A three-dimensional surface extrusion modeling method based on spline interpolation function

Abstract

The present invention discloses a three-dimensional surface extrusion modeling method based on a spline interpolation function, which includes the following specific steps. Step 1): Determine the boundary vertices of the original surface, insert new vertices between the boundary vertices to form a new vertex list SPN after smooth processing. Step 2): Construct the topological connection relationship of the new vertices. Step 3): Traverse each vertex in the vertex list SPN and determine the growth direction of each vertex. Step 4): Each vertex in the vertex list SPN is translated according to its respective growth direction to obtain a new translated surface. Step 5): Generate a side surface between the original surface and the translated surface to obtain a three-dimensional model. When constructing the three-dimensional model in the present invention, the points on the original plane are all translated according to their respective determined growth directions, and the translated surface obtained after translation will not interfere with the original surface. Therefore, the problem of surface interference caused by a single growth direction in the traditional technology is solved.

Description

Technical Field

[0001] The present invention relates to the field of computer application technologies, and particularly relates to a three-dimensional surface extrusion modeling method based on a spline interpolation function. Background Art

[0002] In the field of stomatology, it is necessary to construct a three-dimensional data model of the human oral cavity and teeth by means of computer-aided design, and make a physical model based on the constructed three-dimensional data model, so as to understand and master the appearance of teeth and the internal structure of the human oral cavity, which is convenient for subsequent diagnosis and treatment. This means is widely used in the fields of oral restoration, orthodontics, oral medicine, oral surgery, etc.

[0003] When constructing a three-dimensional model through software, extruding a two-dimensional surface into a three-dimensional body model is a commonly used operation method. The specific method is as shown in the appendix Figure 1 : First, translate the original surface A along a fixed growth direction to form surface B, and then surround the space between surface A and B through the side to complete the construction of the three-dimensional model.

[0004] The existing three-dimensional model construction method has the following deficiencies:

[0005] 1. As shown in the appendix Figure 2 , since surface A is translated and replicated along a single growth direction, the translated and replicated surface B is prone to interference with the original surface A. Due to the interference between surface B and surface A, the construction of the three-dimensional model cannot be completed.

[0006] 2. There is a non-smooth phenomenon at the boundary of the three-dimensional model generated by the traditional method. Since the entity is directly manufactured based on the three-dimensional model constructed by the computer, this is not conducive to the subsequent processing of the product and affects the user experience. It is necessary to further modify the boundary of the constructed three-dimensional model in the three-dimensional modeling software to meet the requirements of users. Summary of the Invention

[0007] The purpose of the present invention is to solve the deficiencies in the prior art and provide a three-dimensional surface extrusion modeling method based on a spline interpolation function.

[0008] The purpose of the present invention is achieved through the following technical solutions: A three-dimensional surface extrusion modeling method based on a spline interpolation function includes the following specific steps.

[0009] Step 1): Determine the boundary vertices of the original surface, insert new vertices between the boundary vertices to form a new vertex list SPN after smooth processing.

[0010] Step 2): Construct the topological connection relationship of the new vertices.

[0011] Step 3): Traverse each vertex in the vertex list SPN and determine the growth direction of each vertex;

[0012] Step 4): Each vertex in the vertex list SPN is translated according to its respective growth direction to generate new translated points, and a new translated surface is obtained through the translated points;

[0013] Step 5): Generate side surfaces between the original surface and the translated surface to obtain a three-dimensional model.

[0014] Preferably, the specific method of Step 1) is as follows:

[0015] S1: Traverse all triangular patches on the original surface and judge each edge in the triangular patches; if the edge is not shared with other triangular patches, the edge is a boundary edge, and the edge is added to the boundary set SE;

[0016] S2: Process each edge in the boundary set SE, take out the two vertices of each edge, remove duplicate vertices and sort them, and store them in the list SP;

[0017] S3: Take out four consecutive vertices (P i-1 , P i , P i+1 , P i+2 ) from the list SP in turn until all vertices are taken out. Insert new vertices between the vertices P i -P i+1 through an interpolation function to obtain the vertex list SPN, and the smoothness requirement of the curve is satisfied after inserting the new vertices.

[0018] Preferably, the interpolation formula is as follows:

[0019]

[0020] where 0 < t < 1, 0 ≤ u ≤ 1, t controls the curve distortion degree, and u is the interpolation parameter.

[0021] Preferably, the interpolation parameter u takes 0.5.

[0022] Preferably, the specific method of Step 2) is as follows: Add corresponding vertices corresponding to the new vertices on the original edge (P i P i+1 ), and add connecting edges between the vertices P i , the vertex P i+1 , the new vertex, and the corresponding vertex to construct the topological connection relationship of the new vertex.

[0023] Preferably, in Step 3), the specific method for determining the vertex growth direction is as follows: For the vertex P i, find the vertex P i of the triangular neighborhoods T1…T i , calculate the normal vector n of each triangular neighborhood i , through the normal vector n of each triangular neighborhood i obtain the growth direction n of the vertex P i pi .

