KR102656989B1 - Recording of holographic data on reflective surfaces - Google Patents

Abstract

Illumination information including reflectance data of at least a plurality of regions of the object surface is generated and printed as a series of relightable holograms. Each of the printed holograms contains reflectance data of a corresponding area of the object. A model of the object is created such that the model also includes a plurality of parts corresponding to regions of the object surface. Each hologram in a series of holograms is attached to a portion of the model such that a particular hologram in the series encoding reflectance data for a particular region of the object is attached to a corresponding portion of the model. In one embodiment, the model of the object is created from metal. The holographic series is engraved directly on the metal model, such that specific holograms of the series encoding reflectance data of specific regions of the object are engraved on corresponding parts of the metal model.

Description

Recording of holographic data on reflective surfaces

Cross-reference to related applications

This application is filed under U.S. Application No. ______ (Attorney Docket No. 139703-011700), filed on the same date as the present application, and titled "APPLYING HOLOGRAPHIC EFFECTS TO PRINTS", and filed on the same date as the present application, titled " RELIGHTABLE HOLOGRAMS", U.S. Application Ser. No. ______ (Attorney Docket No. 139701-011600). The entire disclosures of these applications are incorporated herein by reference.

This disclosure relates to applying holographic effects to two-dimensional and three-dimensional printed materials.

Conventional two-dimensional printers used by computers print data row by row on paper. When this printing method was extended to print multiple layers on top of each other, it enabled the printing of three-dimensional models. Three-dimensional (3D) printing is the process by which a computer model is converted into a physical object. Unlike traditional processes that create models through subtractive processes that primarily chisel away material, 3D printing is a process in which a physical object is built up from multiple layers of material. build up) It is an additive process. The result is less material wastage, in addition to eliminating the costly retooling required to produce different models under conventional subtractive processes. Additive processes are performed by a 3D printer under the control of a computing device containing modules that perform the printing procedure. This makes it possible to quickly and economically acquire models before producing actual objects in the factory. As the technology matures, 3D printers go beyond printing simple models, as well as models of sophisticated mechanical parts, pharmaceutical tablets or even dental crowns used by dentists. It is increasingly being used to print products.

This disclosure relates to systems and methods for creating models of objects that include not only depth information but also illumination information of the object surface. In some embodiments, a method for creating a model of an object is disclosed. The method may be executed by a device that includes one or more processors. The method includes, in a device comprising a processor, a series of printed holograms, each printed hologram comprising at least one holographic pixel encoding illumination information of one of a plurality of regions of the object surface. Contains holographic pixels) - includes the step of receiving. The object may be a real object or a virtual object. The device prints a physical model of the object, where the surface of the physical model includes a plurality of portions, each corresponding to a respective region of the plurality of regions of the object. In some embodiments, the model of the object is a two-dimensional model. In some embodiments, the model of the object is a three-dimensional model. In some embodiments, printing a physical model of the object further includes receiving, by the device, a three-dimensional image of the object and printing a three-dimensional model of the object from the three-dimensional image.

In some embodiments, a series of printed holograms are attached to the physical model such that each printed hologram attaches to that portion of the physical model corresponding to a respective region of the object surface, and the illumination information of the object surface is attached to the attached printed hologram. It is encoded in a hologram. In some embodiments, a holographic sheet comprising at least a subset of the printed hologram series is wrapped on the model. In some embodiments, each of the plurality of printed holograms is affixed to respective portions of the model surface during printing. In some embodiments, the printed hologram series are relightable holograms. In some embodiments, the area of each portion of the printed hologram ranges from 0.000001 square millimeters to 0.25 square millimeters.

In some embodiments, a holographic sheet comprising a series of printed holograms is disclosed. The sheet is divided into a plurality of printed holograms, where each printed hologram includes at least one hologram of the series. Each of the plurality of printed holograms is attached to that portion of the physical model corresponding to a respective region of the object surface, and illumination of the object surface is encoded in the attached printed hologram.

In some embodiments, an apparatus is disclosed that includes a processor and a storage medium tangibly storing program logic for execution by the processor to create a model of an object. The program logic includes receiving logic, executed by a processor, to receive at the device a series of printed holograms, each printed hologram encoding illumination information of one of a plurality of regions of the object surface. Contains at least one holographic pixel. In some embodiments, programming logic includes printing logic, executed by a processor, to print a physical model of an object, wherein a surface of the physical model includes a plurality of portions, Each of the plurality of parts corresponds to a respective object area of the multiple object areas. The programming logic further includes attaching logic, executed by the processor, to attach a series of printed holograms to the physical model, each printed hologram being that portion of the physical model corresponding to a respective region of the object surface. It is attached to the object surface and the illumination information of the object surface is encoded in the attached printed hologram. In some embodiments, the attach logic includes logic, executed by a processor, to wrap a holographic sheet containing at least two printed holograms of a printed hologram series onto the model.

In some embodiments, the processor further executes dividing logic to divide a holographic sheet comprising a series of printed holograms into a plurality of printed holograms, where each printed hologram is at least one hologram of the series. Includes. The processor also executes applying logic to apply each of the plurality of printed holograms to that portion of the physical model corresponding to a respective region of the object surface, the illumination of the object surface being encoded in the attached printed hologram. . In some embodiments, the processor executes image receiving logic to receive a three-dimensional image of the object, and logic to print a three-dimensional model of the object from the three-dimensional image is executed by the processor.

In one embodiment, a non-transitory computer-readable medium comprising processor-executable instructions is disclosed. The instructions include instructions for receiving a series of printed holograms, each printed hologram comprising at least one holographic pixel encoding illumination information of one of a plurality of regions of the object surface. The instructions further include instructions for printing a physical model of the object - the surface of the physical model includes a plurality of portions, each corresponding to a respective region of the plurality of regions - and instructions for attaching a series of print holograms to the physical model. Includes. The instructions attach each printed hologram to that portion of the physical model corresponding to a respective region of the object surface, and the illumination information of the object surface is encoded in the attached printed hologram.

In some embodiments, the instructions for attaching a printed holographic series to a model further include processor-executable instructions for wrapping a holographic sheet comprising at least a subset of the printed holographic series onto the model. In some embodiments, the instructions for attaching a printed hologram series to a model include processor-executable instructions for splitting a holographic sheet comprising a printed hologram series into a plurality of printed holograms, each printed hologram being at least one of the series. further comprising a hologram - and instructions for applying each of the plurality of printed holograms to that portion of the physical model corresponding to a respective region of the object surface - wherein illumination of the object surface is encoded in the attached printed hologram. Includes.

