CN108327287A - A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile - Google Patents

Abstract

The invention discloses a method for quickly generating slice outlines of three-period minimal curved surfaces for three-dimensional printing, which includes inputting the three-period minimal curved surface expression to be sliced, slice thickness, and slice quadrilateral grid resolution; according to the three-period minimal curved surface coordinate distribution Range and slice thickness, generate a sliced quadrilateral grid of the corresponding area of the surface; according to the surface expression, linear interpolation calculates the slice line segment of the surface and each layer of the sliced quadrilateral grid; saves the topological relationship between the slice line segment and the quadrilateral in the corresponding sliced quadrilateral grid; Sort all the slice line segments; finally save all the slice contours generated after sorting in CLI file format. The present invention utilizes sliced quadrilateral grids to realize quick slices of three-period minimal surfaces and quick sorting of sliced scattered line segments, quickly generate three-dimensional printing slice outlines, and avoid the shortcomings of traditional methods that consume a lot of time and memory space for generating STL models.

Description

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

technical field

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

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 and other methods that continuously cut materials to obtain the design shape, 3D printing technology uses various materials and superimposes the design model with the help of computer-aided equipment, which is especially suitable for rapid manufacturing of complex structures. 3D printing slice contour generation is a key link that affects the final accuracy and efficiency of manufacturing.

In order to find an ideal balance between precision and efficiency, scholars at home and abroad have done a lot of work on slice contour generation, 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 approximates the shape of the design model with a large number of triangular faces, and the data structure is simple and easy to handle. But in order to improve the modeling accuracy, the number of facets must be greatly increased, which consumes a lot of memory and processing time. Especially when modeling complex topological structures, the disadvantages of STL are more obvious. A large number of patches and some difficult-to-handle patch defects often lead to the failure of slice contour generation.

Triply Periodic Minimal Surfaces TPMS (Triply Periodic Minimal Surfaces) is an implicit surface with complex topology. Its smooth surface and interconnected pore structure have a wide range of applications in the engineering field. 3D printing has a natural advantage in fabricating such complex structures. Melchels et al. saved the designed TPMS structure as an STL file and manufactured it using a three-dimensional printing process, and then used it 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 printing lightweight (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). In terms of slice line segment sorting, Kim proposed a brute force generation method for slice contours of mesh models. The method is simple to implement but has a time complexity as high as 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 meshed surfaces [J]. The International Journal of Advanced Manufacturing Technology, 2013, 69(1-4):525-530).

According to literature analysis, it is known that the current use of 3D printing technology to manufacture three-period minimal surfaces requires first generating an STL model, and then performing STL-based slicing. Due to the intricate structure, the generally generated STL model file is relatively large, which consumes a lot of memory and processing time. Some current slice line segment sorting algorithms are inefficient when dealing with the sorting problem under a large amount of data, and cannot efficiently generate slice outlines. In addition, no literature was found on the generation method of three-period minimal surface slice contours.

Contents of the invention

In order to solve the shortcomings of low efficiency and large memory consumption of the existing three-period minimal curved surface 3D printing slice based on the STL model, the present invention provides a method for quickly generating the outline of a three-period minimal curved surface 3D printed slice. By constructing a sliced quadrilateral mesh, the direct slice layering of three-period minimal surfaces can be quickly realized, avoiding the generation of the traditional STL model. At the same time, make full use of the topological relationship between the sliced quadrilateral grid and the sliced line segments, quickly sort the sliced line segments to generate the final slice 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 3D 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 quickly generating slice outlines of three-period minimal surfaces for 3D printing, comprising the following steps:

Step 1: Input the expression f(x,y,z)=c of the three-period minimal surface to be sliced, slice thickness h, slice quadrilateral grid resolution n, where c is the surface boundary 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 for the corresponding area of the surface;

Step 3: According to the three-period minimal surface expression f(x, y, z)=c, linear interpolation calculates the slice line segment of the surface and each layer of slice quadrilateral grid;

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

Step 5: Sorting the slice line segments according to the topological relationship between the slice line segment and the quadrilaterals in the slice quadrilateral grid corresponding to the slice line segment;

Step 6: Output and save all sorted slice profiles in CLI file format.

