CN104361246A - Function gradient material hidden model building method based on distance field - Google Patents
Function gradient material hidden model building method based on distance field Download PDFInfo
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Abstract
The invention provides a function gradient material hidden model building method based on a distance field. The method comprises the following concrete steps that (1) a geometric distance field is created: an entity prototype is measured, surface point cloud data is obtained, the point cloud data is a position coordinate value, a surrounding box is used for surrounding the position coordinate, the surrounding box is uniformly divided, and signed distance fields of the point cloud data of all dividing lattice top points in the surrounding box are calculated for displaying a geometric model of the entity; (2) a material distance field is created: the material features are determined according to the material design intention of the function gradient materials, so that the material distance field is calculated; (3) function gradient materials are subjected to hidden modeling. The functional gradient material geometric distance field and the material field modeling are creatively combined, and the hidden function mode of the distance field is used for completely expressing the geometric and material information. Through the self-adaptive characteristic of the distance field, the method is applicable to any complicated models, and the Boolean operation can be conveniently carried out.
Description
Technical field
The invention belongs to Functionally Graded Materials technical field, be specifically related to a kind of Functionally Graded Materials implicit expression modeling method based on distance field.
Background technology
Functionally Graded Materials (Functionally Graded Material, FGM) is that positive sum horizontal well quick hero in Japanese Scientists Xinye can normally work in particular circumstances in order to solve material, a kind of new function material proposed first in 1986.FGM is merged on microcosmic by two or more materials, forms a kind of volume fraction of each component material along certain direction or multiple directions continually varying compound substance.In fusion process, FGM component material self property does not change, and the physical property of this material is relevant with the volume fraction function of various component materials, and along material gradient distribution arrangement consecutive variations, therefore according to the difference of its component material and volume fraction content thereof, there is different physical properties, the request for utilization of particular surroundings can be met, control to improve the various performance of organization internal by material composition, comprise thermomechanical property, toughness and intensity, reduce the loss of weight (fuselage and wing etc.) do not reduced under strength conditions in the layering and crackle and aeronautical product that interfacial stress produces.Along with the continuous expansion of FGM application, its modeling technique becomes the Basic Problems in its design analysis and Study on manufacturing technology.
Current CAD system can not state the functionally gradient model without knowing material boundary, and in order to solve the modeling problem of Functionally Graded Materials, existing functionally gradient modeling method mainly contains following several:
(1), voxelization modeling is a kind of citation form of unit decomposition, and model decomposition is become multiple cubic units of uniform size by voxelization by it, and the size of voxel cell is little of they being considered as a uniform material block.From medical CT(Computerized Tomography) and MRI(Magnetic Resonance Imaging) equipment obtain data normally the type data.The feature of voxelization modeling be it both with distribution of material functional independence, have nothing to do with part geometry shape again.Usually be applicable to the extremely irregular Functionally Graded Materials of material composition distribution, be not too applicable to the Functionally Graded Materials of material with graded.
(2), gridding modeling becomes a series of polyhedron by spatial decomposition, and each polyhedron not only comprises geometric topology information and also comprises its summit material component information.Compared with voxel method, gridding methods stores certain alleviation, but calculate still more time-consuming, be difficult to carry out gridding again, and be the object based on analyzing but not Geometric Modeling and manufacture, thus need when exchanging with cad data to carry out some pre-service (comprising the feature identification of surface smoothing and Layered manufacturing), but the Distribution of materials of complexity, height nonuniformity can be shown flexibly.
(3), the r diversity method of expansion carries out the modeling of heterogeneous material object, and developed the model being analogous to tensor product entity and CSG, is applicable to the modeling of simple non-homogeneous model.
