Method for carrying out visual design on regular wrinkle carrier

Abstract

The invention discloses a method for performing visual design on a regular creased carrier, the regular creased carrier comprises all regular creased three-dimensional carriers, and a regular creased unit of the regular creased carrier consists of three parts, namely an upward convex mountain crease, a downward concave valley crease and a middle unfolded creased unit surface; and on the basis of the size, density and density corresponding to the regular wrinkle units, the regular wrinkle carriers comprise Jiyun wrinkles, Z-shaped wrinkles and Sanpu wrinkles, and visual design including visual rules and translation rules is carried out on various regular wrinkle carriers on the basis of different types of geometrical morphology languages. The invention provides a visual transfer path and a design method of a geometric form language on a regular crumpled carrier, and solves the problem of visual translation of the geometric form language focusing on information transmission on the regular crumpled carrier.

Description

Technical Field

[0001] The invention relates to the technical field of folded carriers, and in particular to a method for performing visual design on a regular folded carrier. Background Art

[0002] With the update of technology and design needs, "flat to three-dimensional" has become one of the design trends. Geometric morphological language has evolved into the art field in line with this trend for a long time, and is widely used in graphic posters, packaging design, installation art, etc. Among them, the geometric origami structure, which is also inspired by geometric concepts, provides a broadening idea of ​​the carrier dimension for geometric morphological language to follow the trend of "flat to three-dimensional".

[0003] "Regular folds" is a broader definition of "geometric origami", including all three-dimensional carriers with regular folds, including origami. They have the advantages of good mechanical properties, simple geometric structure, and high strength. Based on the structural and mechanical properties of these structures themselves, they have been innovatively applied in the fields of building structures, medical equipment, aerospace, robotics, and bioengineering. The above-mentioned regular folded structures also have the formal beauty characteristics of geometry, order, and regularity. A large number of cases have shown that the design of geometric color blocks or abstract geometric patterns on regular folded carriers can enrich the aesthetic expression of visual content while broadening the visual carrier, providing a case basis for exploring the design path of geometric morphological language on such innovative carriers.

[0004] However, when designers try to present the visual representation of geometric morphological language on regular folding carriers, they are mostly based on perceptual, random, and accidental visual representation and aesthetic feelings. Due to the lack of understanding and research on the principles and rules of visual translation of geometric morphological language on regular folding carriers, problems such as pattern deformation and inaccurate pattern information transmission will occur in the actual design process. Therefore, it is necessary to explore a set of methods and procedures for rationally and systematically designing geometric morphological language on regular folding carriers that can be combined with the perceptual aesthetic experience of designers. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the deficiencies in the prior art, the present invention proposes a set of visual transfer paths and design methods for geometric morphological languages ​​on regularly folded carriers, which solves the dilemma of visual translation of geometric morphological languages ​​focusing on information transmission on regularly folded carriers.

[0007] (II) Technical solution

[0008] In recent years, in the field of visual communication in the era of "flat to three-dimensional", the trend of two-way expansion of visual content and visual carriers has become increasingly significant. Geometric forms have attracted much attention due to their strong sense of spatial order. The combination of geometric form language and regular fold carriers born under the influence of geometric forms provides an opportunity for designers to further break through the spatial limitations of visual communication. However, traditional design methods make it impossible for geometric form language to adapt to the concave and convex structure of fold carriers and cause deformation, which affects the effective communication of visual information.

[0009] To achieve the above object, the present invention provides the following technical solutions: a method for performing visual design on a regular folded carrier, wherein the regular folded carrier includes all three-dimensional carriers with regular folds, and the regular folded units thereof are composed of three parts: an upward convex mountain fold, a downward concave valley fold, and an unfolded middle folded unit surface;

[0010] Based on the size and density corresponding to the regular folding units, the regular folding carrier includes:

[0011] Yoshimura fold, the units are mainly polygonal blocks, showing a scattered, stretched, shallow concave-convex fold morphology;

[0012] Z-shaped folds, the units are elongated rectangles, and the whole presents a repeated and dense fold shape;

[0013] Miura folds, the units are parallelograms, the density of the units presents a comfortable regularity, and there is enough space between the units;

[0014] How to carry out visual design on various regular folding carriers based on different types of geometric morphological languages, including visual rules and translation rules, and through the following methods:

[0015] A1. Based on the visual translation of dot matrix and line geometry in geometric morphological language on creases, the combination rules of "shape" are made according to the characteristics of creases 1;

[0016] A2, based on the visual translation of block geometry on the fold unit surface in geometric morphological language, the combination rules of "shape" are carried out according to the arrangement characteristics of the fold unit surface 2;

[0017] A3. Based on inorganic geometric figures in geometric morphological language, mathematical induction is used to explore the inner order, deformation law and visual translation path of square geometry, triangular geometry and circular geometry on the carrier of Miura's regular wrinkle;

[0018] A4. Based on the visual translation and derivation of organic geometric patterns on the fold unit surface in the geometric morphological language, we explored and derived the translation rules 3, 4 and 5 of organic geometric patterns on regular fold carriers.