Wherein, the specific process of generating the slicing quadrilateral mesh of the corresponding area of the curved 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 grid resolution n of the sliced quadrilateral, generate j parallel lines along the x and y directions respectively, where:

parallel lines

parallel lines

The parallel line x _j is orthogonal to the parallel line y _j , generating a sliced quadrilateral mesh of the corresponding area of the surface.

Preferably, the specific process of said step 3 is:

Substitute the vertex coordinates of each sliced quadrilateral grid into the expression of the three-period minimal surface function. For the quadrilateral side P ₁ P ₂ , the three-dimensional coordinates of 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 end point P ₀ of the slice segment:

The surface and all slicing line segments of the slicing quadrilateral mesh are obtained.

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

Preferably, the specific process of said step 4 is:

Establish slice line segment data structure and quadrilateral data structure. The slice line segment data structure stores the two vertex information of the slice line segment and the intersecting quadrilateral information corresponding to the slice line segment. The quadrilateral data structure stores 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 quadrilaterals corresponding to the slice line segments.

Preferably, the specific process of said step 5 is:

Step 5-1: For an unsorted slice line segment, find the intersecting quadrilateral corresponding to the slice line 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: judging 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 the slice line segments, and the ordered slice line segments are the final slice contours.

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

Using the layered slice grid, the layered slice line segment is directly generated according to the function expression of the three-period minimal surface, the coordinate distribution range, and the slice thickness, avoiding the shortcomings of the traditional method that first generates the STL grid model and then slices, saving processing Time and memory consumption. In addition, by making full use of the topological relationship between the slice line segment and the slice grid quadrilateral, the slice line segment is quickly sorted 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 three-dimensional printing slice outlines of three-period minimal curved surfaces.

Description of drawings

Fig. 1 is a flow chart of a method for quickly generating a three-period minimal curved surface 3D printing slice outline provided by an embodiment;

Fig. 2 is the slicing quadrilateral grid of generating the corresponding area of the curved surface provided by the embodiment;

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

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

Fig. 5 is the result of sorting time of slice line segment provided by the embodiment: (a) is the result of sorting time under small amount of data, (b) is the result of sorting time under large amount of data.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here 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 3D printing slice outline provided by the embodiment. As shown in Figure 1, the method provided in 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, slice thickness h, and slice quadrilateral grid resolution n.

Taking the three-period minimal surface P 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 surface, generate a sliced quadrilateral mesh of the corresponding area of the 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 each independent variable In this way, the coordinate distribution range of the three-period minimal surface is determined accordingly, and then the corresponding area of the surface can be obtained according to the slice thickness.

As shown in Figure 2, according to the slice thickness h=0.2mm, respectively on the plane z _i =i×0.2, (i=1,...,40) according to the slice quadrilateral grid resolution n=16, in x, y The directions generate parallel lines of x=j×0.5, (j=0,…,16), y=j×0.5, (j=0,…,16) respectively, and the parallel lines are orthogonal to generate a slice 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, linear interpolation is used to calculate the surface and slice line segments of each layer of sliced quadrilateral grids.

Specifically, substituting the vertex coordinates of each slice quadrilateral grid into the three-period minimal surface function expression f(x, y, z)=c, 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 the linear interpolation method to calculate the endpoint P ₀ of the slice segment:

Using the method above, the surface and all the slice line segments of the quadrilateral mesh of the slice layer 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 calculated by the single-layer slice grid interpolation slice line segment.

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

Specifically, a slice line segment data structure and a quadrilateral data structure are established. The slice line segment data structure stores two vertex information of the slice line segment and the intersecting quadrilateral information corresponding to the slice line segment. The quadrilateral data structure stores four vertex information of the quadrilateral and the corresponding Slice line segment information, so as to establish the corresponding topological relationship between all slice line segments and the quadrilateral corresponding to the slice line segment.

Step 105: Sorting the slice line segments according to the topological relationship between the slice line segment and the quadrilaterals in the slice quadrilateral grid corresponding to the slice line segment.

