CN108327287A - 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 PDF

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CN108327287A
CN108327287A CN201810040995.2A CN201810040995A CN108327287A CN 108327287 A CN108327287 A CN 108327287A CN 201810040995 A CN201810040995 A CN 201810040995A CN 108327287 A CN108327287 A CN 108327287A
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slice
line segment
quadrangle
curved
minimal
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CN108327287B (en
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傅建中
冯嘉炜
林志伟
商策
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Zhejiang University ZJU
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/30Auxiliary operations or equipment
    • B29C64/386Data acquisition or data processing for additive manufacturing
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B33ADDITIVE MANUFACTURING TECHNOLOGY
    • B33YADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00Data acquisition or data processing for additive manufacturing

Abstract

The invention discloses a kind of three period minimal surface 3 D-printing slicing profile rapid generations, including three period minimal surface expression formulas of input slice, slice thickness and slice network of quadrilaterals lattice resolution;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;Preserve the topological relation of slice line segment and 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 formats finally and is preserved.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 models consumption plenty of time and memory headroom is avoided.

Description

A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile
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 periods minimal surface 3 D-printing slicing profile.
Background technology
Three-dimensional printing technology is a kind of advanced manufacturing technology being superimposed based on synusia, and be otherwise known as rapid prototyping technology or increasing Material manufacturing technology.Material is constantly cut down to obtain the process of design shape, 3 D-printing skill different from tradition machining etc. 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 is done, for different three-dimensional modeling datas, it is proposed that 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 disadvantage performance of STL becomes apparent, and a large amount of dough sheet is difficult to some The dough sheet defect of processing often leads to the failure that slicing profile generates.
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 pore space structure 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 structures of design are 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 structures of STL formats 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).In terms of being sliced line segment sequence processing, 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 segments, 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 files generally generated are larger, need to consume Many memories and processing time.Some current slice line segment sort algorithm efficiency in sequencing problem under handling big data quantity are low 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.
Invention content
In order to solve, the existing three period minimal surface 3 D-printing slice efficiencies based on STL models are low, consumption memory is big The shortcomings that, the present invention provides a kind of rapid generations of three periods minimal surface 3 D-printing slicing profile.Pass through structure It is sliced quadrilateral mesh, the direct slicing layering of three period minimal surfaces is fast implemented, avoids the life of conventional method STL models 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 provides following technical scheme:
A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile, includes 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 are 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, cutting for curved surface corresponding region is generated 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 preserving quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment is closed System;
Step 5:It is 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 is exported with CLI file formats and is preserved.
Wherein, the detailed process of the slice quadrilateral mesh for generating curved surface corresponding region is:
First, according to slice thickness h, curved surface corresponding region is divided intoA plane;
Then for planeAccording to slice network of quadrilaterals lattice resolution n, respectively edge X, the directions y generate j parallel lines respectively, wherein:
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 is:
The apex coordinate of every layer of slice quadrilateral mesh is substituted into three period minimal surface function expressions, for four sides Shape side P1P2, the three-dimensional coordinate on two of which vertex is P1(x1,y1,z1), P2(x2,y2,z2), it is calculated using linear interpolation method Obtain slice line segment endpoint P0
It can be obtained the slice line segment of curved surface and all slice quadrilateral mesh.
It can be obtained the slice line segment of curved surface and all slicing layer quadrilateral mesh using this method.
Preferably, the detailed process of the step 4 is:
Slice segment data structure and quadrangle data structure are established, slice segment data structure preserves 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 is:
Step 5-1:For a unsorted slice line segment, intersection quadrangle corresponding with the slice line segment is found;
Step 5-2:According to the quadrangle coordinate, the quadrangle adjacent with the quadrangle is found in quadrilateral mesh;
Step 5-3:Judge to whether there is slice line segment corresponding with the adjacent quadrangle in the adjacent quadrangle;
Step 5-4:Find the adjacent segments for possessing same coordinate with current slice line segment;
Step 5-5:The sequence that slice line segment can be completed in step 5-1 to step 5-4 is repeated, orderly slice line segment is Final slicing profile.
Compared with prior art, the present invention have the advantage that for:
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 models are sliced again, section Processing time and memory consumption are saved.In addition, making full use of slice line segment and the topological relation for being sliced 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.
Description of the drawings
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 generating curved surface corresponding region that embodiment provides;
Fig. 3 is the rapid section result schematic diagram that embodiment provides:(a) it is that P curved surfaces and quadrilateral mesh interpolation are directly raw At slice line segment, (b) be slice result left view, (c) be the slice line segment that is calculated of 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 small data quantity under sorting time as a result, (b) it is the sorting time result under big data quantity.
Specific implementation mode
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, Do not limit protection scope of the present invention.
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 includes the following steps:
Step 101:Input expression formula f (x, y, z)=c, the slice thickness h of three period minimal surfaces of slice, slice 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, curved surface corresponding region is generated It is sliced quadrilateral mesh.
Since when expression formula f (x, y, z)=c of determining three period minimal surfaces, expression formula is not only determined in step 101 The equation of f (x, y, z)=c, further defines the value range of each independent variable, in this way, the coordinate of three period minimal surfaces point Cloth range just accordingly determines, further according to slice thickness, you can obtains 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 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 which 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
It can be obtained the slice line segment of curved surface and all slicing layer quadrilateral mesh using the above method.
If Fig. 3 (a) is P curved surfaces 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:Preserve 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 preserves 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.
Step 105 is as follows:
Step 105-1:For a unsorted slice line segment, intersection quadrangle corresponding with the slice line segment is found;
Step 105-2:According to the quadrangle coordinate, the quadrangle adjacent with the quadrangle is found in quadrilateral mesh;
Step 105-3:Judge to whether there is slice line segment corresponding with the adjacent quadrangle in the adjacent quadrangle;
Step 105-4:Find the adjacent segments for possessing same coordinate with current slice line segment;
Step 105-5:Repeat the sequence that slice line segment can be completed in step 105-1 to step 105-4, orderly slice The as final slicing profile of section.
Step 106:The slicing profile generated after all sequences is exported with CLI file formats and is preserved.
The typical embodiment of the present 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 files preserve.
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 preserve 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, which takes, is considerably less than the violence sequence O (n that Kim is proposed2) method, quicksort O (n) methods 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) methods Sequence with Optimal scheduling O (nlogn) method take it is almost the same at efficiency of algorithm inflection point, hereafter with slice hop count 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 scheme of the present invention and advantageous effect is described in detail in above-described specific implementation mode, Ying Li Solution is not intended to restrict the invention the foregoing is merely presently most preferred embodiment of the invention, all principle models in the present 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 (5)