[0019] As a preferred solution, Rule 1 in A1 includes:

[0020] Mathematical combination: "repetition" and "symmetry";

[0021] Breaking rules combination: "dislocation" and "frame";

[0022] Dynamic combination: "gradient", "diffusion", "emission", "flash".

[0023] As a preferred solution, Rule 2 in A2 includes:

[0024] Geometric pixelation;

[0025] Mathematical combination: "repetition" and "symmetry";

[0026] Breaking rules combination: "dislocation" and "frame";

[0027] Dynamic combination: "gradient", "diffusion", "emission", "flash";

[0028] Among them, "geometric pixelation" means using the "filter" and "balance" methods in Photoshop to pixelate a complete image into geometric shapes, and then translate these pixel geometric color blocks with color information into the carrier unit.

[0029] As a preferred solution, A3 includes an exploration of the intrinsic order of inorganic geometric figures and Miura folds, taking the Miura structure and a horizontal line geometry as an example, experiments are conducted and data are recorded.

[0030] As a preferred solution, A3 also includes an exploration of the initial figure and the plane deformation diagram, and experiments prove that the plane deformation diagram of the square geometry is composed of the plane deformation diagrams of the horizontal line geometry and the vertical line geometry.

[0031] As a preferred solution, Rule 3 in A4 is that each fold unit surface on the regular fold carrier can be regarded as a splicing grid, called a "fold splicing grid", and multiple fold unit surfaces can also be regarded as a splicing grid, depending on the requirements of the final visual effect.

[0032] As a preferred solution, rule 4 in A4 includes:

[0033] Rotational symmetry refers to repeated rotation around a certain point. This fixed point can be inside or outside the element, and can be symmetrical multiple times.

[0034] Translational symmetry refers to the result of a figure (which can be an element, a pattern, or a derived pattern) moving in a specific direction and a specific distance, in which the element itself can rotate and the translation distance can be changed;

[0035] Mirror symmetry refers to a figure (which can be an element, a pattern, or a derived pattern) where one half of the figure is mirrored and repeated with the other half, and the element itself can be rotated and the distance from the axis of symmetry can be changed;

[0036] Sliding mirror symmetry refers to a combination of two symmetries, first translational symmetry and then mirror symmetry along that direction, in which the elements themselves can rotate and the spacing ratio between the two symmetrical behaviors can be changed.

[0037] As a preferred solution, rule 5 in A4 includes:

[0038] Linear symmetry refers to the way symmetry is carried out along a straight line;

[0039] Planar symmetry refers to the symmetry on the plane along two directions, which ultimately allows the pattern to cover the entire surface. The symmetry rule involves the size of the splicing grid, so the size and shape of the splicing grid (i.e. the size and shape of the crease unit of the regular fold carrier) can be changed, and the two translation directions of the plane can be changed;

[0040] Seamless repetition refers to repetitive patterns that appear to have no specific beginning and end. Seamless repetition specifically refers to the activity of translating half of the graphic in the horizontal direction to the other side, and then moving the vertical half to the other side, and then performing the activity of plane symmetry to generate the pattern.

[0041] As a preferred solution, the visual translation path of the organic geometric morphological language on a regular folding carrier is: first, deconstruct the organic morphological language into organic geometric elements; then, the organic geometric elements generate organic geometric patterns; then, the organic geometric patterns generate organic geometric repeating patterns; finally, translate into the folding splicing grid according to the arrangement rules of the folding units.

[0042] As a preferred solution, the visual translation of inorganic geometric morphological language on regular folding carriers is divided into two parts. The first part is the visual translation rules of inorganic point, line and surface geometry on regular folding carriers; the second part is the visual translation path of inorganic geometric figures on the third type of regular folding carrier represented by Miura folds.

