料；将矩阵中将同时满足“在老砂浆内”和“在骨料内”的元素值改为1，即像素所属材料变为老骨料；The old mortar completely surrounds or partially surrounds the old aggregate. In the aggregate delivery center of the old mortar, select a method in steps (3.1), (3.2), (3.3) or (3.4) to establish an equivalent radius smaller than that of the old mortar. Aggregate with equivalent radius of mortar; change the value of elements in the matrix that satisfy both "in the old mortar" and "in the aggregate" to 1, that is, the material to which the pixel belongs becomes the old aggregate; 步骤4、建立基于真实骨料的骨料库Step 4. Build an aggregate library based on real aggregates (4.1)提取前处理(4.1) Pre-extraction processing 使用铁绿色S5605型氧化铁(Fe2O3)和铁红色S190型氧化铁(Fe2O3)对试块中的组分进行染色；经浇筑养护后，使用水磨机对彩色混凝土试块进行逐层打磨，并将打磨平整后的试件使用扫描仪进行扫描，扫描完成后再进行下一次打磨；每次打磨深度为1mm；不局限于以上几种颜料，只要能够形成明显的红色和绿色的颜料都可以用于混凝土的染色；Use iron green S5605 type iron oxide (Fe 2 O 3 ) and iron red S190 type iron oxide (Fe 2 O 3 ) to dye the components in the test block; after pouring and curing, use a water mill to color concrete test blocks. Grind layer by layer, and scan the smoothed specimen with a scanner, and then proceed to the next grinding after scanning; the depth of each grinding is 1mm; it is not limited to the above-mentioned pigments, as long as it can form obvious red and green All pigments can be used for concrete dyeing; (4.2)重构真实三维模型：(4.2) Reconstruct the real 3D model: 将扫描并识别出组分的切片图重构为三维模型，并以实际中1mm的尺寸对应1个像素的矩阵规模，生成与实际尺寸一致的矩阵；Reconstruct the sliced image of the scanned and identified components into a three-dimensional model, and generate a matrix consistent with the actual size with the actual size of 1mm corresponding to a matrix scale of 1 pixel; (4.3)重构真实三维粗骨料：(4.3) Reconstructing the real 3D coarse aggregate: 从三维模型中提取所有的真实骨料作为三维骨料库，用于参数的提取和骨料的投放；在三维空间中，若某体素与其他体素在邻域中相连，则这两个体素为同一连通域；通过提取不同连通域的方法提取出不同骨料，并将该属于骨料的体素单独提取到一个新的矩阵中；All real aggregates are extracted from the 3D model as a 3D aggregate library for parameter extraction and aggregate placement; in 3D space, if a voxel is connected to other voxels in the neighborhood, the two voxels are the same connected domain; different aggregates are extracted by the method of extracting different connected domains, and the voxels belonging to the aggregates are separately extracted into a new matrix; 在矩阵中以坐标的形式存储骨料，各新矩阵和实际尺寸一致；The aggregate is stored in the form of coordinates in the matrix, and each new matrix is consistent with the actual size; (4.4)单个粗骨料拟合前处理：(4.4) Pre-processing of single coarse aggregate fitting: 计算骨料中心点坐标＝各个方向坐标值总和/坐标个数；使用凸包算法，即构造一个包含所有骨料坐标点的多面体，最终得到骨料各外凸顶点坐标，计算骨料内距离最长的两个顶点的连线,记为最长轴；将整个骨料进行三维平移和旋转，使得骨料的中心点与坐标原点重合，最长轴与x轴重合；Calculate the coordinates of the center point of the aggregate = the sum of the coordinate values in each direction/the number of coordinates; use the convex hull algorithm, that is, construct a polyhedron containing all the coordinate points of the aggregate, and finally obtain the coordinates of each convex vertex of the aggregate, and calculate the maximum distance within the aggregate. The line connecting the two long vertices is recorded as the longest axis; the entire aggregate is translated and rotated three-dimensionally, so that the center point of the aggregate coincides with the coordinate origin, and the longest axis coincides with the x-axis; (4.5)选取粗骨料外凸面的各外凸顶点进行拟合：(4.5) Select each convex vertex of the outer convex surface of the coarse aggregate for fitting: 将单个骨料沿x轴平移l次，每次平移±(0.01～0.02)倍最长轴，绕x轴自转m次，每次转360°/k，再关于yz面对称1次，共得到(1+l+m)组不同位置的骨料；使用迭代重加权最小二乘法将各组位置的骨料的外凸顶点分别对标准球、椭球、卵球方程进行拟合；拟合误差参考值取均方误差MSE；多面体跳过拟合处理，每类骨料形态都保存一个拟合误差最小的骨料坐标；Translate a single aggregate along the x-axis for l times, each translation is ±(0.01～0.02) times the longest axis, rotate m times around the x-axis, 360°/k each time, and then symmetrically about the yz plane once, a total of Obtain (1+l+m) aggregates at different positions; use the iterative reweighted least squares method to fit the standard sphere, ellipsoid and egg sphere equations on the convex