1. a kind of rapid generation of three periods minimal surface 3 D-printing slicing profile, which is characterized in that including following step Suddenly:
Step 1:Expression formula f (x, y, z)=c of three period minimal surfaces of slice is inputted, slice thickness h is sliced quadrangle Grid resolution n, wherein c are 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, the slice four of curved surface corresponding region is generated 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;
Step 4:Preserve the topological relation of quadrangle in slice line segment and slice quadrilateral mesh corresponding with the slice line segment;
Step 5:It is 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 is exported with CLI file formats and is preserved.
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 is:
First, according to slice thickness h, curved surface corresponding region is divided intoA 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, wherein:
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 3 is:
The apex coordinate of every layer of slice quadrilateral mesh is substituted into three period minimal surface function expressions, for quadrangle side P1P2, the three-dimensional coordinate on two of which vertex is P1(x1,y1,z1), P2(x2,y2,z2), it is calculated using linear interpolation method It is sliced line segment endpoint P0
It can be obtained the slice line segment of curved surface and all slice quadrilateral mesh.
It can be obtained the slice line segment of curved surface and all slicing layer quadrilateral mesh using this method.
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 4 is:
Slice segment data structure and quadrangle data structure are established, slice segment data structure preserves 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 Slice segment information corresponding with quadrangle establishes all slice line segments and corresponding with slice line segment quadrangle with this Corresponding topological relation.
5. 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 is:
Step 5-1:For a unsorted slice line segment, intersection quadrangle corresponding with the slice line segment is found;
Step 5-2:According to the quadrangle coordinate, the quadrangle adjacent with the quadrangle is found in quadrilateral mesh;
Step 5-3:Judge to whether there is slice line segment corresponding with the adjacent quadrangle in the adjacent quadrangle;
Step 5-4:Find the adjacent segments for possessing same coordinate with current slice line segment;
Step 5-5:The sequence that slice line segment can be completed in step 5-1 to step 5-4 is repeated, orderly slice line segment is as final Slicing profile.
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CN109228353A (en) * 2018-08-06 2019-01-18 上海大学 A kind of Dynamic Slicing algorithm without support 3D printing method
CN109466065A (en) * 2018-11-05 2019-03-15 山东大学 Exempt to support non-homogeneous three periods minimal surface generation method and system towards 3D printing
CN109622958A (en) * 2018-12-20 2019-04-16 华中科技大学 A method of titanium alloy implant is prepared using minimal surface porous structure
CN109977507A (en) * 2019-03-15 2019-07-05 浙江大学 A kind of complex topography porous support efficiently produces method
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