(4), parametric modeling method is the direct extension of conventional parameter curve and parametric surface modeling, it needs a series of reference mark shape function (as B-spline, Bezier, NURBS) to come interpolation curve or curved surface, that reference mark here had both comprised geometric coordinate information also must comprise material composition information with conventional parameter modeling difference.This parametric modeling method, large for any its parametrization of 3D model space burden, and inconvenience carries out boolean operation to model.And reference mark and basis function must be utilized to carry out Presentation Function functionally gradient material (FGM) model, in many cases, Distribution of materials may have nothing to do with geometry reference mark, and must under the geometric model that can represent by parametrization, instead of all complex geometries can represent with parametric curve or curved surface.
(5), feature modeling display material composition and changes in material information, the method only adopts point, straight line and plane as feature, and does not consider the Functionally Graded Materials modeling of any contour feature.
In the modeling method listed by above-mentioned background technology, its solid modelling mainly adopts B reps (method (5)), constructive solid geometry method (method (3)) and space cell representation (method (1) and (2)), for material modeling, parametric method (method (4)) can be adopted, analytical method (method (3)) and material characteristics method (method (5)), these methods are substantially all positive function functionally gradient material (FGM) modeling methods.
Summary of the invention
The present invention, in order to solve weak point of the prior art, provides a kind of topological strong adaptability, structure simple and is convenient to the Functionally Graded Materials implicit expression modeling method based on distance field of boolean operation.
For solving the problems of the technologies described above, the present invention adopts following technical scheme: based on the Functionally Graded Materials implicit expression modeling method of distance field, comprise following concrete steps,
1), the establishment of geometric distance field: measure physical prototypes, obtain surperficial cloud data, cloud data is position coordinate value; Surrounded by position coordinate value with a bounding box, to bounding box evenly son point, what calculate the cloud data on all grid division summits in bounding box has symbolic distance field, in order to the geometric model of display entity;
2), the establishment of material distance field: determine its material characteristics thus Calculating material distance field according to Functionally Graded Materials design idea;
3), the implicit expression modeling of Functionally Graded Materials: Geometric Modeling and material modeling are united, realizes the Functionally Graded Materials implicit expression modeling based on distance field.
In described step 3), the mode of Geometric Modeling comprises B reps, constructive solid geometry method and space cell representation.
In described step 3), the mode of material modeling comprises parametric method, analytical method and material characteristics method.
The acquisition of described step 1) point cloud data is by laser scanning or three coordinate measuring machine.
Symbolic distance field is had to be defined as the bee-line to object geometry or contoured surface of arbitrfary point in three dimensions in described step 1).
Described step 2) in material characteristics be point patterns, line features or region feature.
Described line features is arbitrary curve, and region feature is arbitrary surface.
Described step 1) is specially, for cloud data at random, can adopt implicit expression modeling pattern, be the contour surface of a scalar function by the representation of a surface, randomly topologically structured body surface all can be described by unified distance field, geometric manipulations for body surface provides unified framework, be specially and set up the three-dimensional uniform lattice structure that comprises a cloud, calculate the field value of each net point, field value and distance value, and then extraction zero contour surface is model surface, field model is solid model;
Space a bit to have symbolic measurement to refer to
pto cloud data
shave symbolic distance, the symbol of distance value depends on
ppoint is positioned at
swhich side, for closed model, point
pbeing positioned at model outside is just, point
pbeing positioned at model internal symbol gets negative; Assuming that two-dimensional cam point cloud is stored in 20 × 20 grid spaces,
ppoint be taken as vertex raster (
i,
j),
ppoint coordinate be (
x i ,
y j ), what calculate 400 vertex rasters has symbolic distance value, forms the matrix that 20 row 20 arrange;
（1）
Wherein
poutside at model
sign(
p) be taken as 1,
pinner at model
sign(
p) be taken as-1;
The calculating of formula (1) middle distance value is fairly simple, the judgement of its crucial is-symbol, divides cloud data, be divided into for evenly sub
nxoK
nyrow, altogether (
nx-1) × (
ny-1) individual node, each node is represented by four vertex rasters, and for three-dimensional model, each node is then represented by eight vertex rasters; Be labeled as 0 by what comprise data point, be set to boundary node, what do not comprise data point is labeled as 1, and the node being then 1 by line sweep judge mark is internal node, or external node; If have at least a vertex raster be just and do not comprise data point, be labeled as external node; Otherwise, if having a vertex raster at least for bearing and not comprising data point, be labeled as internal node; Node is divided into three kinds the most at last: external node, boundary node and internal node; To on the four edges of outmost bounding box vertex raster give on the occasion of, namely
i=1,
j=1,2 ...,
ny;
i=
nx, j=1,2 ...,
ny;
i=1,2 ...,
nx,
j=1;
i=1,2 ...,
nx,
j=
ny, all vertex rasters of external node give on the occasion of, all vertex rasters of internal node give negative values.
