CN107845140A - A kind of three-dimensional modeling method and threedimensional model - Google Patents
A kind of three-dimensional modeling method and threedimensional model Download PDFInfo
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Abstract
The present invention provides a kind of three-dimensional modeling method and threedimensional model, wherein method comprise the following steps：Benchmark point set is constructed based on spherical coordinates；Reject the datum mark outside set of keypoints；Positive truncated rectangular pyramids are constructed respectively to the key point in benchmark point set；Truncated rectangular pyramids are aligned to optimize；Triangle gridding is constructed by eight summits of positive truncated rectangular pyramids；Spherical coordinates is converted into cartesian coordinate；It is threedimensional model file by triangle gridding output.This modeling method is used to quickly carry out three-dimensional modeling to discrete point.
Description
Technical field
The present invention relates to the technical field of three-dimensional modeling, particularly a kind of three-dimensional modeling method and threedimensional model.
Background technology
Point shape, it is the morphological feature with the packing space in the form of non-integer dimension, is generally defined as that " one coarse or zero
Broken geometry, there are obvious self-similarity characteristics.Point shape can infinitely amplify, and have unlimited fine structure.
Traditional modeling method, one kind are by modeling software manual creation key point and triangular facet, and then composition model three
Angle grid.But the method can not construct complicated fine fractal structure, because the point coordinates of three-dimensional fractal calculates dependent on formula,
It is extremely difficult by modeling by hand, Procedure modeling can only be passed through.
After some three-dimensional fractal modeling algorithms quote fractal Formula, by constructive geometry body, and daughter element is constantly replaced
Mode creates a point shape threedimensional model, such as door lattice sponge and Xie Erbinsiji pyramids.But the method can not be made through quaternary
Three-dimensional mandelbrot collection and julia collection after number mapping.
Three-dimensional modeling generally use delauney Triangulation Methods based on discrete point, due to three-dimensional fractal model needs pair
Substantial amounts of discrete point carries out three-dimensional modeling, if can be very slow using delauney Triangulation Methods speed, and finally give
Threedimensional model surface and irregular.
Publication No. CN101303770A patent of invention discloses a kind of triangle gridding architecting method and its in ground work
Application in Cheng Jianmo, it is the advantages of this method simply, quickly build the three of compound delauney triangle griddings rule
Angle grid, and grid optimization can be synchronously carried out, suitable for constructing compound delauney according to two dimension or three dimensions discrete point
The triangular network of triangle rule, the construction of irregular Triangle Model can be applied to well, such as the structure of three-dimensional formation FEM layer model
Make.The shortcomings that this method is the calculating for needing to carry out discrete point one by one in order, generates new triangle, when discrete point quantity is huge
Calculating the time when big can be very long, and can not carry out parallelization calculating.
The content of the invention
In order to solve above-mentioned technical problem, the present invention proposes a kind of three-dimensional modeling method, first establishes and is based on spherical coordinates
Equally distributed benchmark point set, overstepping one's bounds form point collection is rejected by the method for solving the discrete point for dividing shape, change can be passed through
The parameter of fractal Formula, different fractal models is generated, or the parameter of datum mark is generated by changing, generate point of different accuracy
Shape model, or stripping and slicing is carried out to fractal model, parallelization Fast Construction three-dimensional fractal model can be passed through.
The present invention provides a kind of three-dimensional modeling method, comprises the following steps：
Step 1：Build set of keypoints；
Step 2：Triangle grid model is established by the set of keypoints；
Step 3：Threedimensional model file is exported according to the triangle gridding.
Preferably, the step 1 includes specifying vertical deflection angle step-length d θ, horizontal deflection angle step-lengthRadius step-length
Dr, distance r maximin, vertical elevation θ maximin and horizontal deflection angle apart from the centre of sphereMinimax
At least one of value.
In any of the above-described scheme preferably, the step 1 also generates base including the use of the parameter in such as claim 2
In the benchmark point set of spherical coordinates.
