A sketch tent design method based on minimal surface
By using a sketch-based minimal surface modeling method, the outline boundary lines of the tent are drawn and a minimal surface mesh is generated, which solves the problem of complex tent modeling in the existing technology and realizes fast and accurate 3D model design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-01-03
- Publication Date
- 2026-06-05
Smart Images
Figure CN119942026B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of 3D modeling technology and relates to a sketch-based tent design method based on minimal surfaces. Background Technology
[0002] 3D modeling has wide applications in animation, games, entertainment, education, architecture, and product design. Current 3D modeling methods generally start with a simple basic geometric shape, manipulating and controlling the geometric elements such as points, edges, and faces of the 3D model to obtain the final 3D model. However, this method has drawbacks such as complex operation and high requirements for spatial imagination. For a tent, which is composed of curved surfaces, existing modeling methods are insufficient for quickly modeling a tent.
[0003] In recent years, sketch-based 3D modeling methods have become a research hotspot. Tents, with their distinct outlines and structures composed of multiple curved surfaces, are well-suited for sketch-based modeling. In geometric modeling, minimal surfaces possess several desirable properties and are frequently used for surface modeling in architectural structures. First, minimal surfaces have the smallest area, making them widely applicable in large-scale and lightweight roof structures. Second, minimal surfaces are separable, meaning any sub-surface of a minimal surface is itself a minimal surface. Third, minimal surfaces exhibit balanced surface tension, resulting in greater structural stability, as the tension is balanced at every point on the surface, much like on a soap film. Finally, minimal surfaces lack an umbilical point, preventing water from remaining on them, making them suitable for applications in architecture, tents, and other fields. The surface properties of tents are similar to those of minimal surfaces; therefore, we can use minimal surfaces for tent modeling.
[0004] Therefore, how to quickly and accurately model tents based on sketch-based 3D modeling methods and minimal surfaces is an urgent problem to be solved. Summary of the Invention
[0005] To address the aforementioned problems, this invention proposes a sketch-based tent design method based on minimal surfaces. This method involves sketching the tent's outline boundary lines, then automatically generating a minimal surface mesh based on the closed region formed by the outline boundary lines, ultimately creating a 3D model of the tent. This invention reduces the difficulty of 3D tent modeling, improves design efficiency, and enables rapid and accurate 3D model design.
[0006] The technical solution adopted in this invention is as follows:
[0007] A sketch-based tent design method based on minimal surfaces includes the following steps:
[0008] 1) Calculate the bounding box of the tent and draw the cuboid frame of the tent;
[0009] 2) Rotate the viewing direction so that the line of sight is aligned with the normal of one of the tent's outline boundaries, and draw a two-dimensional sketch of the outline boundary line;
[0010] 3) Fit the two-dimensional sketch line to a cubic spline curve, and adjust 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) Select multiple contour boundary lines in sequence to form a closed area, creating a curved surface of the tent;
[0013] 6) Generate a minimal surface mesh based on the multiple contour boundary lines;
[0014] 7) Repeat steps 5) to 6) to generate all the minimal surface meshes to obtain the final three-dimensional tent model. Based on the three-dimensional tent model, design and manufacture the tent.
[0015] Furthermore, the two-dimensional sketch line is composed of a discrete number of straight line segments of varying lengths.
[0016] Furthermore, the method for generating the minimal surface mesh is as follows:
[0017] By performing discrete and uniform sampling along the multiple contour boundary lines at a fixed length, several boundary control points are obtained.
[0018] Map the boundary control points onto the boundary of a planar square domain;
[0019] A simple triangular mesh is constructed on the planar square domain based on the boundary control points, and the vertices of the triangles are numbered;
[0020] The triangle vertices are divided into internal vertices and boundary vertices. The three-dimensional coordinates of the internal vertices are calculated based on the three-dimensional coordinates of the boundary vertices.
[0021] Based on the three-dimensional coordinates of the internal vertices and boundary vertices, and combined with the network topology of the square domain, a minimal surface mesh is constructed.
[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 1-neighborhood.