Described step 2) be specially, Distribution of materials is defined as the distance function of each grid point to material characteristics, and the distance value of all vertex rasters is combined into material distance field; Common material characteristics is point patterns, line features and region feature, and real material design is the combination of any one feature or several feature; No matter be that material characteristics, material distance field model is a scalar field model, its value be mapped as surround model grid point to the distance value of material characteristics, this distance value be on the occasion of, the volume proportion of material represents with material distance value;
Material characteristics and the model surface of Functionally Graded Materials match, and namely material composition is along phantom thicknesses dimension linear or nonlinear gradient change, and its Distribution of materials is the function of geometric distance field; For the functionally gradient model that bi-material is formed, distribution of material is:
（2）
Material characteristics and the model surface of Functionally Graded Materials match, and namely material composition is along phantom thicknesses dimension linear or nonlinear gradient change, and its Distribution of materials is the function of geometric distance field; For the functionally gradient model that bi-material is formed, distribution of material is:
Wherein
dit is the lowest distance value from arbitrfary point to model surface;
αit is scale factor;
kit is the distribution index describing gradient attribute; If
kbe 1, material linearly distributes; Usually
αwith
kdecided by design idea and performance test;
To model
sin any grid point (
i,
j), material composition formula is:
（3）
Wherein
represent arbitrfary point (
i,
j) to the absolute value of the distance value of model outside surface, max (
d) be the maximum range value of geometric distance field; In model, the material mixture ratio of arbitrfary point obtains by the distance value of interpolation adjacent gate lattice point; Have and symbolic distance field contour surface or isoline have a little identical material composition.
Described step 3) is specially,
the display of Functionally Graded Materials object, needing the description changing object space, except describing object geometry and topological structure, must increase material dimension, functionally gradient object model space
tit is geometric space
r 3with
ndimension material space
m n tensor product, namely
t=
r 3×
m n; Material space
m nin
mfor often various material component is vectorial:
m =[
m 1,
m 2...,
m n], wherein
,
m i for forming of this point
iplant quality of materials or percent by volume, to formula (3), bi-material
m 1=
f 1(
d),
m 2=
f 2(
d),
m 1+
m 2=1;
For three-dimensional model, geometric distance field and material distance field are united and be can be described as
（4）
Wherein,
d (
i,
j,
k)
(
s) the even son point grid point of expression (
i,
j,
k) to point cloud data
shave symbolic distance value,
f (
i,
j,
k)
(
c) represent this
nx×
ny×
nzindividual net point is to material characteristics
cdistance field; Extract zero isoline for two dimension, three-dimensional zero contour surface (by Marching Cubes algorithm) that extracts obtains model surface; Obtain the functionally gradient model along cam outer face linear distribution according to formula (3), change material composition function
f (
i,
j,
k)
(
c) distribution of material in model can be regulated, obtain the functionally gradient model of different materials distribution, the feature of mobile material also can change the physical attribute of function gradient structure simultaneously.
Adopt technique scheme, the present invention compared with prior art, has the following advantages:
Functionally Graded Materials geometric distance field innovatively combines with yard of material modeling by the present invention, with the form of this implicit function of distance field complete describe geometry and material information.Due to the adaptive characteristic of distance field, be adapted to any complex model, and boolean operation can be carried out easily.
