A method for making a 3D concave sculpture based on inverse perspective

Abstract

The application discloses a kind of based on inverse perspective's 3D inner recess sculpture manufacturing method, comprising: the region of sculpture protruding performance part is recessed design, the rest area is designed with convex, and the sculpture after design is obtained;According to inverse perspective technology and space perspective technology, the sculpture after design is modeled, and 3D inner recess model is obtained;3D inner recess model is constructed to space rendering;After slice processing, the 3D inner recess model after space rendering is printed;The 3D inner recess sculpture printed is light and shadow rendering.The application speeds up the manufacturing speed of inner recess sculpture, and sculpture shows deep spatial sense.

Description

Technical Field

[0001] This invention relates to the field of sculpture production technology, and in particular to a method for producing a 3D concave sculpture based on reverse perspective. Background Technology

[0002] 3D printing is a rapid manufacturing technology that can create physical objects from 3D digital models. Its basic working principle involves slicing the digital model into thin layers and building up material between the layers through a series of steps. 3D printing typically uses modeling software to create a digital model, which is then uploaded to a printer to manufacture the object. Renowned artist Olivier van Herpt has used 3D printing to create a series of concave ceramic sculptures. He uses a homemade 3D printer and self-developed software to realize these sculptures.

[0003] Reverse perspective is an artistic technique that utilizes principles of visual illusion and psychological effects to create an effect opposite to traditional perspective. Its core principle is to represent the size, shape, and position of objects in reverse to traditional perspective, creating a spatial illusion for the viewer—that objects appear distorted or disordered in space—while maintaining realism and lifelikeness. The concave sculpture "Leonardo da Vinci," created by Spanish contemporary sculptor Gabriele Zubilac in 1999 using reverse perspective, fully demonstrates the artistic meaning of this work.

[0004] In concave sculpture, reverse perspective is achieved through the shape and structure of the sculpture, aiming to create an illusory visual effect. Spatial perspective is a technique used to represent the depth and shape of three-dimensional space, commonly used in painting, architecture, and design. It creates a sense of depth and three-dimensionality through principles of perspective, linear perspective, and vanishing points. In the principles of spatial perspective, when a viewer observes an object, light rays emit from various points on the object and form an image on the retina through the naked eye. Under the principles of spatial perspective, the image seen by the naked eye is the result of the combined effects of the relative position, direction, and distance between the light rays emitted from various points on the object and the eye.

[0005] The above technologies have been widely used in the fields of architecture and art, and have had a profound impact and meaning. However, in the current trend of fast-paced art, traditional art forms and customs are not easily disseminated. Therefore, combining the above technologies with the design and creation of shadows, highlights, and textures in artworks can help viewers deeply appreciate the artistic conception conveyed by the artworks and enhance their viewing experience. Summary of the Invention

[0006] To address the issues of slow manufacturing speed and lack of spatial expression in conventional sculptures, a method for creating 3D concave sculptures based on reverse perspective is proposed. This method combines technology with traditional culture and art, accelerates the manufacturing speed of concave sculptures, and enables the sculptures to express a profound sense of space.

[0007] The technical solution of the present invention is as follows:

[0008] A method for creating a 3D concave sculpture based on reverse perspective includes the following steps:

[0009] The prominent parts of the sculpture are designed with an inward concave shape, while the remaining areas are designed with an outward convex shape, resulting in the designed sculpture.

[0010] The designed sculpture is modeled using reverse perspective and spatial perspective techniques to obtain a 3D concave model.

[0011] Perform spatial rendering on the constructed 3D concave model:

[0012] The 3D concave model rendered in space is sliced ​​and then printed.

[0013] The printed 3D concave sculpture is then rendered with light and shadow.

[0014] Preferably, the reverse perspective technology and spatial perspective technology are as follows: the reverse perspective technology converts the model's perspective into a reverse perspective, calculates the position and coordinates of points, and obtains a concave shape or form; the spatial perspective technology calculates the model's proportions and adjusts the perspective effect.

[0015] The projection of the graphic in reverse perspective is calculated using the perspective projection formula, the angle of light reflected on the concave surface is calculated using the light reflection angle formula, and the texture mapping is calculated using the texture mapping formula to enhance the reverse perspective effect.

[0016] The formula for perspective projection is expressed as:

[0017]

[0018]

[0019] Where P = (x, y, z) are the coordinates of the point on the original sculpture, p = (x′, y′) are the coordinates of the point after inverse perspective projection, and d is the distance from the perspective center to the viewer's naked eye;

[0020] The formula for the angle of light reflection is expressed as:

[0021] θi=θr

[0022] Where θi is the angle of incidence of the ray, measured by the angle between the ray and the normal; and θr is the angle of reflection of the ray, measured by the angle between the ray and the normal.

