Sketch type tent design method based on minimal curved surface

Abstract

The invention provides a sketch type tent design method based on a minimal curved surface, which comprises the following steps: calculating a three-dimensional bounding box of a tent, and drawing a cuboid frame of the tent; rotating the view angle direction to enable the sight direction to be consistent with the normal direction of a contour boundary line of the tent, and drawing a two-dimensional sketch line of the contour boundary line; fitting the two-dimensional sketch line into a cubic spline curve, and adjusting the shape of the cubic spline curve to enable the shape of the cubic spline curve to be consistent with the shape of an expected contour boundary line; drawing all contour boundary lines of the tent according to the steps; a plurality of contour boundary lines are selected in sequence, so that a closed area is defined by the contour boundary lines, and a curved surface of the tent is formed; generating a minimum curved surface grid according to the plurality of contour boundary lines; and repeating the steps to generate all minimum curved surface grids, and obtaining a final three-dimensional tent model. The design is simple and convenient, the expected three-dimensional tent model can be rapidly designed, the flexibility of three-dimensional tent modeling operation is improved, and the quality and precision of the three-dimensional tent model are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of three-dimensional modeling and relates to a sketch-type tent design method based on minimal surfaces. Background Art

[0002] 3D modeling is widely used in animation, games, entertainment, education, architecture and product design. The current 3D modeling method generally starts from a simple basic geometric body, and obtains the final 3D model by manipulating and controlling the geometric elements such as points, edges and faces of the 3D model. However, this method has the disadvantages of being complex to operate and requiring high spatial imagination. For a tent, it is composed of curved surface pieces. The existing modeling method makes it difficult to quickly achieve tent modeling.

[0003] In recent years, sketch-based 3D modeling methods have become a hot topic of research. Tents have obvious contours and their structure is composed of multiple surfaces, which is very suitable for sketch-based modeling methods. In geometric modeling, minimal surfaces have some ideal characteristics and are often used for surface modeling in architectural structures. First, minimal surfaces have the characteristic of minimum area, which makes them widely used in large-scale and lightweight roof structures. Second, minimal surfaces have the property of being separable, that is, any subsurface of a minimal surface is its own minimal surface. Third, minimal surfaces have balanced surface tension, which makes the entire structure more stable because the tension is balanced at every point on the surface, just like on a soap film. Finally, minimal surfaces have no umbilical points, and no water can stay on minimal surfaces, making them suitable for applications in buildings, tents, etc. The properties of the tent surface are similar to those of minimal surfaces, so we can use minimal surfaces to model tents.

[0004] Therefore, how to quickly and accurately model the tent based on sketch-like three-dimensional modeling methods and minimal surfaces is an urgent problem to be solved. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a sketch-based tent design method based on minimal surfaces. The method draws the outline boundary line of the tent in a sketch manner, and then automatically generates minimal surface meshes according to the closed area composed of the outline boundary line, and finally forms a three-dimensional model of the tent. The present invention can reduce the difficulty of three-dimensional modeling of the tent, improve the design efficiency of modeling, and realize fast and accurate three-dimensional model design.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A sketch-type tent design method based on minimal surfaces includes the following steps:

[0008] 1) Calculate the three-dimensional bounding box of the tent and draw the rectangular frame of the tent;

[0009] 2) Rotate the viewing angle so that the viewing direction is consistent with the normal direction of a contour boundary line of the tent, and draw a two-dimensional sketch line of the contour boundary line;

[0010] 3) fitting the two-dimensional sketch line into a cubic spline curve, and adjusting the shape of the cubic spline curve to make it consistent with the expected contour boundary line shape;

[0011] 4) Repeat steps 2) to 3) to draw the entire outline of the tent;

[0012] 5) selecting a plurality of contour boundary lines in order so that the plurality of contour boundary lines enclose a closed area to form a curved surface of the tent;

[0013] 6) generating a minimal surface mesh according to the plurality of contour boundary lines;

[0014] 7) Repeat steps 5) to 6) to generate all minimal surface meshes to obtain a final three-dimensional tent model, and design and manufacture a tent based on the three-dimensional tent model.

[0015] Furthermore, the two-dimensional sketch line is composed of a plurality of discrete straight line segments of uneven lengths.

[0016] Furthermore, the method for generating a minimal surface mesh is:

[0017] Performing discrete uniform sampling according to a fixed length on the plurality of contour boundary lines to obtain a plurality of boundary control points;

[0018] Mapping the boundary control points to the boundary of a planar square domain;

[0019] Constructing a simple triangular mesh on the plane square domain according to the boundary control points, and numbering the triangular vertices;

[0020] Divide the triangle vertices into internal vertices and boundary vertices, and solve the three-dimensional coordinates of the internal vertices according to the three-dimensional coordinates of the boundary vertices;

[0021] A minimal surface mesh is constructed according to the three-dimensional coordinates of the internal vertices and the boundary vertices in combination with the network topology of the square domain.