[0043] (III) Beneficial effects

[0044] Compared with the prior art, the present invention provides a method for visual design on a regular folded carrier, which has the following beneficial effects: the regular folded carrier described in the present invention includes all three-dimensional carriers of regular folds, and based on how different categories of geometric morphological languages ​​are used to perform visual design on various regular folded carriers, including visual rules and translation rules, a set of visual transfer paths and design methods of geometric morphological languages ​​on regular folded carriers are proposed, which solves the dilemma of visual translation of geometric morphological languages ​​that focus on information transmission on regular folded carriers. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the visual rules and corresponding translation paths of different geometric morphological languages ​​in regular fold carriers of the present invention;

[0046] Figure 2 A schematic diagram of the visual regularity and translation path of the inorganic geometric figures on the regular wrinkled carrier of the present invention;

[0047] Figure 3 It is a schematic diagram of the visual translation process of the organic geometric morphological language on the regular wrinkled carrier of the present invention;

[0048] Figure 4 Schematic diagrams of three typical carrier folds and unit surfaces of the present invention;

[0049] Figure 5 It is a schematic diagram of the visual translation rules of the geometric correspondence of lines on wrinkle creases of the present invention;

[0050] Figure 6 It is a schematic diagram of the visual translation rules of the block surface geometry corresponding to the creases of the three types of regular fold carriers of the present invention;

[0051] Figure 7 A schematic diagram of the basic generation process of the organic geometric repeating pattern of the present invention;

[0052] Figure 8 Schematic diagram of the cell lattice, splicing lattice and three types of carrier folded splicing lattices of the present invention;

[0053] Fig. 9 Four symmetric schematic diagrams of generating organic geometric patterns for rule 2 organic geometric elements of the present invention;

[0054] Fig.10 Three symmetric schematic diagrams of organic geometric repeating patterns are generated for Rule 3 of the present invention. DETAILED DESCRIPTION

[0055] In order to better understand the purpose, structure and function of the present invention, the present invention will start from the perspectives of information transmission and visual aesthetics at the same time, and with the help of the spatial relationship research mechanism and formal aesthetics of mathematical geometry, further improve the visual translation of geometric morphological language on regular wrinkled surfaces, and obtain a set of systematic visual translation paths with sensibility and rationality, and then gradually deepen and improve the research of the present invention in an interdisciplinary way.

[0056] Example 1

[0057] refer to Figure 1-10The present invention provides a method for visual design on a regular folded carrier, wherein the regular folded carrier includes all three-dimensional carriers with regular folds, wherein the regular folded unit is composed of three parts: an upward convex mountain fold, a downward concave valley fold and an unfolded middle folded unit surface;

[0058] Based on the size and density of the regular folding units, the regular folding carriers include:

[0059] Yoshimura fold, the units are mainly polygonal blocks, showing a scattered, stretched, shallow concave-convex fold morphology;

[0060] Z-shaped folds, the units are elongated rectangles, and the whole presents a repeated and dense fold shape;

[0061] Miura folds, the units are parallelograms, the density of the units presents a comfortable regularity, and there is enough space between the units.

[0062] Specifically, the regular fold carrier in the present invention refers to all three-dimensional carriers with regular folds. A complete regular fold unit consists of three parts: a convex mountain fold, a concave valley fold, and an unfolded fold unit surface in the middle.

[0063] The first type of regular wrinkle carrier is the "Yoshimura fold", with the units mainly in polygonal blocks, showing a dispersed, stretched, and shallowly concave and convex wrinkle shape;

[0064] The second type of regular wrinkle carrier is the "Z-shaped wrinkle", the unit is a slender rectangle, and the whole presents a repeated and dense wrinkle shape;

[0065] The third type of regular fold carrier is the "Miura fold", whose units are parallelograms, the density of the units presents a comfortable regularity, and there is enough space between the units.

[0066] In the present invention, Yoshimura pleats are a type one carrier, and Z-folds and Miura pleats are type two and type three carriers, respectively.

[0067] like Figure 4 As shown in the figure, the reason why the "regular wrinkle carrier" can have regularity and order is due to the regular arrangement of its "wrinkle creases", which plays a decisive role in the final form of the carrier. Specifically, "wrinkle creases" are divided into "mountain creases" and "valley creases". As the name suggests, the "mountain creases" are convex upwards, and the "valley creases" are concave downwards. The unfolded area in the middle becomes the unit surface of the final "regular wrinkle carrier" structure, so a complete "regular wrinkle" unit is always composed of these three parts, namely, the wrinkle crease parts including the convex folding area and the concave folding area, and the unfolded wrinkle unit surface.