[0023] The texture mapping formula is expressed as:

[0024]

[0025] Where U is the x-coordinate of the texture, V is the y-coordinate of the texture, and N is the normal vector obtained by sampling the texture.

[0026] Furthermore, the specific steps for modeling the designed sculpture are as follows:

[0027] The two-dimensional coordinates in the designed sculpture are converted into three-dimensional coordinates using reverse perspective technology. Based on these coordinates, the overall shape of the sculpture model is established using basic geometric shapes. The three-dimensional model is projected onto a two-dimensional screen using a spatial perspective matrix to simulate the human eye's viewing perspective. The model is then refined and adjusted using the principles of light reflection and texture mapping.

[0028] Furthermore, the spatial rendering uses the Glaude shading method to texture the concave sculpture, rendering the 3D concave model by piecing together multiple triangles to form a surface mesh; the Glaude shading method is as follows:

[0029] Interpolation is used to calculate the normal vector inside a triangle. Each triangle stores three normal vectors, representing the normal vectors of points A, B, and C respectively.

[0030] Calculate the illumination intensities ityA, ityB, and ityC of the three vertices A, B, and C; calculate the centroid coordinates to obtain any point P = (1-uv)A + uB + vC.

[0031] Among them u+v<1,u>0,v>0;

[0032] Then replace A, B, and C with ityA, ityB, and ityC to get ityP = (1-uv)ityA + u·ityB + v·ityC; thus completing the lighting and shadow interpolation for the concave sculpture.

[0033] Preferably, the slicing process includes:

[0034] Import the 3D concave model, preprocess the 3D concave model, configure printing parameters, design the support structure, generate slices, select printing materials, import and print the slices, and refine the sculpting details.

[0035] Furthermore, the importing of the 3D concave model specifically involves: opening the slicing software and importing the 3D model created using a mesh into the software;

[0036] The preprocessing of the 3D concave model specifically involves: after importing the model, calibrating the dimensions, fixing mesh errors, eliminating overlapping surfaces, and filling holes;

[0037] The specific steps for configuring printing parameters are: setting printing parameters according to the printer model and material type;

[0038] The printing parameters include printer temperature, fill rate, printing speed, layer height, and material color.

[0039] Furthermore, the specific design support structure is as follows:

[0040] Based on the geometry and printing direction of the object being printed, a corresponding support structure is generated to ensure the stability and accuracy of the printed object.

[0041] The supporting structure is designed manually or automatically generated by slicing software.

[0042] Furthermore, the specific method for generating slices is as follows:

[0043] The 3D model is cut into a series of thin layers, and G-code is generated for each layer;

[0044] The G-code includes information on the path, layer height, temperature, speed, and material usage of the printed object; the preview function allows you to view the slicing effect of each layer.

[0045] Save the sliced ​​G-code file and import it into the 3D printer.

[0046] Furthermore, the importing and printing of the slices specifically involves:

[0047] Import the sliced ​​concave sculpture model into the 3D printer and print it according to the G-code file, the configured printing parameters, and the selected printing material;

[0048] The detailed processing of the sculpture is specifically as follows:

[0049] After printing the concave sculpture, remove the supporting structure, sand it, and paint it.

[0050] Preferably, the lighting and shadow rendering specifically includes:

[0051] Using floodlights or LED light strips, the lighting angle and intensity are designed based on the principle of reverse perspective, so that the light shines on the area below or around the sculpture, creating a contrast between light and shadow.

[0052] The beneficial effects of this invention are:

[0053] 1. 3D printing technology can significantly shorten the production cycle, thereby improving production efficiency; and it can achieve high-precision manufacturing, creating complex shapes and structures.

[0054] 2. By using reverse perspective and spatial perspective, concave sculptures appear to extend backwards as if they are constantly extending, creating a sense of visual distortion and giving the sculpture a profound sense of space.

[0055] 3. By using light and shadow to make the sculpture stand out and attract attention, the sculpture can be made more eye-catching and can also make viewers think about and feel about it. Attached Figure Description

[0056] Figure 1 A flowchart illustrating a method for creating a 3D concave sculpture based on reverse perspective, provided as an example.

[0057] Figure 2 A top view from a reverse perspective provided for an embodiment.

[0058] Figure 3 A front view from a reverse perspective provided for an embodiment.