In any of the above-described scheme preferably, point in the benchmark point set by the distance r apart from the centre of sphere,
The vertical elevation θ and the horizontal deflection angleDetermine its position.
In any of the above-described scheme preferably, the step 1 is including the use of three-dimensional fractal formula or by given discrete
Point searches closest datum mark and extracts key point from the discrete point set.
In any of the above-described scheme preferably, the three-dimensional fractal formula is as follows：
θ=arcos (newPoint.z/r) * power；
R=lenth (newPoint)；
Wherein, power is the parameter that construction difference divides shape, and newPoint is the three-dimensional vector that iteration is tried to achieve, and Point is ginseng
With the datum mark of iteration
In any of the above-described scheme preferably, by the code in iteration such scheme, if r is in limited number of time iteration
It is not reaching to escape value, then it is assumed that this point belongs to a minute form point collection.
In any of the above-described scheme preferably, the alternative manner refers to need to input each datum mark into formula
Participate in calculating, the subset of point set on the basis of the set of keypoints filtered out.
In any of the above-described scheme preferably, the method that closest datum mark is searched by giving discrete point is logical
The distance for calculating given discrete point and datum mark is crossed, the minimum datum mark of selected distance, is added in set of keypoints, in space
2 distance calculation formulas are：Wherein, x1、y1And z1For discrete point
Coordinate, x2、y2And z2On the basis of point coordinates.
In any of the above-described scheme preferably, the step 2 includes first constructing positive four rib respectively by the key point
Platform resettles the triangle grid model.
In any of the above-described scheme preferably, the positive truncated rectangular pyramids are made up of eight summits A, B, C, D, E, F, G and H,
The calculation formula on eight summits is as follows：
A：R=r, θ=θ,
B：R=r, θ=θ+d θ,
C：R=r, θ=θ+d θ,
D：R=r, θ=θ,
E：R=r-dr, θ=θ,
F：R=r-dr, θ=θ+d θ,
G：R=r-dr, θ=θ+d θ,
H：R=r-dr, θ=θ,
In any of the above-described scheme preferably, the positive truncated rectangular pyramids bottom surface is made up of described calculating point A, B, C and D, institute
The top surface for stating positive truncated rectangular pyramids is made up of described calculating point E, F, G and H；The positive truncated rectangular pyramids bottom surface is big, and front is small, and bottom surface is away from ball
The heart.
In any of the above-described scheme preferably, the positive truncated rectangular pyramids of adjacent key point construction share four summits and one
Individual face.
In any of the above-described scheme preferably, the adjacent positive truncated rectangular pyramids are optimized, deletes common surface, with surplus
Under face carry out triangle gridding.
In any of the above-described scheme preferably, the positive truncated rectangular pyramids for not deleting the common surface include 6 faces, each
Face is made up of 2 triangular facets, and each triangular facet is made up of 3 summits adjacent in positive 8 summits of truncated rectangular pyramids, the positive truncated rectangular pyramids
Share 12 triangular facets.
In any of the above-described scheme preferably, T is usednTriangular facet numbering is represented, uses TnTriangular facet numbering is represented, equal sign is right
Side is 3 summits of the positive truncated rectangular pyramids for forming triangular facet, and triangular facet calculation formula is as follows：T1=A, B, F；T2=A, F, E；
T3=D, C, G；T4=D, G, H；T5=H, E, A；T6=H, A, D；T7=B, G, F；T8=B, C, G；T9=B, C, D；T10=B, D,
A；T11=F, G, H；T12=F, H, E；Wherein, n={ 1,12 }.
In any of the above-described scheme preferably, the triangle gridding is made up of the m triangular facets.
In any of the above-described scheme preferably, the step 3 include by the summit of the triangular facet by spherical coordinates r, θ,
Cartesian coordinate x, y, z is converted to, formula is as follows：
Z=r cos θ.
In any of the above-described scheme preferably, the step 3 includes calculating the normal of each triangular facet and generates three-dimensional
Model file, formula are：U=p1‐p0, v=p2‐p0, normal vector tn=nom (u.cross (v)), wherein p1、p2And p0For to
Amount.