[0068] More specifically, according to the size and density of the "wrinkle unit" and the most commonly used origami carrier in each category, the structures commonly used in the regular wrinkle carrier of the present invention are divided into three categories. The first category is "Yoshimura fold", where the unit is mainly polygonal block, showing a dispersed, stretched, and shallowly concave and convex wrinkle form; the second category is "Z-type fold", where the unit is an elongated rectangle, and the whole presents a repeated and dense wrinkle form; the third category is "Miura fold", where the unit is a parallelogram, the density of the unit presents a comfortable regularity, and there is enough space between the units. Based on the above classification, the visual imaging principle of the wrinkle crease and the unit surface of these three types of wrinkle structures is studied, as shown in Table 1 below;

[0069]

[0070] Table 1

[0071] Furthermore, the present invention starts from the perspectives of information transmission and visual aesthetics at the same time, and with the help of the spatial relationship research mechanism and formal aesthetics of mathematical geometry, further improves the visual translation of geometric morphological language on regular wrinkled surfaces, and obtains a set of systematic visual translation paths with sensibility and rationality, and then gradually deepens and improves the research of the present invention in an interdisciplinary way.

[0072] Example 2

[0073] refer to Figure 1-3 Specifically, the method for performing visual design on a regular folded carrier of the present invention includes the following steps:

[0074] A1. Visual translation of dot matrix and line geometry on creases, and combination rules of “shape” according to crease characteristics 1;

[0075] A2, the visual translation of block geometry on the fold unit surface, and the combination rules of "shape" according to the arrangement characteristics of the fold unit surface 2;

[0076] A3. Based on inorganic geometric figures in geometric morphological language, mathematical induction is used to explore the inner order, deformation law and visual translation path of square geometry, triangular geometry and circular geometry on the carrier of Miura's regular wrinkle;

[0077] A4. Based on the visual translation and derivation of organic geometric patterns on the fold unit surface in the geometric morphological language, we explored and derived the translation rules 3, 4 and 5 of organic geometric patterns on regular fold carriers.

[0078] The present invention aims to propose a set of visual transfer paths and design methods for geometric morphological languages ​​on regular wrinkled carriers, which solves the dilemma of visual translation of geometric morphological languages ​​that focus on information transmission on regular wrinkled carriers. The visual translation of the geometric morphological languages ​​of the present invention on regular wrinkled surfaces will be further explained below in combination with specific embodiments.

[0079] Example 3

[0080] Inorganic point, line and surface geometry on regular wrinkle carrier

[0081] Among them, the visual translation of dot matrix and line geometry on the crease is the "crease" of the regular fold carrier, which is mainly divided into two parts, the upper convex folding area and the lower concave folding area, and the arrangement has a sense of order, and it is a collection of "lines" and "dots", so the design method for designing the geometric arrangement of "dots" and "lines" on the two fold areas is the same. "Dot matrix geometry" and "line geometry" in the geometric morphological language are undoubtedly two types of "shapes". There are many visual rules for this type of "shape" on the plane carrier mentioned above, but when they are arranged on the regular fold crease, they must be combined according to the fold characteristics. The present invention summarizes them into Rule 1, that is, Rule 1 in A1, which includes:

[0082] Mathematical combination: "repetition" and "symmetry";

[0083] Breaking rules combination: "dislocation" and "frame";

[0084] Dynamic combination: "gradient", "diffusion", "emission", "flash";

[0085] Among them, "mathematical combination" refers to the combination of "shapes" that combine the distribution rules of folds to express a sense of regular order, and is a means of emphasizing the rhythm of geometric morphological language; "repetition" refers to the repetition of a single geometric figure or form; "symmetry" refers to the symmetry of a single geometric figure or form;

[0086] "Breaking the rules" refers to the combination of "shapes" that break the sense of conventional order by combining the distribution rules of creases. It changes the rhythm of the geometric language without affecting the continuity of the rhythm. "Dislocation" refers to a single geometric figure or form that is displaced from its original position, but still makes people feel the continuity of the extension. "Frame" refers to a single geometric figure or form distributed in an outline state, so as to feel the beauty of the interlacing of the main figure and the negative shape.

[0087] "Dynamic combination" refers to the combination of "shapes" that break the sense of order by combining the distribution law of creases, and more importantly, embody the dynamic rhythm; "gradual change" refers to the gradual change of multiple factors such as density, size, and gap of a single geometric figure or form; "diffusion" refers to a single geometric figure or form that has a certain range limit and spreads outward in a hierarchical and uniform manner; "emission" refers to the distribution of a single geometric figure or form in an emission trajectory, or in a radiation range; "flash" refers to a single figure or form that presents a visual sense of movement with a regular rhythm when it is emitted;

[0088] like Figure 5 As shown, it is a schematic diagram of the visual translation rules of the geometric correspondence of lines on the wrinkle crease. The present invention organizes them, and uses several groups of mountain fold creases as an example to combine color changes for visual design. In addition to a single design method, it can also be superimposed and used as needed, so that the geometric morphological language creates a rich and diverse visual effect on the regular wrinkle carrier crease. However, visual design only on the crease is far from satisfying people's aesthetic psychology and market demand, so it is more important to perform more types of geometric morphological language visual design on the "wrinkle unit surface" in the non-folding area.