[0024] Preferably, the calculation formula for the growth direction n of the vertex P i is as follows: pi

[0025]

[0026] The beneficial effects of the present invention are as follows: The present invention provides a three-dimensional surface extrusion modeling method based on a spline interpolation function. When constructing a three-dimensional model, the points on the original plane are all translated according to their respective determined growth directions, and the translated surface obtained after translation will not interfere with the original surface. Therefore, the problem of surface interference caused by a single growth direction in the traditional technology is solved. Secondly, in the present invention, the boundary of the original surface is smoothed by inserting new vertices, which improves the smoothness at the boundary of the three-dimensional model, meets the user's requirements for the surface smoothness of the product, facilitates subsequent actual processing, and improves the user experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a schematic diagram of generating a three-dimensional model from a two-dimensional surface in the prior art.

[0028] Figure 2 is a schematic diagram when surface interference occurs.

[0029] Figure 3 is a schematic diagram of inserting new vertices between vertices P i -P i+1 .

[0030] Figure 4 is a schematic diagram of constructing a topological connection relationship for the new vertices.

[0031] Figure 5 is a schematic diagram of determining the growth direction of the vertex P i .

[0032] Figure 6 is a schematic diagram of generating a smooth side surface. DETAILED DESCRIPTION OF THE INVENTION

[0033] ​​Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present invention.

[0034] Those skilled in the art should understand that in the disclosure of the present invention, the orientation or positional relationships indicated by the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting the present invention.

[0035] It can be understood that the term "one" should be understood as "at least one" or "one or more". That is, in one embodiment, the number of one element can be one, and in other embodiments, the number of this element can be multiple. The term "one" should not be construed as a limitation on the quantity.

[0036] As Figure 2-4 shown, a three-dimensional surface extrusion molding method based on a spline interpolation function includes the following specific steps.

[0037] Step 1): Determine the boundary vertices of the original surface, insert new vertices between the boundary vertices, and form a new vertex list SPN after smooth processing.

[0038] The specific method of this step is as follows:

[0039] S1: Traverse all triangular patches on the original surface and judge each edge in the triangular patch; if the edge is not shared with other triangular patches, then the edge is a boundary edge, and add the edge to the boundary set SE. It is worth mentioning here that in the existing graphics, the common practice is to divide the surface into several small triangular patches, and approximate the shape of the surface by splicing a certain number of triangular patches.

[0040] S2: Process each edge in the boundary set SE, take out the two vertices of each edge, remove duplicate vertices and sort them, and store them in the list SP.

[0041] S3: Successively take out four consecutive vertices (P i-1 , P i , P i+1 , P i+2), until all vertices are taken; specifically, the four vertices taken for the first time are (P n , P1, P2, P3), the four vertices taken for the second time are (P1, P2, P3, P4) …, and so on. The four vertices taken for the last time are (P n-2 , P n-1 , P n , P1); then new vertices are inserted between the vertices P i -P i+1 through an interpolation function. As shown in the appendix Figure 3 , a vertex list SPN is obtained, and the smoothness requirement of the curve is satisfied after inserting the new vertices. The more new vertices are inserted, the smoother the curve is.

[0042] The interpolation formula is as follows:

[0043]

[0044] where 0 < t < 1, 0 ≤ u ≤ 1, t controls the curve distortion degree, and u is the interpolation parameter. The interpolation parameter u can be determined according to the user's own needs. The larger the value of the interpolation parameter u, the greater the curve distortion degree; the smaller the value of the interpolation parameter u, the smoother the curve. In the present invention, the value of the interpolation parameter u is 0.5.

[0045] Step 2): Construct the topological connection relationship of the new vertices. The specific method is as follows:

[0046] Corresponding vertices corresponding to the new vertices are added to the original edge (P i P i+1 ). Connection edges are added between the vertices P i , the vertex P i+1 , the new vertices, and the corresponding vertices, so as to construct the topological connection relationship of the new vertices. It should be explained here that the original edge (P i P i+1 ) refers to the edge connected between the vertex P i and the vertex P i+1 .

[0047] Specifically, as shown in the appendix Figure 4 , assuming that the new vertices inserted between the vertices P i -P i+1 are respectively p i1 , p i2 , p i3 ......p im , then the corresponding vertices inserted on the original edge (P i P i+1 ) are respectively N i1 , N i2 , N i3......N im , at vertex P i , vertex P i+1 , newly added vertex p i1 , p i2 , p i3 ......p im , corresponding vertex N i1 , N i2 , N i3 ......N im Add connection edges between these points. After connecting the lines between adjacent three points, a newly added triangular patch is formed. For the newly added vertex p i1 , p i2 , p i3 ......p im Connect each other to form a new smooth surface boundary.

[0048] Step 3): Traverse each vertex in the vertex list SPN and determine the growth direction of each vertex.

