Gemstone cutting analysis

Abstract

The present embodiments relate to methods and systems for analyzing and representing the appearance of diamonds, and interactive network-based diamond cutting encyclopedia. These analytical methods involve the use of several unique techniques designed to accurately capture and represent nuance differences of different diamond cuts. Graphical representation converts such complex gemstone data into a format accessible and understandable by non-professional users. Diamond cutting encyclopedia generated by a unique enumeration algorithm provides comprehensive and detailed resources for both experts and amateurs. The present embodiments present a significant progress in the field of gemstone, providing a higher precision, user-friendly interface for diamond analysis, and an efficient method for creating a comprehensive, interactive diamond cutting encyclopedia.

Description

[0001] Cross-references to related applications This application claims priority to U.S. Provisional Patent Application No. 63 / 468,242, filed May 22, 2023, entitled “DIAMOND CUT ANALYSIS”, and U.S. Provisional Patent Application No. 63 / 468,226, filed May 22, 2023, entitled “GENERATION OF GEM CUTS”, the entire contents of which are incorporated herein by reference. Technical Field

[0002] This field encompasses the analysis and graphical representation of the appearance of diamonds or other gemstones, including simulations of light interactions. Furthermore, it includes interactive, web-based encyclopedias of diamond cutting and methodologies and representations for consumer-oriented reporting. Background Technology

[0003] Diamonds and other gemstones are typically evaluated based on their cut, color, clarity, and carat weight (often referred to as the 4Cs). The cut of a diamond can have a significant impact on its brilliance, scintillation, and fire, and is generally considered the most complex and technically difficult criterion to assess.

[0004] There is a need for a robust, accurate, and consumer-friendly method to analyze and represent the appearance of diamonds in models or simulations, which can be interactive or customizable. In particular, there is a need for a system that can translate complex gemological data into a format easily accessible and understandable to the average consumer, while still providing the level of detail and accuracy useful to professionals in the field.

[0005] Given the numerous possible diamond facet arrangements and the variety of techniques available for modeling and precise cutting, a posable diamond cut atlas is extremely useful in diamond modeling and cutting. In many cases, experimentation with different diamond cuts has been hampered by the difficulty in precisely executing certain cuts and the risks involved in cutting diamonds whose properties are unpredictable.

[0006] Limitations of other solutions include cut grading systems that may be applicable to standard round brilliant cuts, and methods tailored to some of the most common facet arrangements. However, developing a cut grading / information system suitable for every diamond cut is a challenging proposition. Furthermore, other systems often lack user-friendly interfaces or formats for non-professional users, limiting their usefulness to consumers or hobbyists.

[0007] Furthermore, while many resources are available for learning about diamond cutting, there is no comprehensive, interactive, web-based encyclopedia specifically dedicated to the subject. Other resources typically provide only basic information, lacking the level of detail or interactivity required to fully understand and appreciate the complexities of diamond cutting. Moreover, generating such an encyclopedia has traditionally been a time-consuming, manual process. More efficient and automated methods are needed to create a comprehensive, interactive encyclopedia of diamond cutting. Summary of the Invention

[0008] The system and method described herein may include generating a virtual faceted model of a gemstone at a computer having a processor and memory; receiving a 3D model file including a scan of the gemstone with facets; receiving first user input from the computer regarding the location of a first light source associated with the 3D model; and determining a first set of illuminated virtual facets and first outgoing beam data by the computer based on ray tracing or beam tracing analysis of the 3D model file and a selected lighting environment (which includes assigning color and / or intensity to individual points on the surrounding hemisphere). A virtual facet pattern is then displayed, wherein the virtual facets are colored and / or illuminated via the outgoing beam data and the lighting environment. Additionally or alternatively, the computer causes an animation sequence of the virtual facet pattern to be displayed corresponding to a sequence of lighting environments. For example, this can be used to model moving light sources or more general animations such as coloring rings moving concentrically away from the poles of a hemisphere. This can also be used to encode information about incident light rays based on angles above the horizon or other criteria.

[0009] In some examples, additionally or alternatively, the systems and methods described herein can be used to reproduce targeted virtual facets in a gemstone, including a hemispherical housing configured to contain the gemstone, the hemispherical housing including an array of multiple lights located at different positions within the hemispherical housing, the array being configured to illuminate the contained gemstone from different angles, and a computer having a processor and memory communicating with the array of multiple lights located at different positions within the hemispherical housing, the computer being configured to turn any one of the multiple lights in the array on and off to generate a virtual facet pattern in the contained gemstone.

[0010] In an example embodiment, additionally or alternatively, a method for generating a virtual faceted model of a gemstone may include receiving a 3D model file, including a scanned image of the gemstone, at a computer having a processor and memory. The method may also include the computer receiving user input regarding a lighting environment associated with the 3D model, which may consist of a single or multiple colored or white light sources, or receiving an arbitrary distribution of light intensity and color to an ideal hemisphere around the virtual model. The method may further include the computer determining the color and illuminance of the virtual facets via outgoing beam data and the lighting environment analyzed from ray tracing or beam tracing analysis of the 3D model file. The method may also include the computer causing the virtual facet illuminance and / or color to be displayed on a user interface showing the 3D model.

[0011] In some instances, additionally or alternatively, the method may include, by a computer, animating a virtual faceted pattern that is tinted and / or illuminated based on a sequence of lighting environments. For example, this could model more general animations such as moving light sources or concentrically moving poles away from a hemisphere, like tinted rings.

[0012] In some instances, additionally or alternatively, the lighting environment represents the total illuminance of the hemisphere surrounding the diamond, with selected darkened portions to model occlusion and contrast.

[0013] In some instances, additionally or alternatively, the method may include computer analysis of the contrast salience of virtual facets.

[0014] In another example embodiment, additionally or alternatively, a system for reproducing targeted virtual facets in a real gemstone is described. The system may include a hemispherical enclosure configured to house the gemstone. The hemispherical enclosure may include an array of multiple lights located at different positions within the hemispherical enclosure, the array being configured to illuminate the housed gemstone from different angles. The system may also include a computer having a processor and memory that communicates with the array of multiple lights located at different positions within the hemispherical enclosure, the computer being configured to turn any one of the multiple lights on and off to generate a virtual facet pattern in the housed gemstone.

[0015] In another example embodiment, additionally or alternatively, a method for generating a virtual faceted model of a gemstone is provided. The method may include receiving a 3D model file, including a scan of the gemstone and its facets, at a computer having a processor and memory. The method may further include having the computer determine a virtual facet pattern and first outgoing beam data based on ray tracing or beam tracing analysis of the 3D model file and an input viewing direction. The method may also include having the computer cause the determined virtual facet pattern to be displayed on a user interface showing the 3D model and the determined virtual facet pattern.

[0016] In some instances, additionally or alternatively, the created virtual faceted pattern is aligned with a selected visual perception angle by utilizing faceted depth information.

[0017] In some instances, additionally or alternatively, the created virtual facet pattern is aligned with a selected visual perception angle by utilizing the actual virtual facet size.

[0018] In some instances, additionally or alternatively, the created virtual faceted pattern is aligned with a selected visual perception angle by utilizing the angle from which the virtual facets draw light.

[0019] In some instances, additionally or alternatively, the method may include displaying virtual facet details by a computer, the virtual facet details including virtual facets colored according to area, virtual facets colored according to beam depth, virtual facet edges colored according to type, and virtual facets colored according to waist-edge interactions.

[0020] In some instances, additionally or alternatively, the method may include a set of metrics calculated by a computer based on the determined virtual facet pattern and the determined first outgoing beam information, including any one of light return, scintillation probability, virtual facet area distribution, virtual facet depth distribution, light entropy, scintillation diffusion, graphic isomorphism class of the virtual facet pattern, Hausdorff distance from the virtual facet pattern to the specified graphic, and / or graphic edit distance from the virtual facet pattern to the specified graphic.

[0021] In some instances, additionally or alternatively, the method may include generating content for a diamond encyclopedia of multiple measures using calculated metrics by automatically generating a list of facet arrangements of a certain complexity using an enumeration algorithm, automatically populating the best guess scale set and displaying charts and interactive content, and creating an interface for the user to adjust the scale set and display newly calculated charts.

[0022] In another example embodiment, additionally or alternatively, a system for reproducing targeted virtual facets in a real gemstone is provided. The system may include a hemispherical housing configured to contain the gemstone. The hemispherical housing may include an array of multiple lights located at different positions within the hemispherical housing, the array being configured to illuminate the contained gemstone from different angles. The system may also include a computer having a processor and memory, the computer communicating with the array of multiple lights located at different positions within the hemispherical housing. The computer may be configured to turn any one of the multiple lights in the array on and off to generate a virtual facet pattern in the gemstone contained within the hemispherical housing.

[0023] In another example embodiment, additionally or alternatively, a method for generating a virtual faceted model of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data.

[0024] The method may also include, additionally or alternatively, receiving user input from a computer regarding the selection of a lighting environment related to the color of the 3D model and an ideal hemisphere surrounding the virtual model. The method may also include determining the facet color and illuminance by a computer using outgoing beam data from the 3D model file, ray tracing analysis of the 3D model file, and the user-input lighting environment selection. The method may further include having a computer display virtual facet illuminance or facet color on a user interface showing the 3D model.