vertices of the aggregates at each group position respectively; The error reference value is the mean square error MSE; the polyhedron skips the fitting process, and each type of aggregate shape saves an aggregate coordinate with the smallest fitting error; (4.6)生成骨料库：(4.6) Generate aggregate library: 获取各个骨料后，统计每个骨料的等效粒径，等效粒径大于等于5mm的骨料根据筛分级配，将真实的骨料分为四类骨料形态以统计各级配骨料的参数；等效粒径小于5mm的骨料计入砂浆部分；After obtaining each aggregate, the equivalent particle size of each aggregate is counted, and the aggregate with an equivalent particle size greater than or equal to 5mm is classified according to the sieve classification, and the real aggregate is divided into four types of aggregate shapes to count the distribution of each grade. Parameters of aggregates; aggregates with equivalent particle size less than 5mm are included in the mortar part; 将骨料中心设为原点，绕x，y，z轴随机旋转t(t≥50)次，每次360°/t，共有超过62500组旋转形式，保存骨料的所有旋转形式；Set the center of the aggregate as the origin, rotate randomly around the x, y, and z axes t (t≥50) times, 360°/t each time, there are more than 62,500 sets of rotation forms, and all the rotation forms of the aggregate are saved; (4.7)用真实骨料库生成骨料：(4.7) Generate aggregate with real aggregate library: 令B＝1，选定骨料形状，等效半径取各级配骨料的半径，随机选择该半径范围内的第几个骨料的第几种旋转形式，将骨料映射到三维像素模型，并三维平移到骨料投放中心，使骨料中心与投放中心重合，三维矩阵中对应坐标的元素值加0.5变为1，即在三维像素模型内对应像素的所属材料从砂浆改变成骨料；Let B=1, select the shape of the aggregate, the equivalent radius is the radius of the aggregates at all levels, randomly select the rotation form of the number of aggregates within the radius range, and map the aggregates to the three-dimensional pixel model , and three-dimensionally translate to the aggregate delivery center, so that the aggregate center coincides with the delivery center, and the element value of the corresponding coordinate in the 3D matrix is increased by 0.5 to become 1, that is, the material of the corresponding pixel in the 3D pixel model is changed from mortar to aggregate. ; 步骤5、手动投放前n个骨料Step 5. Manually put the first n aggregates 若真实模型尺寸三个边界长度均不小于5dmax，则n＝9，在三维像素模型中心点，以及距三维像素模型边界面1/4～1/3边界长度处的8个点投放骨料；If the three boundary lengths of the real model size are not less than 5d max , then n=9, put the aggregate at the center point of the three-dimensional pixel model and 8 points from the boundary surface of the three-dimensional pixel model at 1/4 to 1/3 of the boundary length. ; 若真实模型尺寸某一方向边界长度小于5dmax，则n＝5，在三维像素模型中心点，以及在该方向边界长度的一半，距其他方向边界面1/4～1/3边界长度处的4个点投放骨料；If the boundary length in a certain direction of the real model size is less than 5d max , then n=5, at the center point of the three-dimensional pixel model, and at half of the boundary length in this direction, 1/4 to 1/3 of the boundary length from the boundary surface in other directions 4 points to put the aggregate; 若真实模型尺寸两个方向边界长度均小于5dmax，则n＝3，在三维像素模型中心点，以及在距这些边界长度的一半，距其他方向边界面1/4～1/3边界长度处的2个点投放骨料；If the boundary lengths in both directions of the real model size are less than 5d max , then n=3, at the center point of the three-dimensional pixel model, and at half the length from these boundaries, and 1/4 to 1/3 of the boundary length from the boundary surfaces in other directions The 2 points of the aggregate are put in; 若真实模型尺寸三个边界长度均小于5dmax，则n＝1，在三维像素模型中心点投放骨料；If the three boundary lengths of the real model size are all less than 5d max , then n=1, and the aggregate is placed at the center point of the three-dimensional pixel model; 步骤6、选取三维剩余空间生成骨架Step 6. Select the remaining three-dimensional space to generate the skeleton 在三维矩阵中获取垂直于z方向的Zmax层切片，获取方法为每隔一个像素切一层，每一层切片中z方向上只有一个单位长度；在每一层切片上选取未投放骨料的空间即三维剩余空间，通过骨架算法获取骨架，即目标轮廓的最大内切圆的圆心的集合；在切片的骨架像素点中，若某个像素点沿正x、正y、负x、负y四个方向相邻位置的像素均为骨架像素点，则该像素点为骨架的分支点，记录位置和中心点坐标；再把每一层切片按原位置组合到三维像素模型；Obtain the Z max layer slices perpendicular to the z direction in the three-dimensional matrix. The method of obtaining is to cut one layer every other pixel. There is only one unit length in the z direction in each layer slice; The space is the three-dimensional remaining space, and