CN108327287B - A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile - Google Patents
A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile Download PDFInfo
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- CN108327287B CN108327287B CN201810040995.2A CN201810040995A CN108327287B CN 108327287 B CN108327287 B CN 108327287B CN 201810040995 A CN201810040995 A CN 201810040995A CN 108327287 B CN108327287 B CN 108327287B
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Abstract
The invention discloses a kind of three period minimal surface 3 D-printing slicing profile rapid generations, three period minimal surface expression formulas, slice thickness and slice network of quadrilaterals lattice resolution including inputting slice；According to three period minimal surface coordinate distributions and slice thickness, the slice quadrilateral mesh of curved surface corresponding region is generated；According to curved surface expression formula, linear interpolation calculates the slice line segment of curved surface and every layer of slice quadrilateral mesh；Save the topological relation of slice line segment with quadrangle in corresponding slice quadrilateral mesh；All slice line segments are ranked up；The slicing profile generated after all sequences is exported with CLI file format finally and is saved.The present invention realizes the quicksort of the rapid section and slice line segment at random to three period minimal surfaces using slice quadrilateral mesh, 3 D-printing slicing profile is quickly generated, the shortcomings that conventional method must generate STL model consumption plenty of time and memory headroom is avoided.
Description
Technical field
The present invention relates to 3 D-printing computer-aided manufacturing (Computer aided manufacturing, CAM) skills
Art field, more particularly, to a kind of rapid generation of three period minimal surface 3 D-printing slicing profiles.
Background technique
Three-dimensional printing technology is a kind of advanced manufacturing technology based on synusia superposition, and be otherwise known as rapid prototyping technology or increasing
Material manufacturing technology.Cut down material constantly different from tradition machining etc. to obtain the process of design shape, 3 D-printing skill
Art utilizes various types of materials, is layering and is designed a model by computer-aided equipment, is particularly suitable for the quick of labyrinth
It is manufactured.It is the key link for influencing to manufacture final precision and efficiency that 3 D-printing slicing profile, which generates,.
In order to find more satisfactory equalization point between precision and efficiency, domestic and foreign scholars are in terms of slicing profile generation
A large amount of work has been done, for different three-dimensional modeling datas, has proposed all kinds of slice generation methods.Currently led in 3 D-printing
Domain, STL are the most commonly used model data formats.STL approaches the shape that designs a model, data structure letter with a large amount of tri patch
It is single, convenient for processing.But in order to improve modeling accuracy, it is necessary to greatly increase dough sheet quantity, and then consume a large amount of memory and place
Manage the time.Especially when modeling complex topology structure, the performance of the disadvantage of STL is become apparent, and a large amount of dough sheet and some is difficult to
The dough sheet defect of processing often will lead to the failure of slicing profile generation.
Three period minimal surface TPMS (Triply Periodic Minimal Surfaces) are that one kind is opened up with complexity
Flutter the implicit surface of structure.The hole configurations of its smooth surface and inside and outside connection has a wide range of applications in engineering field.
3 D-printing has the inherent advantage for manufacturing such labyrinth.The TPMS structure of design is saved as STL by Melchels et al.
