Parameterized origami modeling method for obtaining Miura crease graph from folding form curve

Abstract

The invention provides a parameterized origami modeling method for obtaining a Miura crease graph from a folding form curve, which comprises the following steps of: S1, drawing a folding form two-dimensional curve in interactive modeling software, and averagely segmenting the curve to obtain a target polyline similar to the curve in shape; s2, for the generated target polyline, calculating a mathematical transformation relation between the polyline and a line segment of the crease graph by adopting a mathematical method, and generating a crease strip graph; s3, carrying out simulation folding on the generated crease graph; and S4, observing the model structure obtained by simulation folding, adjusting the parameter values of the crease graph, ensuring the reasonability of the folding structure in mathematics and the aesthetic property of the folding structure in design, and obtaining a printable and directly-foldable crease graph drawing. According to the method, efficient conversion from the polyline form to the crease graph can be achieved, and the operation threshold of non-professional designers and paper folding beginners is remarkably lowered.

Description

Technical Field

[0001] This invention relates to the field of folding morphology curve analysis technology, and in particular to a parametric origami modeling method for obtaining the Miura crease diagram from the folding morphology curve. Background Technology

[0002] Origami is an art and engineering method that creates three-dimensional forms by folding planar materials. Due to its flexible parametric modeling, foldable and deformable structures, and combination of aesthetics and functionality, it has been applied in product design, architectural components, aerospace and other fields. In the field of industrial design, origami-inspired product designs have advantages such as lightweight structures, high space utilization, and customizable forms. For example, lampshade products designed using parametric origami can achieve efficient transformation from two-dimensional planes to three-dimensional shapes, while reducing development costs.

[0003] When designing products inspired by origami, most designers typically adopt a forward design approach, starting from basic crease units to build complex shapes, or a reverse design approach, which works by solving for crease patterns from the perspective of target function and three-dimensional form. Forward and reverse design have become the two mainstream paths in origami design.

[0004] However, origami is actually a highly spatial and procedural handicraft. Its complex folding logic and spatial changes result in a high learning threshold and low learning efficiency, which can easily dampen users' enthusiasm for learning. Therefore, non-professional designers and origami beginners often need to use auxiliary design methods to learn origami structures and design origami products.

[0005] Existing origami design aids and tools include Rhino-Grasshopper, Oripa, Biomorpher, etc., but they each have problems such as high technical threshold (e.g., Rhino-Grasshopper requires mastery of programming logic), limitations in parametric adjustment (e.g., Oripa only supports classic crease patterns), and insufficient algorithm optimization efficiency. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve, so as to solve the problems of high technical threshold and insufficient algorithm optimization efficiency of existing origami design auxiliary methods and tools.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] A parametric origami modeling method for obtaining the Miura crease pattern from the folding shape curve includes the following steps:

[0009] Step S1: In the interactive modeling software, draw a folded two-dimensional curve, and obtain a target polyline that closely resembles the curve shape by dividing the curve into equal segments.

[0010] Step S2: For the generated target polyline, use mathematical methods to calculate the mathematical transformation relationship between the polyline and the line segments of the crease diagram, and generate a crease strip diagram;

[0011] Step S3: Simulate folding on the generated crease pattern;

[0012] Step S4: Observe the model structure obtained by simulation folding, adjust the parameter values ​​of the crease diagram to ensure the mathematical rationality and aesthetics of the folding structure, and obtain a printable and directly foldable crease diagram drawing.

[0013] Preferably, step S1 specifically includes the following steps:

[0014] S101: Design a folded two-dimensional curve: Input control points to generate a curve on a two-dimensional plane;

[0015] S102: The curve is divided into several key points by average segmentation.

[0016] S103: Connect the key points of the curve in sequence to draw a polyline;

[0017] S104: Complete the drawing of the target polyline by adding, deleting and moving points.

[0018] Preferably, step S2 specifically includes the following steps:

[0019] S201: Treat polylines as multiple separate line segments, and crease units are irregular trapezoidal units with known height (h). Each line segment is the midline of the crease unit.