the skeleton is obtained by the skeleton algorithm, that is, the set of the centers of the largest inscribed circles of the target contour; The pixels in the adjacent positions in the four directions of y are all skeleton pixel points, then the pixel point is the branch point of the skeleton, and the position and center point coordinates are recorded; then each layer of slices is combined into the three-dimensional pixel model according to the original position; 使用与上述相同的方法获取垂直于x和y方向切片的骨架分支点，并记录位置和中心点坐标；Use the same method as above to obtain the skeleton branch points sliced perpendicular to the x and y directions, and record the position and center point coordinates; 步骤7、对骨架的分支点进行聚类Step 7. Cluster the branch points of the skeleton (7.1)将垂直于x、y、z三个方向的切片的骨架分支点按原位置组合到三维像素模型；删掉重复的分支点；(7.1) Combine the skeleton branch points of the slices perpendicular to the three directions of x, y, and z into the three-dimensional pixel model according to the original position; delete the repeated branch points; (7.2)骨料边角的分支点采用凸包算法，即生成一个包含所有分支点的外包多面体，删除重复面，取该外包多面体顶点作为聚类点，删掉已经位于边界的顶点；(7.2) The branch points of the aggregate edges and corners adopt the convex hull algorithm, that is, an outsourcing polyhedron containing all the branch points is generated, the duplicate faces are deleted, the vertices of the outsourcing polyhedron are taken as the clustering points, and the vertices that are already located on the boundary are deleted; (7.3)骨架中间部分的分支点采用基于欧几里得的点云聚类算法：(7.3) The branch point in the middle part of the skeleton adopts the point cloud clustering algorithm based on Euclid: 将所有分支点代入欧几里得点云聚类算法，距离参数取骨料粒径的1/10，若小于1mm则取1mm，获取所有类簇的分支点作为聚类点，若某类簇中的分支点数量大于或等于3个，取该类簇中所有分支点中心点坐标的均值作为聚类点；Substitute all branch points into the Euclidean point cloud clustering algorithm. The distance parameter takes 1/10 of the aggregate particle size, and if it is less than 1mm, take 1mm, and obtain the branch points of all clusters as clustering points. The number of branch points is greater than or equal to 3, and the mean of the coordinates of the center points of all branch points in this cluster is taken as the cluster point; (7.4)骨架边缘的分支点：(7.4) Branch points at the edge of the skeleton: 获取最靠近边界面的所有骨架分支点，采用基于欧几里得的点云聚类算法，距离参数取1mm，将各类簇中所有分支点中心点坐标的均值作为聚类点；Obtain all the skeleton branch points closest to the boundary surface, adopt the point cloud clustering algorithm based on Euclid, take the distance parameter as 1mm, and take the mean value of the center point coordinates of all branch points in various clusters as the clustering point; (7.5)记录所有聚类点的坐标；(7.5) Record the coordinates of all clustering points; 步骤8、开始投放骨料Step 8. Start adding aggregate (8.1)依次选取聚类点的坐标，使用步骤3或步骤4生成的骨料进行投放：(8.1) Select the coordinates of the clustering points in turn, and use the aggregates generated in step 3 or step 4 for delivery: (8.2)是否超出边界或重叠(8.2) Whether out of bounds or overlapping 若三维矩阵中有不小于1.5的元素值，则骨料超出边界或与已投放骨料重叠，删除本次投放的骨料，即在三维矩阵中将本次投放骨料对应位置的元素值减0.5；If there is an element value of not less than 1.5 in the three-dimensional matrix, the aggregate exceeds the boundary or overlaps with the already placed aggregate, and the aggregate placed this time will be deleted, that is, the element value at the corresponding position of the placed aggregate will be subtracted in the three-dimensional matrix. 0.5; 否则投放成功，计算当前体积率L；Otherwise, the delivery is successful, and the current volume rate L is calculated; (8.3)所有聚类点都经过选取后，该轮投放结束；该轮投放过程中，若当前体积率未达到投放含量的要求、且在该轮投放中有骨料投放成功，则模型生成过程未结束，接着选取该轮投放结束后的三维剩余空间进行步骤6、7、8的操作；(8.3) After all clustering points have been selected, this round of delivery ends; during this round of delivery, if the current volume rate does not meet the requirements of the delivery content, and the aggregate delivery is successful in this round of delivery, the model generation process If it is not over, then select the three-dimensional remaining space after the round of delivery is over to carry out the operations of steps 6, 7, and 8; (8.4)若该轮所有聚类点均不能成功投放骨料或L满足含量要求时，投放终止，保存最终的三维像素模型。