In any of the above-described scheme preferably, parallel computation side is applied at least one step in step 1 to step 3
Method improves modeling speed.
In any of the above-described scheme preferably, it is to use any one method in the above method to generate.
Method proposed by the present invention can by divide shape discrete point carry out three-dimensional modeling, while use improved parallel computation
Method, a point calculating speed for shape discrete point can be greatly improved, by changing fractal Formula parameter, different point shape moulds can be generated
Type.
Brief description of the drawings
Fig. 1 is the flow chart according to a preferred embodiment of the three-dimensional modeling method of the present invention.
Fig. 2 is the positive truncated rectangular pyramids demonstration graph according to the embodiment as shown in Figure 1 of the three-dimensional modeling method of the present invention.
Fig. 3 is to divide the shape discrete point diagram according to the embodiment as shown in Figure 1 of the three-dimensional modeling method of the present invention.
Fig. 4 is the triangle gridding mould ultimately generated according to the embodiment as shown in Figure 1 of the three-dimensional modeling method of the present invention
Type figure.
Fig. 5 is the triangular facet normal map according to the embodiment as shown in Figure 1 of the three-dimensional modeling method of the present invention.
Fig. 6 is the threedimensional model side ultimately generated according to the embodiment as shown in Figure 1 of the three-dimensional modeling method of the present invention
View.
Fig. 6 A are to be overlooked according to the threedimensional model that ultimately generates of the embodiment as shown in Figure 6 of the three-dimensional modeling method of the present invention
Figure.
Fig. 6 B are to be faced upward according to the threedimensional model ultimately generated of the embodiment as shown in Figure 6 of the three-dimensional modeling method of the present invention
View.
Embodiment
The present invention is further elaborated with specific embodiment below in conjunction with the accompanying drawings.
Embodiment one
The present invention establishes a kind of method that point shape discrete point is quickly carried out to three-dimensional modeling, three-dimensional available for Fast Construction
Fractal model.
As shown in figure 1, performing step 100, the benchmark point set based on spherical coordinates is constructed.Specify vertical deflection angle step-length d
θ, horizontal deflection angle step-lengthRadius step-length dr, the distance r maximin apart from the centre of sphere, vertical elevation θ it is maximum most
Small value and horizontal deflection angleMaximin, use these parameters generation the benchmark point set based on spherical coordinates, Mei Geji
On schedule by r, θ andIt is determined that r represents the distance apart from the centre of sphere, θ represents vertical elevation,Represent horizontal deflection angle.
Step 110 is performed, set of keypoints is extracted and rejects the datum mark outside set of keypoints.It is public using three-dimensional fractal
Formula or the method for searching closest datum mark by giving discrete point, key point is extracted from the benchmark point set.1) pass through
The method that three-dimensional fractal formula extracts key point from the benchmark point set is to search to divide shape using following three-dimensional fractal formula
Discrete point set θ=arcos (newPoint.z/r) * power；
R=lenth (newPoint)；
Wherein, power is the parameter that construction difference divides shape, and newPoint is the three-dimensional vector that iteration is tried to achieve,
Point is the initial point for participating in iteration.By the above-mentioned code of iteration, if r is not reaching in limited number of time iteration
Escape value, then it is assumed that this point belongs to a minute form point collection.Alternative manner refers to need to input each datum mark joins into formula
With calculating, the subset of point set on the basis of the set of the key point filtered out.2) closest base is searched by given discrete point
Method on schedule, key point is extracted from the benchmark point set, specific method is as follows：By calculating given discrete point and benchmark
The distance of point, the minimum datum mark of selected distance, is added in set of keypoints, 2 distance calculation formulas are in space：Wherein, x1、y1And z1To give discrete point coordinates, x2、y2And z2For
Benchmark point coordinates.