In some embodiments, a model of an object is disclosed. The model includes a plurality of parts, where each part of the model corresponds to a respective region of the plurality of regions of the object. The model further includes a plurality of holographic prints attached to the plurality of model parts, where each of the holographic prints includes illumination information of a respective region of the plurality of regions of the object. At least one of the plurality of holographic prints is attached to one of the plurality of model parts corresponding to each of the plurality of areas of the object, and lighting information of the object is included in the at least one holographic print. In some embodiments, the lighting information included in the at least one holographic print is a bi-directional reflectance distribution function (BRDF) of a respective object region of the plurality of object regions. The area of each holographic print of the holographic prints ranges from 0.000001 square millimeters to 0.25 square millimeters. The model of the object may be a two-dimensional model or a three-dimensional model. In some embodiments, the properties of light reflected from the surface of a model are similar to the properties of light reflected from the surface of an object.

In one embodiment, a method for creating a 3D model of an object is disclosed. The method includes obtaining a metal model of the object. An object includes a plurality of regions. The model is made of metal and includes a plurality of parts such that each part of the model corresponds to a respective region of the object's regions. In one embodiment, the first processor receives illumination information of an object, where the illumination information includes reflectance data of object regions. The illumination information of the object is printed by the first processor as a series of holograms, each hologram of the series comprising at least one holographic pixel encoding reflectance data of a respective object region. Each hologram is printed on a portion of the model corresponding to its respective object region. In some embodiments, the model of the object is printed by a three-dimensional printer capable of printing metal models with metals such as gold or silver.

In one embodiment, a method for generating a metal model including reflectance data of an object is disclosed. The method includes receiving, by a device comprising a processor, illumination information of an object comprising a plurality of regions, wherein the illumination information includes reflectance data of the portions. A model of the object is printed by a device where the model is made of metal and the surface of the model includes a plurality of parts, each part of the model surface corresponding to a respective region of the areas of the object. The illumination information of the object is transferred by the device to the model as a series of holograms, each hologram of the series comprising at least one holographic pixel encoding reflectance data of a respective region of the regions, each hologram They are printed on a part of the model corresponding to each area.

In some embodiments, the device receives a three-dimensional image of an object and prints a three-dimensional model of the object from the three-dimensional image. Similarly, when the device receives a two-dimensional image of an object, a two-dimensional model of the object is printed from the two-dimensional image.

In one embodiment, a method for generating a hologram of an object including a plurality of regions is disclosed. The method includes acquiring, from a single fixed viewpoint, a plurality of reflectance data sets of the object surface for each of the plurality of light sources. The method further includes illuminating the surface of the object with one light source among a plurality of light sources located at a specific position with respect to the object and recording respective reflectance data of the surface of the object by the light source at the specific position. Includes. The light source is moved to a new location adjacent to the specific location, for example, a distance of 0.5 mm to 1.0 mm, and the illuminating, recording, and moving steps are repeated a predetermined number of times for each of the plurality of light sources. do.

Aggregated reflectance data for each area of the object surface is generated by the computing device by overlaying reflectance data obtained from a plurality of reflectance data sets for each area of the object surface. A light sensitive medium is illuminated using aggregated reflectance data of at least one of a plurality of regions of the object surface and a hologram of the at least one region is fabricated from the light sensitive medium. In some embodiments, the hologram is included on a substrate having an area between 0.000001 square millimeters and 0.25 square millimeters.

In some embodiments, the object is a real-world object and a light stage apparatus is used to acquire multiple sets of reflectance data. In some embodiments, the object is a virtual object and a computing device is used to acquire multiple sets of reflectance data.

In one embodiment, a substrate comprising a diffraction structure that is a hologram is disclosed. A hologram includes a plurality of images of a virtual or real object overlaid on one another, each image of the plurality of images encoding reflectance data of a region of the object surface recorded from a single viewpoint under respective lighting conditions. In some embodiments, the substrate spans between 0.000001 square millimeters and 0.25 square millimeters. In some embodiments, the respective lighting conditions include at least a light source located at a respective location relative to the object and viewpoint. A reflected ray is generated by the hologram from light incident on the hologram from the light source, and the reflected ray generated by the hologram has the same characteristics as the reflected ray generated by the area of the object surface when illuminated by the light source. .

These and other embodiments will be apparent to those skilled in the art upon reference to the following detailed description and accompanying drawings.

In the drawings that are not to scale, like reference numbers identify like elements across the several drawings.
1 is a flow chart illustrating a method of creating a model of an object according to some embodiments.
2 is a flow chart detailing a method for creating a model of an object according to some embodiments.
3 is a flow chart detailing a method for creating a model of an object according to some embodiments.
4 is a flow chart detailing a method for generating lighting information for a reilluminable hologram that can be used in a 3D printed model of an object according to some embodiments.
FIG. 5 is a diagram detailing a method for generating a reilluminable hologram according to some embodiments.
6 is a diagram illustrating lighting information including a series of images acquired for a person according to some embodiments.
Figure 7 is a diagram illustrating a model of an object created according to the embodiments described above.
8 is a diagram illustrating the internal architecture of a computing device according to some embodiments.
9 is a diagram illustrating a 3D printer device for printing 3D models according to some embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS The subject matter will now be more fully described below with reference to the accompanying drawings, which form a part hereof and show, by way of example, certain exemplary embodiments. However, the subject matter may be embodied in a variety of different forms, and thus the stated or claimed subject matter is intended to be construed as not limited to any of the exemplary embodiments set forth herein; The exemplary embodiments are provided by way of example only. Likewise, a reasonably broad scope of the claimed or stated subject matter is intended. Among other things, for example, the subject matter may be implemented as methods, devices, components, or systems. Accordingly, embodiments may take the form of, for example, hardware, software, firmware, or any combination thereof. Accordingly, the following detailed description is not intended to be interpreted in a limiting sense.

In the accompanying drawings, some features may be exaggerated to illustrate details of certain components (and any sizes, materials and similar details shown in the drawings are intended to be illustrative and not restrictive). Accordingly, the specific structural and functional details disclosed herein should not be construed as limiting, but only as a representative basis for teaching those skilled in the art to make various uses of the disclosed embodiments.