[0089] Example 4

[0090] Visual translation of “block geometry” on the wrinkled unit surface

[0091] In designing geometric morphological language on "wrinkle unit surface", in addition to specific organic geometric repeating patterns, the most basic is the visual translation of "block geometry" on the unit surface. The present invention summarizes a lot of visual rules for designing "block geometry" on a plane carrier, but when they are arranged on regular wrinkles and creases, they must be combined according to the arrangement characteristics of the wrinkle unit surface. Different from the "dot matrix and line geometry", the present invention summarizes them into Rule 2, that is, Rule 2 in A2, which includes:

[0092] Geometric pixelation;

[0093] Mathematical combination: "repetition" and "symmetry";

[0094] Breaking rules combination: "dislocation" and "frame";

[0095] Dynamic combination: "gradient", "diffusion", "emission", "flash";

[0096] Among them, "geometric pixelation" refers to pixelating a complete image into geometric shapes using the "filter" and "balance" methods in Photoshop, and then translating these pixel geometric blocks with color information onto the carrier unit. "mathematical combination", "rule-breaking combination" and "dynamic combination" are the combination rules of the three types of "shapes" in Rule 1 above.

[0097] The present invention arranges them and takes the wrinkled unit surfaces of several groups of units as an example to combine color changes for visual design, and the effect is as follows Figure 6 The figure shows the schematic diagram of the visual translation rules of the block surface geometry corresponding to the creases of three types of regular folded carriers.

[0098] Example 5

[0099] Generation of organic geometric patterns combined with wrinkled unit surfaces

[0100] The definition of organic geometric morphology language is relative to inorganic geometric morphology language. Therefore, the organic geometry studied in this embodiment, that is, the geometric morphology language other than inorganic geometry, is more inclined to be called "organic geometric pattern". The pattern we usually refer to is actually often a repeat pattern. In this embodiment, "organic geometric repeat pattern" will be used to replace the broad organic geometric morphology language.

[0101] Therefore, the present invention defines that an "organic geometric element" is the smallest constituent atom of an organic geometric repeating pattern, an "organic geometric pattern" is composed of two or more organic geometric elements, and an "organic geometric derived pattern" or "organic geometric repeating pattern" is generated by two or more organic geometric patterns through any one or more repetitive symmetry rules, such as Figure 7 shown.

[0102] As for how to distribute organic geometric repeating patterns on regular folded carriers, this embodiment also draws on the concepts of "cell grid" and "patchwork grid" of Paul Jackson. The two are very similar, sometimes even identical, and have the same functions. They are all polygons that allow patterns to be connected to each other and cover the entire plane. Without them, there would be no repeating patterns, but the difference is that the boundaries of the "cell grid" are defined by the designed elements, patterns, or derived patterns; while the boundaries of the "patchwork grid" already exist before the design of the elements, patterns, or derived patterns is completed. Therefore, the "creases" and "fold unit surfaces" of regular folded carriers can be considered equivalent to the "patchwork grid" of regular folded carriers. Therefore, this embodiment converts the fold unit surfaces of three types of regular folded carriers into "folded patchwork grids". The first type is a dispersed and stretched fold patchwork grid, the second type is a fine and continuous fold patchwork grid, and the third type is a regular and orderly fold patchwork grid, such as Figure 8 shown.

[0103] In summary, this embodiment obtains the translation rule 3 of the organic geometric pattern on the regular wrinkled carrier:

[0104] Each fold unit surface on the regular fold carrier can be regarded as a splicing grid, called a "fold splicing grid", and multiple fold unit surfaces can also be regarded as a splicing grid, depending on the requirements of the final visual effect.

[0105] Example 6

[0106] Visual translation and derivation of organic geometric patterns on the folded unit surface

[0107] Furthermore, this embodiment will discuss in detail the visual translation rules of organic geometric repeating patterns (i.e., organic geometric morphological language) on a regularly folded carrier. In the process, leaf shapes are selected as organic geometric elements to demonstrate the final generated effect.