[0023] Furthermore, the step of solving for the three-dimensional coordinates of the interior points based on the three-dimensional coordinates of the boundary points specifically involves:
[0024] By treating the internal vertices as unknowns and the boundary vertices as knowns, a system of equations is constructed. The three-dimensional coordinates of the boundary vertices are then substituted into the system of equations to solve for 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, adjusting the shape of the cubic spline curve specifically involves modifying the shape of the cubic spline curve by moving, adding, or deleting the control vertices of the cubic spline curve.
[0027] This invention can be applied to the design of 3D models for tents. Based on the tent design drawings, a sketch-based modeling method can be used to quickly design a 3D mesh model. Compared with existing technologies, the advantages of this invention are reflected in the following two points:
[0028] 1. The present invention proposes a sketch-based 3D modeling method based on minimal surfaces. Designers draw 2D sketch boundary lines on the screen using a mouse or drawing pen, and fit them into cubic spline curves. Designers then select multiple spline curves that can form closed regions to generate a minimal surface mesh model. Compared with existing technologies, this method simplifies the design of tent models and enables the rapid design of the desired 3D tent model.
[0029] 2. The sketch-based 3D modeling method based on minimal surfaces proposed in this invention automatically fits the boundary lines of the 2D sketch into cubic spline curves. By adding, deleting, and moving control vertices, the shape of the spline curves can be arbitrarily changed, thereby controlling the shape of the 3D model. Compared with existing technologies, this improves the flexibility of 3D tent modeling operations and enhances the quality and accuracy of 3D tent models. Attached Figure Description
[0030] Figure 1 This is a flowchart illustrating the process of generating a 3D tent model in an embodiment of the present invention.
[0031] Figure 2 This is a schematic diagram of the tent frame in an embodiment of the present invention.
[0032] Figure 3 This is a schematic diagram illustrating the principle of minimum surface generation in an embodiment of the present invention.
[0033] Figure 4 This is a schematic diagram of the outline of the tent surface in an 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 extremely small curved surfaces in an embodiment of the present invention.
[0036] Figure 7 This is a model diagram of a tent with the frame hidden and the curved surfaces joined together, as shown in an embodiment of the present invention. Detailed Implementation
[0037] The method of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples.
[0038] A sketch-based tent design method based on minimal surfaces includes the following steps:
[0039] 1) Calculate the bounding box of the tent and draw the cuboid frame of the tent;
[0040] 2) Rotate the viewing direction so that the line of sight is aligned with the normal of one of the tent's outline boundaries, and draw a two-dimensional sketch of the outline boundary line;
[0041] 3) Fit the two-dimensional sketch line to a cubic spline curve, and adjust 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) Select multiple contour boundary lines in sequence to form a closed area, creating a curved surface of the tent;
[0044] 6) Generate a minimal surface mesh based on the multiple contour boundary lines;
[0045] 7) Repeat steps 5) to 6) to generate all the minimal surface meshes to obtain the final three-dimensional tent model. Based on the three-dimensional tent model, design and manufacture the tent.
[0046] The method for generating minimal surface meshes is as follows:
[0047] By performing discrete and uniform sampling along the multiple contour boundary lines at a fixed length, several boundary control points are obtained.
[0048] Map the boundary control points onto the boundary of a planar square domain;
[0049] A simple triangular mesh is constructed on the planar square domain based on the boundary control points, and the vertices of the triangles are numbered;
[0050] The triangle vertices are divided into internal vertices and boundary vertices. The three-dimensional coordinates of the internal vertices are calculated based on the three-dimensional coordinates of the boundary vertices.
[0051] Based on the three-dimensional coordinates of the internal vertices and boundary vertices, and combined with the network topology of the square domain, a minimal surface mesh is constructed.
[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 1-neighborhood.
[0053] The process of solving the three-dimensional coordinates of the interior points based on the three-dimensional coordinates of the boundary points specifically involves:
[0054] By treating the internal vertices as unknowns and the boundary vertices as knowns, a system of equations is constructed. The three-dimensional coordinates of the boundary vertices are then substituted into the system of equations to solve for the three-dimensional coordinates of the internal vertices.