The present disclosure is described below with reference to block diagrams and operational examples of methods and devices for selecting and presenting media related to a particular subject matter. It will be appreciated that each block in the block diagrams or operational examples, and combinations of blocks in the block diagrams or operational examples, may be implemented by analog or digital hardware and computer program instructions. These computer program instructions are such that the instructions executed through a processor of a computer or other programmable data processing device implement the functions/operations specified in the block diagrams or operation block or blocks, such as a general purpose computer, special purpose computer, ASIC, or ASIC. Or it may be provided to a processor of another programmable data processing device.

In some alternative implementations, the functions/operations shown in the blocks may be performed other than the order shown in the operation examples. For example, depending on the functions/operations involved, two blocks shown in succession may in fact be executed substantially simultaneously, or the blocks may sometimes be executed in the opposite order. Additionally, embodiments of the methods described and presented as flowcharts in this disclosure are provided as examples to provide a more complete understanding of the technology. The disclosed methods are not limited to the operations and logical flow presented herein. Alternative embodiments are contemplated in which the order of the various operations is changed and suboperations described as part of a larger operation are performed independently.

A computing device may transmit or receive signals, such as over a wired or wireless network, or may process or store signals, such as physical memory states, in memory and thus act as a server. Accordingly, devices capable of operating as servers include, for example, dedicated rack-mounted servers, desktop computers, laptop computers, set-top boxes, and features of two or more of the foregoing devices. It may include integrated devices having the same various features. Servers can vary greatly in configuration or capability, but generally a server may include one or more central processing units and memory. The server may also include one or more mass storage devices, one or more power supplies, one or more wired or wireless network interfaces, one or more input/output interfaces, or one or more storage devices, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. It may include more than one operating system.

Throughout the specification and claims, terms may have nuanced meanings that are implied or implied by context beyond the explicitly stated meaning. Likewise, the phrase “in one embodiment,” as used herein, does not necessarily refer to the same embodiment, and the phrase “in another embodiment,” as used herein, does not necessarily refer to a different embodiment. It does not refer to . For example, it is intended that the claimed subject matter includes combinations of exemplary embodiments, in whole or in part. Generally, terms can be understood, at least in part, from their use in context. For example, terms such as “and,” “or,” or “and/or,” as used herein, depend at least in part on the context in which such terms are used. It can contain a variety of meanings that can be relied upon. Typically, when "or" is used to associate a list, such as A, B, or C, A, B, and C - here used in the inclusive sense - as well as A, B, or C - here Used in an exclusive sense - is intended to mean. Additionally, the term “one or more”, as used herein, may be used to describe any feature, structure, or characteristic in a singular sense, or may be used in a plural sense, depending at least in part on the context. Can be used to describe combinations of features, structures, or properties. Similarly, terms such as “a,” “an,” or “the” may convey singular or plural usage, again depending at least in part on the context. It can be understood that Additionally, it may be understood that the term "based on" is not necessarily intended to convey an exclusive set of arguments, and again, depends at least in part on the context, which is not necessarily explicitly stated. can allow the presence of additional arguments.

Improvements in printing technology have transformed two-dimensional printing of data on paper into an additive process for printing three-dimensional models from image data fed to computers. Currently used three-dimensional printers build three-dimensional models by layering printing materials, for example, one micrometer at a time. Models produced by 3D printing can include robust internal structures that would not otherwise be possible with conventional molds. Models can be built through a three-dimensional printing process using different materials such as plastics, metals or resins of different colors. Despite the availability of a variety of colors and materials for use in 3D printing, current 3D printing technologies primarily produce simple reflectance surfaces that do not convey the true reflectance behavior of the actual objects being modeled. For example, it is limited to printing models with Lambertian surfaces.

Although a 3D printer may be able to model the detailed structure of the Eiffel Tower, the model does not capture the actual reflectance characteristics of the metal that makes up the tower. Another example of a complex structure with reflectance properties that is not properly captured by a 3D printer is the human (or other species) face. The face of a living entity contains a complex collection of hues and shades and reflects light in complex ways that cannot be captured by even the best high-resolution 3D printers. For example, three-dimensional printers are currently available with resolutions as fine as 16 to 30 micrometers. Therefore, when printing a face, features such as hair and pores can be printed. However, even models printed with the finest resolution 3D printers do not look lifelike, despite accurately replicating object structures. This is because the light reflectance properties of objects are determined by a complex set of factors that include not only physical properties such as the object's microscopic surface details and color, but also chemical properties of the object itself. These details of how an object interacts with light cannot be accurately captured by 3D printed models without the improvements described herein.

Technologies now exist to capture and record the detailed light reflectance properties of objects such as the face or skin of a living being. An example is a light stage, which will be described in further detail below. Similarly, techniques exist for generating reflectance properties of objects by computing devices. For example, image based relighting techniques are used to generate photorealistic images of objects under arbitrary lighting conditions. Applications of these techniques include, inter alia, inserting characters into scenes in movies.

Devices such as dome-like light stages or mobile light stages are used to capture reflectance data of an object by illuminating the object from different directions. Multiple images of an object are captured, where the object in each image is illuminated by light coming from a different direction than the other images. Thus, for each pixel the intensities of light coming from various directions can be captured, which, through the use of mathematical models, reconstructs an image of the object under any other lighting conditions not captured by a device such as an illumination stage. makes it possible to do so. This can be achieved by fitting a reflectance model to the reflectance measurements for the object surface obtained from the illumination stage. In addition, the set of reflectance measurements obtained for specific directions can be extrapolated using models such as Lambertian, Phong or Ward models to obtain intensities for angles of incidence not included in the set of measurements. ) can be.

The interaction of light with various surfaces can be described by the bidirectional reflectance distribution function (BRDF). In general, the extent to which light is reflected (or transmitted) depends on the viewer and light position relative to the surface normal and tangent. Because the BRDF describes how light is reflected, the BRDF must capture the view and light-dependent properties of reflected light. As a result, the BRDF is a function of the incoming (light) direction and the outgoing (view) direction with respect to the local orientation at the point of light interaction. However, techniques do not currently exist for imparting various light reflectance properties to 3D printed models, such as those conveyed by the BRDF of the object surface.