[0059] Figure 4 A schematic diagram of the internal normal vectors of a triangle provided for an embodiment.

[0060] Figure 5 A schematic diagram of an existing sculpture sample provided for an embodiment. Detailed Implementation

[0061] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0062] Example 1

[0063] In this embodiment, as Figure 1 As shown, a method for creating a 3D concave sculpture based on reverse perspective includes the following steps:

[0064] The prominent parts of the sculpture are designed with an inward concave shape, while the remaining areas are designed with an outward convex shape, resulting in the designed sculpture.

[0065] The designed sculpture is modeled using reverse perspective and spatial perspective techniques to obtain a 3D concave model.

[0066] Perform spatial rendering on the constructed 3D concave model:

[0067] The 3D concave model rendered in space is sliced ​​and then printed.

[0068] The printed 3D concave sculpture is then rendered with light and shadow.

[0069] More specifically, such as Figure 2 , Figure 3 As shown, the reverse perspective technique and spatial perspective technique are specifically as follows: the reverse perspective technique converts the model's perspective into a reverse perspective, calculates the position and coordinates of points, and obtains the concave shape or form; the spatial perspective technique calculates the model's proportions and adjusts the perspective effect.

[0070] The projection of the graphic in reverse perspective is calculated using the perspective projection formula, the angle of light reflected on the concave surface is calculated using the light reflection angle formula, and the texture mapping is calculated using the texture mapping formula to enhance the reverse perspective effect.

[0071] The formula for perspective projection is expressed as:

[0072]

[0073]

[0074] Where P = (x, y, z) are the coordinates of the point on the original sculpture, p = (x′, y′) are the coordinates of the point after inverse perspective projection, and d is the distance from the perspective center to the viewer's naked eye;

[0075] The formula for the angle of light reflection is expressed as:

[0076] θi=θr

[0077] Where θi is the angle of incidence of the ray, measured by the angle between the ray and the normal; and θr is the angle of reflection of the ray, measured by the angle between the ray and the normal. In the specific creation of a concave sculpture, factors such as the concave shape, curvature, material properties, surface roughness, and light characteristics of the envisioned concave image must be considered to calculate the precise reflection angle based on the specific shape.

[0078] The texture mapping formula is expressed as:

[0079]

[0080] Where U is the x-coordinate of the texture, V is the y-coordinate of the texture, and N is the normal vector obtained by sampling the texture.

[0081] In this embodiment, modeling the designed sculpture specifically involves:

[0082] The two-dimensional coordinates of key points in the designed sculpture are converted into three-dimensional coordinates using reverse perspective technology. Based on these coordinates, the overall shape of the sculpture model is established using basic geometric shapes. The three-dimensional model is projected onto a two-dimensional screen using the spatial perspective matrix in the modeling software, thereby simulating the human eye's viewing perspective. The preliminary model is refined and adjusted using the principles of light reflection and texture mapping.

[0083] In this embodiment, the spatial rendering uses the Glaude shading method to design the texture of the concave sculpture. The 3D concave model is rendered by stitching together multiple triangles to form a surface mesh. The Glaude shading method is as follows:

[0084] like Figure 4 As shown, interpolation is used to calculate the normal vector inside a triangular face. Each triangle stores three normal vectors, representing the normal vectors of points A, B, and C respectively;

[0085] Calculate the illumination intensities ityA, ityB, and ityC of the three vertices A, B, and C; calculate the centroid coordinates to obtain any point P = (1-uv)A + uB + vC.

[0086] Among them u+v<1,u>0,v>0;

[0087] Then replace A, B, and C with ityA, ityB, and ityC to get ityP = (1-uv)ityA + u·ityB + v·ityC; thus completing the lighting and shadow interpolation for the concave sculpture.

[0088] Preferably, the slicing process includes:

[0089] Import the 3D concave model, preprocess the 3D concave model, configure printing parameters, design the support structure, generate slices, select printing materials, import and print the slices, and refine the sculpting details.

[0090] More specifically, importing the 3D concave model involves: opening the slicing software and importing the 3D model created using a mesh into the software;

[0091] The preprocessing of the 3D concave model specifically involves: after importing the model, calibrating the dimensions, fixing mesh errors, eliminating overlapping surfaces, and filling holes;

[0092] The specific steps for configuring printing parameters are: setting printing parameters according to the printer model and material type;

[0093] The printing parameters include printer temperature, fill rate, printing speed, layer height, and material color.