[0022] Furthermore, for each internal vertex, its three-dimensional coordinates are equal to the weighted average of the three-dimensional coordinates of all vertices in its neighborhood.

[0023] Furthermore, solving the three-dimensional coordinates of the internal points according to the three-dimensional coordinates of the boundary points is specifically:

[0024] The internal vertices are taken as unknown quantities and the boundary vertices are taken as known quantities, a set of equations is constructed, and the three-dimensional coordinates of the boundary vertices are substituted into the set of equations to solve the three-dimensional coordinates of the internal vertices.

[0025] Furthermore, LR decomposition is used to accelerate the solution speed of the equation system.

[0026] Furthermore, the adjusting the shape of the cubic spline curve is specifically: modifying the shape of the cubic spline curve by moving, adding, or deleting control vertices of the cubic spline curve.

[0027] The present invention can be applied to the design of a three-dimensional model of a tent. According to the design drawing of the tent, a three-dimensional grid model can be quickly designed by using a sketch modeling method. Compared with the existing technology, the advantages of the present invention are reflected in the following two points:

[0028] 1. The sketch-based 3D modeling method based on minimal surfaces proposed in the present invention allows the designer to draw the boundary line of the 2D sketch on the screen with a mouse or drawing pen and fit it into a cubic spline curve. The designer selects multiple spline curves that can form a closed area and then generates a minimal surface mesh model. Compared with the existing technology, this method makes the design of the tent model simpler and can quickly design the expected 3D tent model.

[0029] 2. The sketch-based 3D modeling method based on minimal surfaces proposed by the present invention automatically fits the boundary line of the 2D sketch into a cubic spline curve. The shape of the spline curve can be arbitrarily changed by adding, deleting and moving control vertices, thereby controlling the shape of the 3D model. Compared with the existing technology, the flexibility of the 3D tent modeling operation is improved, and the quality and accuracy of the 3D tent model are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart for generating a three-dimensional tent model in an embodiment of the present invention.

[0031] Figure 2 Schematic diagram of a tent frame in an embodiment of the present invention.

[0032] Figure 3 Schematic diagram of the principle of generating minimal surfaces in an embodiment of the present invention.

[0033] Figure 4 Schematic diagram of the outline of the curved surface of the tent in the embodiment of the present invention

[0034] Figure 5 This is a diagram of a minimal surface mesh model automatically generated in an embodiment of the present invention.

[0035] Figure 6 This is a model diagram of a tent composed of multiple minimal surfaces in an embodiment of the present invention.

[0036] Figure 7 This is a tent model diagram with the frame hidden and the curved surfaces completed in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The method of the present invention is further described in detail below with reference to the accompanying drawings and specific examples.

[0038] A sketch-type tent design method based on minimal surfaces includes the following steps:

[0039] 1) Calculate the three-dimensional bounding box of the tent and draw the rectangular frame of the tent;

[0040] 2) Rotate the viewing angle so that the viewing direction is consistent with the normal direction of a contour boundary line of the tent, and draw a two-dimensional sketch line of the contour boundary line;

[0041] 3) fitting the two-dimensional sketch line into a cubic spline curve, and adjusting the shape of the cubic spline curve so that the two-dimensional sketch line is consistent with the expected contour boundary line shape;

[0042] 4) Repeat steps 2) to 3) to draw the entire outline of the tent;

[0043] 5) selecting a plurality of contour boundary lines in order so that the plurality of contour boundary lines enclose a closed area to form a curved surface of the tent;

[0044] 6) generating a minimal surface mesh according to the plurality of contour boundary lines;

[0045] 7) Repeat steps 5) to 6) to generate all minimal surface meshes to obtain a final three-dimensional tent model, and design and manufacture a tent based on the three-dimensional tent model.

[0046] The method for generating a minimal surface mesh is:

[0047] Performing discrete uniform sampling according to a fixed length on the plurality of contour boundary lines to obtain a plurality of boundary control points;

[0048] Mapping the boundary control points to the boundary of a planar square domain;

[0049] Constructing a simple triangular mesh on the plane square domain according to the boundary control points, and numbering the triangular vertices;

[0050] Divide the triangle vertices into internal vertices and boundary vertices, and solve the three-dimensional coordinates of the internal vertices according to the three-dimensional coordinates of the boundary vertices;

[0051] A minimal surface mesh is constructed according to the three-dimensional coordinates of the internal vertices and the boundary vertices in combination with the network topology of the square domain.

[0052] For each internal vertex, its three-dimensional coordinates are equal to the weighted average of the three-dimensional coordinates of all vertices in its neighborhood.