Embodiments disclosed herein provide a model of an object that has the light reflectance characteristics of the object, such that the model also reflects light in a similar manner to the object and thereby appears more like a real object when compared to a model printed from a conventional 3D printer. makes it possible to do so. More specifically, the embodiments described herein make it possible to record the light interaction properties of an object and apply these properties to a model of the object. This makes the model look virtually identical to the object by giving it the light reflectance properties of the object. In one embodiment, a model may be printed by a 3D printer such that depth information of the object surface is captured in data received by the 3D printer, and the 3D printer transfers the depth information of the object surface to the model it prints. In one embodiment, the captured reflectance data is transferred to the 3D printed model via relightable holographic techniques as detailed herein. A 3D printed model that includes both the depth and light interaction properties of a real object will look more realistic than a model obtained from a 3D printer.

In some embodiments, the object's reflectance data is printed as a reilluminable hologram that is attached to the 3D printed model. Holography is a technique that creates the illusion that an object exists by recording the illumination information of the object and later reproducing it when the object is not present. To create a hologram of an object, the object is illuminated with a light source, such as a coherent light source such as a laser or a spectrally filtered light source. The light reflected from the object is combined with a reference beam, which can be direct light from the light source. A pattern resulting from the interference of a reflected beam and a reference beam is captured on a recording medium such as a photograph. However, recorded patterns captured using holography contain much more information than simple focused images, such as photographs. This makes it possible to reproduce a three-dimensional image of an object, creating the illusion that the object exists.

1 is a flowchart 100 illustrating a method for creating a model of an object according to some embodiments. The method begins at step 102 where a model of the object is obtained. In some embodiments, the object may be a real-world object such as, but not limited to, a person, animal, or other real-world animate/inanimate object. In some embodiments, an object may be a virtual/imaginary object that may or may not exist in the real world, which may include (but is not limited to) living or inanimate entities. . The properties of these virtual objects, such as appearance, which may include shape, size, colors, texture, reflectance characteristics, and other visible and invisible characteristics, are of interest to the creators/designers of virtual objects. can be determined by A model of a real or virtual object may be obtained at 102 through subtractive or additive processes as described herein. The image of the object is input into the 3D printer. Again, based on whether the object is real or virtual, the image input to the 3D printer may be a photo from a camera or a processor-generated image. Models are created from images received by a 3D printer by repeatedly layering materials, such as powdered resin, in an additive process. Because the detailed structure of an object can be reproduced by a 3D printer, the depth information of the object's surface can be accurately represented by the 3D model. In one embodiment, the model includes a colored surface including one or more of red, green, blue, cyan, yellow, etc. In one embodiment, the model is made the same size as the object.

At 104, illumination information of the object is obtained. The lighting information obtained from 104 can represent not only reflection but also other complex phenomena that occur when light interacts with the surface of an object. This may include other phenomena such as light absorption and/or transmission, including but not limited to diffraction and scattering effects. In one embodiment, lighting information at 104 may be obtained from an imaging apparatus, such as an illumination stage. In one embodiment, the lighting stage includes, in addition to other components, a camera and light sources with controllable intensities. The lighting stage is configured to generate gradient illumination patterns. The light sources are configured and arranged to illuminate the surface of the object with gradient illumination patterns. Light reflected from the illuminated surface of an object is received by a camera that generates data representing the reflected light. In some embodiments, the data may include interference patterns to create holograms of the object surface. In some embodiments, data from the camera is processed by the computing system to estimate a surface normal map of the object's surface.

Specular normal map of the surface of an object by positioning polarizers on the light sources and in front of the camera to illuminate the surface of the object with polarized spherical gradient illumination patterns. normal map and diffuse normal map can be created separately. In one embodiment, data from the illumination stage can be used to estimate other properties of the object surface. For example, techniques can be used to model layered facial reflectance consisting of specular reflectance, single scattering, and shallow and deep subsurface scattering. there is. The parameters of appropriate reflectance models can be estimated using models as mentioned above for each of these layers, for example from only 20 pictures recorded by the illumination stage over a few seconds from a single viewpoint.

In one embodiment, lighting information at 104 may be obtained from a computing device. For example, object surface appearance can be modeled using bidirectional reflectance distribution functions (“BRDF”). As described herein, the BRDF of a surface can be evaluated from mathematical functions derived using analytical models. Different models can be used to determine the reflectance properties of different types of materials. In fact, libraries of measured BRDF data can also be accessed from multiple sources. In one embodiment, the light interaction properties of an object surface can be calculated mathematically on a computer using path tracing. Path tracing is a computer graphics Monte Carlo method for rendering images of three-dimensional scenes. In fact, techniques exist in computer graphics (CG) rendering that calculate even complex light interaction properties, such as diffusion and scattering, at sub millimeter resolution, such as for one pixel. Illumination information of multiple regions of the object surface may thus be obtained through one or more physical or mathematical procedures at 104.

Illumination information for a plurality of regions of the object surface is obtained at 104. In some embodiments, illumination information for regions of the object surface may be collected at 104. The area of each region can be determined based on the desired resolution of the resulting image. The greater the desired resolution, the smaller the area of each region. Accordingly, the object surface can be hypothetically divided into a plurality of regions to obtain lighting information.

The lighting information for the plurality of object areas obtained at 104 may encode multiple viewing angles or multiple lighting conditions depending on the method employed to obtain the lighting information. For example, each pixel of a digital hologram encodes multiple viewing angles for a given light source. Lighting information for this digital hologram is captured through incremental camera movements while keeping the object and light source at fixed positions.

In some embodiments, lighting information for each region of an object's surface may encode multiple lighting conditions that can be used to print a reilluminable hologram. This can be achieved by changing light sources and regional aggregation of lighting information while keeping the camera and object at fixed positions, according to embodiments as further detailed below.

At 106, illumination information of areas of the object surface acquired at 104 is printed as a hologram series. Each hologram in the series contains or encodes illumination information of one of the regions of the object surface. By way of example and not limitation, each hologram in the series may include illumination information, such as reflectance data of one of the regions of the object surface. Accordingly, the reflectance data for each area of the object surface acquired at 104 is printed as a hologram at 106. In one embodiment, reflectance data for each region of the object surface is represented by a BRDF. Accordingly, the hologram series printed at 106 encodes BRDFs of regions of the object surface. The printed hologram at 106 is configured to generate the correct wave front, thereby ensuring that the hologram encodes all of the different lighting conditions to which the object may be exposed. In one embodiment, a single sheet containing a series of holograms is printed at 106. Various known methods, such as those used by ZEBRA IMAGING, can be used to acquire a hologram series.