[0025] In some instances, additionally or alternatively, the lighting environment selection is at least one of a single or multiple colored or white light sources, or an arbitrary allocation of light intensity.

[0026] In some instances, additionally or alternatively, the method may include an animation by which a computer causes a programmable sequence of lighting environments to display virtual faceted illuminance or faceted color.

[0027] In some instances, additionally or alternatively, the programmed lighting environment sequence includes at least one of a model of a moving light source or a model of a shading ring that moves concentrically away from the model's hemispherical poles.

[0028] In some instances, additionally or alternatively, the lighting environment is selected to model the total illuminance of the hemisphere surrounding the gem model, with selected darkened portions to model occlusion and contrast.

[0029] In some instances, additionally or alternatively, the method may include using a computer to analyze the contrast of virtual facets in a 3D model using a model of the emitted beam data.

[0030] In another example embodiment, additionally or alternatively, a method for generating a virtual faceted model of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include determining a virtual faceted pattern and first outgoing beam data by the computer based on ray tracing or beam tracing analysis of the 3D gemstone model and an input viewing direction. The method may also include the computer causing the determined virtual faceted pattern to be displayed on a user interface showing the 3D model and the determined virtual faceted pattern.

[0031] In some instances, additionally or alternatively, the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing facet depth information.

[0032] In some instances, additionally or alternatively, the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing the actual virtual facet size from the 3D model.

[0033] In some instances, additionally or alternatively, the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing the angle from which light is drawn from the virtual facets of the 3D model.

[0034] In some instances, additionally or alternatively, the method may include displaying virtual facet details by a computer.

[0035] In some instances, additionally or alternatively, facet details include at least one of the following: virtual facets colored according to area, virtual facets colored according to beam depth, virtual facet edges colored according to type, or virtual facets colored according to waist-edge interactions.

[0036] In some instances, additionally or alternatively, the method may include having a computer calculate a set of metrics based on a determined virtual facet pattern and determined first outgoing beam data, the set of metrics including at least one of the following: light return, scintillation probability, virtual facet area distribution, virtual facet depth distribution, light entropy, scintillation diffusion, graphic isomorphism class of the virtual facet pattern, Hausdorff distance from the virtual facet pattern to a specified graphic, or graphic edit distance from the virtual facet pattern to a specified graphic.

[0037] In some instances, additionally or alternatively, the method may also include generating multiple simplified diagrams of a virtual faceted pattern using a computed metric by generating a list of faceted arrangements by using an enumeration algorithm to do so; determining an optimal scale prediction set; displaying a graph of the multiple simplified diagrams of the virtual faceted pattern; and receiving instructions to adjust the scale set of the virtual faceted pattern, and displaying the graph based on the received instructions.

[0038] In another example embodiment, additionally or alternatively, a method for generating a gemstone model is provided. The method may include receiving input regarding gemstone parameters, wherein the gemstone parameters include at least one of light return, contrast enhancement, or light entropy. The method may also include generating the gemstone model using an algorithm and the input parameters, wherein the algorithm is at least one of a linear approximation constrained optimization (COBYLA) algorithm, a genetic algorithm, or a machine learning technique.

[0039] In another example embodiment, additionally or alternatively, a method for determining contrast in a gemstone model is provided. The method may further include receiving data about a scanned gemstone at a computer having a processor and memory. The method may further include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include generating ray-tracing data on the 3D gemstone model by the computer. The method may further include generating virtual facet decomposition by the computer from multiple angles based on the generated ray-tracing data. The method may further include calculating the angle between the incident light ray and the horizon for each virtual facet for each ray tracing using the geometry of the model and refraction and reflection data.

[0040] In some instances, additionally or alternatively, the method may also include having a computer return the total percentage area of ​​the occluded facets for each ray trace and generate an occlusion score.

[0041] In another example embodiment, additionally or alternatively, a method for generating a scintillation diffusion map for a gemstone model is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include receiving a selection of an angular radius by the computer. The method may further include generating a pixelated image of the 3D gemstone model by the computer. The method may further include assigning color to each pixel of the pixelated image of the 3D gemstone model by the computer based on a modeling light source from the angular radius and the calculated relative area of ​​the convex hull of the illuminated facets.

[0042] In some instances, additionally or alternatively, the color is a linear gradient from 0 to 1, where 0 is no virtual facet illumination and 1 is the maximum virtual facet illumination.

[0043] In another example embodiment, additionally or alternatively, a method for generating a scintillation diffusion map for a gemstone model. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing beam tracing on the 3D gemstone model by the computer. The method may further include generating a digital image of a hemisphere surrounding the 3D gemstone model by the computer in a face-down configuration. The method may further include receiving the angular radius of a modeling light source by the computer. The method may further include assigning color to each pixel in the digital image by the computer based on the convex hull of a virtual faceted outgoing beam and the virtual faceted centroid calculated from the received angular radius.

[0044] In some instances, additionally or alternatively, the method may include determining the relative area of ​​the convex hull with respect to the total visible area of ​​the 3D gem model by a computer.

[0045] In some instances, additionally or alternatively, the method may include assigning a color code to each pixel by a computer using a linear gradient from 0 to 1.

[0046] In some instances, additionally or alternatively, the method may include computer-generated total area to produce a thermal map of light source visibility across the surface of a 3D gemstone model.

[0047] In some instances, additionally or alternatively, the method may include computer-generated a number of virtual facets illuminated in a 3D gem model and generating a thermal map of the amount of scintillation as a function of the location of the light source.

[0048] In another example embodiment, additionally or alternatively, a method for generating a visualization of a gemstone model is described. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing beam tracing on a set of modeling beams by the computer through the generated 3D gemstone model. The method may further include calculating virtual facets within the 3D gemstone model by the computer using beam tracing. The method may further include assigning color to each calculated virtual facet in the 3D gemstone model by the computer based on relative size. In some instances, the method may include displaying virtual facets and colors by the computer. In some instances, the method may include displaying a percentage area of ​​the size category of the virtual facets by the computer. In some instances, the method may include displaying a graph of the count of the size categories of the virtual facets by the computer.

[0049] In another example embodiment, additionally or alternatively, a method for mapping optical entropy in a gemstone model is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing beam tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may also include generating a fraction for each virtual facet using the area of ​​virtual facets in the 3D gemstone model and the beam tracing, including generating the dot product of the outgoing beam from each virtual facet with the outgoing beams from adjacent virtual facets.

[0050] In some instances, additionally or alternatively, the method may include assigning a color to each virtual facet by a computer based on a classification of ray tracing and the direction of ray tracing.

[0051] In some instances, additionally or alternatively, the method may include generating a continuous color gradient by a computer based on a fraction of each virtual facet, and displaying the color gradient along with the 3D gem model.

[0052] In another example embodiment, additionally or alternatively, a method for generating a gemstone model is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may also include displaying the 3D gemstone model and the ray tracing. The method may further include highlighting each virtual facet having an optical path that interacts with the girdle facets of the 3D gemstone model.

[0053] In another example embodiment, additionally or alternatively, a method for generating a virtual gem facet isomorphic map is provided. The method may include receiving data about a scanned gem at a computer having a processor and memory. The method may also include generating a 3D gem model by the computer using the received scanned gem data. The method may further include generating variants of the 3D gem model with different scales by the computer. The method may further include performing ray tracing on the 3D gem model and the generated variants of the 3D gem model by the computer using geometric, refraction, and reflection rules. The method may further include spatially segmenting all virtual facet patterns in the 3D gem model and the variants of the 3D gem model into virtual facet types. The method may further include creating a map that displays the virtual facet types of the 3D gem model and the variants of the 3D gem model.

[0054] In some instances, additionally or alternatively, different proportions are at least one of the crown height, pavilion depth, platform dimensions, or shape parameters.

[0055] In some instances, additionally or alternatively, a virtual facet type map is a map of regions colored according to isomorphic types.

[0056] In some instances, additionally or alternatively, the virtual facet type map is a 3D drawing colored according to the isomorphic type.

[0057] In another example embodiment, additionally or alternatively, a method for modeling the boundaries of a gemstone is provided. This method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include generating a 2D image of the 3D gemstone model by the computer using an alignment routine to best fit the axis of symmetry to align the gemstone. The method may also include fitting a Bezier curve to the four quadrants of the 3D gemstone model defined by parameters kappa, theta, and mu by the computer.

[0058] The method may also include using, additionally or alternatively, characteristics of the shape profile of the 3D gemstone model as input, determined by a computer, wherein the shape characteristics are fitted to narrow, standard, or wide categories. The method may also include assigning color parameters to the categories.

[0059] In some instances, the method may include, by computer, additionally or alternatively, displaying a 3D gemstone model with color parameters assigned to its shape contours.

[0060] In another example embodiment, additionally or alternatively, a method for generating a scintillation diffusion map of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing beam tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include having the computer display a digitally pixelated image of the 3D gemstone model and a hemisphere surrounding the 3D gemstone model in a face-down orientation. The method may further include receiving a selection of an angular radius (in degrees) for a modeling light source by the computer. The method may further include having the computer analyze the emitted beams from each virtual facet of the 3D gemstone model intersecting selected pixels of the digitally pixelated image using the selected angular radius. The method may further include having the computer determine the convex hull of the centroid of the virtual facets in the 3D gemstone model. The method may further include having the computer determine the relative area of ​​the convex hull with respect to the total visible area of ​​the 3D gemstone model. The method may further include having the computer assign color codes to selected pixels using the convex hull.