File is manufactured using 3 D-printing technique, and then carries out cell culture (referring to Melchels F as tissue engineering bracket
P W,Bertoldi K,Gabbrielli R,et al.Mathematically defined tissue engineering
scaffold architectures prepared by stereolithography[J].Biomaterials,2010,31
(27):6909-6916.)；Interstitital texture of the Li et al. life at the TPMS structure of STL format as 3 D-printing model, realization are beaten
Lightweight purpose is printed (referring to Li D, Dai N, Jiang X, et al.Interior structural optimization
based on the density-variable shape modeling of 3D printed objects[J].The
International Journal of Advanced Manufacturing Technology,2016,83(9-12):
1627-1635).It is sliced line segment sequence processing aspect, Kim proposes a kind of slicing profile violence generation method of grid model,
Method implements simple but time complexity and is up to O (n2) (referring to Kim H C.Tool path generation for
contour parallel milling with incomplete mesh model[J].The International
Journal of Advanced Manufacturing Technology,2010,48(5):443-454)；Lin et al. is proposed
A kind of Optimal scheduling algorithm for STL slice line segment, time complexity O (nlogn) (referring to Lin Z, Fu J, Shen H,
et al.Efficient cutting area detection in roughing process for meshed
surfaces[J].The International Journal of Advanced Manufacturing Technology,
2013,69(1-4):525-530)。
It is both needed to first generate STL it is found that currently manufacturing three period minimal surfaces using three-dimensional printing technology according to document analysis
Model, then carry out the slice based on STL.Since structure is intricate, the STL model file generally generated is larger, needs to consume
Many memories and processing time.Current some slice line segment sort algorithms low efficiency in sequencing problem under handling big data quantity
Under, slicing profile can not be efficiently produced.In addition, not finding any text about three period minimal surface slicing profile generation methods
It offers.
Summary of the invention
In order to solve, the existing three period minimal surface 3 D-printing slice efficiencies based on STL model are low, consumption memory is big
The shortcomings that, the present invention provides a kind of rapid generations of three period minimal surface 3 D-printing slicing profiles.Pass through building
It is sliced quadrilateral mesh, the direct slicing layering of three period minimal surfaces is fast implemented, avoids the life of conventional method STL model
At.Slice quadrilateral mesh is made full use of simultaneously and is sliced the topological relation of line segment, is quickly carried out slice line segment sequence and is generated most
Whole slicing profile, time complexity are only linear O (n).This method is reliable and stable, and three period minimal surface three-dimensionals may be implemented and beat
Print slicing profile quickly generates.
For achieving the above object, the present invention the following technical schemes are provided:
A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile, comprising the following steps:
Step 1: expression formula f (x, y, z)=c of three period minimal surfaces of slice is inputted, slice thickness h, slice four
Side shape grid resolution n, wherein c is the critical numerical constant of curved surface, x ∈ [a0,a1], y ∈ [b0,b1], z ∈ [c0,c1]；
Step 2: according to the coordinate distribution and slice thickness of three period minimal surfaces, generating cutting for curved surface corresponding region
Piece quadrilateral mesh；
Step 3: according to three period minimal surface expression formula f (x, y, z)=c, linear interpolation calculates curved surface and every layer of slice
The slice line segment of quadrilateral mesh；
Step 4: the topology for saving quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment is closed
System；
Step 5: being closed according to the topology of quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment
System is ranked up slice line segment；
Step 6: the slicing profile generated after all sequences being exported with CLI file format and is saved.
Wherein, the detailed process of the slice quadrilateral mesh for generating curved surface corresponding region are as follows:
Firstly, curved surface corresponding region is divided into according to slice thickness hA plane；
Then for planeAccording to slice network of quadrilaterals lattice resolution n, respectively edge
X, the direction y generates j parallel lines respectively, in which:
Parallel lines
Parallel lines
Parallel lines xjWith parallel lines yjIt is orthogonal, generate the slice quadrilateral mesh of curved surface corresponding region.
Preferably, the detailed process of the step 3 are as follows:
The apex coordinate that every layer is sliced quadrilateral mesh is substituted into three period minimal surface function expressions, for four sides
Shape side P1P2, the three-dimensional coordinate on two of them vertex is P1(x1,y1,z1), P2(x2,y2,z2), it is calculated using linear interpolation method
Obtain slice line segment endpoint P0:
The slice line segment of curved surface and all slice quadrilateral mesh can be obtained.
The slice line segment of curved surface and all slicing layer quadrilateral mesh can be obtained using this method.
Preferably, the detailed process of the step 4 are as follows:
Slice segment data structure and quadrangle data structure are established, slice segment data structure saves the 2 of slice line segment
A vertex information and it is corresponding with slice line segment intersect quadrangle information, 4 vertex of quadrangle data structure preservation quadrangle
Information and slice segment information corresponding with quadrangle establish all slice line segments and four side corresponding with the slice line segment with this
The correspondence topological relation of shape.