Step 120 is performed, positive truncated rectangular pyramids are constructed respectively to the point in set of keypoints.Positive truncated rectangular pyramids by eight summit A, B,
C, D, E, F, G and H are formed, and the calculation formula on eight summits is as follows：
A：R=r, θ=θ,
B：R=r, θ=θ+d θ,
C：R=r, θ=θ+d θ,
D：R=r, θ=θ,
E：R=r-dr, θ=θ,
F：R=r-dr, θ=θ+d θ,
G：R=r-dr, θ=θ+d θ,
H：R=r-dr, θ=θ,
As shown in Fig. 2 positive truncated rectangular pyramids are made up of eight summits A, B, C, D, E, F, G and H, it is characterized in that bottom surface is big, top surface
Small, positive truncated rectangular pyramids of the bottom surface away from the centre of sphere, wherein tetra- points of A, B, C and D form the bottom surface of positive truncated rectangular pyramids, and E, F, G and H are formed just
The top surface of truncated rectangular pyramids, the positive truncated rectangular pyramids that adjacent key point is formed share four summits and a face.
Step 130 is performed, adjacent positive truncated rectangular pyramids are optimized, shared face is deleted, triangle is carried out with remaining face
Gridding.
Step 140 is performed, triangle gridding is constructed by eight summits of truncated rectangular pyramids, does not delete the positive truncated rectangular pyramids bag of common surface
Containing 6 faces, each face is made up of 2 triangular facets, and each triangular facet forms totally 12 three by 3 in positive 8 summits of truncated rectangular pyramids
Edged surface.Triangular facet is represented with Tn to number, it is as follows for 3 points of composition triangular facet, triangular facet calculation formula on the right of equal sign：T1=A,
B,F；T2=A, F, E；T3=D, C, G；T4=D, G, H；T5=H, E, A；T6=H, A, D；T7=B, G, F；T8=B, C, G；T9=B,
C,D；T10=B, D, A；T11=F, G, H；T12=F, H, E；Wherein, n={ 1,12 }.
Step 150 is performed, spherical coordinates is converted into cartesian coordinate.By the summit of the triangular facet by spherical coordinates r, θ,
Cartesian coordinate x, y, z is converted to, formula isZ=rcos θ.Calculate each three
The normal of edged surface simultaneously generates threedimensional model file, and formula is：U=p1‐p0, v=p2‐p0, normal vector tn=nom (u.cross
(v)), wherein p1、p2And p0For vector.
Step 160 is performed, is threedimensional model file by triangle gridding output.
Changed point by point instead of original in above-mentioned steps 110 to each sub-steps application parallel calculating method in step 150
For computing, can significantly improve the extraction set of keypoints in modeling speed, including step 110 and reject set of keypoints it
Outer datum mark, being constructed respectively in positive truncated rectangular pyramids, step 130 to the point in set of keypoints in step 120 align truncated rectangular pyramids
Optimize, eight summits construction triangle gridding by positive truncated rectangular pyramids in step 140, the calculating normal in step 150.
Embodiment two
Beneficial effects of the present invention are as follows：
1. this method can will divide shape discrete point to carry out three-dimensional modeling.
2. the model of generation has the characteristics of from the centre of sphere to space all directions homogeneous radiation.
3. using improved parallel calculating method, instead of the method for original node-by-node algorithm, avoid when discrete point quantity
It is excessive, the problem of consuming the plenty of time is calculated one by one, can greatly improve a point calculating speed for shape discrete point, is greatly shortened
Modeling time.
4. the three-dimensional fractal model in the range of the specified datum mark of output can be only calculated, to dividing shape stripping and slicing.
5. the fractal model of exportable designated precision.
6. by changing fractal Formula parameter, different three-dimensional fractal models can be generated.
7. threedimensional model file can be exported directly, 3D printer production is supported.