[0061] In some instances, additionally or alternatively, color codes are based on illuminance from 0 to 1.

[0062] In some instances, additionally or alternatively, the method may include generating a visible light thermal map over the total area of ​​the 3D gem model by a computer.

[0063] In some instances, additionally or alternatively, the method may include drawing the scintillation amount of a number of virtual facets of an illuminated 3D gem model generated by a computer.

[0064] In another example embodiment, additionally or alternatively, a method for virtual facet edge coloring of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may also include recording clipping edge data of any polygonal regions in the 3D gemstone model by the computer during ray tracing. The method may further include assigning color codes to edge types by the computer. The method may further include creating a simplified map of edge codes by the computer using the color codes.

[0065] In some instances, additionally or alternatively, the range of edge types extends from the countertop to the waistline.

[0066] In some instances, additionally or alternatively, the method may include a computer-generated virtual facet diagram of a 3D gemstone model containing color codes.

[0067] In another example embodiment, a method for contrast / sparkle analysis of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing beam tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include generating a virtual facet pattern model by the computer and displaying the virtual facet pattern model. The method may further include receiving a selection of virtual facets in the virtual facet pattern model by the computer. The method may further include receiving a color selection for the selected virtual facets by the computer. The method may further include generating a single frame of a sparkle movie by the computer using the selected color and beam tracing of the 3D gemstone model. The method may further include storing the single frame of the sparkle movie. The method may further include repeatedly receiving the virtual facet selection and color selection by the computer. The method may further include generating a unique lighting configuration sequence around a hemisphere of the 3D gemstone model and a series of additional frames of the sparkle movie by the computer. The method may further include displaying the first frame of the sparkle movie and the series of additional frames of the sparkle movie.

[0068] In some instances, additionally or alternatively, the method may include sending instructions to a hemispherical light system to illuminate a gemstone based on scintillation movie data.

[0069] In another example embodiment, additionally or alternatively, a method for determining the contour characteristics of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may also include determining 2D shadows of the 3D model by the computer. This determination may include selecting an axis of symmetry with the minimum area, calculating the area of ​​the convex hull for each axis and for shadows and reflections, and iterating over potential axes of symmetry.

[0070] The method may also include, additionally or alternatively, rotating the 3D gem model to a horizontal axis by a computer. The method may also include, by a computer, fitting Bézier curves to the four quadrants of the 3D gem model. The method may further include, by a computer, determining the aspect ratio as the difference between the maximum and minimum x-coordinates in the 3D gem model divided by the difference between the maximum and minimum y-coordinates.

[0071] In some instances, additionally or alternatively, for oval gemstone models, the control points of the Bézier curves are located at constant fractions of kappa in the width and height of the profile.

[0072] In some instances, additionally or alternatively, the method may include having a computer center the 3D gem model at the origin and align it with four control points (0, a), (kappa×b, a), (a, kappa×b), and (b, 0) of the axis and curve.

[0073] In some instances, additionally or alternatively, for marquise gemstone models, all four quadrants are roughly identical and fitted to a family of two parameters, where parameter mu controls the curvature and parameter theta controls the angle of the tangent drawn at the tip of the 3D gemstone model.

[0074] In some instances, additionally or alternatively, for pear-shaped gemstone models, the elliptical half is controlled by the parameter kappa, while the marquise half is controlled by the parameter mu.

[0075] In another example embodiment, additionally or alternatively, a method for determining the virtual facet depth distribution of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include determining and recording the number of ray-facet interactions (defined as combined depth) for each virtual facet by the computer. The method may further include determining the relative percentage of areas with high depth and the percentage of areas with low depth by the computer.

[0076] In some instances, additionally or alternatively, the method may include measuring the physical length of the ray path for each virtual facet by a computer.

[0077] In some instances, additionally or alternatively, the method may include classifying the fire of a 3D gem model by a computer based on a determined relative percentage of high and low depths.

[0078] In another example embodiment, additionally or alternatively, a method for determining the distribution of virtual facet areas of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include grouping virtual facets in the 3D gemstone model by the computer according to a predetermined size threshold. The method may further include determining a measure of the total area of ​​the grouped virtual facets.

[0079] In another example embodiment, additionally or alternatively, a method for determining the contrast and saturation of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include creating a virtual facet decomposition by the computer from multiple angles. The method may further include determining the angle between the incident ray and the horizon for each virtual facet for each ray tracing by the computer. The method may further include determining whether any virtual facets are occluded by the computer based on a predetermined threshold for the incident ray. The method may further include determining the total percentage area of ​​occluded facets for each ray tracing by the computer and creating an occlusion score based on the determined total percentage area.

[0080] In some instances, additionally or alternatively, the predetermined threshold for the incident ray is 15 degrees or less.

[0081] In another example embodiment, additionally or alternatively, a method for determining the scintillation score of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing beam tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include creating a virtual facet breakdown from multiple angles by the computer using beam tracing. The method may further include drawing incident rays for each virtual facet on a virtual hemisphere surrounding the 3D gemstone model by the computer. The method may further include determining the total area of ​​all points within a predetermined angular threshold at each point by the computer and dividing the determined total area by the area of ​​the hemisphere. The method may further include determining a measure of the likelihood that the 3D gemstone model will exhibit scintillation by the computer based on the total area divided by the area of ​​all points and the hemisphere.

[0082] In some instances, additionally or alternatively, the method may include a measurement determined by a computer on a portion of the hemisphere to represent the angle relative to the horizontal line within upper and lower limits.

[0083] In some instances, additionally or alternatively, the method may include having a computer count the number of virtual facets illuminated by a light source having a fixed given angle threshold in order to determine the average number of flicker events of a randomly placed light source at each point in the hemisphere.

[0084] In some instances, additionally or alternatively, the method may include having a computer calculate the total area of ​​the illuminated virtual facets and then having the computer average that total area over the area of ​​the hemisphere.

[0085] In another example embodiment, additionally or alternatively, a method for determining the optical performance score of a gemstone is provided. The method may include receiving data about a scanned gemstone at a computer having a processor and memory. The method may also include generating a 3D gemstone model by the computer using the received scanned gemstone data. The method may further include performing ray tracing on the 3D gemstone model by the computer using geometric, refraction, and reflection rules. The method may further include creating virtual facet decomposition from multiple angles by the computer using ray tracing. The method may further include calculating the angle between the incident ray and the horizon for each virtual facet for each ray tracing by the computer. The method may further include determining whether each virtual facet is illuminated by the computer based on previously defined lower and upper limits. The method may further include determining the light return score of the 3D gemstone model by the computer based on the total percentage area of ​​the illuminated facets returned by each ray tracing.

[0086] In some instances, additionally or alternatively, the lower limit is 15 degrees and the upper limit is 45 degrees. Attached Figure Description

[0087] This patent or application document contains at least one color-drawn drawing. Upon request and payment of the necessary fees, the Patent Office will provide a copy of this patent or patent application publication with the color-drawn drawing.

[0088] To better understand the embodiments described in this application, reference should be made to the following detailed description in conjunction with the accompanying drawings, wherein the same reference numerals identify corresponding parts throughout the drawings.

[0089] Figure 1 This is an example virtual facet pattern of a round brilliant diamond according to the embodiments described herein; Figure 2 These are example wireframe diagrams based on the embodiments described herein; Figure 3 This is an example symmetry comparison based on the embodiments described herein; Figure 4 This is an example symmetry comparison based on the embodiments described herein; Figure 5 This is an example of symmetry grading using a neural network according to the embodiments described herein; Figure 6 This is an example waistline interaction mapping diagram according to the embodiments described herein; Figure 7 These are examples of optical path visualization tools according to the embodiments described herein; Figure 8 These are examples of light source visualization tools according to the embodiments described herein; Figure 9This is an example of an angular spectrum analysis tool based on the embodiments described herein; Figure 10 These are examples of flicker probability tools according to the embodiments described herein; Figure 11 These are examples of beam depth analysis tools according to embodiments described herein; Figure 12 This is an example of a weight ratio chart based on the embodiments described herein; Figure 13 This is an example of a contour analysis chart according to the embodiments described herein; Figure 14 These are examples of light patterns and virtual facet size diagrams according to embodiments described herein; Figure 15 This is an example of a diamond contrast mapping diagram according to the embodiments described herein; Figures 16A-16C Example normal, color gradient, and monochrome diamond evaluation images are shown according to embodiments described herein; Figure 17 This is an example scintillation diffusion map of a standard round brilliant diamond according to the embodiments described herein; Figure 18 This is an example optical entropy map of an octagonal diamond according to the embodiments described herein; Figure 19 These are illustrations of example networked systems based on certain aspects described herein; and Figure 20 These are illustrations of example computer systems based on certain aspects described in this article. Detailed Implementation

[0090] Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. Numerous specific details are set forth in the following detailed description to provide a full understanding of the subject matter presented herein. However, those skilled in the art will understand that the subject matter can be practiced without these specific details. Furthermore, the specific embodiments described herein are provided as examples only and are not intended to limit the scope of the particular embodiments. In other instances, well-known data structures, timing protocols, software operations, processes, and components have not been described in detail so as not to unnecessarily obscure some aspects of the embodiments herein.