[0020] S202: Based on the included angle (β) between two adjacent line segments, an isosceles triangle solution model is established to obtain the base angle (α) of the crease trapezoidal unit. The formula for calculating the base angle is as follows:

[0021]

[0022] S203: Based on the length of the line segment (m), establish a solution model for the midline of the trapezoid, regard the line segment as the midline of the trapezoidal unit, and combine the base angle obtained in S22 to obtain the length of the corresponding base (a) of the crease trapezoidal unit.

[0023] S204: Solve the trapezoidal element parameters sequentially and draw the crease element strip diagram.

[0024] Preferably, step S203, calculating the length of the base (a), specifically involves: when the line segment (m) is the first line segment, the base angle of the trapezoidal unit is 90 degrees and α, then the formula for calculating side a is as follows:

[0025]

[0026] At this point, the target polyline consists of two connected line segments, and the trapezoidal crease unit is a right trapezoid.

[0027] Preferably, step S203, which calculates the length of the base (a), specifically involves the following: when the left base angle of the trapezoidal unit is an obtuse angle (180°-α1) and the right base angle is an acute angle α2, the formula for calculating side a is as follows:

[0028]

[0029] At this point, the target polyline is "z" shaped, and the trapezoidal crease unit is a parallelogram-like shape.

[0030] Preferably, step S203, calculating the length of the base (a), specifically involves: when both base angles of the trapezoidal unit are acute angles, denoted as the left base angle (180°-α1) and the right base angle α2, the formula for calculating side a is as follows:

[0031]

[0032] At this point, the target polyline is an "n" shape with its opening to the left, and the trapezoidal crease unit is a square trapezoid.

[0033] Preferably, step S203, calculating the length of the base (a), specifically involves the following: when the left base angle of the trapezoidal unit is an acute angle (180°-α1) and the right base angle is an obtuse angle α2, the formula for calculating side a is as follows:

[0034]

[0035] At this point, the target polyline is an inverted "z" shape, and the trapezoidal crease unit is a parallelogram-like shape.

[0036] Preferably, step S203, calculating the length of the base (a), specifically involves: when both base angles of the trapezoidal unit are obtuse angles, denoted as the left base angle (180°-α1) and the right base angle α2, the formula for calculating side a is as follows:

[0037]

[0038] At this point, the target polyline is an "n" shape with its opening to the left, and the trapezoidal crease unit is an inverted trapezoid.

[0039] Preferably, step S3 specifically includes the following steps:

[0040] S301: Mirror the crease unit strip pattern along the bottom edge to obtain the crease strip pattern;

[0041] S302: Analyze the circumferential angle of the crease center on the center line of the crease strip diagram to confirm the direction of the valley crease line;

[0042] S303: Simulate folding of the crease strip diagram.

[0043] Preferably, step S302 specifically includes the following steps:

[0044] S3021: In the angle of the circumferential angle, when the two angles obtained by mirroring the bottom side are obtuse angles, the three obtuse angle sides are in the same direction and are set as the mountain line;

[0045] S3022: In the angle of the circumferential angle, when the two angles obtained by mirroring about the bottom side are acute angles, the direction of the side shared by the two acute angles is opposite to the direction of the side of the obtuse angle, and is set as the valley line.

[0046] Beneficial effects

[0047] Compared with the prior art, the present invention has at least the following beneficial effects: The parametric origami modeling method proposed in this invention, which obtains the Miura crease diagram from the folding shape curve, achieves efficient conversion from polyline shape to crease diagram on the Rhino-Grasshopper platform, significantly reducing the operating threshold for non-professional designers and origami beginners. Attached Figure Description

[0048] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate embodiments of the present disclosure and, together with the specification, further serve to explain the principles of the present disclosure and enable those skilled in the art to implement and use the present disclosure.

[0049] Figure 1 This is a schematic diagram of the process of the present invention.

[0050] Figure 2 A schematic diagram showing the base angle (α) of the crease trapezoidal unit obtained by establishing an isosceles triangle solution model based on the included angle (β) between two adjacent line segments.

[0051] Figure 3 This is a schematic diagram of the first type of trapezoidal unit.

[0052] Figure 4 This is a schematic diagram of the second type of trapezoidal unit.