[0094] More specifically, the design support structure is as follows:

[0095] Based on the geometry and printing direction of the object being printed, a corresponding support structure is generated to ensure the stability and accuracy of the printed object.

[0096] The supporting structure is designed manually or automatically generated by slicing software.

[0097] More specifically, the generated slices are as follows:

[0098] The 3D model is cut into a series of thin layers, and G-code is generated for each layer;

[0099] The G-code includes information on the path, layer height, temperature, speed, and material usage of the printed object; the preview function allows you to view the slicing effect of each layer.

[0100] Save the sliced ​​G-code file and import it into the 3D printer.

[0101] More specifically, the importing and printing of slices refers to:

[0102] Import the sliced ​​concave sculpture model into the 3D printer and print it according to the G-code file, the configured printing parameters, and the selected printing material;

[0103] The detailed processing of the sculpture is specifically as follows:

[0104] After printing the concave sculpture, remove the supporting structure, sand it, and paint it.

[0105] Preferably, the lighting and shadow rendering specifically includes:

[0106] Using floodlights or LED light strips, the lighting angle and intensity are designed based on the principle of reverse perspective, so that the light shines on the area below or around the sculpture, creating a contrast between light and shadow.

[0107] Example 2

[0108] In this embodiment, the creation of the sculpture is divided into the following stages:

[0109] 1. Sculpture design and modeling stage;

[0110] The design of the concave sculpture provided in this technical solution differs from that of a fully concave sculpture. This embodiment uses a concave design for specific areas of the sculpture (e.g., the face of a human figure) to better highlight the facial features, while other parts (e.g., headdress, clothing) can use a conventional convex design to enhance the realism of the sculpture. The modeling stage employs inverse perspective technology, converting the model's viewpoint into an inverse perspective viewpoint to calculate the position and coordinates of points, thereby deriving the desired concave shape or form. Combining the principles of spatial perspective, the model's proportions are calculated and the perspective effect is adjusted.

[0111] 2. Sculpture production stage;

[0112] Import the model into 3D printing slicing software, select the appropriate material for the target printing object, and use a CNC engraving machine to cut and carve; carve out a concave shape, apply psychological principles to adjust the perspective effect, and put yourself in the viewer's perspective to feel the light and shadow and visual center of gravity, so as to ensure that the three-dimensionality and realism of the sculpture can be felt from any angle.

[0113] 3. Spatial rendering stage;

[0114] Place the concave sculpture in a suitable environment, such as an art gallery or temple; design appropriate lighting to illuminate the area below or around the sculpture, creating a contrast between light and shadow to enhance its three-dimensionality; use floodlights or LED light strips, and design the lighting angle and intensity based on the principle of reverse perspective.

[0115] Example 3

[0116] Based on Embodiments 1 and 2, in this embodiment, during the sculpture design stage, such as Figure 5 As shown, the base is a trapezoidal cone, with the top rectangle having L = 7.5cm and W = 4cm, the bottom rectangle having L = 12cm and W = 9cm, and the trapezoidal cone having H = 19cm; it is sculpted based on Michelangelo's work "David" and scaled down proportionally.

[0117] Regarding the selection of printing materials:

[0118] For works requiring high-quality texture and fine surface detail, resin 3D printing materials, such as photosensitive resin (SLA), can be selected. SLA offers excellent precision and surface texture, enabling the printing of highly realistic details and textures. For works requiring good strength and hardness, heat-resistant plastics, such as ABS and PETG, can be chosen, as they possess good mechanical properties and durability. In the case of the concave sculpture in this technical solution, different materials can be combined. For example, resin materials can be used to print highly realistic surface details, while heat-resistant plastics are used as the supporting structure to enhance the strength and durability of the artwork.

[0119] Furthermore, reverse perspective techniques also need to consider some psychological principles of human visual perception, such as the light and shadow effect. When the naked eye observes an object, light shines on its surface, and some light is reflected back into the eye, forming the image seen by the viewer. When light encounters raised parts of an object's surface, highlights are created, while shadows are created in recessed areas. This distribution of shadows and highlights plays a crucial role in the viewer's perception of an object's shape, surface contours, and three-dimensionality. This principle helps viewers better understand the human visual system's processing of light and the mechanisms of visual perception. Additionally, the principle of visual center of gravity posits that when observing an object, the viewer naturally focuses their visual attention on the object's center of gravity. When the human brain processes visual information, it focuses on the center of gravity of an object to better understand and process information such as its shape, size, orientation, and position. By flexibly applying these principles, the viewer's visual perception can be more precisely controlled, thereby creating a more realistic convex effect.