[0055] Furthermore, LR decomposition is used to accelerate the solution speed of the system of equations.
[0056] Furthermore, adjusting the shape of the cubic spline curve specifically involves modifying the shape of the cubic spline curve by moving, adding, or deleting the control vertices of the cubic spline curve. Example
[0057] like Figure 1 As shown, a sketch-based tent design method based on minimal surfaces includes the following steps:
[0058] Step 1: Calculate the tent's 3D bounding box based on the tent's length, width, and height. The tent's 3D bounding box is a cuboid. Draw the tent's cuboid frame based on the 3D bounding box, as shown below. Figure 2 As shown. Each edge of the frame is a spline, which allows for precise positioning during tent modeling.
[0059] Step 2: Since the outline of each tent falls on a plane, before drawing a 2D sketch line, you need to rotate the viewpoint to a suitable direction so that the line of sight is consistent with the normal of the plane containing one of the tent's outline boundaries.
[0060] Use a mouse, pen, or finger to draw two-dimensional sketch lines within the tent frame. A two-dimensional sketch line consists of several discrete straight line segments of varying lengths, the endpoints of which are determined by the position of the mouse or pen as it moves across the display screen.
[0061] Step 3: Fit the 2D sketch lines to cubic spline curves. The purpose is to edit the 2D sketch lines for precise control of the 3D model's shape. The cubic spline curve is obtained through a cubic spline interpolation function, generated using a cubic equation to control the curves at the vertices, resulting in smooth boundaries for the 2D contour lines. After fitting the 2D sketch lines to cubic spline curves, if the endpoints of the cubic spline curve are found to be very close to the endpoints of other spline curves, the endpoints of the frame, or the boundary lines (e.g., within 10 pixels), the endpoint will automatically snap to the nearby endpoints or boundary lines.
[0062] By moving, adding, or deleting the control vertices of cubic splines, the shape of the cubic spline can be modified to better fit the outline of the desired tent model. Similarly, relevant attribute information in the attribute box, such as endpoint position and normal, can be modified and applied to the spline to obtain the desired 3D mesh model shape.
[0063] Step 4: Repeat steps 2-3 to draw all the outline boundary lines of the tent. When drawing each 2D sketch line, you need to rotate the viewpoint to a suitable direction so that the line of sight is consistent with the normal of the plane containing the outline boundary line of the tent.
[0064] Step 5: Select all the contour boundary lines in a clockwise or counterclockwise order to form a closed area, such as... Figure 4 As shown.
[0065] Step 6: Automatically generate a minimal surface mesh based on the selected multiple contour boundary lines, such as... Figure 5 As shown. The algorithm steps for generating the minimum surface are as follows:
[0066] a) Select multiple contour boundary lines are discretely and uniformly sampled according to a fixed length (e.g., 10 pixel units) to obtain several boundary control points, and then mapped onto the boundary of a square domain in the plane.
[0067] b) Construct a simple triangular mesh on the square domain and number the vertices; the numbering rules are as follows:
[0068] A layered mesh is constructed on a square domain, with the total number of layers being n divided by 4. The zeroth layer is the center point of the square, numbered 0. Starting from the first layer, the number of control points in each layer is 4 more than the previous layer. That is, the first layer has 4 control points, numbered 1-4; the second layer has 8 control points, numbered 5-12; the third layer has 12 control points, numbered 13-24; and so on, up to the n / 4th layer with n control points. The numbering order in each layer is top left, bottom left, bottom right, top right, and so on, with all control points in that layer being sampled evenly. For each internal point, it is connected to the top left, bottom left, top right, bottom right, and two adjacent control points in the same layer to form mesh edges, 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 that layer, excess control points can be connected to the last internal control point, thus handling cases with an arbitrary number of control points. The generated control point topology is as follows: Figure 3 As shown.