[0053] Figure 5 This is a schematic diagram of the third type of trapezoidal unit.

[0054] Figure 6 This is a schematic diagram of the fourth type of trapezoidal unit.

[0055] Figure 7 This is a schematic diagram of the fifth type of trapezoidal unit.

[0056] Figure 8 This is a schematic diagram of step S3021.

[0057] Figure 9 This is a schematic diagram of step S3022. Detailed Implementation

[0058] The parametric origami modeling method for obtaining Miura crease diagrams from folding shape curves, provided by the present invention, will be described in detail below with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more detailed, the following embodiments are the best and preferred embodiments; those skilled in the art can also use other alternative methods to implement some known technologies; and the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0059] It should be noted that the use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0060] like Figure 1 As shown, an embodiment of the present invention provides a parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve, including the following steps:

[0061] Step S1: In the interactive modeling software, draw a folded 2D curve, and obtain a target polyline that closely resembles the curve shape by dividing the curve into equal segments. Both the curve drawing and polyline operations are performed in Rhinoceros software, and then the line segments are picked up into the Grasshopper plugin. Specifically, the steps include:

[0062] S101: Design a folded two-dimensional curve: Input control points to generate a curve on a two-dimensional plane;

[0063] S102: The curve is divided into several key points by average segmentation. The average segmentation is the equal division of the length of several segments, which is independent of the position and number of control points in S101.

[0064] S103: Connect the key points of the curve in sequence and draw polylines. The polylines are selectively connected points to form lines. It is not necessary to completely connect all the key points of S102. The goal is to achieve an aesthetically pleasing result and approximate the target curve.

[0065] S104: Complete the drawing of the target polyline by adding, deleting and moving points.

[0066] Step S2: For the generated target polyline, a mathematical transformation relationship between the polyline and the crease diagram segments is calculated using mathematical methods to generate a crease strip diagram. The mathematical method used is the median line model of an isosceles triangle and a trapezoid; specifically, it includes the following steps:

[0067] S201: Treat polylines as multiple separate line segments, and crease units are irregular trapezoidal units with known height (h). Each line segment is the midline of the crease unit.

[0068] S202: As Figure 2 As shown, based on the included angle (β) between two adjacent line segments, an isosceles triangle solution model is established to obtain the base angle (α) of the crease trapezoidal unit. The formula for calculating the base angle is as follows:

[0069]

[0070] S203: Based on the length of the line segment (m), establish a solution model for the midline of the trapezoid, regard the line segment as the midline of the trapezoidal unit, and combine the base angle obtained in S22 to obtain the length of the corresponding base (a) of the crease trapezoidal unit.

[0071] We will discuss the calculation of the base (a) side length in five different cases:

[0072] The first method: Step S203, which calculates the length of the base (a), specifically involves the following: When the line segment (m) is the first line segment, the base angle of the trapezoidal unit is 90 degrees and α. The formula for calculating side a is as follows:

[0073]

[0074] like Figure 3 As shown, the target polyline at this time consists of two connected line segments, and the trapezoidal crease unit is a right trapezoid.

[0075] The second method: Step S203, which calculates the length of the base (a), is as follows: When the left base angle of the trapezoidal unit is an obtuse angle (180°-α1) and the right base angle is an acute angle α2, the formula for calculating side a is as follows:

[0076]

[0077] like Figure 4 As shown, the target polyline is "z" shaped, and the trapezoidal crease unit is a parallelogram-like shape.

[0078] The third method: Step S203, which calculates the length of the base (a), specifically involves the following: When both base angles of the trapezoidal unit are acute angles, let them be the left base angle (180°-α1) and the right base angle α2. Then, the formula for calculating side a is as follows:

[0079]

[0080] like Figure 5 As shown, the target polyline is an "n" shape with an opening to the left, and the trapezoidal crease unit is a square trapezoid.

[0081] The fourth method: Step S203, which calculates the length of the base (a), is as follows: When the left base angle of the trapezoidal unit is an acute angle (180°-α1) and the right base angle is an obtuse angle α2, the formula for calculating side a is as follows:

[0082]

[0083] like Figure 6 As shown, the target polyline is an inverted "z" shape, and the trapezoidal crease unit is a parallelogram-like shape.

