CN108327287B - A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile - Google Patents

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

A fast generation method of three-period minimal surface 3D printing slice profile

technical field

The invention relates to the technical field of three-dimensional printing computer aided manufacturing (CAM), in particular to a method for rapidly generating three-period minimal curved surface three-dimensional printing slice profiles.

Background technique

3D printing technology is an advanced manufacturing technology based on layer stacking, also known as rapid prototyping technology or additive manufacturing technology. Different from traditional machining methods that continuously cut materials to obtain design shapes, 3D printing technology uses various materials to obtain design models with the help of computer-aided equipment layer by layer, which is especially suitable for rapid manufacturing of complex structures. The generation of 3D printing slice contour is a key link that affects the final precision and efficiency of manufacturing.

In order to find an ideal balance between accuracy and efficiency, scholars at home and abroad have done a lot of work in the generation of slice contours, and proposed various slice generation methods for different 3D model data. Currently in the field of 3D printing, STL is the most commonly used model data format. STL uses a large number of triangular patches to approximate the shape of the design model, and the data structure is simple and easy to handle. However, in order to improve the modeling accuracy, the number of patches must be greatly increased, which in turn consumes a lot of memory and processing time. Especially when modeling complex topological structures, the disadvantage of STL is more obvious. A large number of patches and some intractable patch defects often lead to the failure of slice contour generation.

Triply Periodic Minimal Surfaces (TPMS) are implicit surfaces with complex topology. Its smooth surface and internal and external connected hole structure have a wide range of applications in the engineering field. 3D printing has a natural advantage in making such complex structures. Melchels et al. saved the designed TPMS structure as an STL file for fabrication using a three-dimensional printing process, and then used as a tissue engineering scaffold for cell culture (see Melchels FP W, Bertoldi K, Gabbrielli R, et al. Mathematically defined tissue engineering scaffold architectures prepared by stereolithography [J].Biomaterials,2010,31(27):6909-6916.); Li et al. generated the TPMS structure in STL format as the filling structure of the 3D printing model to achieve the purpose of lightweight printing (see 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). For the processing of slice line segment sorting, Kim proposed a method for violent generation of slice contours for mesh models. The method is simple to implement but has a time complexity of up to O(n ² ) (see 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. proposed an optimized sorting algorithm for STL slice line segments with a time complexity of O(nlogn) (see Lin Z , Fu J, Shen H, et al. Efficient cutting area detection in roughing process for meshedsurfaces[J]. The International Journal of Advanced Manufacturing Technology, 2013, 69(1-4):525-530).

According to literature analysis, the current use of 3D printing technology to manufacture three-period minimal surfaces requires first generating STL models, and then performing STL-based slicing. Due to the intricate structure, the generally generated STL model file is large, which consumes a lot of memory and processing time. Some current slicing line sorting algorithms are inefficient when dealing with large data volumes and cannot efficiently generate slicing contours. Furthermore, no literature was found on the method for generating the profile of three-period minimal surface slices.

SUMMARY OF THE INVENTION

In order to solve the shortcomings of low efficiency and large memory consumption of the existing three-period minimal surface 3D printing slices based on the STL model, the present invention provides a rapid generation method for three-period minimal surface 3D printing slice profiles. By constructing a slicing quadrilateral mesh, the direct slicing and layering of three-period minimal surfaces can be quickly realized, avoiding the generation of STL models by traditional methods. At the same time, the topological relationship between the slicing quadrilateral grid and the slicing line segment is fully utilized, and the slicing line segment is quickly sorted to generate the final slicing outline, and the time complexity is only linear O(n). The method is stable and reliable, and can realize the rapid generation of three-period minimal surface three-dimensional printing slice contours.

In order to realize the above-mentioned purpose of the invention, the present invention provides the following technical solutions:

A method for rapidly generating slice profiles for three-period minimal surface three-dimensional printing, comprising the following steps:

Step 1: Input the expression f(x,y,z)=c of the three-period minimal surface to be sliced, the slice thickness h, the slice quadrilateral mesh resolution n, where c is the surface critical value constant, x∈[ a ₀ ,a ₁ ], y∈[b ₀ ,b ₁ ], z∈[c ₀ ,c ₁ ];

Step 2: According to the coordinate distribution range and slice thickness of the three-period minimal surface, generate a sliced quadrilateral grid of the corresponding area of the surface;

Step 3: According to the three-period minimal surface expression f(x,y,z)=c, linearly interpolate the surface and slice line segments of each layer of sliced quadrilateral grid;

Step 4: Save the topological relationship between the slice line segment and the quadrilateral in the slice quadrilateral grid corresponding to the slice line segment;

Step 5: Sort the sliced line segments according to the topological relationship between the sliced line segment and the quadrilateral in the sliced quadrilateral grid corresponding to the sliced line segment;

Step 6: Save all sorted slice contours as output in CLI file format.