Preferably, the detailed process of the step 5 are as follows:
Step 5-1: the slice line segment unsorted for one finds intersection quadrangle corresponding with the slice line segment；
Step 5-2: according to the quadrangle coordinate, the quadrangle adjacent with the quadrangle is found in quadrilateral mesh；
Step 5-3: judge in the adjacent quadrangle with the presence or absence of slice line segment corresponding with the adjacent quadrangle；
Step 5-4: the adjacent segments for possessing same coordinate with current slice line segment are found；
Step 5-5: repeating step 5-1 to step 5-4 can be completed the sequence of slice line segment, and orderly slice line segment is
Final slicing profile.
Compared with prior art, the present invention has the advantage that are as follows:
Using hierarchy slicing grid, according to the function expression of three period minimal surfaces, coordinate distribution and slice
Thickness directly generates hierarchy slicing line segment, avoids conventional method and needs to firstly generate the shortcomings that STL grid model is sliced again, section
Processing time and memory consumption are saved.In addition, making full use of slice line segment and being sliced the topological relation of grid quadrangle, quickly arrange
Sequence is sliced line segment and generates slicing profile, and time complexity is only linear O (n).The method of the present invention is reliable and stable, can efficiently produce
The 3 D-printing slicing profile of three period minimal surfaces.
Detailed description of the invention
Fig. 1 is the flow chart for the three period minimal surface 3 D-printing slicing profile rapid generations that embodiment provides；
Fig. 2 is the slice quadrilateral mesh for the generation curved surface corresponding region that embodiment provides；
Fig. 3 is the rapid section result schematic diagram that embodiment provides: (a) being that P curved surface and quadrilateral mesh interpolation are directly raw
At slice line segment, be (b) left view of slice result, the slice line segment (c) being calculated for monolayer slices gridding interpolation；
Fig. 4 is the rapid section time result that embodiment provides；
Fig. 5 is the slice line segment sorting time result that embodiment provides: (a) be the sorting time under small data quantity as a result,
It (b) is the sorting time result under big data quantity.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention more comprehensible, with reference to the accompanying drawings and embodiments to this
Invention is described in further detail.It should be appreciated that the specific embodiments described herein are only used to explain the present invention,
And the scope of protection of the present invention is not limited.
Fig. 1 is the flow chart for the three period minimal surface 3 D-printing slicing profile rapid generations that embodiment provides.
As shown in Figure 1, method provided in this embodiment the following steps are included:
Step 101: inputting expression formula f (x, y, z)=c, the slice thickness h of three period minimal surfaces of slice, be sliced
Network of quadrilaterals lattice resolution n.
By taking three period minimal surface P curved surfaces as an example, function expression is f (x, y, z)=cos (0.25 π x)+cos (0.25 π
Y)+cos (0.25 π z)=0, slice thickness h=0.2mm, grid resolution n=16, x ∈ [0,8], y ∈ [0,8], z ∈ [0,
8]。
Step 102: according to the coordinate distribution and slice thickness of three period minimal surfaces, generating curved surface corresponding region
It is sliced quadrilateral mesh.
Since when expression formula f (x, y, z)=c of three period minimal surfaces of determination, expression formula has not only been determined in step 101
F (x, y, z)=c equation, further defines the value range of each independent variable, in this way, the coordinate of three period minimal surfaces point
Cloth range has just accordingly determined, further according to slice thickness, can be obtained curved surface corresponding region.
As shown in Fig. 2, according to slice thickness h=0.2mm, respectively in zi=i × 0.2, in the plane of (i=1 ..., 40)
According to slice network of quadrilaterals lattice resolution n=16, x=j × 0.5 is generated respectively in the direction x, y, (j=0 ..., 16), y=j ×
0.5, the parallel lines of (j=0 ..., 16), the orthogonal slice quadrilateral mesh for generating curved surface corresponding region of parallel lines.
Step 103: according to three period minimal surface expression formula f (x, y, z)=c, linear interpolation calculates curved surface and every layer is cut
The slice line segment of piece quadrilateral mesh.