[0091] It should be noted that the use of the terms "diamond" or "gemstone" in this disclosure is not intended to be limiting. Since the systems and methods described herein work with and relate to both naturally occurring and laboratory-grown rough gemstones and cut gemstones (including diamonds), the interchangeable use of these terms is for illustrative purposes only and is not intended to limit the scope in any way.

[0092] Overview This embodiment relates to analyzing and presenting the appearance characteristics of diamonds and generating various outputs of light models and computerized simulations derived from the gem facets. Example outputs may include a computerized model of a visual light display of a virtual facet pattern that appears in the physical gemstone at least in part due to the reflection and refraction of light in and through the physical facets of the gemstone.

[0093] Other example outputs could include consumer-facing diamond reports using metrics derived from these models, interactive web-based diamond cut encyclopedias, and / or other interactive representations illustrating the characteristics of various diamond facets and the modeled light interactions with these facets. These techniques could leverage enumeration algorithms that can be used to generate the outputs described herein.

[0094] The techniques described herein may include analyzing models of actual physical gemstones or diamonds, such as three-dimensional (3D) computer-generated models. Diamonds can be scanned using various scanning hardware to produce 3D models, such as silhouette scanning using computerized image capture. In some instances, various 3D modeling or virtual gemstone cutting techniques can be used to generate models. In some examples, 3D models may be generated from computer software layouts rather than from scans of actual physical gemstones.

[0095] These models can be used to simulate the interaction of light within the model, within facets and virtual facets, and through facets and virtual facets. These techniques can be used to understand the characteristics of diamond cutting and the behavior of light entering a gemstone at any of various angles or directions. This light can generate visual light patterns in the gemstone's appearance, referred to here as virtual facet patterns, which can be modeled on computer simulations. Data is collected from these models and displayed to the user, changing and updating as the modeling light source is moved and directed at different parts and directions of the modeled gemstone. This modeled virtual facet pattern can vary depending on the viewing angle of the human eye or camera, or the modeled viewing direction. Some of the systems and methods described in this paper can be used to model and display gemstones at a fixed eye position to show which virtual facets will be illuminated as the direction of the light source moves.

[0096] These features can be provided to diamond consumers or owners, and can also be used for education about the appearance of diamonds. Outputs can include an interactive encyclopedia that provides insights into the characteristics of diamonds.

[0097] These characteristics can be used to score or grade gemstones and various optical properties based on their cut and light interaction, as well as their symmetry.

[0098] This embodiment can also relate to cutting optimization based on software-based products and services. Example use cases for this technology may include software-related products supporting manufacturers and equipment manufacturers providing cutting or recutting planning equipment to factories. A technical challenge in providing cloud-based software solutions may be generating 3D wireframe models that conform to the physical constraints of the gemstone material from which the gemstone will be polished. In many cases, the database of unique facet arrangements of submitted diamonds may include thousands of unique designs (facet arrangements). For each possible facet arrangement, there may be unique parameters defining the geometry of the diamond. These include parameters such as table size, crown angle, girdle thickness, various ratios, and parameters defining the shape of the diamond.

[0099] Another aspect of this embodiment relates to the design and planning of virtual facets in gemstone cutting. When facets are cut on a particular gemstone, light entering the gemstone from any of a variety of angles and directions can cause changes in the gemstone's internal appearance. Light not only passes through the gemstone but also interacts with facets, reflecting, refracting, and bouncing, thus creating different patterns in the internal appearance. This virtual facet design is not only a computer representation of the gemstone facets in virtual space but also the physical appearance of the virtual facets within the gemstone as seen by a human or camera observer in physical space. Such virtual facets can be modeled and displayed, analyzed, and classified using the systems and methods described herein.

[0100] Another objective of this embodiment relates to educational, gem design, and cutting report products for retailers, designers, consumers, etc. This embodiment can be used to create an encyclopedia of gem cutting, which can be incorporated into core curricula and integrated into digital platforms to help protect and inform consumers. The techniques described herein can be used with a variety of devices to enhance diamond grading reports, visualize diamond performance, and create educational tools on diamond cutting for consumers and trade. Users can also use the encyclopedia to research and create designs for diamonds that have not been cut before.

[0101] Among the tool's users, many diamond designers are able to easily generate diamond designs with patterned or sparkling effects to create unique and one-of-a-kind gemstone and jewelry designs. These custom-designed diamonds can be submitted for grading, where they receive interactive digital reports highlighting their unique design attributes. New terminology, scales, and other data can be used to understand all aspects of diamond cutting education and standards.

[0102] Analysis method example This embodiment utilizes analytical methods to evaluate the appearance of a diamond based on ray or beam tracing models of a scanned or virtual diamond. Virtual facet patterns can be facet patterns appearing in a cut gemstone, and can include reflections, refractions, actual facet cuts, and combinations thereof. Therefore, virtual facet patterns are presented to the viewer when observed on a physical stone based on light and the interaction of light with various actual physical facets on the stone. In some examples, a designer or gem cutter / poliss can cut specific facets to generate patterns, shapes, designs, or other artworks in the gemstone that appear under specific lighting conditions within the virtual facets. These designs can be the central focus of a gemstone cutting design.

[0103] Therefore, in some examples, it may be advantageous to model not only the actual physical facet cut of the gemstone, but also the virtual facet pattern that will be presented to an observer of the physically cut gemstone. This modeling may be affected by the arrangement of light beams or rays illuminating the gemstone from various angles or directions, at different wavelengths, and at different intensities.

[0104] The system and method described in this paper can be used to model virtual facet patterns that can be derived from ray or ray tracing techniques based on physical facet patterns cut into or modeled in a wireframe model of a gemstone. For example, Figure 1 Image 100 is an example of a virtual facet pattern of a round brilliant diamond. Furthermore, the virtual facet pattern can be derived from a computer-generated model and the facet cuts programmed into it, or it can be based on the actual facet cuts of an actual physical diamond. Various scanning hardware techniques can be used to derive models of the facet patterns of physical diamonds to generate models of the virtual facet patterns described herein. Additionally, various insights can be gathered from the intersections of light rays generated within a physical sphere or hemisphere surrounding the physical gemstone. The results can be translated into an insightful graphical representation.

[0105] The components may include virtual facet patterns calculated based on physical facets cut into the gemstone. For example, the polygonal decomposition of a gemstone or diamond surface is due to refraction and internal reflection as a beam of light passes through, reflects, and refracts around the physical facets of the gemstone. Virtual facet patterns can serve as a basis for further analysis because each virtual facet can correspond to a backward-tracing beam of light leaving the diamond and striking the surrounding hemisphere. This information can form the basis for several analyses and visualizations.

[0106] Various metrics can be derived from data collected from gemstone models. Example metrics could include light return, flicker probability (e.g., ... Figure 10 (as shown in 1000), contrast salience (e.g., as shown in 1000), Figure 15 As shown), virtual facet area distribution (e.g., as shown) Figure 14 As shown), virtual facet depth distribution (e.g., as shown) Figure 11 As shown), contour characteristics (e.g., Figure 13 As shown), weight ratio (e.g., as shown) Figure 12 The figure shown is 1200, which has a height of 1202, a width of 1205, and a weight ratio (chart 1206), symmetry fraction, etc. Other example metrics may include virtual facet comparison metrics, which may include isomorphism classes, Hausdorff distance, graphic editing distance, ice footprint, bowtie analysis, waistline reflection analysis, optical entropy, blaze diffusion, and / or optical symmetry fraction or virtual facet (VF) symmetry fraction.

[0107] Computerized simulations of various virtual facet arrangements can take into account many aspects of gem facet design in order to model the virtual facet patterns that a user will see under different lighting conditions. Any combination of these aspects can be used for the virtual facet modeling described in this paper.

[0108] For example, light return can help measure how bright a diamond appears and can be a factor in assessing diamond quality. Additionally, scintillation probability can help measure the likelihood that a virtual facet will capture a light source, thus measuring its scintillation. Contrast scintillation can indicate whether this contrast makes a diamond appear dark, or it can be an indicator of the design created by the pattern of contrast, such as classic heart and arrow patterns, and bow ties, which are dark virtual facet bands that cross the belly of some stones.

[0109] Virtual facet area distribution can measure ice inclusions without any judgment. Many small virtual facets can cause so-called ice inclusions, a pattern in a diamond that some consumers like while others may not. Profile characteristics can include information provided to consumers regarding the curvature of the diamond's profile. Weight ratio can measure whether a diamond presents a reasonable cross-sectional area based on its weight. This prevents manufacturers from artificially inflating carat weight, even if the difference may be subtle. Symmetry fraction can quantify the symmetry of a diamond. Virtual facet comparison metrics can include measures that allow researchers to search diamond cuts to find patterns that are as close as possible to the desired pattern.

[0110] Visual score example Light return can be measured using computer simulations to determine the percentage of light rays originating from a light source within a typical angular range that strike an observer's eye. Light performance metrics have been used in many different solutions. Light return can measure how bright a stone appears.