Accompanying drawing explanation
Fig. 1 is the schematic diagram that Functionally Graded Materials description is carried out in applications distances field;
Fig. 2 is schematic flow sheet of the present invention;
Fig. 3 is the schematic diagram that under 2D state, cam has symbolic distance (20 × 20 grid);
Fig. 4 a is the schematic diagram of 2D state lower node in Fig. 3;
Fig. 4 b is the schematic diagram of 3D state lower node in Fig. 3;
Fig. 5 is the schematic diagram of three kinds of node division;
Fig. 6 is cam distance field sign flag under 2D state;
The schematic diagram of the functionally gradient model of Fig. 7 formula cam through-thickness linear distribution;
Fig. 8 is the schematic diagram of functionally gradient model.
Embodiment
As shown in Figure 1, application has symbolic distance field can describe the geometric topology information of homogeneous object, consider the attribute of Functionally Graded Materials, describe in object geometric shape feature base at distance field, give material characteristics attribute to each three dimensional network lattice point, each like this grid point had both comprised the geometry describing geometrical property symbolic distance field, comprises again the material distance field describing material behavior, thus form unified augmentation distance field, carry out representation function functionally gradient material (FGM).
As shown in Figure 2, the Functionally Graded Materials implicit expression modeling method based on distance field of the present invention, comprises following concrete steps:
1), the establishment of geometric distance field: measure physical prototypes, obtain surperficial cloud data, cloud data is position coordinate value; Surrounded by position coordinate value with a bounding box, to bounding box evenly son point, what calculate the cloud data on all grid division summits in bounding box has symbolic distance field, in order to the geometric model of display entity;
2), the establishment of material distance field: determine its material characteristics thus Calculating material distance field according to Functionally Graded Materials design;
3), the implicit expression modeling of Functionally Graded Materials: Geometric Modeling and material modeling are united, realizes the Functionally Graded Materials implicit expression modeling based on distance field.
In step 3), the mode of Geometric Modeling comprises B reps, constructive solid geometry method and space cell representation.
In step 3), the mode of material modeling comprises parametric method, analytical method and material characteristics method.
The acquisition of step 1) point cloud data is by laser scanning or three coordinate measuring machine.
Symbolic distance field is had to be defined as the bee-line to object geometry or contoured surface of arbitrfary point in three dimensions in step 1).
Step 2) in material characteristics be point patterns, line features or region feature.Line features is arbitrary curve, and region feature is arbitrary surface.
Step 1) is specially, for cloud data at random, can adopt implicit expression modeling pattern, be the contour surface of a scalar function by the representation of a surface, randomly topologically structured body surface all can be described by unified distance field, geometric manipulations for body surface provides unified framework, be specially and set up the three-dimensional uniform lattice structure that comprises a cloud, calculate the field value of each net point, field value and distance value, and then extraction zero contour surface is model surface, field model is solid model;
Space a bit to have symbolic measurement to refer to
pto cloud data
shave symbolic distance, the symbol of distance value depends on
ppoint is positioned at
swhich side, for closed model, point
pbeing positioned at model outside is just, point
pbeing positioned at model internal symbol gets negative; As shown in Figure 3, assuming that two-dimensional cam point cloud is stored in 20 × 20 grid spaces,
ppoint be taken as vertex raster (
i,
j),
ppoint coordinate be (
x i ,
y j ), what calculate 400 vertex rasters has symbolic distance value, forms the matrix that 20 row 20 arrange.