[0108] Symmetry can be divided into "zero-dimensional", i.e. symmetry with a single point; "one-dimensional", i.e. symmetry with a line segment; "two-dimensional", i.e. symmetry with two line segments to form a two-dimensional plane; "three-dimensional", i.e. symmetry with three line segments to form a three-dimensional space. The derivative rules involved in the generation of organic geometric repeating patterns are essentially symmetry rules. Among them, organic geometric elements generate organic geometric patterns using four basic symmetries: rotational symmetry, translational symmetry, mirror symmetry, and sliding mirror symmetry, such as Fig. 9 As shown in Figure 4, it can be summarized as translation rule 4.

[0109] (1) Rotational symmetry refers to repeated rotation around a certain point. This fixed point can be inside or outside the element, and can be symmetrical multiple times.

[0110] (2) Translational symmetry refers to the result of a figure (which can be an element, a pattern, or a derived pattern) moving in a specific direction and a specific distance, in which the element itself can rotate and the translation distance can be changed;

[0111] (3) Mirror symmetry refers to a figure (which can be an element, a pattern, or a derived pattern) in which one half is a mirror copy of the other half, and the elements themselves can be rotated and the distance from the symmetry axis can be changed;

[0112] (4) Sliding mirror symmetry refers to a combination of two symmetries: translational symmetry followed by mirror symmetry along the same direction, in which the elements themselves can rotate and the spacing ratio between the two symmetric behaviors can be changed.

[0113] It can be seen that when applying the above symmetry rules, there are many variable factors, and there is a superposition of the rule of the element's own symmetry change. Therefore, in order to control this variable and facilitate the derivation of the next step of organic geometric repeating patterns, the elements are defined to be placed vertically here. If the elements themselves rotate, the subsequent derivation rules can be verified in the same way.

[0114] When organic geometric patterns generate organic geometric repeating patterns, the three rules of linear symmetry, planar symmetry, and seamless repeating patterns are used, such as Fig.10 As shown. It can be summarized as translation rule 5:

[0115] (1) Linear symmetry refers to the way of symmetry along a straight line;

[0116] (2) Planar symmetry refers to the symmetry on the plane along two directions, which ultimately allows the pattern to cover the entire surface. The symmetry rule involves the size of the splicing grid, so the size and shape of the splicing grid (i.e., the size and shape of the crease unit of the regular fold carrier) can be changed, and the two translation directions of the plane can be changed;

[0117] (3) Seamless repetition refers to repetitive patterns that appear to have no specific beginning or end. Seamless repetition specifically refers to the activity of translating half of the pattern horizontally to the other side, and then moving the other half vertically to the other side, and then performing the activity of generating the pattern in plane symmetry.

[0118] Furthermore, this embodiment summarizes the systematic visual generation rules of organic geometric patterns, that is, the visual translation path of organic geometric morphological language on regular folded carriers is: first, deconstruct the organic morphological language into organic geometric elements; then, the organic geometric elements generate organic geometric patterns; then, the organic geometric patterns generate organic geometric repeating patterns; finally, according to the arrangement rules of the folding units, they are translated into folding splicing grids. In addition, because the organic geometric repeating pattern is mainly based on visual aesthetics, the ups and downs of the carrier will not affect its visual effect presentation, but will create light and shadow effects due to the sense of space.

[0119] Example 7

[0120] Inorganic Geometry and the Inner Order of Miura Folding

[0121] Since both inorganic geometric figures and Miura folds are orderly, regular, and rational, in order to explore their internal order, the present invention proposes assumption 1: the folding degree of Miura folds and the deformation degree of inorganic geometric figures must have a definite logical and mathematical relationship between the two.

[0122] To verify hypothesis 1, the present invention A3 includes an exploration of the intrinsic order of inorganic geometric figures and Miura folds, and takes the Miura structure and a horizontal line geometry as an example to conduct experiments and record data. The process of experiment 1 is as follows:

[0123] B1. Define the angles between the Miura fold unit and the line geometry l. The Miura fold unit is composed of four parallelograms with equal sides and internal angles of 60° and 120° respectively. In this process, a model with half of the Miura structural unit is established with the help of shaper3D software;

[0124] B2. Perform the operation of plane cutting into solid. Draw line segment l on the XY axis plane. Pull down in the Z axis direction to cut the model and hollow out the line geometry l. When the half Miura unit is flattened, it is found that the position of line segment l is offset;

[0125] B3. Mirror the model with the vertical direction as the symmetry axis to obtain a complete Miura wrinkle unit, and observe the deformed line geometry l on the surface at this time;