Embodiment three
Specify vertical deflection angle step-length d θ, horizontal deflection angle step-lengthRadius step-length dr, apart from the centre of sphere distance r most
Big minimum value, vertical elevation θ maximin and horizontal deflection angleMaximin, to generate the base based on spherical coordinates
Gather on schedule.Point in benchmark point set passes through the distance r, vertical elevation θ and horizontal deflection angle apart from the centre of sphereDetermine its position
Put.By taking three-dimensional mandelbrot collection as an example：Three-dimensional fractal discrete point set (as shown in Figure 3) is searched using formula below
θ=arcos (newPoint.z/r) * power；
R=lenth (newPoint)；
Wherein, power is the parameter that construction difference divides shape, and newPoint is the three-dimensional vector that iteration is tried to achieve, and Point is ginseng
With the initial point of iteration.If r is not reaching to escape value in limited number of time iteration, then it is assumed that this point belongs to a minute form point collection.Iteration
Method refers to need to input each datum mark to be participated in calculating into formula, the quantity and benchmark point set of the key point filtered out
The subset of point set on the basis of the directly proportional set of quantity of point.
Positive truncated rectangular pyramids are first constructed by the key point, after aligning truncated rectangular pyramids optimization, resettle triangle grid model.Positive four
Terrace with edge is made up of eight summits A, B, C, D, E, F, G and H, and the calculation formula on eight summits is as follows：
A：R=r, θ=θ,
B：R=r, θ=θ+d θ,
C：R=r, θ=θ+d θ,
D：R=r, θ=θ,
E：R=r-dr, θ=θ,
F：R=r-dr, θ=θ+d θ,
G：R=r-dr, θ=θ+d θ,
H：R=r-dr, θ=θ,
Example IV
By each summit for each triangular facet being calculated by spherical coordinates r, θ,Be converted to cartesian coordinate x, y,
Z, formula are as follows：Z=r cos θ.Calculate the normal of each triangular facet and generation
Threedimensional model file, formula are：U=p1‐p0, v=p2‐p0, normal vector tn=nom (u.cross (v)), wherein p1、p2And p0For
Vector.The threedimensional model file that exports is built up after grid model by above-mentioned steps, it can be seen that by all discrete points
Carry out three-dimensional modeling (as shown in Figure 4).
Embodiment five
As shown in figure 5, p1, p2 and p0 are vector.Calculate the normal of each triangular facet and generate threedimensional model file, formula
For：U=p1-p0, v=p2-p0, wherein normal vector tn=nom (u.cross (v)), p1, p2 and p0 are vector.
Embodiment six
The threedimensional model being calculated according to the method in embodiment one, angle precision PI/400, radius precision are
0.01, face number is 3367456, is counted as 1615367, and usage time is 510 seconds, and the file size of generation is 168.4MB.This three
The allocation of computer that dimension module uses is：CPU is the core IntelCore i7 of 2.8GHz tetra- processing reason devices, and video card is Radeon Pro
455 video cards.Shown in Fig. 6 is the side view of the threedimensional model ultimately generated, and shown in Fig. 6 A is the threedimensional model ultimately generated
Top view, shown in Fig. 6 B is the upward view of the threedimensional model ultimately generated.
Embodiment seven
The three-dimensional modeling method proposed by the application uses the Method Modeling of parallel computation.The speed of modeling can be improved
Degree, the threedimensional model details rule of generation is neat, and by adjusting datum mark dr, d θ,Size, can flexibly carry
Precision that is high and reducing modeling, by adjusting datum mark r, θ,Span, can flexibly to divide shape carry out stripping and slicing.Gram
Taken traditional modeling method and excessively relied on manual creation key point and triangular facet, can not construct complicated fine fractal structure and
Delauney Triangulation Method speed is slow, and can not parallelization the shortcomings that.
For a better understanding of the present invention, it is described in detail above in association with the specific embodiment of the present invention, but is not
Limitation of the present invention.Every technical spirit according to the present invention still belongs to any simple modification made for any of the above embodiments
In the scope of technical solution of the present invention.What each embodiment stressed in this specification be it is different from other embodiments it
Locate, same or analogous part cross-reference between each embodiment.For system embodiment, due to itself and method
Embodiment corresponds to substantially, so description is fairly simple, the relevent part can refer to the partial explaination of embodiments of method.