（1）
Wherein
poutside at model
sign(
p) be taken as 1,
pinner at model
sign(
p) be taken as-1;
The calculating of formula (1) middle distance value is fairly simple, the judgement of its crucial is-symbol, divides cloud data, be divided into for evenly sub
nxoK
nyrow, altogether (
nx-1) × (
ny-1) individual node, each node is represented by four vertex rasters, and as shown in fig. 4 a, for three-dimensional model, each node is then represented by eight vertex rasters, as shown in Figure 4 b; Be labeled as 0 by what comprise data point, be set to boundary node, what do not comprise data point is labeled as 1, and the node being then 1 by line sweep judge mark is internal node, or external node; If have at least a vertex raster be just and do not comprise data point, be labeled as external node; Otherwise, if having a vertex raster at least for bearing and not comprising data point, be labeled as internal node; Node is divided into three kinds the most at last: external node, boundary node and internal node; As shown in Figure 5,2. 1. white be internal node, black is boundary node, and 3. white be external node.To on the four edges of outmost bounding box vertex raster give on the occasion of, namely
i=1,
j=1,2 ...,
ny;
i=
nx, j=1,2 ...,
ny;
i=1,2 ...,
nx,
j=1;
i=1,2 ...,
nx,
j=
ny, all vertex rasters of external node give on the occasion of, all vertex rasters of internal node give negative values, and as shown in Figure 6, "+" represents vertex raster distance value symbol for just, and " o " represents vertex raster distance value symbol is negative in last symbol display.
Step 2) be specially, Distribution of materials is defined as the distance function of each grid point to material characteristics, and the distance value of all vertex rasters is combined into material distance field; Common material characteristics is point patterns, line features and region feature, and real material design is the combination of any one feature or several feature; No matter be that material characteristics, material distance field model is a scalar field model, its value be mapped as surround model grid point to the distance value of material characteristics, this distance value be on the occasion of, the volume proportion of material represents with material distance value;
Material characteristics and the model surface of Functionally Graded Materials match, and namely material composition is along phantom thicknesses dimension linear or nonlinear gradient change, and its Distribution of materials is the function of geometric distance field; For the functionally gradient model that bi-material is formed, distribution of material is:
（2）
Material characteristics and the model surface of Functionally Graded Materials match, and namely material composition is along phantom thicknesses dimension linear or nonlinear gradient change, and its Distribution of materials is the function of geometric distance field; For the functionally gradient model that bi-material is formed, distribution of material is:
Wherein
dit is the lowest distance value from arbitrfary point to model surface;
αit is scale factor;
kit is the distribution index describing gradient attribute.If
kbe 1, material linearly distributes.Usually
αwith
kdecided by design idea and performance test;
To model
sin any grid point (
i,
j), material composition formula is:
（3）
Wherein
represent arbitrfary point (
i,
j) to the absolute value of the distance value of model outside surface, max (
d) be the maximum range value of geometric distance field.In model, the material mixture ratio of arbitrfary point obtains by the distance value of interpolation adjacent gate lattice point.Have and symbolic distance field contour surface or isoline have a little identical material composition.
Described step 3) is specially,
the display of Functionally Graded Materials object, needing the description changing object space, except describing object geometry and topological structure, must increase material dimension, functionally gradient object model space
tit is geometric space
r 3with
ndimension material space
m n tensor product, namely
t=
r 3×
m n.Material space
m nin
mfor often various material component is vectorial:
m =[
m 1,
m 2...,
m n], wherein
,
m i for forming of this point
iplant quality of materials or percent by volume, to formula (3), bi-material
m 1=
f 1(
d),
m 2=
f 2(
d),
m 1+
m 2=1.
For three-dimensional model, geometric distance field and material distance field are united and be can be described as
（4）
Wherein,
d (
i,
j,
k)
(
s) represent evenly son point grid point
to point cloud data
shave symbolic distance value,
f (
i,
j,
k)
(
c) represent this
nx×
ny×
nzindividual net point is to material characteristics
cdistance field.Extract zero isoline for two dimension, three-dimensional zero contour surface (by Marching Cubes algorithm) that extracts obtains model surface.Obtain the functionally gradient model along cam outer face linear distribution according to formula (3), as shown in Figure 7, change material composition function
f (
i,
j,
k)
(
c) distribution of material in model can be regulated, obtain the functionally gradient model of different materials distribution, the feature of mobile material also can change the physical attribute of function gradient structure simultaneously, as shown in Figure 8, material characteristics is point patterns, range points O (0,0).