Wherein, the specific process of generating the sliced quadrilateral mesh of the corresponding area of the surface is as follows:

First, according to the slice thickness h, the corresponding area of the surface is divided into a plane;

then for the plane According to the slicing quadrilateral grid resolution n, j parallel lines are generated along the x and y directions respectively, where:

parallel lines

parallel lines

Parallel lines x _j and parallel lines y _j are orthogonal to generate a sliced quadrilateral grid of the corresponding area of the surface.

Preferably, the specific process of step 3 is:

Substitute the vertex coordinates of each sliced quadrilateral mesh into the three-period minimal surface function expression, for the quadrilateral side P ₁ P ₂ , the three-dimensional coordinates of the two vertices are P ₁ (x ₁ , y ₁ , z ₁ ), P ₂ (x ₂ , y ₂ , z ₂ ), using the linear interpolation method to calculate the endpoint P ₀ of the slice line segment:

You can get the sliced segments of the surface and all sliced quad meshes.

Using this method, the slice segments of the surface and quadrilateral meshes of all slice layers can be obtained.

Preferably, the specific process of step 4 is:

Establish a slice line segment data structure and a quadrilateral data structure. The slice line segment data structure saves the 2 vertex information of the slice line segment and the intersecting quadrilateral information corresponding to the slice line segment, and the quadrilateral data structure saves the four vertex information of the quadrilateral and the slice line segment information corresponding to the quadrilateral , so as to establish the corresponding topological relationship between all slice line segments and the quadrilateral corresponding to the slice line segment.

Preferably, the specific process of step 5 is:

Step 5-1: For an unsorted slice segment, find the intersecting quadrilateral corresponding to the slice segment;

Step 5-2: According to the coordinates of the quadrilateral, find the quadrilateral adjacent to the quadrilateral in the quadrilateral grid;

Step 5-3: determine whether there is a slice line segment corresponding to the adjacent quadrilateral in the adjacent quadrilateral;

Step 5-4: Find the adjacent line segment with the same coordinates as the current slice line segment;

Step 5-5: Repeat steps 5-1 to 5-4 to complete the sorting of slice line segments, and the ordered slice line segments are the final slice outlines.

Compared with the prior art, the present invention has the following advantages:

Using the layered slice grid, the layered slice line segment is directly generated according to the function expression, coordinate distribution range and slice thickness of the three-period minimal surface, avoiding the disadvantage of the traditional method that needs to generate the STL grid model first and then slice it, and saves the processing time. time and memory consumption. In addition, making full use of the topological relationship between the slice line segment and the slice grid quadrilateral, quickly sort the slice line segment to generate the slice outline, and the time complexity is only linear O(n). The method of the invention is stable and reliable, and can efficiently generate a three-dimensional printing slice profile of a three-period minimal curved surface.

Description of drawings

1 is a flowchart of a method for quickly generating a three-period minimal curved surface three-dimensional printing slice profile provided by an embodiment;

Fig. 2 is the sliced quadrilateral mesh of the corresponding area of the generation surface provided by the embodiment;

Figure 3 is a schematic diagram of the fast slicing result provided by the embodiment: (a) is the slice line segment directly generated by the interpolation of the P surface and the quadrilateral grid, (b) is the left view of the slicing result, (c) is the single-layer slice grid interpolation calculation the obtained slice segment;

Fig. 4 is the fast slice time result that the embodiment provides;

FIG. 5 shows the sorting time results of slice line segments provided by the embodiment: (a) is the sorting time result under a small data amount, and (b) is the sorting time result under a large data amount.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and do not limit the protection scope of the present invention.

FIG. 1 is a flow chart of a method for quickly generating a three-period minimal curved surface three-dimensional printing slice profile provided by an embodiment. As shown in Figure 1, the method provided by this embodiment includes the following steps:

Step 101: Input the expression f(x, y, z)=c of the three-period minimal surface to be sliced, the slice thickness h, and the slice quadrilateral mesh resolution n.

Taking the three-period minimal surface P surface as an example, the function expression is f(x,y,z)=cos(0.25πx)+cos(0.25πy)+cos(0.25πz)=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 range and slice thickness of the three-period minimal curved surface, generate a sliced quadrilateral grid of the corresponding area of the curved surface.

Since the expression f(x,y,z)=c of the three-period minimal surface is determined in step 101, not only the equation of the expression f(x,y,z)=c is determined, but also each independent variable is determined In this way, the coordinate distribution range of the three-period minimal surface is determined accordingly, and then according to the slice thickness, the corresponding area of the surface can be obtained.