[0111] Example procedures for generating a light return score may include scanning the gemstone using a non-contact measuring device. In some instances, the non-contact measuring device can provide various measurements of the gemstone to generate a 3D model. In other examples, the measurements and / or the 3D model may be obtained from another computing device.

[0112] Ray tracing or beam tracing can be performed on 3D models to create virtual facet decomposition from multiple angles. Ray tracing, based on Snell's law, can be achieved by following the path of the main ray passing backward through the eye from the ray mesh and by interacting with the diamond through refraction and reflection. Beam tracing can be done at the beam level by tracing a parallel ray and creating a sub-beam in a tree-like data structure each time the beam hits a facet junction.

[0113] Each virtual facet can be a polygon in an image of the diamond, representing a class of nearly parallel rays that interact with the diamond and strike the viewer's eye. The angle between the incident ray and the horizon can be calculated for each virtual facet for each ray tracing. Virtual facets with angles between defined lower and upper limits can be considered illuminated. For example, virtual facets with incident light angles between 15 and 45 degrees can be considered illuminated. The total percentage area of ​​the illuminated facets can be returned for each ray tracing, thus creating a light return fraction for faceted and tilted diamonds.

[0114] A flicker score can involve the probability distribution of one, two, three, or more virtual facets of a gemstone that can be illuminated under a given randomly placed light source. This probability distribution can be used as a flicker score metric to determine the average number of flicker events (e.g., flashes) of a randomly placed source. More specifically, the metric can include analyzing the points on a hemisphere corresponding to each virtual facet. The flicker score can be the probability that a light source facing x degrees can illuminate one of these points. The flicker score can be calculated by considering the set of all points on the hemisphere less than x degrees from the intersection of the virtual facets. The flicker score can include the area of ​​the x-neighborhood divided by the total area of ​​the hemisphere. More generally, the flicker score can be limited to angles above the horizon where the light source would normally be located.

[0115] An example process for gemstone scintillation scoring may include using a non-contact measuring device to scan the gemstone or obtain measurements to generate a 3D model of the gemstone. Ray tracing or beam tracing can then be performed on this model to create a virtual facet breakdown from multiple angles.

[0116] The incident ray for each virtual facet can be plotted on a virtual hemisphere surrounding the diamond. The total area of ​​the set of all points within a set angular threshold for each point can be calculated and divided by the area of ​​the hemisphere. The resulting scintillation score provides a measure of the likelihood that the diamond will exhibit a scintillation event.

[0117] In some instances, the calculations described herein can be performed within a portion of the described hemisphere to represent the angle with respect to the horizontal line within set upper and lower limits. This can refine the flicker score, capturing only light sources within a limited range of positions above the horizontal line. In some embodiments, to capture the average number of flicker events from randomly placed light sources, the number of virtual facets illuminated by the light source can be counted for each point in the hemisphere at a fixed, given angular threshold. The average can be taken over the hemisphere or a selected subset. In some instances, the visual area of ​​flicker events can be captured for each point in the hemisphere. The total area of ​​the illuminated virtual facets can be calculated and averaged over the hemisphere or a selected subset.

[0118] Contrast intensity can be measured by the percentage of light that hits the observer's eye, which comes from near-vertical lines and typically appears darker in the stone when viewed.

[0119] An example process for determining the contrast and saturation of a gemstone may include using a non-contact measuring device to scan the gemstone or obtain measurements to generate a 3D model of the gemstone. Ray tracing or beam tracing can be performed on this model to create a virtual facet breakdown from multiple angles. Using the geometry of the model and the physical properties of refraction and reflection, the angle of the incident ray to the horizon can be calculated for each virtual facet for each ray tracing. Virtual facets where the incident ray falls within a set angular threshold (such as 15 degrees) on the vertical line can be considered occluded. The total percentage area of ​​the occluded facets can be returned for each ray tracing, thus creating an occlusion score for faceted and tilted diamonds. For example, a diamond might have 10% visual area occluded, a relatively small amount of occlusion, or 40% occlusion, indicating a very dark diamond.

[0120] The virtual facet area distribution can include a list of virtual facet areas, which can be further divided into small facets, medium facets, and large facets.

[0121] The process of determining the virtual facet area distribution may involve using non-contact measuring devices to scan the gemstone or obtain measurements to generate a 3D model of the gemstone. Ray tracing or beam tracing can be performed on this model to create virtual facet breakdowns from multiple angles. Virtual facets can be grouped into different sizes based on set thresholds. The total area occupied by small facets can provide a measure of how much ice (i.e., the industry term referring to the smaller areas of virtual facets on a stone, which can have an optical effect similar to observing ice or glass) is present. The area distribution provides a judgment of the stone's overall appearance.

[0122] Virtual facet depth distribution can include classifying diamonds by beam length and / or combination depth. Beam length can be the apparent distance between the virtual facet and the eye, while combination depth measures the amount of interaction (reflection and / or refraction) between the beam and the diamond surface. Diamonds with a higher percentage of low-depth facets can have a sharper virtual facet profile. Longer beam lengths can be associated with a greater dispersion probability (also known in the industry as fire). Example procedures for determining virtual facet depth distribution can include using a non-contact measuring device to scan the gemstone or obtain measurements of the gemstone to produce a 3D model of the gemstone. Ray tracing or beam tracing can be performed on this model to create a virtual facet breakdown from multiple angles. The number of ray-facet interactions for each virtual facet can be recorded, which can be defined as the combination depth. In some instances, the physical length of the ray path for each virtual facet can be measured. The relative percentage of area at high depths can give the probability of more washed virtual facets and increased fire. The percentage of area at low depths can give a measure of the sharpness of the perceived pattern.

[0123] Contour characteristics can include analyzing the convexity and other factors of a diamond's contour. This can include finding the best-fit Bézier curves for the four quadrants of the contour. For an oval shape, this can involve a one-dimensional family of fitted Bézier curves indexed by the parameter κ. A value of κ = 0.55 will give a perfect ellipse, while higher and lower values ​​will make the result more convex or more pointed. For a marquise shape, there can be two parameters. κ controls the curvature of its wings, while the angle θ controls the angle between the two tips. Finally, a pear shape can have three parameters: the curvature κ of the paired shoulders, the curvature µ of the wings, and the angle θ of the points.

[0124] The process for determining the contour features of a gemstone may include scanning the gemstone or obtaining measurements of it and generating a 3D model of the gemstone. This process may also include aligning the 2D shading of the diamond. Aligning the shading of a diamond may include: for each potential axis of symmetry, calculating the convex hull of the shading plus the area of ​​its reflection. The axis of symmetry with the smallest area can be selected, and the diamond can be rotated so that this axis is horizontal. Bézier curves can be fitted to the four quadrants of the diamond. For an oval shape, the curves can all be approximately identical. The curves can be fitted to a family of single parameters from kappa=0 to kappa=1, where kappa=0.55 is an ellipse. The control points of the Bézier curves can be located on constant fractions of kappa for the width and height of the contour. More specifically, if the stone is modeled to be centered at the origin and aligned with the axes, the four control points of the curve may include (0, a), (kappa×b, a), (a, kappa×b), and (b, 0). For a marquise shape, the four quadrants can also be approximately identical. The marquise shape can be fitted to a family of two parameters, where the parameter mu controls the curvature (a smaller mu means a flatter shape), and the parameter theta controls the angle of the tangent drawn at the tip of the marquise shape.

[0125] A pear shape can have a marquise half and an oval half. The oval half can be controlled by the parameter kappa, while the marquise half can be controlled by the parameter mu. The aspect ratio can be calculated as the difference between the maximum and minimum x-coordinates in the aligned diamond divided by the difference between the maximum and minimum y-coordinates. A pear shape can have two independent aspect ratios, one for the marquise half and another for the oval half, and also has an independent culet position.

[0126] Weight ratio can refer to the ratio of surface area to volume when viewed from above. A lower weight ratio means fewer visible diamonds per carat. Figure 11 The output 1100 shows the weight ratio. The weight ratio may include identifying the diamond's dimensions (e.g., 1102, 1104) and determining the weight ratio via chart 1106.

[0127] An example process for generating the weight ratio of a gemstone may include scanning the stone and generating a 3D model of it. The process may also include uniformly scaling the model so that the 2D footprint is a predefined fixed area, or the weight is a predefined fixed weight. The area of ​​the shape profile can be calculated with the table face up and divided by the volume of the diamond.

[0128] A symmetry score can be calculated by matching facets across a line of symmetry and calculating the deviation of each facet from its matching facet version mapped along the line of symmetry. These two facets can be superimposed, and the symmetry difference in their areas can be calculated. A score of 0 indicates perfect symmetry.

[0129] Various metrics can be used to determine the closeness of virtual facet patterns. A first example metric could be isomorphism class. Two virtual facet patterns are said to be close if their abstract graphical types are isomorphic. The process for determining isomorphism class could involve scanning the stone and generating a 3D model of it. Ray tracing or ray tracing could be performed on this model to create virtual facet decompositions from multiple perspectives. The virtual facet decomposition could be transformed into an abstract mathematical graph consisting of nodes and edges. The similarity of two diamonds can be compared by examining whether there is mathematical isomorphism between their virtual facet patterns.

