CN110889903B - Three-dimensional model fast voxelization method based on slicing strategy - Google Patents
Three-dimensional model fast voxelization method based on slicing strategy Download PDFInfo
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Abstract
A three-dimensional model fast voxelization method based on a slicing strategy comprises the steps of firstly, establishing a three-dimensional model voxelization space based on a model bounding box; cutting the three-dimensional model layer by using a plane vertical to the Z axis to obtain a cut section; secondly, cutting the obtained section layer by layer on a two-dimensional plane by using a straight line perpendicular to the Y axis to obtain a plurality of section lines; all voxel cells on the resulting tangent are then lit up in the X-direction. And repeating the steps to achieve the aim of realizing the voxelization of the three-dimensional model by illuminating all the three-dimensional model occupying voxel units from line to surface to body. The method can realize direct integral cutting of the model and can quickly process the model with complex geometric characteristics.
Description
Technical Field
The invention belongs to the technical field of computer aided engineering and finite element meshing, and particularly relates to a three-dimensional model fast voxelization method based on a slicing strategy.
Background
Computer Aided Engineering (CAE) uses computer technology to perform design and manufacturing process analysis of products, and the computational analysis process generally adopts a finite element analysis method and utilizes a mathematical approximation method to simulate a real physical system (geometric and load working conditions). With simple and interacting elements (i.e., grid cells), a finite number of unknowns can be used to approximate a real system of infinite unknowns. The mesh division is to divide the model into a plurality of small units, which are used as the important factor in the pretreatment of finite element analysis, and the matching degree of the mesh division and the calculation target and the quality of the mesh determine the quality of the later finite element calculation. Therefore, the element partition processing for the three-dimensional model is a key problem for developing finite element analysis and performing CAE calculation. The invention provides a new grid division technology based on a voxelization method, which is used for quickly and accurately converting a three-dimensional grid model into grid units for finite element calculation.
Disclosure of Invention
The invention aims to overcome the defects of the existing voxelized grid partitioning algorithm in the aspects of partitioning precision and partitioning efficiency, and provides a three-dimensional model fast voxelization method based on a layer cutting strategy.
In order to achieve the purpose, the invention adopts the following technical scheme:
a three-dimensional model fast voxelization method based on a slicing strategy is characterized by comprising the following steps:
step 1: reading in vertex coordinate information of the three-dimensional model;
step 2: traversing coordinate information to obtain maximum value X of three-direction coordinates of modelmax、Ymax、ZmaxAnd minimum value Xmin、Ymin、ZminEstablishing a model bounding box;
and step 3: establishing a model voxel space based on the model bounding box, setting the side length of each voxel unit as dx, and respectively obtaining the number of the voxel units in the direction X, Y, Z;
and 4, step 4: setting a switch value for each voxel unit, wherein the initial switch values are all 0, and labeling each voxel unit in sequence;
and 5: a plane Z' vertical to the Z axis is tangent with the model to obtain a section J, and the boundary contour of the section J is the section contour; setting the coordinate of the plane Z 'along the Z direction as M, wherein the plane Z' is not overlapped with the surface of the voxel unit;
step 6: a straight line Y 'vertical to the Y axis is tangent to the section J under a two-dimensional coordinate system to obtain all intersection points p of the straight line Y' and the section J; setting the coordinate of the straight line Y 'along the Y direction as N, wherein the straight line Y' is not overlapped with the edge of the voxel unit;
and 7: lighting all voxel units between the intersection points p along the one-dimensional X direction, namely setting the switch values of the voxel units as 1;
and 8: and (6) looping steps 6 and 7, wherein the initial M is 1/2dx, and each loop increases the dx by N, namely N is N + dx, and if N is N>YmaxStopping circulation, and finally lighting the voxel units of all the sections J;
and step 9: and (5) looping steps 5 and 8, wherein the initial N is 1/2dx, and each loop increases M by dx, namely M is M + dx, and if M is M>ZmaxThe circulation is stopped;
step 10: and traversing all voxel units in the voxel space, wherein all voxel units with the switch value of 1 are the model voxel set.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in step 3, the number nx of voxel units in the X direction, the number ny of voxel units in the Y direction, and the number nz of voxel units in the Z direction are calculated according to the following formula:
nx＝(Xmax-Xmin)/dx
ny＝(Ymax-Ymin)/dx
nz＝(Zmax-Zmin)/dx
and obtaining a model voxel space with the number of voxel units of nx x ny x nz in the model bounding box by taking integers of nx, ny and nz.
Further, in step 4, the order formula of the voxel unit is expressed as follows:
P＝k×nx×ny+j×nx+i
wherein k, j and i are serial numbers of the voxel units in Z, Y, X three directions in the bounding box space, k is more than or equal to 0 and is less than nz, j is more than or equal to 0 and is less than ny, i is more than or equal to 0 and is less than nx, and P is more than or equal to 0 and is less than nz x nx x ny + ny x nx + nx.