Specifically, by every layer of slice quadrilateral mesh apex coordinate substitute into three period minimal surface function expression f (x, y,
Z) in=c, for quadrangle side P1P2, the three-dimensional coordinate on two of them vertex is P1(x1,y1,z1), P2(x2,y2,z2), it utilizes
The endpoint P of slice line segment is calculated in linear interpolation method0:
The slice line segment of curved surface and all slicing layer quadrilateral mesh can be obtained using the above method.
If Fig. 3 (a) is P curved surface and the slice line segment that slice quadrilateral mesh interpolation directly generates, if Fig. 3 (b) is to cut
The left view of piece result, if Fig. 3 (c) is the slice line segment that monolayer slices gridding interpolation is calculated.
Step 104: saving the topology of quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment
Relationship.
Specifically, slice segment data structure and quadrangle data structure are established, slice segment data structure saves slice
2 vertex informations of line segment and it is corresponding with slice line segment intersect quadrangle information, the 4 of quadrangle data structure preservation quadrangle
A vertex information and slice segment information corresponding with quadrangle establish all slice line segments and corresponding with the slice line segment with this
Quadrangle correspondence topological relation.
Step 105: according to the topology of quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment
Relationship is ranked up slice line segment.
Specific step is as follows for step 105:
Step 105-1: the slice line segment unsorted for one finds intersection quadrangle corresponding with the slice line segment；
Step 105-2: according to the quadrangle coordinate, the quadrangle adjacent with the quadrangle is found in quadrilateral mesh；
Step 105-3: judge in the adjacent quadrangle with the presence or absence of slice line segment corresponding with the adjacent quadrangle；
Step 105-4: the adjacent segments for possessing same coordinate with current slice line segment are found；
Step 105-5: repeating step 105-1 to step 105-4 can be completed the sequence of slice line segment, orderly slice
Section is final slicing profile.
Step 106: the slicing profile generated after all sequences being exported with CLI file format and is saved.
Typical embodiment of the invention is as follows:
The three period minimal surface P toroidal function expression formulas for inputting slice are f (x, y, z)=cos (0.25 π x)+cos
(0.25 π y)+cos (0.25 π z)=0, x ∈ [0,8], y ∈ [0,8], z ∈ [0,8], slice thickness h=0.2mm, setting are different
Grid resolution n obtain different number of slice line segment, obtain the slicing profile of different accuracy after slice line segment sequence, generate
Synusia CLI file saves.
Rapid section method and traditional dicing method are tested on the computer of Intel to strong CPU@3.40GHz, 8GB memory
Slice time difference.It is sliced again as shown in figure 4, rapid section obviously first generates three period minimal surface STL models than tradition
Method it is more efficient, while also save save stl file memory consumption.
In addition, in terms of being sliced line segment sequence, as shown in Fig. 5 (a), quicksort O (n) under smaller slice segment data amount
Method time-consuming is considerably less than the violence sequence O (n of Kim proposition2) method, quicksort O (n) method and Lin et al. propose excellent
It is little to change sequence O (nlogn) method divergence；As shown in Fig. 5 (b), under larger slice segment data amount, quicksort O (n) method
It is almost the same at efficiency of algorithm inflection point with the sequence time-consuming of Optimal scheduling O (nlogn) method, hereafter with slice number of segment mesh
Increase, quicksort method can save more and more sorting times compared to O (nlogn) method.Three period minimal surface knots
Structure is complicated, and the slice segment data amount generally generated is larger, and the method for the present invention can quickly be sliced curved surface, and then quickly
It sorts to slice line segment at random and generates slicing profile.
Technical solution of the present invention and beneficial effect is described in detail in above-described specific embodiment, Ying Li
Solution is not intended to restrict the invention the foregoing is merely presently most preferred embodiment of the invention, all in principle model of the invention
Interior done any modification, supplementary, and equivalent replacement etc. are enclosed, should all be included in the protection scope of the present invention.