[0126] B4. It is found that the deformation occurs at the intersection of the unit crease and the line geometry l, which is concave in the middle and forms an angle, which is defined as the shape deformation angle In addition, when the Miura fold unit is folded at any angle, the angle formed by the two unit faces below the structure on the same plane is defined as the folding forming angle α (line angle, not dihedral angle);

[0127] B5. After clarifying the parameters, angles and experimental process, the control variable method is used to control the length, position and recording angle of the line geometry l, change the folding angle and take the special moment of α=90° as an example, increase or decrease the angle at intervals of 5°, carry out experimental measurements and record each folding angle α and the corresponding shape deformation angle The data records are shown in Table 2 below;

[0128]

[0129] Table 2

[0130] B6. Through data observation and analysis, it is found that there is indeed a functional relationship between the two, and there is an optimal range. When the folding forming angle α is between 80° and 110°, it is linearly correlated.

[0131] It is proved through experiments that the plane deformation diagram of square geometry is composed of the plane deformation diagrams of horizontal line geometry and vertical line geometry. The process of Experiment 2 is as follows:

[0132] C1. Starting from two parallel horizontal lines, draw a plane deformation diagram of line segment geometry. Using the control variable method, keep the shape, position and recording angle unchanged, change the folding angle α, and find that there is an initial figure of horizontal line geometry at a certain angle;

[0133] C2, draw two parallel vertical lines, still control the shape, position and recording angle unchanged, change the folding angle α, and find that they remain vertical throughout the process without deformation;

[0134] C3. Based on the deformation of the horizontal and vertical line geometry, draw a plane deformation diagram of the square geometry. Similarly, keep the shape, position and recording perspective unchanged, change the folding angle α, and continue to fold to find that there is a specific angle that presents the initial figure of the square geometry.

[0135] Based on the results obtained in the above embodiments, Figure 1 As shown in the figure, in order to explore how different types of geometric morphological languages ​​can be used for visual design on various regular folding carriers, a set of visual translation paths is summarized. Figure 1 Schematic diagram of the visual rules and corresponding translation paths of different geometric languages ​​in regular folding carriers.

[0136] The visual translation process of the inorganic geometric morphological language and the regular folding carrier is as follows:

[0137] The visual translation of inorganic geometric morphological language on regular folding carriers is divided into two parts. The first part is the visual translation rules of inorganic point, line and surface geometry on regular folding carriers, which is mainly based on the visual laws and visual principles in Chapter 3; the second part is the visual translation path of inorganic geometric figures on the third type of regular folding carrier, which is a typical example of Miura folds.

[0138] according to Figure 2 As shown, it is a schematic diagram of the visual rules and translation paths of inorganic geometric figures on regular wrinkled carriers. Designers can choose corresponding conclusions for visual translation according to different types of design requirements:

[0139] In addition, the visual translation of organic geometric morphological language on the regular folding carrier is divided into two parts. The first part is the visual generation law of organic geometric repeating patterns, and the second part is the translation onto the regular folding carrier. The specific translation process is summarized as follows: Figure 3 shown.

[0140] Finally, we will explain the conclusions of the visual translation path of geometric morphological language on the regular fold carrier, as shown in the following table:

[0141]

[0142]

[0143] Table 3

[0144]

[0145] Table 4

[0146] The present invention will conduct practical verification based on the above-mentioned overall research conclusions on the visual translation path, including visual laws, visual imaging principles, visual translation rules, and visual translation methods. This shows that this set of theories is feasible, and takes into account both "vision" and "communication", giving full play to the advantages of combining regular wrinkle carriers with geometric morphological language, while solving existing problems.

[0147] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for performing visual design on a regularly folded carrier, characterized in that: The regular fold carrier includes all three-dimensional carriers with regular folds, and its regular fold units are composed of three parts: a convex mountain fold, a concave valley fold, and an unfolded fold unit surface in the middle; Based on the size and density corresponding to the regular folding units, the regular folding carrier includes: Yoshimura fold, the units are mainly polygonal blocks, showing a scattered, stretched, shallow concave-convex fold morphology; Z-shaped folds, the units are elongated rectangles, and the whole presents a repeated and dense fold shape; Miura folds, the units are parallelograms, the density of the units presents a comfortable regularity, and there is enough space between the units; Based on different types of geometric morphological languages, visual design is carried out on various regular folding carriers, including visual rules and translation rules, and is carried out in the following ways: A1. Based on the visual translation of dot matrix and line geometry on creases in geometric morphological language, the combination rules of "shape" are made according to the crease characteristics 1; A2, based on the visual translation of block geometry on the fold unit surface in geometric morphological language, the combination rules of "shape" are carried out according to the arrangement characteristics of the fold unit surface 2; A3. Based on inorganic geometric figures in geometric morphological language, mathematical induction is used to explore the inner order, deformation law and visual translation path of square geometry, triangular geometry and circular geometry on the carrier of Miura's regular wrinkle; A4. Based on the visual translation and derivation of organic geometric patterns on the wrinkle unit surface in the geometric morphological language, we explored and derived the translation rules 3, 4 and 5 of organic geometric patterns on regular wrinkle carriers.