Further, in step 5, the Z-direction sequence numbers of all voxel units on the cross section J are k, k is an integer, and k is M/dx.
Further, in step 6, the serial numbers of all voxel units on the straight line Y' in the Y direction are j, j is an integer, and j is N/dx;
cutting the section J with a straight line Y' to obtain an intersection point p of the straight line and the section profile1、p2Point of intersection p1、p2The coordinates in the X direction are X respectively1、x2；
Let the point of intersection p1Serial number in X direction of i1Point of intersection p2Serial number in X direction of i2，i1、i2Taking an integer, the formula is as follows:
i1＝x1/dx
i2＝x2/dx
let the point of intersection p1、p2The number of the occupied voxel unit in the voxel space is P1、P2And then:
P1＝k×nx×ny+j×nx+i1
P2＝k×nx×ny+j×nx+i2。
further, in step 7, P is marked1、P2I.e. with the sequence number P1、P2The switch value of a voxel unit is 1.
The invention has the beneficial effects that:
1. the triangular mesh model is directly cut integrally, and voxelization is completed in a line-to-face-to-body mode, so that compared with a method of voxelizing the outer surface of the model and then voxelizing the inner space of the model, more traversal processes are saved, and the voxelization efficiency is higher;
2. only one variable dx needs to be set, the operation is convenient, and the smaller the distance dx between each node is set, the more accurate the voxelization of the model is;
3. and each voxel unit is labeled, so that the coordinates of each node and the corresponding position of the voxel unit can be searched, and the establishment of a topological relation and the finite element calculation are facilitated.
Drawings
Fig. 1a to 1d are plane node lighting flowcharts: FIG. 1a is a view of the entire mold cut perpendicular to the Z-axis plane; FIG. 1b is a cross-sectional profile after cutting; FIG. 1c is a two-dimensional planar lower cross-sectional profile; fig. 1d is a diagram of lighting all voxel cells within the cross-sectional profile.
Fig. 2 is a schematic diagram of the spatial relationship of a cross section to a triangular patch.
FIG. 3 is a schematic diagram of the intersection of the straight line Y' with the plane.
Fig. 4 is a schematic diagram of a labeled boundary voxel unit error case 1 when a section J is cut straight.
Fig. 5 is a schematic diagram of a labeled boundary voxel cell error case 2 when a section J is cut straight.
Fig. 6 is a schematic diagram of labeling boundary voxel cells for error 1.
Fig. 7 is a schematic diagram of labeling boundary voxel cells for error 2.
Fig. 8 is a schematic diagram of lighting a voxel cell between two labeled voxel cells.
Fig. 9 is a schematic diagram of the lit cross section J occupying all voxel units.
FIG. 10 is a schematic representation of the results of somatization.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
The invention provides a three-dimensional model fast voxelization method based on a slicing strategy, which specifically comprises the following steps:
step 1: and reading in vertex coordinate information of the three-dimensional model.
Step 2: establishing a triangular mesh model bounding box, which specifically comprises the following steps: traversing coordinate information of all vertexes of the triangular mesh model, comparing the coordinate size of each point in three directions, and finding the maximum value and the minimum value in the three directions, namely: xmin、Xmax、Ymin、Ymax、Zmin、Zmax. According to the maximum vertex (X)max，Ymax，Zmax) Minimum vertex (X)min，Ymin，Zmin) A model bounding box is available.
And step 3: establishing a model voxel space: the side length dx of each voxel unit is set. The number nx of voxel units in the X direction, the number ny of voxel units in the Y direction and the number nz of voxel units in the Z direction are shown in the following formula:
nx＝(Xmax-Xmin)/dx (1)
ny＝(Ymax-Ymin)/dx (2)
nz＝(Zmax-Zmin)/dx (3)
and taking integers of nx, ny and nz to obtain a voxel space with the number of nx × ny × nz voxel units in the bounding box.
And 4, step 4: each voxel unit establishes a switch value, and the initial switch values are all 0. Each voxel cell is labeled sequentially. The order formula for voxel unit is as follows:
P＝k×nx×ny+j×nx+i (4)
k. j and i are serial numbers of the voxel units in Z, Y, X three directions in the bounding box space, k is more than or equal to 0 and less than nz, j is more than or equal to 0 and less than ny, i is more than or equal to 0 and less than nx, and P is more than or equal to 0 and less than nz x ny + ny x nx + nx.