In some embodiments, the method moves directly to step 110 of identifying portions of the 3D printed model that correspond to regions of the object surface so that appropriate lighting information can be applied to the 3D printed model. The surface of a 3D printed model can be virtually divided into parts in a manner similar to the surface of an object. By way of example and not limitation, the number of regions of the object surface may be equal to the number of hypothetical portions of the 3D model surface. Accordingly, each hypothetical region of the object surface corresponds to a respective portion of the model surface.

The method then proceeds to step 112 of attaching the holographic sheet to the model, so step 108 can be omitted. At 112, the sheet of holograms generated at 106 is displayed in 3D, such that each of the holograms containing illumination data of one particular region of the object surface corresponding to that particular portion of the model is positioned and attached to that particular portion of the model. Attached to the printed model. For example, a sheet of holograms can be placed and shrink wrapped over a model, such that a specific hologram containing illumination data of a specific area of the object's surface is attached to a corresponding part of the model.

In some embodiments, the method moves to step 108 where the sheet containing the holographic series is cut or divided into a plurality of segments or a plurality of holographic flakes. In one embodiment, the sheet is divided such that each segment or flake contains one hologram in a series of printed holograms. As a result of this separation, a plurality of printed holograms are obtained at 108, where each printed hologram includes reflectance data of one of the regions of the object surface. Again, it can be seen that the number of printed holograms or holographic flakes generated in step 108 may be equal to the number of object surface areas or correspondingly the number of model surface portions. By way of example and not limitation, the area of the printed holograms obtained at 108 may range from 0.000001 square millimeters to 0.25 square millimeters. In one embodiment, the sheet may be split so that one sheet contains two or more holograms. Accordingly, it can be seen that the holograms generated at 108 may include one or more holograms, each encoding reflectance data of respective regions of the object surface.

In some embodiments, the method moves from step 108 to step 110 where portions of the 3D model that correspond to regions of the object surface are identified. The flakes of the holographic sheet created at 108 are attached or affixed to corresponding parts of the model at 112. Because the 3D printing process is an additive process, the 3D printer can be programmed to attach flakes of the holographic sheet to corresponding parts of the 3D model when the final layer of the model is printed. For example, a 3D printer's mechanical inkjet can be programmed to eject multiple flakes of a holographic sheet as it builds individual parts of the 3D model.

As a result of the process detailed in Figure 1, a 3D printed model is obtained that not only conveys depth information of the object surface but is also endowed with the reflectance properties of the object surface. When light is incident on these 3D printed models, the light is reflected in substantially the same way as the real object. This is because the holographic pieces on the model are encoded with the reflectance properties of the real object surface and thus mimic the reflectance properties of the object surface.

It can be seen that the procedures for wrapping or separating the holographic sheet as a whole are individually described in the flowchart 100 by way of example and not limitation. In fact, the steps do not have to be mutually exclusive when creating a 3D model and can be used together to create a single 3D model. For example, a holographic sheet containing multiple holograms may be attached or wrapped around one part of a 3D model, while segments or flakes of the holographic sheet containing individual holograms may be attached to other parts of the same 3D model. There may be attached parts.

2 is a flowchart 200 detailing a method for creating a model of an object according to some embodiments. The method begins at 202 where a model consisting of a reflective material, such as a metal, is obtained. The model may be made of metals such as gold or silver. In some embodiments, the model is the same size as the object and can be obtained from a 3D printer through additive processes or by etching or chiseling a metal block/sheet. At 204, lighting information including reflectance data of regions of the object is obtained. In one embodiment, the reflectance data acquired at 204 is similar to the reflectance data acquired at 104. In one embodiment, once the object's reflectance data is recorded at 104, this data can be reused, thereby making step 204 redundant. At 206, various portions of the model surface are identified that correspond to respective regions of the object. In one embodiment, the model surface may be the same size as the object area, such that the plurality of portions identified on the model may be the same size as the identified areas on the object surface. At 210, the obtained illumination information for each region of the object surface is encoded on a corresponding portion of the model surface.

In one embodiment, the lighting information includes reflectance data of an area for rays of light incident on the area from different directions. Accordingly, reflectance data for multiple lighting conditions are encoded on the model surface for each region. In one embodiment, the model may be printed by a 3D printer and lighting information, including reflectance data, may be etched onto the model, for example by a holographic printer.

In one embodiment, the reflectance data may include a BRDF of each area of the object surface, and the holographic printer may etch a diffraction grating on the surface of the metal model that changes the index of refraction of the model surface. When the metal model is illuminated by a light source that serves as a reference beam, the diffraction grating will operate to create a hologram that reflects light in a way that mimics light reflection by an object. This alleviates the need to print, section, and adhere holographic films to the model surface as described in Figure 1. In one embodiment, a metal model as described herein can be used to model metal objects.

It can be seen that different parts of the surface of an object may have different properties. Some areas of the object surface may be diffuse, while other parts of the object surface may be more shiny. Accordingly, Figure 3 is a flow chart 300 detailing a method for creating a model of an object according to some embodiments. The method begins at 302 where lighting information, including, for example, reflectance data of a region of an object's surface, is obtained by a computing device attached to a 3D printer. In one embodiment, reflectance data of an object is acquired using a device such as an illumination stage. In one embodiment, reflectance data is analyzed by a computing device at 304 to determine the nature of the object surface. At 306, it is determined whether the object surface has a matte finish or a more glossy finish based on the analysis at 304. For example, if the reflectance data fits a Lambertian model, it may be determined at 306 that the object surface has a matte finish; otherwise, it may be determined that the object surface has a glossy finish. If the object surface has a matte finish, as shown at 308, ink of the appropriate color may be squirted to create the layers of the 3D model. If it is determined that a portion of the object surface of the object is glossier, that particular portion of the object surface is printed or built up by ejecting ink at 310 and then at 312, for example, in the embodiments described herein. Holographic data is applied by attaching small flakes of holographic film according to the method. Accordingly, it can be seen that in accordance with the embodiments described herein, the entire model need not be covered by the holographic imprint. Rather, portions of the model surface corresponding to the more glossy surfaces of the objects may be covered with holographic imprints created according to embodiments detailed further below, while the portions of the model surface corresponding to the more diffuse object surfaces Parts of can receive a matte finish through conventional 3D printing.