[0130] Another example metric could be the Hausdorff distance. Two virtual faceted patterns are said to be close if the Hausdorff distance between them is small (e.g., within 1% or 2% of the diamond's diameter). The Hausdorff distance could be a metric defined as follows: For each point x in the first group, let d(x) be the minimum distance from x to points in the second group. Then the Hausdorff distance could be defined as the maximum of all d(x).

[0131] The process of determining Hausdorff distance may involve scanning the stone and generating a 3D model of it. Ray tracing or beam tracing can be performed on this model to create a virtual facet breakdown from multiple angles. The similarity of two diamonds can be compared by examining the Hausdorff distance of their virtual facet patterns. As an example, Hausdorff distance can be used to maximize other performance metrics while keeping the virtual facet pattern as close as possible to the desired virtual facet pattern.

[0132] Graphical edit distance can include a combination of distance definitions. This distance can be the minimum number of edits required to move from one graphic to another, including the deletion or addition of vertices and edges. The process for determining the graphical edit distance can include scanning the stone and generating a 3D model of it. Ray tracing or ray tracing can be performed on this model to create a virtual facet decomposition from multiple angles. The virtual facet decomposition can be transformed into an abstract mathematical graph composed of nodes and edges. By calculating the graphical edit distance between two virtual facet patterns of a diamond, their similarity can be compared. As an example, graphical edit distance can be used to maximize other performance metrics while keeping the virtual facet pattern as close as possible to the desired virtual facet pattern.

[0133] An ice footprint can be a measure of how much of the visible area of ​​a diamond is occupied by ice (a term used for areas with small virtual facets). The process for measuring an ice footprint can involve scanning the gemstone and generating a 3D model of it. Ray tracing or beam tracing can be performed on this model to create a virtual facet breakdown from multiple angles. The percentage of the virtual facet pattern occupied by small virtual facets gives a measure of the ice footprint.

[0134] Bowtie analysis can include metrics to measure the presence of a bowtie, which is a band of covering across the belly of a stone of a particular shape, such as pear or oval. The process for performing bowtie analysis can include scanning the gemstone and generating a 3D model of it. Ray tracing or beam tracing can be performed on this model to create a virtual facet breakdown from multiple angles. A virtual facet with a band of covering across the belly of the stone near the culet can be considered part of the bowtie pattern. The area of ​​the bowtie can be calculated and output.

[0135] Girdle reflection analysis can include a measure of the extent to which the light path reflected from the diamond's girdle at a given point traverses the visible area of ​​the diamond. This area can be important because it represents the area of ​​the stone where dirt on the girdle might become visible.

[0136] The process for performing girdle reflection analysis may involve scanning the gemstone and generating a 3D model of it. Ray tracing or beam tracing can be performed on this model to create a virtual facet breakdown from multiple angles. The principal ray path of each virtual facet can be analyzed to see if it contacts the girdle at any point. If so, this virtual facet can be considered to have girdle reflection.

[0137] Optical entropy is a measure of the combined dispersion of light. It measures whether virtual facets near a given virtual facet represent incident light rays approaching or moving away from the selected virtual facet.

[0138] The process for measuring optical entropy may involve scanning the gemstone and generating a 3D model of it. Ray tracing or beam tracing can be performed on this model to create virtual facet decompositions from multiple angles. A score can be assigned to each virtual facet as follows: Let n denote the unit vector of a given virtual facet in the direction of the back-tracing outgoing beam. For each adjacent facet f, consider the unit vector n(f) representing its back-tracing outgoing beam. Let A be the area percentage of a given virtual facet (2D area divided by the total 2D area of ​​all virtual facets), and let A(f) be the area percentage of adjacent virtual facets. A score can be assigned, which is the sum of the dot products A × A(f) × (Arccos(v1.DotProduct(v2)) / PI). The larger this number, the smaller the spread between adjacent facets. The total score can be the average score for each virtual facet. This can be defined as the optical entropy.

[0139] Blaze diffusion can be defined as a measure of the diffusion of a virtual facet illuminated by a single light source. Given a light source, the centroid of the illuminated facet can be calculated, the convex hull can be calculated, and the area can be determined. A larger area corresponds to greater diffusion and enhanced blaze. This can be calculated on an illuminance grid within two selected upper and lower polar angle limits in the upper hemisphere.

[0140] The process for measuring scintillation diffusion can involve scanning the gemstone and generating a 3D model of it. Ray tracing or beam tracing can be performed on this model to create virtual facet breakdowns from multiple angles. Polar meshes can be overlaid in annulus between two selected angles from the horizon in the upper hemisphere. For example, the meshes can be overlaid between 45 and 85 degrees, or between 0 and 90 degrees, and so on. Each cell in the polar mesh can be analyzed to determine the incident rays of light on the virtual facets that intersect it. The centroid of each such virtual facet can be calculated, and their convex hulls can be formed. In some instances, the convex hulls of a set of illuminated virtual facets can be calculated, rather than the convex hull of their centroids. The area of ​​this polygon can be calculated, and a relative area (the area of ​​the polygon divided by the total visible area of ​​the diamond) can be calculated. An average area can be calculated on the polar mesh, giving a scintillation diffusion score, which measures the typical distribution of a single light source on the diamond.

[0141] In some examples, virtual facet modeling can be considered source-dependent or source-independent. Source-dependent can mean that the shading of the virtual facets is (partially) determined by the location of (one or more) sources, allowing us to create a map with illuminated virtual facets. Source-independent can mean that the shading of the virtual facets is completely independent of the location / intensity of any particular source.

[0142] Examples of symmetric fractions In some examples, symmetry scores can be used to practice the systems and methods described herein. Such symmetry scores may be used in determining further measures using modeled virtual facets. In the 4Cs (color, clarity, cut, and carat weight), cut may include symmetry assessment. In some cases, symmetry can be assessed manually in the laboratory. Graders can assess symmetry by crossing appropriate symmetry lines (such as...). Figure 3 (As shown) Symmetry deviations are visually assessed by comparing the size, shape, and orientation of facets, facet edges, and facet junctions. Recently, efforts have been made to automate the assessment of symmetry. This can be done more easily with round brilliant diamonds that have a consistent facet arrangement, such as... Figure 4 An example of creating an asymmetric image is shown in the image.

[0143] Figure 3 The first example compares symmetry at 300, and Figure 4This is the second example of symmetry comparison 400. (e.g.) Figure 3 As shown, the symmetry 304, 306 between the first diamond image 302 and the virtual facets 308, 310.

[0144] Many methods for automatically assessing symmetry deviations do so by analyzing deviations in conventional measurement parameters. Many of these measurements do not directly measure visual deviations, but rather the deviations in the metric are proxies of the actual visual defects the grader is assessing. For example, measuring the maximum deviation of the pavilion angle could be a good indicator that the facet edges and joints on the pavilion may not typically align across the eight (8) axes of symmetry of a round brilliant diamond. A fundamental drawback of this approach is that all diamond facets may have to be identified and sorted to ensure alignment across the eight (8) axes of symmetry. Figure 3 Make appropriate comparisons using the lines of symmetry shown. For fancy shapes, this method may often be untenable, because, as... Figure 4 Each of the gemstone shapes shown may have countless different facet arrangements.

[0145] A more direct approach could involve the use of viewing devices. Viewing devices can be used to specifically assess aspects of symmetry, and other devices include symmetry assessment as part of pattern analysis (“heart-and-arrow” viewer). Other viewer can measure various aspects of a diamond’s appearance, which may include aspects of symmetry.

[0146] In some examples, the evaluation can be based on 2D or 3D models of the diamond, rather than directly capturing aspects of symmetry from the diamond itself. To construct a 3D model, the scale and angles of each facet can be captured as... Figure 2 The 3D wireframe file shown depends on the 2D representation of the model facing upwards.

[0147] For example, 3D mesh files of gemstones can be used in various applications, but primarily for measuring these potentially tiny objects with a high level of accuracy. These 3D files can be referred to as wireframes, for example... Figure 2 An example of a 3D wireframe model is shown. Figure 2 This is an example wireframe diagram 200 based on the embodiments described herein.

[0148] The system and method described herein can be used to first convert wireframe files into a list of various vertices and isolated vertex indices representing the faces or facets of a given gemstone, as needed. These faces can be polygons with at least three vertices existing in 3D space. Due to the optical measurement system capturing the wireframe, the wireframe file may itself be face-down in orientation. The following steps can be taken for wireframe files.

[0149] These steps may include transforming the list of XYZ points and facet vertices as needed. These steps may also include flipping the wireframe to an upward orientation by inverting the X and Z coordinates. These steps may also include determining the convex hull of the gemstone in XY space. These steps may also include determining the centroid of the convex hull. These steps may also include offsetting all points in XY space such that the centroid of the convex hull lies at XY=0, 0. These steps may also include rotating the gemstone to the desired orientation in XY space.

[0150] The result of this process can include a 3D gem frame considered to be facing upwards. It can be rotated to a symmetrical orientation, where the centroid of the XY profile is 0, 0. At this point, the process of evaluating the symmetry of the facets can be performed.

[0151] Symmetry processes can be performed along various axes of symmetry. The following process applies to all axes of symmetry; however, a vertical axis of symmetry can be used to describe the process. A vertical axis of symmetry can divide a gemstone into a left and right half.