[0053] The step of solving the three-dimensional coordinates of the internal points according to the three-dimensional coordinates of the boundary points is specifically as follows:

[0054] The internal vertices are taken as unknown quantities and the boundary vertices are taken as known quantities, a set of equations is constructed, and the three-dimensional coordinates of the boundary vertices are substituted into the set of equations to solve the three-dimensional coordinates of the internal vertices.

[0055] Furthermore, LR decomposition is used to accelerate the solution speed of the equation system.

[0056] Furthermore, the adjusting the shape of the cubic spline curve is specifically: modifying the shape of the cubic spline curve by moving, adding, or deleting control vertices of the cubic spline curve.

[0057] Example

[0058] like Figure 1 As shown in the figure, a sketch-based tent design method based on minimal surfaces is shown in the figure. The steps are as follows:

[0059] Step 1: Calculate the three-dimensional bounding box of the tent according to the parameters of the length, width and height of the tent. The three-dimensional bounding box of the tent is a cuboid. Draw the cuboid frame of the tent according to the three-dimensional bounding box, such as Figure 2 As shown in the figure, each edge of the frame is a spline, which can be used for precise positioning of the tent modeling.

[0060] Step 2: Since the outline boundary line of each tent falls within a plane, before drawing a 2D sketch line, you need to rotate the view to an appropriate direction so that the line of sight is consistent with the normal of the plane where one of the tent's outline boundary lines is located.

[0061] Use a mouse, drawing pen or finger to draw a two-dimensional sketch line within the frame of the tent. The two-dimensional sketch line is composed of a number of discrete straight line segments of uneven length, and the end point positions of the straight line segments are determined according to the position of the mouse or drawing pen when it moves on the display screen.

[0062] Step 3: Fit the 2D sketch line to a cubic spline curve. The purpose is to edit the 2D sketch line so as to precisely control the shape of the 3D model. The cubic spline curve is obtained by the cubic spline interpolation function, which uses a cubic equation to generate a curve passing through control vertices so that the boundary of the 2D contour line is smooth. After fitting the 2D sketch line to a cubic spline curve, if it is found that the endpoint of the cubic spline curve is very close to the endpoint of other spline curves or the endpoint or boundary line of the frame, such as within 10 pixels, the endpoint is automatically adsorbed to the nearby endpoint or boundary line.

[0063] The shape of the cubic spline curve can be modified by moving, adding, or deleting its control vertices, so that the shape of the two-dimensional sketch line can better fit the contour boundary line of the expected tent model. Similarly, the relevant attribute information in the attribute box, such as endpoint position, normal, etc., can be modified and applied to the spline to obtain the expected three-dimensional mesh model shape.

[0064] Step 4: Repeat steps 2 to 3 to draw all the outlines of the tent. When drawing each 2D sketch line, you need to rotate the view to the appropriate direction so that the line of sight is consistent with the normal of the plane where the outline of the tent is located.

[0065] Step 5: Select all contour boundary lines in a clockwise or counterclockwise order to enclose a closed area, such as Figure 4 shown.

[0066] Step 6: Based on the selected multiple contour boundary lines, a minimal surface mesh is automatically generated, such as Figure 5 The algorithm steps for generating minimal surfaces are as follows:

[0067] a) performing discrete uniform sampling on the selected multiple contour boundary lines according to a fixed length (e.g., 10 pixel units) to obtain a number of boundary control points, and mapping them to the boundary of the square domain of the plane;

[0068] b) Construct a simple triangular mesh on the square domain and number the constructed vertices; the numbering rules are as follows:

[0069] The grid is constructed in layers on the square domain, and the total number of layers is the number of boundary control points n divided by 4. The zeroth layer is the center point of the square, which is numbered 0. Starting from the first layer, the number of control points in each layer is 4 more than the number of control points in the previous layer. That is, the number of control points in the first layer is 4, numbered 1 to 4; the number of control points in the second layer is 8, numbered 5 to 12; the number of control points in the third layer is 12, numbered 13 to 24; and the number of control points in the n / 4th layer is n. The numbering order in each layer is upper left corner, lower left corner, lower right corner, upper right corner, and all the control points of the layer are uniformly sampled in this order. For each internal point, it is connected to the upper left, lower left, upper right, lower right and two adjacent control points in the same layer to form the edge of the grid, ensuring that the out-degree of each internal point is 6. Since the number of control points in each layer is 4 times the number of the level, the redundant control points can be connected to the last internal control point, so that the situation with any number of control points can be handled. The generated control point topology is as follows Figure 3 shown.