[0120] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for fabricating a 3D concave sculpture based on reverse perspective, characterized in that, Includes the following steps: The prominent parts of the sculpture are designed with an inward concave shape, while the remaining areas are designed with an outward convex shape, resulting in the designed sculpture. The designed sculpture is modeled using reverse perspective and spatial perspective techniques to obtain a 3D concave model. Specifically, the reverse perspective technique converts the model's viewpoint into a reverse perspective viewpoint, calculates the position and coordinates of points, and obtains the concave shape or form; the spatial perspective technique calculates the model's proportions and adjusts the perspective effect. The projection of a graphic in reverse perspective is calculated using the perspective projection formula. The angle of light reflection on a concave surface is calculated using the light reflection angle formula. Texture mapping is used to calculate texture maps and enhance the reverse perspective effect. The perspective projection formula is expressed as: in These are the coordinates of points on the original sculpture. These are the coordinates of the point after inverse perspective projection. It is the distance from the perspective center to the viewer's naked eye; The formula for the angle of light reflection is expressed as: in, It is the angle of incidence of a ray, measured by the angle between the ray and the normal. It is the angle of reflection of a ray of light, measured by the angle between the ray and the normal. The texture mapping formula is expressed as: Where U is the x-coordinate of the texture, V is the y-coordinate of the texture, and N is the normal vector obtained by sampling the texture. Perform spatial rendering on the constructed 3D concave model: The 3D concave model rendered in space is sliced ​​and then printed. The printed 3D concave sculpture is then rendered with light and shadow.

2. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 1, characterized in that, The specific steps for modeling the designed sculpture are as follows: The two-dimensional coordinates in the designed sculpture are converted into three-dimensional coordinates using reverse perspective technology. Based on these coordinates, the overall shape of the sculpture model is established using basic geometric shapes. A spatial perspective matrix is ​​used to project a 3D model onto a 2D screen, thereby simulating the human eye's perspective. The model is refined and adjusted using the principles of light reflection and texture mapping.

3. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 2, characterized in that, The spatial rendering described above uses the Glaude shading method to design the texture of the concave sculpture. It renders the 3D concave model by piecing together multiple triangles to form a surface mesh. The Glaude shading method is detailed below: Interpolation calculates the normal vector inside a triangle facet. Each triangle facet stores three normal vectors, representing... The normal vector of each point; work out The light intensity of each of the three vertices ; Calculate the centroid coordinates to obtain any point. ; in ; Reuse Alternative ,get Complete the interpolation of lighting and shadows for the concave sculpture.

4. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 1, characterized in that, The slicing process includes the following steps: Import the 3D concave model, preprocess the 3D concave model, configure printing parameters, design the support structure, generate slices, select printing materials, import and print the slices, and refine the sculpting details.

5. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 4, characterized in that, The specific steps for importing the 3D concave model are as follows: Open the slicing software and import the 3D model created using a mesh into the software; The preprocessing of the 3D concave model specifically involves: after importing the model, calibrating the dimensions, fixing mesh errors, eliminating overlapping surfaces, and filling holes; The specific steps for configuring printing parameters are: setting printing parameters according to the printer model and material type; The printing parameters include printer temperature, fill rate, printing speed, layer height, and material color.

6. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 5, characterized in that, The specific design support structure is as follows: Based on the geometry and printing direction of the object being printed, a corresponding support structure is generated to ensure the stability and accuracy of the printed object. The supporting structure is designed manually or automatically generated by slicing software.

7. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 6, characterized in that, The specific process of generating slices is as follows: The 3D model is cut into a series of thin layers, and G-code is generated for each layer; The G-code includes information on the path, layer height, temperature, speed, and material usage of the printed object; the preview function allows you to view the slicing effect of each layer. Save the sliced ​​G-code file and import it into the 3D printer.

8. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 7, characterized in that, The specific steps for importing and printing slices are as follows: Import the sliced ​​concave sculpture model into the 3D printer and print it according to the G-code file, the configured printing parameters, and the selected printing material; The detailed processing of the sculpture is specifically as follows: After printing the concave sculpture, remove the supporting structure, sand it, and paint it.

9. The method for fabricating a 3D concave sculpture based on reverse perspective as described in claim 1, characterized in that, The aforementioned lighting and shadow rendering specifically refers to: Using floodlights or LED light strips, the lighting angle and intensity are designed based on the principle of reverse perspective, so that the light shines on the area below or around the sculpture, creating a contrast between light and shadow.

Images