And 5: as shown in fig. 1a, 1b, and 1c, a plane Z' perpendicular to the Z axis is taken, the plane Z-direction coordinate is set to M, and M is initialized to 1/2dx so that the plane does not overlap the plane of the voxel unit. Setting the sequence numbers of all voxel units in the Z direction on the plane P as k, wherein k is an integer, and the formula of k is shown as formula (5):
k＝M/dx (5)
and (3) cutting the model into layers by using a plane Z ', wherein when the plane Z' cuts each triangular mesh, a line segment is obtained by traversing a triangular patch in the patch container on the current layer, and if the triangular patch is tangent to the layer, the line segment of the triangular patch and the line segment of the layer is obtained. First, the spatial positions of the current triangular patch Tri and the cross section Z' need to be determined, as shown in fig. 2, T1，T2And T3Three vertexes, Z, of the triangular patch respectively1And Z2Respectively adjacent Z' planes. If the triangle Tri has two nodes Z at a level higher than the Z' section, e.g. Z1Crossing with Tri, the section line intersection point S1、E1From Z1And line segment T2T3And a line segment T1T3Respectively solving; if the triangle Tri has a node Z at a level higher than the Z' section, e.g. Z2Crossing with Tri, the section line intersection point S2、E2From Z2And line segment T1T2And a line segment T1T3Respectively obtaining. To find S1For example, the coordinates can be obtained by a linear equation as shown in equation (6):
T2the coordinate is (x)2,y2,z2)，T3The coordinate is (x)3,y3,z3)，S1The coordinate is (x)s,ys,zs) M is the section Z1Z-direction coordinates of (a).
And finally obtaining a plane P which is composed of a plurality of line segments and surrounds completely after traversal is finished, wherein the boundary contour of the plane P is the section contour of the model cut by the Z' plane.
Step 6: taking a straight line Y' perpendicular to the Y axis, the coordinates in the direction of the straight line Y are set to N, and N is initialized to 1/2dx in order to ensure that the straight line does not coincide with the edge of a voxel cell. Let the serial numbers of all nodes in the Y direction on the straight line Y' be j, j is an integer, and the formula for solving j is shown in formula (7):
j＝N/dx (7)
cutting the section J in step 5 with a straight line Y' to obtain an intersection point p of the straight line and the section profile as shown in FIG. 31、p2From the formula (8), two point coordinates x can be obtained1、x2：
Line segment ScEcPoint ScThe coordinate is (x)Sc，ySc) Point EcThe coordinate is (x)Ec，yEc)。ScEcPoint p of intersection with straight line Y1The coordinate is (x)1，N)，p2The coordinate is (x)2And N) is the Y-direction coordinate of the straight line Y'.
Let node p1Serial number in X direction of i1Node p2Serial number in X direction of i2，i1、i2Taking an integer, the formula is as follows:
i1＝x1/dx (9)
i2＝x2/dx (10)
setting a node p according to the voxel space ordering criterion established in the step 3 and the step 41、p2The number of the occupied voxel unit in the voxel space is P1、P2Then, the following equations (4), (5), (7), (9) and (10) can be obtained:
P1＝k×nx×ny+j×nx+i1(11)
P2＝k×nx×ny+j×nx+i2(12)
sign P1、P2I.e. with the sequence number P1、P2The switch value of a voxel unit is 1.
Two error cases can occur during the labeling of boundary voxel cells:
1. marking a point P after the value i is integer according to a formula (10)2Deviation from the voxel unit occupied by the actual curve, resulting in P2The right voxel cell is not labeled and the voxelization results are not accurate (fig. 4).
2. When the straight line Y 'cuts the section J, and the intersection a of the straight line Y' and the section intersects with the voxel cell boundary, X is determined according to the formula (9)1Dx can be divided equally, when P1The left voxel cell is not labeled, leading to inaccurate voxelization results (fig. 5).
And 7: and 6, executing the step (4):
if error case 1 occurs: let P3＝P2+1, with the tag number P3Let the switch value of the voxel unit of (1). The cancellation mark having a sequence number P2Let the switch value of the voxel unit (2) be 0 (fig. 6).
If error case 2 occurs: let P4＝P1-1, with a tag number P4Let the switch value of the voxel unit of (1). The cancellation mark having a sequence number P1Let the switch value of the voxel unit (2) be 0 (fig. 7).
And 8: in the one-dimensional X direction, all voxel units between the two labeled voxel units in step 7 are lighted, i.e. their switch value is 1, and at this time, all voxel units on a straight line are lighted (fig. 8).
And step 9: and 7, looping steps 7 and 8, wherein the initial N is 1/2dx, and each loop increases the dx by N, namely N is N + dx, and if N is N>YmaxThe loop is stopped and eventually all voxel cells of the P-plane can be lit up (fig. 9, fig. 1 d).
Step 10: and (5) looping steps 5 and 9, wherein the initial M is 1/2dx, and each loop increases the dx of M, namely M is M + dx, and if M is M + dx>ZmaxThe cycle is stopped.