2. The method for performing visual design on a regular wrinkled carrier according to claim 1, characterized in that: Rule 1 in A1 includes: Mathematical combination: "repetition" and "symmetry"; Breaking the rules combination: "dislocation" "frame"; Dynamic combination: "gradual change", "diffusion", "emission" and "flash".

3. The method for performing visual design on a regular wrinkled carrier according to claim 1, characterized in that: Rule 2 in A2 includes: Geometric pixelation; Mathematical combination: "repetition" and "symmetry"; Breaking the rules combination: "dislocation" "frame"; Dynamic combination: "gradual change", "diffusion", "emission" and "flash".

4. The method for performing visual design on a regularly folded carrier according to claim 1, characterized in that: The A3 includes the exploration of the intrinsic order of inorganic geometric figures and Miura folds. Taking the Miura structure and a horizontal line geometry as an example, experiments are conducted and data are recorded.

5. The method for performing visual design on a regularly folded carrier according to claim 4, characterized in that: The A3 also includes the exploration of the initial figure and the plane deformation diagram, and proves through experiments that the plane deformation diagram of the square geometry is composed of the plane deformation diagrams of the horizontal line geometry and the vertical line geometry.

6. The method for performing visual design on a regularly folded carrier according to claim 1, characterized in that: Rule 3 in A4 is that each fold unit surface on the regular fold carrier can be regarded as a splicing grid, called a "fold splicing grid", and multiple fold unit surfaces can also be regarded as a splicing grid, depending on the requirements of the final visual effect.

7. The method for performing visual design on a regularly folded carrier according to claim 1, characterized in that: Rule 4 in A4 includes: Rotational symmetry refers to repeated rotation around a certain point. This fixed point can be inside or outside the element, and can be symmetrical multiple times. Translational symmetry refers to the result of a figure (which can be an element, a pattern, or a derived pattern) moving in a specific direction and a specific distance, in which the element itself can rotate and the translation distance can be changed; Mirror symmetry refers to a figure (which can be an element, a pattern, or a derived pattern) where one half of the figure is mirrored and repeated with the other half, and the element itself can be rotated and the distance from the axis of symmetry can be changed; Sliding mirror symmetry refers to a combination of two symmetries, first translational symmetry and then mirror symmetry along that direction, in which the elements themselves can rotate and the spacing ratio between the two symmetrical behaviors can be changed.

8. The method for performing visual design on a regularly folded carrier according to claim 1, characterized in that: Rule 5 in A4 includes: Linear symmetry refers to the way symmetry is carried out along a straight line; Planar symmetry refers to the symmetry on the plane along two directions, which ultimately allows the pattern to cover the entire surface. The symmetry rule involves the size of the splicing grid, so the size and shape of the splicing grid (i.e. the size and shape of the crease unit of the regular fold carrier) can be changed, and the two translation directions of the plane can be changed; Seamless repetition refers to repetitive patterns that appear to have no specific beginning and end. Seamless repetition specifically refers to the activity of translating half of the graphic in the horizontal direction to the other side, and then moving the vertical half to the other side, and then performing the activity of plane symmetry to generate the pattern.

9. The method for performing visual design on a regularly folded carrier according to claim 1, characterized in that: The visual translation path of organic geometric morphological language on the regular folding carrier is: first, deconstruct the organic morphological language into organic geometric elements; then, the organic geometric elements generate organic geometric patterns; then, the organic geometric patterns generate organic geometric repeating patterns; finally, translate it into the folding splicing grid according to the arrangement rules of the folding units.

10. The method for performing visual design on a regularly folded carrier according to claim 1, characterized in that: The visual translation of inorganic geometric morphological language on regular folding carriers is divided into two parts. The first part is the visual translation rules of inorganic point, line and surface geometry on regular folding carriers; the second part is the visual translation path of inorganic geometric figures on the third type of regular folding carrier represented by Miura fold.

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