The concrete steps of step 105 are as follows:

Step 105-1: For an unsorted slice line segment, find the intersecting quadrilateral corresponding to the slice 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: judging whether there is a slice line segment corresponding to the adjacent quadrilateral in the adjacent quadrilateral;

Step 105-4: Find an adjacent line segment that has 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 contours.

Step 106: Output and save all sorted slice contours in CLI file format.

Typical implementation examples of the present invention are as follows:

Input the three-period minimal surface P surface function expression to be sliced as 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 get different numbers of slice line segments, and get slice contours with different precision after sorting the slice line segments , to generate a slice CLI file and save it.

Test the slicing time difference between the fast slicing method and the traditional slicing method on a computer with an Intel Xeon CPU@3.40GHz and 8GB of 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 terms of slice line sorting, as shown in Figure 5(a), the quick sort O(n) method consumes significantly less time than the violent sort O(n ² ) method proposed by Kim under a small slice line segment data volume, and the quick sort There is little difference between the O(n) method and the optimized sorting O(nlogn) method proposed by Lin et al.; 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 quick sorting method will save more and more sorting time than the O(nlogn) method. The structure of the three-period minimal curved surface is complex, and the amount of slice line segment data generally generated is large. The method of the present invention can quickly slice the surface, and then quickly sort the scattered slice line segments to generate a slice outline.

The above-mentioned specific embodiments have described the technical solutions and beneficial effects of the present invention in detail. It should be understood that the above-mentioned are only the most preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, supplements and equivalent replacements made within the scope shall be included in the protection scope of the present invention.

Claims (5)

1. A method for rapidly generating three-period minimal curved surface three-dimensional printing slice outlines, characterized in that it comprises the following steps: Step 1: Input the expression f(x,y,z)=c of the three-period minimal surface to be sliced, slice thickness h, slice quadrilateral grid resolution n, where c is the surface boundary 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 for the corresponding area of the surface; Step 3: According to the three-period minimal surface expression f(x, y, z)=c, linear interpolation calculates the slice line segment of the surface and each layer of slice quadrilateral grid; Step 4: Save the slice line segment and the topological relationship of the quadrilaterals in the slice quadrilateral grid corresponding to the slice line segment; Step 5: Sorting the slice line segments according to the topological relationship between the slice line segment and the quadrilaterals in the slice quadrilateral grid corresponding to the slice line segment; Step 6: Output and save all sorted slice profiles in CLI file format. 2. The rapid generation method of three-period minimal curved surface 3D printing slice outline as claimed in claim 1, is characterized in that, the specific process of the slice quadrilateral grid of described generation curved surface corresponding area is: 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 grid resolution n of the sliced quadrilateral, generate j parallel lines along the x and y directions respectively, where: parallel lines The parallel line x _j is orthogonal to the parallel line y _j , generating a sliced quadrilateral mesh of the corresponding area of the surface. 3. The rapid generation method of three-period minimal curved surface 3D printing slice outline as claimed in claim 1, characterized in that, the specific process of the step 3 is: Substitute the vertex coordinates of each sliced quadrilateral grid into the expression of the three-period minimal surface function. For the quadrilateral side P ₁ P ₂ , the three-dimensional coordinates of 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 end point P ₀ of the slice segment: The surface and all slicing line segments of the slicing quadrilateral mesh are obtained. Using this method, the surface and the slice line segments of the quadrilateral meshes of all slice layers can be obtained. 4. The rapid generation method of three-period minimal curved surface 3D printing slice outline as claimed in claim 1, characterized in that, the specific process of the step 4 is: Establish slice line segment data structure and quadrilateral data structure. The slice line segment data structure stores the two vertex information of the slice line segment and the intersecting quadrilateral information corresponding to the slice line segment. The quadrilateral data structure stores 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 quadrilaterals corresponding to the slice line segments. 5. The rapid generation method of three-period minimal curved surface 3D printing slice contour as claimed in claim 1, characterized in that, the specific process of the step 5 is: Step 5-1: For an unsorted slice line segment, find the intersecting quadrilateral corresponding to the slice line 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: judging 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 the slice line segments, and the ordered slice line segments are the final slice contours.