In some embodiments, reilluminable holograms are used for glossier surfaces, as detailed in Figure 3. Generally, holograms encode changing viewpoints under fixed lighting conditions. For example, given a stationary object and a light source, a camera is programmed to make microscopic, incremental movements to generate data for printing a digital hologram. Therefore, if an observer changes the viewing position while viewing a printed hologram, the hologram appears to have moved relative to the observer. FIG. 4 shows a flowchart 400 detailing a method for generating lighting information for a reilluminable hologram that can be used in a 3D printed model of an object according to some embodiments. A reilluminable hologram according to some embodiments encodes multiple lighting conditions from a single viewpoint. According to some embodiments, reflectance data for a reilluminable hologram may be physically collected by moving the light source(s) around the real world object and the camera while maintaining the camera at fixed positions. Devices as known in the art for collecting reflectance data include, for example, but are not limited to, a lighting stage or portable lighting stage that can be used to perform the method as detailed in FIG. It can be included. In some embodiments, reflectance data for either a real-world object or a virtual object for a plurality of lighting conditions may be generated entirely by a computing device. In some embodiments, reflectance data may also be generated in part by programming the computing device to extrapolate data obtained for real-world objects for a subset of a plurality of lighting conditions using known mathematical models.

Collecting reflectance data for a real-world object using a physical procedure begins at 402 where the object for which illumination information is to be collected is illuminated from one or more directions by one or more light source(s). In some embodiments, the light source(s) are fixed to the dome-shaped structure of the lighting stage, and the object is positioned in the center of the dome. In other embodiments, the light sources are independently movable. At 404, area information of the object surface is obtained. For example, regions may include micro-regions on the surface of an object, where the number of pixels included in an image of the region or micro-region is estimated, for example, by a computing device. The light source(s) used to illuminate the object are programmed to move at 406 based on the area information obtained at 404. In one embodiment, the light source is programmed for minute movements in the range of 0.5 mm to 1.0 mm, and the number of times the light source moves may depend on the number of areas on the object surface. For example, if the desired resolution of the image of the object surface is 300 pixels per inch (PPI), the light source may be moved 300 times per inch when collecting reflectance data of the object surface. At 408, illumination information of a region of the object surface is captured. In one embodiment, lighting information may include data associated with reflectance of a plurality of light rays coming from a plurality of light sources and incident on a region of the surface of an object.

When lighting information of an area is obtained at 408, it is determined at 410 whether there are more areas for which lighting information needs to be collected. If yes, the light source is moved as shown at 412, and the procedure returns to 408 where lighting information for the next area is obtained. The loop including steps 408, 410, and 412 may be repeated until all areas of the object surface have been imaged. At 414, it is determined whether there are further lighting conditions that need to be applied to the object to collect reflectance data. If yes, the method moves to 416 where new lighting conditions are selected. The new lighting conditions selected at 416 may include, but are not limited to, different light sources, where various RGB values may be applied to the object to obtain additional reflectance data. Upon selecting new lighting conditions at 416, the method loops back to step 402 where the object is illuminated using the newly selected lighting conditions and reflectance data is acquired by moving the light sources as previously detailed.

The imaging procedure described in Figure 4 generates multiple images of the object for each lighting condition. For example, the procedure of Figure 4, when run for a single lighting condition, can produce approximately 8000 images. FIG. 5 details a method of generating a reilluminable hologram according to some embodiments. The method begins at 502 by obtaining illumination information of a plurality of regions of an object under a plurality of lighting conditions as detailed in FIG. 4. In one embodiment, area-wise reflectance data at 502 may be acquired as a series of images of an object illuminated by one or more light sources from different locations. At 504, the illumination information of the plurality of regions of the object surface thus obtained is aggregated. In some embodiments, images of each area of an object collected under a plurality of lighting conditions are overlaid on top of each other to aggregate lighting information. Because the images are taken from a single camera viewpoint (but under different lighting conditions), when the images are overlaid on top of each other, the object appears to be illuminated by white light. This is in contrast to conventional methods of collecting lighting information from multiple viewpoints to create a digital hologram, where aggregating this lighting information results in a fuzzy, out-of-focus image. focus images will be obtained. Those of ordinary skill in the art will appreciate that for small regions or regions of an object surface as described herein, viewing angle may not contribute as much to the appearance of the model as appropriate reflectance.

A holographic print of the aggregated illumination information for each region of the object is obtained at 506. In some embodiments, aggregated illumination information for each of the plurality of regions is recorded on a photosensitive medium from which a holographic print is created using known methods. Examples of photosensitive media that can be used to create holograms may include, but are not limited to, photographic emulsions, photopolymers, photoresists, and similar materials. The holographic print obtained at 506 includes a plurality of reilluminable holograms, each encoding multiple illumination conditions for each area of the object, unlike multiple viewing angles encoded in a typical holographic pixel. Accordingly, while a conventional hologram can provide image data from different viewing angles, a reilluminable hologram according to embodiments described herein provides reflectance data when illuminated by appropriate lighting conditions.

In some embodiments, if the reilluminable hologram generated at 506 is illuminated with a light source from a direction substantially similar to those present when the reflectance data was collected, the light may be substantially similar to the object for which light interactions were recorded at 502. reflected in a way. Therefore, when a 3D model of an object is covered with reilluminable holograms as described herein, both depth and light interaction data are captured, thereby creating a more realistic representation of the object than would otherwise have been created by a 3D printer alone. Creates an enemy copy.

6 is an example 600 showing lighting information including a series of images 602 of an object acquired in accordance with some embodiments. One or more light sources can be programmed for slight movements while the camera and object remain in fixed positions. It will be appreciated that image series 602 with 25 images is shown and discussed herein by way of example only and not limitation. Any number of images for image series 602 can be generated based on various positions of the light source(s). Each image 604 of the plurality of images 602 captures illumination information of regions or micro-regions of the object for a given location of the light source(s). A plurality of images 602 were created by moving the light sources sequentially, for example, from the left side of the object to the right side of the object, while keeping the object and camera at fixed positions. Accordingly, if the image series 602 is considered a 5x5 matrix, the image at the 5x5 position is a mirror image of the image at the 1x1 position. A plurality of such image series 606 may be generated by using a plurality of lighting conditions. To generate multiple image series 606, light sources with various properties may be used, such as, but not limited to, intensities, colors/wavelengths, and types of light.