(8.4) If all the clustering points in this round cannot be successfully put into aggregate or L meets the content requirements, the putting in is terminated and the final three-dimensional pixel model is saved. 2.根据权利要求1所述的一种高效的混凝土三维骨料生成与投放方法——三维剩余空间法，其特征在于，开始生成三维骨料时，分别在每一个粒径范围内取一个等效半径，以所取的最大半径作为三维骨料的等效半径，所有类型的半径均乘以B作为编程所用的半径；步骤8中每次有三维骨料投放成功，若L不满足投放含量要求，且L大于该粒径范围的累计体积占比百分数时，将等效半径改为下一粒径范围的等效半径，重新计算三维骨料参数；若为再生混凝土，先投放再生骨料，当再生骨料体积率满足v×p时，下一次投放天然骨料，当天然骨料体积率满足(1-v)×p时，下一次投放再生骨料，若同时满足下一次投放再生骨料。2. a kind of efficient concrete three-dimensional aggregate generation and throwing method according to claim 1---three-dimensional residual space method, it is characterized in that, when starting to generate three-dimensional aggregate, take one etc. in each particle size range respectively. Effective radius, take the maximum radius taken as the equivalent radius of 3D aggregate, all types of radii are multiplied by B as the radius used for programming; in step 8, every time 3D aggregate is successfully delivered, if L does not meet the delivery content requirements, and L is greater than the cumulative volume percentage of the particle size range, change the equivalent radius to the equivalent radius of the next particle size range, and recalculate the three-dimensional aggregate parameters; if it is recycled concrete, put recycled aggregate first , when the volume ratio of recycled aggregate satisfies v×p, the natural aggregate is put in the next time; when the volume ratio of natural aggregate satisfies (1-v)×p, the recycled aggregate is put in the next time, if it also meets the requirements of the next feeding of recycled aggregate aggregate. 3.根据权利要求1所述的一种高效的混凝土三维骨料生成与投放方法——三维剩余空间法，其特征在于，生成钢筋混凝土模型时，在步骤1中预先记录钢筋的位置并将对应位置矩阵元素值设为1，不执行步骤5的手动投放骨料；三维骨料投放结束后，将钢筋对应像素位置的元素值改为2，即对应像素的所属材料变为钢筋。3. a kind of efficient concrete three-dimensional aggregate generation and throwing method according to claim 1---three-dimensional residual space method, it is characterized in that, when generating reinforced concrete model, in step 1, pre-record the position of steel bar and correspondingly. The element value of the position matrix is set to 1, and the manual aggregate placement in step 5 is not performed; after the 3D aggregate placement is completed, the element value of the corresponding pixel position of the steel bar is changed to 2, that is, the material of the corresponding pixel becomes the steel bar. 4.根据权利要求1所述的一种高效的混凝土三维骨料生成与投放方法——三维剩余空间法，其特征在于，若需生成其他截面的混凝土，且该截面必须在xmax×ymax×zmax的范围内，根据截面所在面从o、p、q中选取两个矩阵代入形状公式，在映射到三维像素模型中，将对应三维矩阵元素值改为0.5，其他位置的元素值改为1，作为三维矩阵扩大区域。4. a kind of efficient concrete three-dimensional aggregate generation and throwing method according to claim 1 - three-dimensional residual space method, it is characterized in that, if need to generate the concrete of other section, and this section must be in x max × y max Within the range of ×z max , select two matrices from o, p, and q according to the surface of the section and substitute them into the shape formula. In the mapping to the three-dimensional pixel model, change the element value of the corresponding three-dimensional matrix to 0.5, and change the element value of other positions. is 1, as the three-dimensional matrix expands the area. 5.根据权利要求1所述的一种高效的混凝土三维骨料生成与投放方法——三维剩余空间法，其特征在于，保存模型时，允许超边界的模型可直接保存，不允许超边界的模型需对投放结束后的三维矩阵进行以下处理：5. a kind of efficient concrete three-dimensional aggregate generation and throwing method according to claim 1---three-dimensional residual space method, it is characterized in that, when saving model, the model that allows superboundary can be saved directly, does not allow superboundary model. The model needs to perform the following processing on the 3D matrix after delivery: 将三维矩阵扩大区域的元素删除，使三维像素模型和真实的三维骨料模型一致。The elements in the enlarged area of the 3D matrix are deleted to make the 3D pixel model consistent with the real 3D aggregate model.
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