Above embodiment is the unrestricted technical scheme of the present invention in order to explanation only, although with reference to above-described embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that: still can modify to the present invention or equivalent replacement, and not departing from any modification or partial replacement of the spirit and scope of the present invention, it all should be encompassed in the middle of right of the present invention.
Claims (10)
1., based on the Functionally Graded Materials implicit expression modeling method of distance field, comprise following concrete steps,
1), the establishment of geometric distance field: measure physical prototypes, obtain surperficial cloud data, cloud data is position coordinate value; Surrounded by position coordinate value with a bounding box, to bounding box evenly son point, what calculate the cloud data on all grid division summits in bounding box has symbolic distance field, in order to the geometric model of display entity;
2), the establishment of material distance field: determine its material characteristics thus Calculating material distance field according to Functionally Graded Materials design idea;
3), the implicit expression modeling of Functionally Graded Materials: Geometric Modeling and material modeling are united, realizes the Functionally Graded Materials implicit expression modeling based on distance field.
2. in step 3) described in, the mode of Geometric Modeling comprises B reps, constructive solid geometry method and space cell representation.
3. in step 3) described in, the mode of material modeling comprises parametric method, analytical method and material characteristics method.
4. the acquisition of step 1) point cloud data described in is by laser scanning or three coordinate measuring machine.
5. in step 1) described in, there is symbolic distance field to be defined as the bee-line to object geometry or contoured surface of arbitrfary point in three dimensions.
6. step 2 described in) in material characteristics be point patterns, line features or region feature.
7. line features described in is arbitrary curve, and region feature is arbitrary surface.
8. described in, step 1) is specially, for cloud data at random, can adopt implicit expression modeling pattern, be the contour surface of a scalar function by the representation of a surface, randomly topologically structured body surface all can be described by unified distance field, geometric manipulations for body surface provides unified framework, be specially and set up the three-dimensional uniform lattice structure that comprises a cloud, calculate the field value of each net point, field value and distance value, and then extraction zero contour surface is model surface, field model is solid model;
Space a bit to have symbolic measurement to refer to
pto cloud data
shave symbolic distance, the symbol of distance value depends on
ppoint is positioned at
swhich side, for closed model, point
pbeing positioned at model outside is just, point
pbeing positioned at model internal symbol gets negative; Assuming that two-dimensional cam point cloud is stored in 20 × 20 grid spaces,
ppoint be taken as vertex raster (
i,
j),
ppoint coordinate be (
x i ,
y j ), what calculate 400 vertex rasters has symbolic distance value, forms the matrix that 20 row 20 arrange;
（1）
Wherein
poutside at model
sign(
p) be taken as 1,
pinner at model
sign(
p) be taken as-1;
The calculating of formula (1) middle distance value is fairly simple, the judgement of its crucial is-symbol, divides cloud data, be divided into for evenly sub
nxoK
nyrow, altogether (
nx-1) × (
ny-1) individual node, each node is represented by four vertex rasters, and for three-dimensional model, each node is then represented by eight vertex rasters; Be labeled as 0 by what comprise data point, be set to boundary node, what do not comprise data point is labeled as 1, and the node being then 1 by line sweep judge mark is internal node, or external node; If have at least a vertex raster be just and do not comprise data point, be labeled as external node; Otherwise, if having a vertex raster at least for bearing and not comprising data point, be labeled as internal node; Node is divided into three kinds the most at last: external node, boundary node and internal node; To on the four edges of outmost bounding box vertex raster give on the occasion of, namely
i=1,
j=1,2 ...,
ny;
i=
nx, j=1,2 ...,
ny;
i=1,2 ...,
nx,
j=1;
i=1,2 ...,
nx,
j=
ny, all vertex rasters of external node give on the occasion of, all vertex rasters of internal node give negative values.