Step 11: and traversing all voxel units in the voxel space, wherein all voxel units with the switch value of 1 are the model voxel set. Finally, the whole voxel of the three-dimensional model can be realized from line to surface to volume (figure 10).
It should be noted that the terms "upper", "lower", "left", "right", "front", "back", etc. used in the present invention are for clarity of description only, and are not intended to limit the scope of the present invention, and the relative relationship between the terms and the terms is not limited by the technical contents of the essential changes.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.
Claims (6)
1. A three-dimensional model fast voxelization method based on a slicing strategy is characterized by comprising the following steps:
step 1: reading in vertex coordinate information of the three-dimensional model;
step 2: traversing coordinate information to obtain maximum value X of three-direction coordinates of modelmax、Ymax、ZmaxAnd minimum value Xmin、Ymin、ZminEstablishing a model bounding box;
and step 3: establishing a model voxel space based on the model bounding box, setting the side length of each voxel unit as dx, and respectively obtaining the number of the voxel units in the direction X, Y, Z;
and 4, step 4: setting a switch value for each voxel unit, wherein the initial switch values are all 0, and labeling each voxel unit in sequence;
and 5: a plane Z' vertical to the Z axis is tangent with the model to obtain a section J, and the boundary contour of the section J is the section contour; setting the coordinate of the plane Z 'along the Z direction as M, wherein the plane Z' is not overlapped with the surface of the voxel unit;
step 6: a straight line Y 'vertical to the Y axis is tangent to the section J under a two-dimensional coordinate system to obtain all intersection points p of the straight line Y' and the section J; setting the coordinate of the straight line Y 'along the Y direction as N, wherein the straight line Y' is not overlapped with the edge of the voxel unit;
and 7: lighting all voxel units between the intersection points p along the one-dimensional X direction, namely setting the switch values of the voxel units as 1;
and 8: and (6) looping steps 6 and 7, wherein the initial M is 1/2dx, and each loop increases the dx to N, namely N is N + dx, when N is N>YmaxStopping time loop, and finally lighting the voxel units of all the sections J;
and step 9: and (5) circulating the steps (5) and (8), wherein the initial N is 1/2dx, and each circulation increases M by dx, namely M is M + dx, when M is M>ZmaxStopping the time cycle;
step 10: and traversing all voxel units in the voxel space, wherein all voxel units with the switch value of 1 are the model voxel set.
2. The three-dimensional model fast voxelization method based on the slicing strategy as claimed in claim 1, characterized in that: in step 3, the number nx of voxel units in the X direction, the number ny of voxel units in the Y direction and the number nz of voxel units in the Z direction are calculated according to the following formula:
nx＝(Xmax-Xmin)/dx
ny＝(Ymax-Ymin)/dx
nz＝(Zmax-Zmin)/dx
and obtaining a model voxel space with the number of voxel units of nx x ny x nz in the model bounding box by taking integers of nx, ny and nz.
3. The three-dimensional model fast voxelization method based on the slicing strategy as claimed in claim 2, characterized in that: in step 4, the order formula of the voxel unit is as follows:
P＝k×nx×ny+j×nx+i
wherein k, j and i are serial numbers of the voxel units in Z, Y, X three directions in the bounding box space, k is more than or equal to 0 and is less than nz, j is more than or equal to 0 and is less than ny, i is more than or equal to 0 and is less than nx, and P is more than or equal to 0 and is less than nz x nx x ny + ny x nx + nx.
4. The three-dimensional model fast voxelization method based on the slicing strategy as claimed in claim 3, characterized in that: in step 5, the sequence numbers of all voxel units on the section J in the Z direction are k, k is an integer, and k is M/dx.
5. The three-dimensional model fast voxelization method based on the slicing strategy as claimed in claim 4, wherein: in step 6, the serial numbers of all voxel units in the Y direction on the straight line Y' are j, j is an integer, and j is N/dx;
cutting the section J with a straight line Y' to obtain an intersection point p of the straight line and the section profile1、p2Point of intersection p1、p2The coordinates in the X direction are X respectively1、x2；
Let the point of intersection p1Serial number in X direction of i1Point of intersection p2Serial number in X direction of i2，i1、i2Taking an integer, the formula is as follows:
i1＝x1/dx
i2＝x2/dx
let the point of intersection p1、p2The number of the occupied voxel unit in the voxel space is P1、P2And then:
P1＝k×nx×ny+j×nx+i1
P2＝k×nx×ny+j×nx+i2。
6. the three-dimensional model fast voxelization method based on the slicing strategy as claimed in claim 5, wherein: in step 7, P is marked1、P2I.e. with the sequence number P1、P2The switch value of a voxel unit is 1.
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