As shown in Figure 2, according to the slice thickness h=0.2mm, on the plane of _zi =i×0.2, (i=1,...,40), according to the slice quadrilateral grid resolution n=16, in x, y The directions respectively generate parallel lines of x=j×0.5, (j=0,…,16), y=j×0.5, (j=0,…,16), and the parallel lines are orthogonal to generate the sliced quadrilateral network of the corresponding area of the surface grid.

Step 103 : According to the three-period minimal surface expression f(x, y, z)=c, linearly interpolate the surface and slice line segments of each layer of sliced quadrilateral grids.

Specifically, the vertex coordinates of each sliced quadrilateral mesh are substituted into the three-period minimal surface function expression f(x, y, z)=c, and for the quadrilateral side P ₁ P ₂ , the three-dimensional coordinates of the two vertices are P ₁ (x ₁ , y ₁ , z ₁ ), P ₂ (x ₂ , y ₂ , z ₂ ), use linear interpolation to calculate the endpoint P ₀ of the slice line segment:

Using the above method, the slicing line segments of the surface and quadrilateral meshes of all slice layers can be obtained.

Figure 3(a) is the slice line segment directly generated by the interpolation of the P surface and the sliced quadrilateral grid, Figure 3(b) is the left view of the slice result, and Figure 3(c) is the calculation of the single-layer slice grid interpolation slice line segment.

Step 104: Save the topological relationship between the slice line segment and the quadrilateral in the slice quadrilateral grid corresponding to the slice line segment.

Specifically, a slicing line segment data structure and a quadrilateral data structure are established. The slicing line segment data structure preserves 2 vertex information of the slicing line segment and the intersecting quadrilateral information corresponding to the slicing line segment, and the quadrilateral data structure preserves the 4 vertex information of the quadrilateral and the corresponding quadrilateral information. Slice line segment information, thereby establishing the corresponding topological relationship between all slice line segments and the quadrilateral corresponding to the slice line segment.

Step 105: Sort the slicing line segments according to the topological relationship between the slicing line segments and the quadrilaterals in the slicing quadrilateral grid corresponding to the slicing line segments.

The specific steps of step 105 are as follows:

Step 105-1: For an unsorted slicing line segment, find the intersecting quadrilateral corresponding to the slicing line segment;

Step 105-2: According to the coordinates of the quadrilateral, find the quadrilateral adjacent to the quadrilateral in the quadrilateral grid;

Step 105-3: Determine whether there is a slice line segment corresponding to the adjacent quadrilateral in the adjacent quadrilateral;

Step 105-4: Find the adjacent line segment with the same coordinates as the current slice line segment;

Step 105-5: Repeat steps 105-1 to 105-4 to complete the sorting of slice line segments, and the ordered slice line segments are the final slice outlines.

Step 106: Output and save all the slicing contours generated after sorting in a CLI file format.

Typical embodiments of the present invention are as follows:

The surface function expression of the input three-period minimal surface P to be sliced is f(x,y,z)=cos(0.25πx)+cos(0.25πy)+cos(0.25πz)=0, x∈[0,8 ], y∈[0,8], z∈[0,8], slice thickness h=0.2mm, set different grid resolutions n to obtain different numbers of slice line segments, and get slice outlines with different precisions after the slice line segments are sorted , and save the generated slice CLI file.

Test the slicing time difference between the fast slicing method and the traditional slicing method on a computer with Intel Xeon CPU@3.40GHz and 8GB memory. As shown in Figure 4, fast slicing is obviously more efficient than the traditional method of first generating a three-period minimal surface STL model and then slicing, and it also saves the memory consumption of saving STL files.

In addition, in the sorting of slice line segments, as shown in Figure 5(a), the O(n) method of quick sort with a small amount of slice line segment data is significantly less time-consuming than the O(n ² ) method of brute force sorting proposed by Kim. There is little difference between the O(n) method and the optimized sorting O(nlogn) method proposed by Lin et al. As shown in Figure 5(b), with a large amount of sliced line segment data, the quick sorting O(n) method is different from the optimized sorting O(n) method. The sorting time of the (nlogn) method is basically the same at the inflection point of the algorithm efficiency. After that, as the number of slice line segments increases, the quicksort method will save more and more sorting time compared with the O(nlogn) method. The three-period minimal surface is complex in structure, and generally generates a large amount of slice line segment data. The method of the invention can quickly slice the surface, and then quickly sort the scattered slice line segments to generate slice outlines.

The above-mentioned specific embodiments describe in detail the technical solutions and beneficial effects of the present invention. It should be understood that the above-mentioned embodiments are only the most preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, additions and equivalent substitutions made within the scope shall be included within 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 x_jWith parallel lines y_jIt 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.