9. step 2 described in) be specially, Distribution of materials is defined as the distance function of each grid point to material characteristics, and the distance value of all vertex rasters is combined into material distance field; Common material characteristics is point patterns, line features and region feature, and real material design is the combination of any one feature or several feature; No matter be that material characteristics, material distance field model is a scalar field model, its value be mapped as surround model grid point to the distance value of material characteristics, this distance value be on the occasion of, the volume proportion of material represents with material distance value;
Material characteristics and the model surface of Functionally Graded Materials match, and namely material composition is along phantom thicknesses dimension linear or nonlinear gradient change, and its Distribution of materials is the function of geometric distance field; For the functionally gradient model that bi-material is formed, distribution of material is:
（2）
Material characteristics and the model surface of Functionally Graded Materials match, and namely material composition is along phantom thicknesses dimension linear or nonlinear gradient change, and its Distribution of materials is the function of geometric distance field; For the functionally gradient model that bi-material is formed, distribution of material is:
Wherein
dit is the lowest distance value from arbitrfary point to model surface;
αit is scale factor;
kit is the distribution index describing gradient attribute; If
kbe 1, material linearly distributes; Usually
αwith
kdecided by design idea and performance test;
To model
sin any grid point (
i,
j), material composition formula is:
（3）
Wherein
represent arbitrfary point (
i,
j) to the absolute value of the distance value of model outside surface, max (
d) be the maximum range value of geometric distance field; In model, the material mixture ratio of arbitrfary point obtains by the distance value of interpolation adjacent gate lattice point; Have and symbolic distance field contour surface or isoline have a little identical material composition.
10. described in, step 3) is specially,
the display of Functionally Graded Materials object, needing the description changing object space, except describing object geometry and topological structure, must increase material dimension, functionally gradient object model space
tit is geometric space
r 3with
ndimension material space
m n tensor product, namely
t=
r 3×
m n; Material space
m nin
mfor often various material component is vectorial:
m =[
m 1,
m 2...,
m n], wherein
,
m i for forming of this point
iplant quality of materials or percent by volume, to formula (3), bi-material
m 1=
f 1(
d),
m 2=
f 2(
d),
m 1+
m 2=1;
For three-dimensional model, geometric distance field and material distance field are united and be can be described as
（4）
Wherein,
d (
i,
j,
k)
(
s) the even son point grid point of expression (
i,
j,
k) to point cloud data
shave symbolic distance value,
f (
i,
j,
k)
(
c) represent this
nx×
ny×
nzindividual net point is to material characteristics
cdistance field; Extract zero isoline for two dimension, three-dimensional zero contour surface (by Marching Cubes algorithm) that extracts obtains model surface; Obtain the functionally gradient model along cam outer face linear distribution according to formula (3), change material composition function
f (
i,
j,
k)
(
c) distribution of material in model can be regulated, obtain the functionally gradient model of different materials distribution, the feature of mobile material also can change the physical attribute of function gradient structure simultaneously.
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| CN107886464A (en) * | 2017-11-09 | 2018-04-06 | 哈尔滨工业大学 | A kind of method that point cloud model is generated by two-phase composite material meso-mechanical model |
| CN109117504A (en) * | 2018-07-09 | 2019-01-01 | 哈尔滨工程大学 | A kind of two-way function gradient song shell vibration analysis method |
| CN109767495A (en) * | 2017-11-09 | 2019-05-17 | 达索系统公司 | The increasing material manufacturing of 3D component |
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| WO2020215533A1 (en) * | 2019-04-26 | 2020-10-29 | 大连理工大学 | Structural topology optimization method based on material-field reduction series expansion |
| CN111319266A (en) * | 2020-03-10 | 2020-06-23 | 嘉兴学院 | Functional gradient material 3D printing path planning method based on contour line |
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