[0049] In this step, the specific method for determining the vertex growth direction is as follows: For vertex P i , find the triangular neighborhoods T1…T l , one of the vertices of the triangular neighborhood is vertex P i , calculate the normal n of each triangular neighborhood i , through the normal n of each triangular neighborhood i Obtain the growth direction n of vertex P i ; pi ;

[0050] Vertex P i 's growth direction n pi The calculation formula is as follows:

[0051]

[0052] Specifically as shown in the appendix Figure 5 , around vertex P i , find five triangular neighborhoods. These five triangular neighborhoods are T1, T2, T3, T4, and T5 respectively. These five triangular neighborhoods surround vertex P i , and the normal vectors of these five triangular neighborhoods are n1, n2, n3, n4, and n5 respectively. Then, according to the calculation formula, the growth direction n of vertex P i can be obtained. pi .

[0053] Step 4): Each vertex in the vertex list SPN is translated according to its respective growth direction to generate new translated points, and a new translated surface is obtained through the translated points. Among them, the boundary of the translated surface is determined by connecting the translated points, and then a new translated surface is obtained.

[0054] Step 5): Generate a side surface between the original surface and the translated surface to obtain a three-dimensional model.

[0055] In the traditional three-dimensional model construction method, there is no curvature in the growth direction when generating the side surface, and there will be a right-angle transition between the side surface and the original surface and the translated surface, as shown in the appendix Figure 6 shown; this right-angle transition method is not convenient for actual processing, and the processed product will affect the user experience. In the present invention, when generating the side surface, the side surface is smoothed by using a spline interpolation function to generate a side surface with a curvature. The specific processing method is the same as that in Step 1). In this way, the side surface can be smoothly transitioned with the original surface and the translated surface, which is convenient for processing and also improves the experience of the product.

[0056] The present invention provides a three-dimensional surface extrusion modeling method based on a spline interpolation function. When constructing a three-dimensional model, the points on the original plane are all translated according to their respective determined growth directions, and the translated surface obtained after translation will not interfere with the original surface. Therefore, the problem of surface interference caused by a single growth direction in the traditional technology is solved; secondly, in the present invention, the boundary of the original surface is smoothed by inserting new vertices, which improves the smoothness at the boundary of the three-dimensional model and meets the user's demand for the smoothness of the product surface, facilitating subsequent actual processing and improving the user experience.

[0057] The present invention is not limited to the above best implementation manner. Anyone can obtain other various forms of products under the inspiration of the present invention. However, no matter what changes are made in its shape or structure, as long as it has the same or similar technical solutions as the present application, it falls within the protection scope of the present invention.

Claims

1. A three-dimensional surface extrusion modeling method based on spline interpolation function, characterized in that, It includes the following specific steps: Step 1): Determine the boundary vertices of the original surface, insert new vertices between the boundary vertices, and form a new vertex list SPN after smooth processing. The specific method is as follows: S1: Traverse all triangular patches on the original surface and judge each edge in the triangular patch; if the edge is not shared with other triangular patches, the edge is a boundary edge, and the edge is added to the boundary set SE; S2: Process each edge in the boundary set SE, take out the two vertices of each edge, remove duplicate vertices, sort them, and store them in the list SP; S3: Sequentially take out four consecutive vertices (P i-1 , P i , P i+1 , P i+2 ) from the list SP until all vertices are taken out. Insert new vertices between the vertices P i -P i+1 through an interpolation function to obtain the vertex list SPN, and the smoothness requirement of the curve is satisfied after inserting the new vertices; Step 2): Construct the topological connection relationship of the newly added vertices; Step 3): Traverse each vertex in the vertex list SPN and determine the growth direction of each vertex; Step 4): Each vertex in the vertex list SPN is translated according to its respective growth direction to generate new translated points, and a new translated surface is obtained through the translated points; Step 5): Generate side surfaces between the original surface and the translated surface to obtain a three-dimensional model.

2. The three-dimensional surface extrusion modeling method based on spline interpolation function according to claim 1, wherein The interpolation formula is as follows: where \(0 < t < 1\), \(0\leq u\leq1\), \(t\) controls the curve distortion degree, and \(u\) is the interpolation parameter.

3. The three-dimensional surface extrusion modeling method based on the spline interpolation function according to claim 2, wherein, The interpolation parameter \(u\) takes 0.

5.

4. A three-dimensional surface extrusion molding method based on a spline interpolation function according to claim 1, characterized in that, The specific method of step 2) is as follows: On the original edge (P i P i+1 ), corresponding vertices corresponding to the newly added vertices are added, and connection edges are added between these points such as vertex P i , vertex P i+1 , the newly added vertices, and the corresponding vertices, so as to construct the topological connection relationship of the newly added vertices.

5. A three-dimensional surface extrusion modeling method based on a spline interpolation function according to claim 1, characterized in that, In step 3), the specific method for determining the vertex growth direction is as follows: For vertex P i , find the triangular neighborhoods T1…T i of vertex P l , calculate the normal vectors n i of each triangular neighborhood, and obtain the growth direction n i of vertex P i through the normal vectors n pi .

6. The three-dimensional surface extrusion modeling method based on the spline interpolation function according to claim 5, characterized in that Vertex P i Growth direction n pi The calculation formula is as follows:

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