[0152] The first step in the example process may include determining which pairs of facets will be compared along the axis of symmetry. That is, if the gemstone is divided along the axis of symmetry, it can be determined which pairs of facets should be compared to each other. The XY centroids of each facet can be determined, and the centroids can be grouped according to their XY arrangement relative to the axis of symmetry. All centroids existing to the left of Y=0 (all centroids with Y coordinates less than 0) can be considered to be located in the left half of the gemstone. All centroids existing to the right of Y=0 (all centroids with Y coordinates greater than or equal to 0) can be considered to be located in the right half of the gemstone.

[0153] In some examples, the methods described herein can be generalized from facet-level analysis of a gemstone to virtual facet-level analysis of the same diamond. In these embodiments, instead of comparing pairs of facets, pairs or groups of virtual facets are compared. Symmetry maps and similar metrics, associated with what is generally considered optical symmetry, provide a method, for example, for assessing the symmetry of an arrow in a standard circle or the symmetry of a bow tie in a fancy cut that displays these patterns. Furthermore, the same virtual facet-level analysis can be performed on diamonds in a face-down orientation; for example, this might be necessary for analyzing heart-shaped patterning of standard round brilliant cuts and related shapes.

[0154] One example difference in the overall flow of this algorithm is that ray tracing or beam tracing of the diamond can be performed first on the face-up and face-down orientations to create virtual facet maps of these orientations. These maps can then be used as input to the symmetry algorithm described earlier.

[0155] Before evaluating any pairings, in some examples, certain facets may not be paired. One such example is a table facet, because it has only one table facet and typically intersects the axis of symmetry. Computerized routines can be implemented to identify these facets and remove them as an option in the following pairing algorithm, although they are still considered paired in subsequent steps. These facets can be called lonely facets. Lonely facets can be paired using the following methods: If a lonely facet intersects the axis of symmetry, the facet can be divided into two polygons along the axis of symmetry and identified as a pair. If a lonely facet does not intersect the axis of symmetry, the facet can be considered "completely asymmetric," and non-overlapping polygons can be created by inverting the lonely facet across the axis of symmetry (as described in the next section). The Euclidean distance in XY space between the centroids of all facets to the left of the axis of symmetry and the centroids of all facets to the right of the axis of symmetry can be calculated. For this calculation, the coordinates of the centroids of the facets on the right side can be inverted along the axis of symmetry to attempt to find the closest centroids for pairing on the opposite side. This distance matrix can then be sorted in ascending order.

[0156] Centroid pairs with the minimum Euclidean distance can be stored, and these two facets can be removed from any further possible pairings. Minimum distance pairs can be repeatedly extracted until no possible pairs exist between the left and right halves. Any remaining unpaired facets can then be considered isolated facets. In some instances, best-fit matching algorithms, such as the Hungarian Algorithm, can be used. Once all paired facets are identified, asymmetric image creation can begin. Paired facets are reversed along the axis of symmetry, and the symmetry differences between the original facets and their reversed counterparts are collected as non-overlapping polygons. These non-overlapping polygons can then be superimposed onto the original 2D face-up wireframe image. The original wireframe is colored green. Non-overlapping polygons on the crown (upper part of the stone) are colored red. Non-overlapping polygons on the pavilion (lower part of the stone) are colored blue. The entire process of superimposing symmetry differences can be completed along all axes of symmetry.

[0157] The resulting asymmetric image can be used as input to a pre-trained convolutional neural network, which then produces probability-based predictions for the symmetry grade of the gemstone. Figure 5 An example of this process is shown, where a convolutional neural network is used for symmetry reasoning to obtain the symmetry grade. For example... Figure 5As shown, image 502 can be fed into a trained neural network 504 to generate a symmetry grade 506. The trained neural network 504 may include multiple elements 504A-S, such as convolutional + ReLU blocks (504A, 504C-D, 504F-H, 504J-L, and 504N-P), max pooling blocks (e.g., 504B, 504E, 504I, 504M, 504Q), fully connected -ReLU blocks (e.g., 504R), and softmax blocks (e.g., 504S).

[0158] Symmetry grades can include the total area of ​​symmetry differences (non-overlapping areas), possibly expressed as a percentage of the area of ​​the outline. In this metric, a gemstone with perfect symmetry can have a score of 0%, while a stone with very low symmetry will have a score of 100% or higher because the non-overlapping area may exceed the area of ​​the outline. This metric can be further subdivided to measure only the non-overlapping area of ​​the crown or pavilion.

[0159] Examples of graphical representation and visual modeling The analytical methods, supplemented by various graphical representations, are designed to transform complex gemological data into a format that is easily accessible and understandable to both experts and non-experts.

[0160] In some examples, the systems and methods described herein can be used to model shimmering patterning or flickering. This modeling can show what would be observed in a darker environment with some bright sources. This embodiment provides a tool for demonstrating such patterning by selectively illuminating virtual facets for display. Another aspect of optical performance is contrast patterning, which is typically viewed in a uniformly lit environment with a panoramic area obstructed by the viewer.

[0161] This embodiment can be used to model and display any input gemstone cut wireframe, model, volume, etc. Example displays may include virtual facet patterns highlighted by virtual facet areas (e.g., such as...). Figure 14 The 1400 shown), and the virtual facet pattern highlighted by the beam depth (e.g., as shown) Figure 11 The 1100 shown), a virtual faceted pattern with edges highlighted by contrast (e.g., as shown in Figure 1100), Figure 15 1500 shown).

[0162] Other example outputs may include symmetry maps, contour assessments (e.g., ... Figure 13 The diagram shown is 1300°, and the simplified angular spectrum diagram is as follows (e.g., as shown in the figure). Figure 9 The diagram shown is 900), isomorphic mapping diagram, and simplified diagram of the emitted beam (e.g., as shown). Figure 8 The 800 shown), interactive optical path and light source visualizer (e.g., as shown in the image) Figure 7The 700 shown and Figure 8 800 with virtual facets 802, 804), contrast / sparkle presentation tools, waistline interaction maps (e.g., ... Figure 6 The 600 shown), optical entropy mapping (e.g., Figure 18 1800 in the middle), blaze diffusion map (e.g., Figure 17 (1700), optical symmetry map or VF symmetry map.

[0163] Virtual facet maps can be the backbone of many of the techniques proposed in this paper. They can be displayed on a computer user interface as a simple black-and-white image or with various levels of detail. Ray tracing or beam tracing can generate a series of virtual facets, each facet maintaining a record of the reverse light path to it and the outgoing path into the surrounding hemisphere. Virtual facets can divide a view of a diamond into individual polygons, each with a unique ray path leading to it. A bare polygonal image without any color or other markings can be referred to as a black-and-white contour virtual facet map.

[0164] A virtual facet map (with the reverse ray path for each virtual facet and the outgoing beam that reverse-tracks the intersection with the virtual hemisphere) can represent the complete first-order optical information of a diamond from a specified viewing position. The following analyses can all be derived from this data, and therefore only require a single ray tracing or beam tracing operation.

[0165] The model displaying the black-and-white outline of a virtual faceted pattern can vary depending on the viewer's eye position relative to the stone. The stone can be tilted, and different patterns will be visible. The light source does not affect the outline. The choice of light source can influence how the virtual facets are illuminated, which can be important for many tools and analyses.

[0166] Systems and methods may include the use of reverse ray / beam tracing. Instead of starting from the light source and following all the beams that leave the source, most of which never reach the observer's eye, we reverse the path of light from the eye, through the diamond, and back to the world. Each virtual facet can represent a different path of light from the eye to the world, which is modeled as a hemisphere around the diamond, sometimes referred to as a virtual hemisphere.

[0167] Tools that modify the light source can examine which of these paths hit the light source in the hemisphere. This can include light source analyzers, shimmer / contrast tools, and diamond evaluation maps. Many other tools, such as light path analyzers, start with a virtual facet and trace its final position on the hemisphere.

[0168] Figure 7 Example output 700 of the tool used to visualize the light path corresponding to the selected visual facets is shown. Figure 7As shown, the output can be used to identify the facets 702 and optical path 704 of a diamond using the system and method described herein. The virtual facet pattern 702 can be displayed on a UI screen. The system and method can acquire input from a user (e.g., a mouse or other cursor position on the screen) and use it as an indication of where a light source might be aligned with the facet pattern. The system and method of this paper can then use the user input about the light source to generate a virtual facet pattern to display the resulting optical path (e.g., 704) based on that information.

[0169] For example, the process of determining the light path of a gemstone may involve scanning the stone and generating a 3D model of it. Beam tracing can be performed on this model by using the stone's geometry and the physical properties of refraction and reflection to trace the light beam passing through the stone in reverse. A virtual facet map can be displayed on one side of the screen. The outline of the 3D diamond model can be displayed on the other side of the screen. The user can move the mouse over different virtual facets, and the corresponding light path can be displayed within the 3D model.

[0170] Figure 8 An example UI display or output 800 is shown for a tool used to visualize virtual facets illuminated by a light source at a specific location. For example, if a light source is to be shown or exposed to any particular direction or portion of a gemstone, the systems and methods of this paper can model which virtual facets are illuminated. For example, in Figure 8 In this process, the user hovers the mouse or other UI pointer over a portion of the model surrounding the hemisphere of the gemstone, and the resulting beam of light to be illuminated is displayed on a virtual facet map 802 of the gemstone itself. The user's cursor or mouse hovering over the model indicates the indicated location of the light source's direction, and the program can calculate which virtual facets intersect with that light source and then illuminate them on the UI, thus modeling the virtual facets that a person watching such a gemstone cut would see while viewing the model.