Claims (4)
1. a kind of rapid generation of three period minimal surface 3 D-printing slicing profiles, which is characterized in that including following step
It is rapid:
Step 1: inputting expression formula f (x, y, z)=c, the slice thickness h of three period minimal surfaces of slice, be sliced quadrangle
Grid resolution n, wherein c is the critical numerical constant of curved surface, x ∈ [a0,a1], y ∈ [b0,b1], z ∈ [c0,c1]；
Step 2: according to the coordinate distribution and slice thickness of three period minimal surfaces, generating the slice four of curved surface corresponding region
Side shape grid；
Step 3: according to three period minimal surface expression formula f (x, y, z)=c, linear interpolation calculates curved surface and every layer of four side of slice
The slice line segment of shape grid, specific steps are as follows:
The apex coordinate that every layer is sliced quadrilateral mesh is substituted into three period minimal surface function expressions, for quadrangle side
P1P2, the three-dimensional coordinate on two of them vertex is P1(x1,y1,z1), P2(x2,y2,z2), it is calculated using linear interpolation method
It is sliced line segment endpoint P0:
The slice line segment of curved surface and all slice quadrilateral mesh can be obtained；
The slice line segment of curved surface and all slicing layer quadrilateral mesh can be obtained using this method；
Step 4: saving the topological relation of quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment；
Step 5: right according to the topological relation of quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment
Slice line segment is ranked up；
Step 6: the slicing profile generated after all sequences being exported with CLI file format and is saved.
2. the rapid generation of three periods minimal surface 3 D-printing slicing profile as described in claim 1, feature exist
In the detailed process of the slice quadrilateral mesh for generating curved surface corresponding region are as follows:
Firstly, curved surface corresponding region is divided into according to slice thickness hA plane；
Then for planeAccording to slice network of quadrilaterals lattice resolution n, respectively along x, the side y
To j parallel lines of generation respectively, in which:
Parallel lines
Parallel lines
Parallel lines xjWith parallel lines yjIt is orthogonal, generate the slice quadrilateral mesh of curved surface corresponding region.
3. the rapid generation of three periods minimal surface 3 D-printing slicing profile as described in claim 1, feature exist
In the detailed process of the step 4 are as follows:
Slice segment data structure and quadrangle data structure are established, slice segment data structure saves 2 tops of slice line segment
Point information and it is corresponding with slice line segment intersect quadrangle information, 4 vertex informations of quadrangle data structure preservation quadrangle
With slice segment information corresponding with quadrangle, all slice line segments and corresponding with slice line segment quadrangle are established with this
Corresponding topological relation.
4. the rapid generation of three periods minimal surface 3 D-printing slicing profile as described in claim 1, feature exist
In the detailed process of the step 5 are as follows:
Step 5-1: the slice line segment unsorted for one finds intersection quadrangle corresponding with the slice line segment；
Step 5-2: according to the quadrangle coordinate, the quadrangle adjacent with the quadrangle is found in quadrilateral mesh；
Step 5-3: judge in the adjacent quadrangle with the presence or absence of slice line segment corresponding with the adjacent quadrangle；
Step 5-4: the adjacent segments for possessing same coordinate with current slice line segment are found；
Step 5-5: the sequence that step 5-1 to step 5-4 completes slice line segment is repeated, orderly slice line segment is final
Slicing profile.
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| CN109228353B (en) * | 2018-08-06 | 2021-01-12 | 上海大学 | Unsupported 3D printing method of dynamic slicing algorithm |
| CN109466065B (en) * | 2018-11-05 | 2019-12-27 | 山东大学 | Support-free non-uniform three-period extremely-small curved surface generation method and system for 3D printing |
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| CN111062166B (en) * | 2019-12-16 | 2021-10-22 | 浙江大学 | Three-period minimum curved surface porous structure topology optimization method based on variable density method |
| CN111695259B (en) * | 2020-06-12 | 2024-04-30 | 重庆大学 | Processing method of TPMS structure with continuous gradient wall thickness based on 3D printing |
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