[0069] c) Using the definition of a minimal surface, for each interior point, its coordinates are equal to the weighted average of the coordinates of all vertices in its 1-neighborhood, i.e., V. i = 1 / n * (V1 + V2 + V3 + ... + V n );exist Figure 3 The specific expression for the example is:
[0070] V0 = 1 / 4 * (V1 + V2 + V3 + V4);
[0071] V1 = 1 / 6 * (V0 + V2 + V4 + V5 + V6 + V 12 );
[0072] V2 = 1 / 6 * (V0 + V1 + V3 + V6 + V8);
[0073] V3 = 1 / 6 * (V0 + V2 + V4 + V8 + V9 + V 10 );
[0074] V4 = 1 / 6 * (V0 + V1 + V3 + V 10 + V 11 + V 12 );
[0075] V5 = 1 / 6 * (V1 + V6 + V 12 + V 13 + V 14 + V 24 ); ...
[0076] V 24 = 1 / 6 * (V5 + V 12 + V 13 + V 23 + V 39 + V 40 );
[0077] The generated mesh can be further optimized using the Laplacian operator on a two-dimensional manifold.
[0078] d) Divide the triangle vertices into internal vertices and boundary vertices. In step c, V0~V24 are internal vertices, and V25~V40 are external vertices. Treat the internal vertices as unknowns and the boundary vertices as knowns. Place the 25 internal vertices on the left side of the equation and the 16 boundary vertices on the right side to construct a system of equations. Substitute the 3D coordinates of the boundary vertices into the right side of the equation and use LR decomposition to accelerate the solution of the sparse system of equations to solve for the 3D coordinates of the internal vertices.
[0079] e) After obtaining the three-dimensional coordinates of the interior points, and in conjunction with the grid topology of the square domain in step b, construct the minimal surface grid with the smallest area.
[0080] Step 7: Repeat steps 5-6 to generate all the minimum surfaces, such as... Figure 6 As shown; finally, the frame is removed from display, and the required 3D tent model is created, as follows. Figure 7 As shown, the tent is then designed and manufactured based on the three-dimensional tent model.
[0081] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.
Claims
1. A sketch-based tent design method based on minimal curved surfaces, characterized in that, Includes the following steps: 1) Calculate the bounding box of the tent and draw the cuboid frame of the tent; 2) Rotate the viewing direction so that the line of sight is aligned with the normal of one of the tent's outline boundaries, and draw a two-dimensional sketch of the outline boundary line; 3) Fit the two-dimensional sketch line to a cubic spline curve, and adjust 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) Select multiple contour boundary lines in sequence to form a closed area, creating a curved surface of the tent; 6) Generate a minimal surface mesh based on the multiple contour boundary lines; 7) Repeat steps 5) to 6) to generate all the minimal surface meshes to obtain the final three-dimensional tent model. Based on the three-dimensional tent model, design and manufacture the tent. The method for generating minimal surface meshes is as follows: By performing discrete and uniform sampling along the multiple contour boundary lines at a fixed length, several boundary control points are obtained. The boundary control points are mapped onto the boundary of a planar square domain. A simple triangular mesh is constructed on the planar square domain based on the boundary control points, and the vertices of the triangles are numbered. The vertices of the triangles are divided into internal vertices and boundary vertices. The three-dimensional coordinates of the internal vertices are solved based on the three-dimensional coordinates of the boundary vertices. Specifically, the internal vertices are treated as unknowns, and the boundary vertices are treated as knowns. A system of equations is constructed. The three-dimensional coordinates of the boundary vertices are substituted into the system of equations to solve for the three-dimensional coordinates of the internal vertices. Based on the three-dimensional coordinates of the internal vertices and the boundary vertices, and combined with the network topology of the square domain, a minimal surface mesh is constructed.
2. The sketch-based tent design method based on minimal curved surfaces according to claim 1, characterized in that, The two-dimensional sketch line is composed of discrete straight line segments of varying lengths.
3. The sketch-based tent design method based on minimal curved surfaces according to claim 1, 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 1-neighborhood.
4. The sketch-based tent design method based on minimal curved surfaces according to claim 1, characterized in that, The solution speed of the system of equations is accelerated by using LR decomposition.
5. The sketch-based tent design method based on minimal curved surfaces according to claim 1, characterized in that, The adjustment of the shape of the cubic spline curve specifically involves modifying the shape of the cubic spline curve by moving, adding, or deleting the control vertices of the cubic spline curve.