Claims (10)
1. a kind of three-dimensional modeling method, comprises the following steps：
Step 1：Build set of keypoints；
Step 2：Triangle grid model is established by the set of keypoints；
Step 3：Threedimensional model file is exported according to the triangle gridding.
2. three-dimensional modeling method as claimed in claim 1, it is characterised in that：The step 1 includes specifying vertical deflection angle to walk
Long d θ, horizontal deflection angle step-lengthRadius step-length dr, the distance r maximin apart from the centre of sphere, vertical elevation θ maximum
Minimum value and horizontal deflection angleAt least one of maximin.
3. three-dimensional modeling method as claimed in claim 2, it is characterised in that：The step 1 is also including the use of such as claim 2
In parameter generation the benchmark point set based on spherical coordinates.
4. three-dimensional modeling method as claimed in claim 3, it is characterised in that：Point in the benchmark point set by it is described away from
From centre of sphere distance r, the vertical elevation θ and the horizontal deflection angleDetermine its position.
5. three-dimensional modeling method as claimed in claim 4, it is characterised in that：The step 1 is including the use of three-dimensional fractal formula
Or closest datum mark is searched by given discrete point and extracts key point from the benchmark point set.
6. three-dimensional modeling method as claimed in claim 5, it is characterised in that：The three-dimensional fractal formula is as follows：
θ=arcos (newPoint.z/r) * power；
R=lenth (newPoint)；
Wherein, power is the parameter that construction difference divides shape, and newPoint is the three-dimensional vector that iteration is tried to achieve, and Point changes for participation
The datum mark in generation.
7. three-dimensional modeling method as claimed in claim 6, it is characterised in that：By the code in iteration claim 6, if
R is not reaching to escape value in limited number of time iteration, then it is assumed that this point belongs to a minute form point collection.
8. three-dimensional modeling method as claimed in claim 7, it is characterised in that：The alternative manner refers to need to input each
Datum mark participates in calculating into formula, the subset of point set on the basis of the set of keypoints filtered out.
9. three-dimensional modeling method as claimed in claim 5, it is characterised in that：It is described to be looked into by given discrete point
The method for looking for closest datum mark be by calculating given discrete point and the distance of datum mark in space, choose away from
From the datum mark of minimum, it is added in set of keypoints, the calculation formula of two point distances is in space：Wherein, x1、y1And z1For discrete point coordinates, x2、y2And z2On the basis of
Point coordinates.
A kind of 10. threedimensional model, it is characterised in that：It is to use any one method in claim 1-9 to generate.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110084887A (en) * | 2019-04-15 | 2019-08-02 | 北京空间飞行器总体设计部 | A kind of space non-cooperative target Relative Navigation model three-dimensional rebuilding method |
| CN110111375A (en) * | 2019-03-29 | 2019-08-09 | 中国地质大学（武汉） | A kind of Image Matching elimination of rough difference method and device under Delaunay triangulation network constraint |
| CN116050032A (en) * | 2023-04-03 | 2023-05-02 | 陕西空天信息技术有限公司 | Blade grid slice generation method and device, storage medium and electronic equipment |
-
2017
- 2017-11-22 CN CN201711175678.3A patent/CN107845140A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110111375A (en) * | 2019-03-29 | 2019-08-09 | 中国地质大学（武汉） | A kind of Image Matching elimination of rough difference method and device under Delaunay triangulation network constraint |
| CN110084887A (en) * | 2019-04-15 | 2019-08-02 | 北京空间飞行器总体设计部 | A kind of space non-cooperative target Relative Navigation model three-dimensional rebuilding method |
| CN110084887B (en) * | 2019-04-15 | 2022-10-28 | 北京空间飞行器总体设计部 | Three-dimensional reconstruction method for space non-cooperative target relative navigation model |
| CN116050032A (en) * | 2023-04-03 | 2023-05-02 | 陕西空天信息技术有限公司 | Blade grid slice generation method and device, storage medium and electronic equipment |
| CN116050032B (en) * | 2023-04-03 | 2023-06-20 | 陕西空天信息技术有限公司 | Blade grid slice generation method and device, storage medium and electronic equipment |
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