Illumination information from each corresponding individual image 604 from each series 602 of the plurality of series 606 for a given image pixel is overlaid, and the resulting images are formed according to some embodiments. It is printed as a sheet of reilluminable holograms 608 including small holograms 610 of . For example, assuming that each image at a 1x1 position in the plurality of series 606 represents illumination information of the imaged object surface when the light sources and the object are at a specific position, a re-illuminable hologram of the object surface may be created by overlapping or overlaying each of the 1x1 images from the plurality of image series 606. Accordingly, by overlapping each NxN image representing a particular light source/object location with other images representing the same location in the various image series 606, a reilluminable hologram is created.

Because each hologram 610 of reilluminable hologram 608 encodes illumination information of a plurality of illumination conditions of a single corresponding region of the object surface, one of the plurality of illumination conditions is displayed on the sheet of reilluminable hologram 608. When applied to , the result is a view that will substantially replicate how the object surface looks when illuminated under those lighting conditions. This effect can be further enhanced to look more realistic by applying reilluminable holographic pixels on a 3D printed model of the object surface. The process as outlined in the embodiments herein allows objects such as, but not limited to, human faces, to be thus created from 3D printed models that are endowed with depth information as well as human facial reflectance data. It can help create more realistic replicas of objects.

Figure 7 shows a model 700 of an object created according to the embodiments described above. In some embodiments, depth and illumination information of an object may be obtained by executing a physical data collection process using tools such as an illumination stage. The physical structure of the model showing depth information is created by a 3D printer. Illumination information is transferred to the model via a holographic sheet containing a reilluminable hologram as detailed herein. Based on the illumination information of the object, there may be certain parts, such as the tires 702 of the model 700, for example, which may have a matte finish and do not require holograms, whereas the body 704 of the car and other parts such as windshield 706 can have holographic flakes/sheets attached thereto.

Figure 8 illustrates the internal architecture of computing device 800 according to some embodiments. Computing device 800 or another device substantially similar thereto may include modules for creating a model and properties of a virtual object by an artist for further modeling in accordance with embodiments described herein. Computing device 800 may be further configured to include programming logic to generate reflectance data for virtual or real objects. In some embodiments, certain reflectance information of a real-world object may be obtained through performing a physical procedure as detailed herein, while other reflectance information is generated by programming logic executed by computing device 800. It can be. In some embodiments, computing device 800 may also be used to operate a data collection device, such as a lighting stage as detailed herein. Moreover, computing device 800 may include modules that drive a printer, which may include, but is not limited to, a 3D printer, to print a 3D model of an object and attach a holographic sheet containing lighting information to the printed model. It can be included.

The internal architecture of the computing device includes one or more processing units (also referred to herein as CPUs) 812 that interface with at least one computer bus 802. Persistent storage medium/media 806, optional audio devices 808, network interface 814, memory 804, such as random access memory (RAM), run-time transient memory, A media disk drive interface 820, monitor or other device for a drive capable of reading and/or writing to media, including removable media such as read only memory (ROM), floppies, CD-ROMs, DVDs, and other media. Display interface 810 as an interface to a display device, input device interface 818 to input devices such as pointing devices such as a keyboard, mouse, and parallel and serial port interfaces, universal serial bus (USB) interface, etc. Other interfaces 822, not individually shown, also interface with computer bus 802.

Memory 804 includes an operating system, application programs, device drivers, and program code and/or computer-executable process steps that include one or more of the functions described herein, e.g., process flows described herein. Interfaces with computer bus 802 to provide information stored in memory 804 to CPU 812 during execution of software programs, such as software modules. CPU 812 first loads software modules for computer-executable process steps from storage, such as memory 804, storage medium/media 806, removable media drive, and/or other storage device. CPU 812 may then execute software modules to execute computer-executable process steps. Stored data, such as data stored by a storage device, may be accessed by CPU 812 during execution of computer-executable process steps.

Persistent non-transitory storage medium/media 806 is a computer-readable storage medium(s) that can be used to store software and data, such as an operating system and one or more application programs. Persistent storage media/mediums 806 may also be used to store device drivers, content and other files, such as one or more of a digital camera driver, monitor driver, printer driver, scanner driver, or other device drivers. there is. Persistent storage medium/media 806 may further include program modules and data files used to implement one or more embodiments of the disclosure.

9 is a 3D printer 900 for printing 3D models using holographic data according to some embodiments described herein. As previously described, 3D printer 900 may be connected to a controller, such as computing device 900, that provides software for creation and/or selection of models to be printed. Specialized 3D printing software packages are available that enable creating models on the display screen of computing device 900. Based on the model created/selected by the user, the computing device 900 may control the 3D printer 900 to create or print the model. Although shown herein as separate units, it can be seen that computing device 800 may also be integrated with a 3D printer to form a single unit according to some embodiments.

The electronics 912 of the 3D printer 900 include at least a processor 914 and a non-transitory processor or computer-readable non-transitory storage medium 916. Processor 914 controls various components of 3D printer 900 based on programming logic stored on non-transitory storage medium 916 to generate 3D printed models with attached holographic data. A holographic sheet cutter to separate a sheet containing a plurality of reilluminable holograms containing illumination information of the surface of the object to be printed into a plurality of printed holograms for attachment to the 3D printed model when the 3D printed model is being printed. It is fed to (holographic sheet cutter) 904. In some embodiments, multiple printed holograms may be obtained externally from a separate device to separate them into multiple printed, relightable holograms.

A plurality of reilluminable printed holograms, obtained either from a cutter 904 or externally, are fed to an extruder 906 in accordance with embodiments described herein. Extruder 904 consists of an extrusion mechanism that includes a tank containing 3D printing ink, which may contain plastics such as colored resins, and a nozzle that extrudes the 3D printing ink to create a 3D printing model. The extrusion mechanism may be further configured to emit or output each of the reilluminable holograms of the series when the corresponding portion of the model is printed. In some embodiments, the electronics 912 of the 3D printer 900 are programmed to enable the extruder 904 to emit a specific reilluminable hologram when the outer surface of a corresponding portion of the 3D model is printed.