[0070] c) Using the definition of a minimal surface, for each internal point, its coordinates are equal to the weighted average of the coordinates of all vertices in the neighborhood of 1, that is, V i =1 / n*(V1+V2+V3+...+V n );exist Figure 3 The specific expression of the example is:

[0071] V0 = 1 / 4 * (V1 + V2 + V3 + V4);

[0072] V1=1 / 6*(V0+V2+V4+V5+V6+V 12 );

[0073] V2 = 1 / 6 * (V0 + V1 + V3 + V6 + V8);

[0074] V3=1 / 6*(V0+V2+V4+V8+V9+V 10 );

[0075] V4=1 / 6*(V0+V1+V3+V 10 +V 11 +V 12 );

[0076] V5=1 / 6*(V1+V6+V 12 +V 13 +V 14 +V 24 ); ...

[0078] V 24 =1 / 6*(V5+V 12 +V 13 +V 23 +V 39 +V 40 );

[0079] The generated mesh can be further optimized using the Laplacian operator on a two-dimensional manifold.

[0080] d) Divide the triangle vertices into internal vertices and boundary vertices. V0 to V24 in step c are internal vertices, and V25 to V40 are external vertices. Take the internal vertices as unknown quantities and the boundary vertices as known quantities. Put the 25 internal vertices on the left side of the equation and the 16 boundary vertices on the right side of the equation to construct the equation system. Substitute the 3D coordinates of the boundary vertices into the right side of the equation, and use LR decomposition to speed up the solution of the sparse equation system to solve the 3D coordinates of the internal vertices.

[0081] https: / / max.book118.com / html / 2017 / 0912 / 133521933.shtm discloses the method for solving the system of equations.

[0082] e) After obtaining the three-dimensional coordinates of the internal points, a minimal surface mesh with the smallest area is constructed in combination with the mesh topology of the square domain in step b.

[0083] Step 7: Repeat steps 5 to 6 to generate all minimal surfaces, such as Figure 6 As shown; finally, the frame is cancelled and the three-dimensional tent model required by the user is established, as shown Figure 7 As shown, a tent is then designed and manufactured based on the three-dimensional tent model.

[0084] The above specific implementation modes are used to explain the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A sketch-type tent design method based on minimal surfaces, characterized in that: The following steps are involved: 1) Calculate the three-dimensional bounding box of the tent and draw the rectangular frame of the tent; 2) Rotate the viewing angle so that the viewing direction is consistent with the normal direction of a contour boundary line of the tent, and draw a two-dimensional sketch line of the contour boundary line; 3) fitting the two-dimensional sketch line into a cubic spline curve, and adjusting the shape of the cubic spline curve to make it consistent with the expected contour boundary line shape; 4) Repeat steps 2) to 3) to draw the entire outline of the tent; 5) selecting a plurality of contour boundary lines in order so that the plurality of contour boundary lines enclose a closed area to form a curved surface of the tent; 6) generating a minimal surface mesh according to the plurality of contour boundary lines; 7) Repeat steps 5) to 6) to generate all minimal surface meshes to obtain a final three-dimensional tent model, and design and manufacture a tent based on the three-dimensional tent model.

2. The sketch-type tent design method based on minimal surfaces according to claim 1, characterized in that: The two-dimensional sketch line is composed of a plurality of discrete straight line segments of uneven lengths.

3. The sketch-type tent design method based on minimal surfaces according to claim 1, characterized in that: The method for generating a minimal surface mesh is: Performing discrete uniform sampling according to a fixed length on the plurality of contour boundary lines to obtain a plurality of boundary control points; Mapping the boundary control points to the boundary of a planar square domain; Constructing a simple triangular mesh on the plane square domain according to the boundary control points, and numbering the triangular vertices; Divide the triangle vertices into internal vertices and boundary vertices, and solve the three-dimensional coordinates of the internal vertices according to the three-dimensional coordinates of the boundary vertices; A minimal surface mesh is constructed according to the three-dimensional coordinates of the internal vertices and the boundary vertices in combination with the network topology of the square domain.

4. The sketch-type tent design method based on minimal surfaces according to claim 3 is characterized in that: For each internal vertex, its three-dimensional coordinates are equal to the weighted average of the three-dimensional coordinates of all vertices in its neighborhood.

5. The sketch-type tent design method based on minimal surfaces according to claim 3 is characterized in that: The step of solving the three-dimensional coordinates of the internal points according to the three-dimensional coordinates of the boundary points is specifically as follows: The internal vertices are taken as unknown quantities and the boundary vertices are taken as known quantities, a set of equations is constructed, and the three-dimensional coordinates of the boundary vertices are substituted into the set of equations to solve the three-dimensional coordinates of the internal vertices.

6. The sketch-type tent design method based on minimal surfaces according to claim 5, characterized in that: LR decomposition is used to speed up the solution of the system of equations.

7. The sketch-type tent design method based on minimal surfaces according to claim 1, characterized in that: The adjusting the shape of the cubic spline curve specifically includes: modifying the shape of the cubic spline curve by moving, adding, or deleting control vertices of the cubic spline curve.

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