[0084] Fifth method: Step S203, calculating the length of the base (a), specifically involves: when both base angles of the trapezoidal unit are obtuse angles, denoted as the left base angle (180°-α1) and the right base angle α2, the formula for calculating side a is as follows:

[0085]

[0086] like Figure 7 As shown, the target polyline is an "n" shape with an opening to the left, and the trapezoidal crease unit is an inverted trapezoid.

[0087] In the first case, the target polyline is the initial broken line segment; in the second and fourth cases, the target polylines are symmetrical about the horizontal line; and in the third and fifth cases, the target polylines are centrally symmetrical. The symmetry here refers to basic symmetry in a general sense, not strict symmetry in a narrow sense.

[0088] S204: Solve the trapezoidal element parameters sequentially and draw the crease element strip diagram.

[0089] Step S3: Simulate folding on the generated crease pattern using the Crane plugin in Grasshopper; specifically, this includes the following steps:

[0090] S301: Mirror the crease unit strip pattern along the bottom edge to obtain the crease strip pattern;

[0091] S302: Analyze the circumferential angle of the crease center on the center line of the crease strip diagram to confirm the direction of the valley crease lines. The circumferential angle is the central vertex of the crease unit. Miura Origami is classified as four-fold origami, which means that four crease lines extend from the central vertex. The task here is to determine the valley classification of these four crease lines; specifically, the following steps are included:

[0092] S3021: In the angle of the circumferential angle, when the two angles obtained by mirroring the bottom side are obtuse angles, the three obtuse angle sides are in the same direction and are set as the mountain line;

[0093] The three obtuse-angled sides consist of two separate sides and one shared side, where the shared side is the last side of the crease vertex, such as... Figure 8 As shown;

[0094] S3022: In the angle of the circumferential angle, when the two angles obtained by mirroring about the bottom side are acute angles, the direction of the side shared by the two acute angles is opposite to the direction of the side of the obtuse angle, and is set as the valley line;

[0095] After determining the direction of the valley line at one vertex, use the other vertices of the crease segment as crease vertices to determine the directions of other valleys;

[0096] The valley direction is a relative direction. That is, if a line segment is an obtuse-angled shared side when viewed from vertex 1, but an acute-angled shared side when viewed from vertex 2, then this line segment at vertex 2 is the aforementioned "last side," with a single direction, while the other three sides share the same direction. Figure 9 As shown;

[0097] S303: Simulate folding of the crease strip map. The simulation folding is performed using the Crane plugin. This step must be manually re-simulated after each adjustment of the crease map parameters to determine the specific shape after folding. It should be noted that the simulated folding must be classified according to the valley line direction as a necessary prerequisite operation. If the valley line is classified incorrectly, the folding will not be able to be simulated.

[0098] Step S4: Observe the model structure obtained by simulation folding, adjust the parameter values ​​of the crease diagram to ensure the mathematical rationality and aesthetics of the folding structure, and obtain a printable and directly foldable crease diagram. Mathematical rationality means that the crease diagram can indeed be folded and conforms to the folding rules.

[0099] The crease diagram can be further optimized and fine-tuned using the biomorpher plugin with a genetic algorithm to obtain a fold shape and corresponding crease diagram that better matches the design. The optimization is performed on the crease diagram by automatically adjusting parameters. After obtaining the crease diagram, a new simulation folding is required.

[0100] The crease pattern conversion process is carried out on the rhinoceros-grasshopper platform, and its implementation carrier is the battery connection; in each key step, the parts other than the parameters can be integrated into components, and the crease pattern can be adjusted by adjusting the parameters.

[0101] The uses of this invention include, but are not limited to, lighting design, exhibition stand design, etc. For example, the origami structure obtained by this invention can be applied to product design, including product structure design by professional designers and simple designs in daily life by non-professional designers.

[0102] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0103] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc.