Adjustable printer bed 908, together with extruder movement mechanism 902, enables 3D printing by extruder 2004. Extruder movement mechanism 902 may include one or more adjustable frames 922 and X-Y-Z motors 924. Extruder 902 is mounted on frames 922 equipped with X-Y-Z motors that enable movement of extruder 904 along one or more of the X-Y-Z axes on frames 922. Additionally, the adjustable printer bed 908—from which the extruder 906 ejects ink onto the adjustable printer bed 908—can be adjusted to add another level of flexibility to the 3D printer 900. A cooling mechanism 910, such as a fan, is also included in the 3D printer 900 to keep the 3D model cool when printed. Accordingly, the 3D printer 900 can print realistic models using depth information and lighting information according to embodiments described herein.

For the purposes of this disclosure, a computer-readable medium stores computer data, which may include computer program code executable by a computer, in machine-readable form. By way of example, and not limitation, computer-readable media may include computer-readable storage media for tangible or fixed storage of data, or communication media for transient interpretation of code-bearing signals. You can. Computer-readable storage media, as used herein, refers to physical or tangible storage (rather than signals) and tangible storage of information such as computer-readable instructions, data structures, program modules or other data. This includes, but is not limited to, volatile and non-volatile, removable and non-removable media implemented in any method or technology. Computer readable storage media may include RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices. , or any other physical or material medium that can be used to tangibly store desired information or data or instructions and that can be accessed by a computer or processor.

For the purposes of this disclosure, a module refers to software that performs or facilitates the processes, features, and/or functions described herein (with or without human interaction or augmentation). , hardware, or firmware (or combinations thereof) is a system, process, or function, or a component thereof. A module may include sub-modules. The software components of the module may be stored on a computer-readable medium. Modules may be integrated into one or more servers or loaded and executed by one or more servers. One or more modules may be grouped into engines or applications.

Those skilled in the art will recognize that the methods and systems of this disclosure can be implemented in many ways and therefore should not be limited by the illustrative embodiments and examples described above. In other words, functional elements performed by single or multiple components in various combinations of hardware and software or firmware, and individual functions may be distributed among software applications on the client or server or both. In this regard, any number of the features of the different embodiments described herein may be combined into a single or multiple embodiments having less or more than all of the features described herein. Alternative embodiments are possible. Functionality may also be distributed, in whole or in part, among multiple components in ways now known or to become known. Accordingly, numerous software/hardware/firmware combinations are possible to achieve the functions, features, interfaces and preferences described herein. Moreover, the scope of the present disclosure extends to conventionally known ways of performing the described features and functions and interfaces as well as those described herein as will now and hereafter be understood by a person skilled in the art. Includes variations and modifications that may be made to hardware or software or firmware components.

Although the system and method have been described in terms of one or more embodiments, it should be understood that the disclosure is not necessarily limited to the disclosed embodiments. This disclosure is intended to cover various modifications and similar arrangements included within the spirit and scope of the claims, and the scope thereof should be construed in the broadest manner to encompass all such modifications and similar structures. This disclosure includes all embodiments of the following claims.

Claims (15)

A method of generating models of objects, comprising:
Obtaining a physical model of an object - the object includes a plurality of regions, the physical model is made of metal and further includes a plurality of physical model parts, and each physical model part is a respective one of the object regions. Corresponds to the object area of -;
Receiving, by a first processor, lighting information of the object, the lighting information including reflectance data of regions of the object; and
Printing, by the first processor, the illumination information of the object as a holographic sheet divided into a plurality of separate physical holographic flakes, the number of the divided holographic flakes. corresponds to the number of the object regions, each holographic flake comprising a respective hologram of a series of holograms, and each hologram of the series is the reflectance of the respective object region of the object regions. At least one holographic pixel encoding data as one or more bi-directional reflectance distribution functions (BRDFs), each hologram in a respective one of the object regions. Printed and attached to the corresponding part of the physical model -
A method for generating models of objects, including. According to paragraph 1,
A method of generating models of objects, wherein the physical model of the object is printed by a three-dimensional printer. According to paragraph 1,
A method of creating models of objects, wherein the metal is gold. According to paragraph 1,
The metal is silver, a method for creating models of objects. According to paragraph 1,
A method of generating models of objects, wherein the physical model of the object is a two-dimensional model. A method of generating models of objects, comprising:
Receiving, by a device comprising a processor, illumination information of an object comprising a plurality of regions, the illumination information including reflectance data of the plurality of regions of the object;
Printing, by the device, a physical model of an object, wherein the physical model is made of metal, the surface of the physical model includes a plurality of parts, each part of the physical model surface is a region of the object. Each corresponds to its own area -; and
Transferring, by the device, the illumination information of the object to the physical model as a holographic series, wherein transferring the illumination information of the object is divided into a plurality of separate physical holographic flakes. printing with a second physical material as a holographic sheet, wherein the number of segmented holographic flakes corresponds to the number of regions of the object, each holographic flake comprising a respective hologram of the holographic series; , each hologram of the series comprising at least one holographic pixel encoding the reflectance data of the respective one of the regions as one or more bi-directional reflectance distribution functions (BRDFs), and , each hologram is printed and attached to the part of the physical model corresponding to its respective area -
A method for generating models of objects, including. According to clause 6,
A method of generating models of objects, wherein the physical model of the object is printed by a three-dimensional printer. In clause 7,
A method of generating models of objects, wherein the physical model is a two-dimensional model. In clause 7,
A method of generating models of objects, wherein the physical model is a three-dimensional model. According to clause 9,
The step of printing the physical model of the object includes:
receiving, by the device, a three-dimensional image of the object; and
Printing, by the device, the three-dimensional model of the object from the three-dimensional image.
A method for generating models of objects, including. According to clause 6,
A method of creating models of objects, wherein the metal is gold. In clause 7,
The metal is silver, a method for creating models of objects. As a model of an object,
a plurality of parts made of a first physical material on the outer surface of the model, each part corresponding to a respective part of the plurality of parts located on the outer surface of the object; and
A plurality of holographic flakes on the plurality of portions - the holographic flakes are divided from a holographic sheet of a second material, the number of divided holographic flakes being dependent on the number of the plurality of portions of the surface of the object. Correspondingly, each of the holographic flakes includes reflectance data for a plurality of lighting conditions of a respective portion of the plurality of portions of the surface of the object corresponding to a respective portion on the outer surface of the model. Each of the holographic flakes is printed and attached to the first physical material of a corresponding portion of the model, and the reflectance data is one or more bi-directional reflectance distribution functions. , BRDFs) -
A model containing . According to clause 13,
A model wherein the first physical material is gold. According to clause 13,
The first physical material is the benefactor model.

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