[0104] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve, characterized in that, Includes the following steps: Step S1: In the interactive modeling software, draw a folded two-dimensional curve, and obtain a target polyline that closely resembles the curve shape by dividing the curve into equal segments. Step S2: For the generated target polyline, use mathematical methods to calculate the mathematical transformation relationship between the polyline and the line segments of the crease diagram, and generate a crease strip diagram; Step S3: Simulate folding on the generated crease pattern; Step S4: Observe the model structure obtained by simulation folding, adjust the parameter values ​​of the crease diagram to ensure the mathematical rationality and aesthetics of the folding structure, and obtain a printable and directly foldable crease diagram drawing.

2. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 1, characterized in that, Step S1 specifically includes the following steps: S101: Design a folded two-dimensional curve: Input control points to generate a curve on a two-dimensional plane; S102: The curve is divided into several key points by average segmentation. S103: Connect the key points of the curve in sequence to draw a polyline; S104: Complete the drawing of the target polyline by adding, deleting and moving points.

3. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 1, characterized in that, Step S2 specifically includes the following steps: S201: Treat polylines as multiple separate line segments, and crease units are irregular trapezoidal units with known height (h). Each line segment is the midline of the crease unit. S202: Based on the included angle (β) between two adjacent line segments, an isosceles triangle solution model is established to obtain the base angle (α) of the crease trapezoidal unit. The formula for calculating the base angle is as follows: S203: Based on the length of the line segment (m), establish a solution model for the midline of the trapezoid, regard the line segment as the midline of the trapezoidal unit, and combine the base angle obtained in S22 to obtain the length of the corresponding base (a) of the crease trapezoidal unit. S204: Solve the trapezoidal element parameters sequentially and draw the crease element strip diagram.

4. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 3, characterized in that, The specific steps for calculating the length of the base (a) in step S203 are as follows: When the line segment (m) is the first line segment, the base angle of the trapezoidal unit is 90 degrees and α, then the formula for calculating the length of the base (a) is as follows: At this point, the target polyline consists of two connected line segments, and the trapezoidal crease unit is a right trapezoid.

5. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 3, characterized in that, The specific steps for calculating the length of the base (a) in step S203 are as follows: When the left base angle of the trapezoidal unit is an obtuse angle (180°-α1) and the right base angle is an acute angle α2, the formula for calculating side a is as follows: At this point, the target polyline is "z" shaped, and the trapezoidal crease unit is a parallelogram-like shape.

6. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 3, characterized in that, The specific steps for calculating the length of the base (a) in step S203 are as follows: When both base angles of the trapezoidal unit are acute angles, let them be the left base angle (180°-α1) and the right base angle α2. Then, the formula for calculating side a is as follows: At this point, the target polyline is "z" shaped, and the trapezoidal crease unit is a square trapezoid.

7. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 3, characterized in that, The specific steps for calculating the length of the base (a) in step S203 are as follows: When the left base angle of the trapezoidal unit is an acute angle (180°-α1) and the right base angle is an obtuse angle α2, the formula for calculating side a is as follows: At this point, the target polyline is an inverted "z" shape, and the trapezoidal crease unit is a parallelogram-like shape.

8. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 3, characterized in that, The specific steps for calculating the length of the base (a) in step S203 are as follows: When both base angles of the trapezoidal unit are obtuse angles, let them be the left base angle (180°-α1) and the right base angle α2. Then, the formula for calculating side a is as follows: At this point, the target polyline is an "n" shape with the opening to the left, and the trapezoidal crease unit is an inverted trapezoid.

9. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 3, characterized in that, Step S3 specifically includes the following steps: S301: Mirror the crease unit strip pattern along the bottom edge to obtain the crease strip pattern; S302: Analyze the circumferential angle of the crease center on the center line of the crease strip diagram to confirm the direction of the valley crease line; S303: Simulate folding of the crease strip diagram.

10. The parametric origami modeling method for obtaining the Miura crease diagram from the folding shape curve according to claim 9, characterized in that, Step S302 specifically includes the following steps: S3021: In the angle of the circumferential angle, when the two angles obtained by mirroring the bottom side are obtuse angles, the three obtuse angle sides are in the same direction and are set as the mountain line; S3022: In the angle of the circumferential angle, when the two angles obtained by mirroring about the bottom side are acute angles, the direction of the side shared by the two acute angles is opposite to the direction of the side of the obtuse angle, and is set as the valley line.

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