[0171] The process for calculating the outgoing beams that intersect with the light source can include scanning the gemstone and generating a 3D model of it. Beam tracing can be performed on this model by using the stone's geometry and the physical properties of refraction and reflection to trace the beams of light passing through the stone in reverse. A virtual facet map can be displayed on one side of the screen. A map of a virtual hemisphere indicating the location where the reverse-traced outgoing beams strike the hemisphere can be created and displayed on the other side of the screen. The user can hover a light source with an adjustable angular radius above the virtual hemisphere. The program can calculate which outgoing beams intersect with the light source and illuminate the corresponding virtual facets in the virtual facet map.

[0172] By modeling what light would do from the hemispherical dome surrounding this gem, it can be recreated in the real world by physical components. Figure 8Modeling of virtual facets in a dome. For example, a physical dome with multiple arrays of different lights in different quadrants and sectors of the dome can communicate with a computer. The computer can be programmed to illuminate certain lights in the dome, which are pointed at the physical gemstone in the dome at different angles to illuminate different virtual facet designs of the gemstone itself. In this way, the system and method of this paper can be used to create a computerized model of virtual facet illumination by user-input light sources and / or by creating a physically real-space dome for housing a gemstone, where light from different angles is displayed into the gemstone to produce the desired virtual facet design for the user's eye and / or camera in the physical reality space.

[0173] A simplified diagram of the outgoing beam can include a diagram that models how the outgoing beam from each virtual facet intersects with a simulated or real outer hemisphere. This can provide a visualization of how a diamond collects light from its environment. One process for generating this visualization can include scanning the stone and generating a 3D model of the stone. Beam tracing can be performed on this model by using the geometry of the stone and the physical properties of refraction and reflection to trace the beams passing through the stone in reverse. The location where each beam strikes a virtual hemisphere can be plotted as the intersection of the beam and the hemisphere. This gives a spherical polygon, for example, which can be... Figure 8 It was seen at position 804.

[0174] Figure 9 This shows an example output of 900 from a tool used to visualize the distribution (angular spectrum) of angles at which a diamond collects light and directs it to the viewer's eye. Figure 9 In this context, circles with the same area can be shown instead of the exact intersection of the beams.

[0175] The process for determining the distribution of angles may involve scanning the stone and generating a 3D model of it. Beam tracing can be performed on this model by using the stone's geometry and the physical properties of refraction and reflection to trace beams of light passing through the stone in reverse. The location where each beam strikes a virtual hemisphere can be plotted as a circle with the same area as the virtual facet.

[0176] also, Figure 10 This shows an example output of 1000 from a tool used to visualize and calculate the probability of flickering events. Figure 10 In this tool, you can view the set of points where rays intersect with the outer hemisphere and calculate the set of all points within a specified angular distance. This can include looping over a radial grid.

[0177] The process for calculating scintillation events may involve scanning the stone and generating a 3D model of it. Beam tracing can be performed on this model by backtracking a beam of light passing through the stone using the stone's geometry and the physical properties of refraction and reflection. The user can define the angular radius of the light source, such as 1 degree or 2.1 degrees. The program can use a radial grid search to display a set of points within a specified angular radius of one of the outgoing beams. The covered area can represent the location of light sources with a given angular radius that will illuminate at least one virtual facet of the diamond. The relative area can provide the probability that a randomly placed light source with a given angular radius will illuminate at least one virtual facet. Additionally or alternatively, the tool can be further refined to limit it to certain angles above the horizontal line where the light source would typically be located.

[0178] Figure 11 Example output 1100 is shown for a tool used to visualize and calculate the depth of virtual facets. (e.g., ...) Figure 11 As shown, virtual facets 1102 can be identified, where the depth of each virtual facet is represented in the diamond's characterization (e.g., 1104). Figure 11 The tools in the document can use the same beam tracing information by listing the number of interactions for each light ray.

[0179] The process for calculating the depth of a virtual facet can involve scanning the stone and generating a 3D model of it. This model can be beam-traced by using the stone's geometry and the physical properties of refraction and reflection to trace the light beams passing through the stone in reverse. Each virtual facet can be colored based on the amount of interaction between the light ray path and the diamond.

[0180] Additionally or alternatively, the system and method described herein may include an Angle Spectrum Evaluation Tool (ASET) map. The ASET map records the angle of the outgoing beam to the horizon and colors each virtual facet accordingly. Outgoing beams originating within 15 degrees of the vertical line are given a blue virtual facet. Outgoing beams originating within 45 degrees of the horizon are given a green virtual facet, and outgoing beams located between these two (typically where the light source is located) are colored red. Outgoing beams originating below the horizon, corresponding to leakage, are colored black, gray, or white. The percentage of ASET values ​​analyzed as red, green, or blue can be used to predict visual characteristics such as brightness or contrast.

[0181] Other versions of ASET have continuous color gradients between different colors, making boundary cases easier to understand. Another version uses monochrome encoding. For example, one could take the fourth power of the cosine of the angle relative to the vertical line. Figures 16A-16C A view showing an example diamond evaluation image. For example, Figure 16A Example normal image 1600A is shown. Figure 16B An example color gradient image 1600B is shown, and Figure 16C Example monochrome diamond image 1600C is shown.

[0182] The process of generating visualizations using ASET can include scanning a stone and creating a 3D model. Beam tracing can be performed on this model by back-tracing a beam of light passing through the stone using the stone's geometry and the physical properties of refraction and reflection. The polar angle of the outgoing beam is calculated for each virtual facet. The virtual facets can be colored according to the ASET scheme, a continuous color gradient scheme, or a monochromatic scheme.

[0183] These examples can be used to capture the phenomenon of contrast. When viewing a diamond facets up, the virtual facets with light rays originating from near-vertical lines tend to appear dark because the viewer's head blocks these light paths. The dark patterns seen in a diamond are called contrast. Generally, a little contrast is needed to make the patterns in a diamond interesting, but too much contrast will make the diamond appear too dark.

[0184] In standard round brilliant diamonds, the contrast often creates a pleasing 8-fold arrow pattern. The related phenomenon in oblong diamonds is sometimes referred to as a bowtie, and its desirability is an aesthetic choice.

[0185] Contrast can be calculated using a method similar to the ASET angle cutoff method, displaying a virtual facet with a near-vertical outgoing beam as dark. See also Figure 15 .

[0186] This can result in a virtual facet pattern colored by a contrast map, which can be used to predict bow ties or view an 8x / 8-fold arrow pattern in a standard round brilliant diamond. An 8x / 8-fold arrow pattern can be associated with a well-cut round brilliant diamond. A bow tie can be a term used to describe the contrast along a band in the middle of some fancy cut. How much a consumer likes a bow tie can be subjective, and the tool can visualize this without labeling it as good or bad.

[0187] Another use of virtual facets is for modeling a phenomenon known as ice shards. This is an optical effect found in some rocks that is said to resemble ice shards. Ice shards can be represented as clusters of small virtual facets.

[0188] To represent qualitative aspects of how virtual facets appear (including ice-breaking effects), virtual facets can be categorized into three types: small, medium, and large. Then, in addition to a graph showing the facet size distribution, a color-coded map can be displayed. See also Figure 14 This can result in virtual facet patterns colored according to the area map.

[0189] A virtual facet edge coloring chart can be constructed as follows. The diamond's wireframe model can be assigned edge colors to distinguish edge types: table, girdle, and edges in between. A simplified virtual facet diagram containing this color coding can be displayed.

[0190] The process for generating a virtual faceted edge color map may include scanning the gemstone, generating a 3D model, and performing beam tracing on the model by back-tracing a beam of light passing through the stone using the stone's geometry and the physical properties of refraction and reflection. At each stage of beam tracing, the shear edges of polygonal regions can be recorded. Color coding of the edge types can be used to create an edge coding map.

[0191] A symmetry map can include a map indicating deviations from symmetry, determined by identifying matching pairs of facets and displaying the deviations in reflections through shaded regions. This map can be used for AI training and is internally referred to as a symmetry map.

[0192] Contour analysis can analyze bulginess just like segment analysis, using sliders to indicate severity or curvature. Figure 13 The output of the example contour property is 1300. (Example:) Figure 13 As shown, the tip 1302, wing 1304, belly 1306, shoulder 1308, and head 1310 of the diamond can be identified. Additionally, wing outline diagram 1312 and shoulder outline diagram 1314 can be shown. Figure 13 The output can be generated by modeling the boundary with a Bézier curve and measuring its curvature.

[0193] The process for generating the contour characteristics of a gemstone may involve creating a 3D model of the gemstone and creating a 2D image of the model via an alignment routine that aligns the diamonds using the best-fit axis of symmetry. Specifically, pear, oval, and marquise shapes are aligned such that their long axes are horizontal. Bézier curves can be fitted to the four diamond quadrants within the family of curves defined by the previously mentioned parameters kappa, theta, and mu. These parameters can be used as input to determine the characteristics of the shape contour, fitting it to a narrow, standard, or wide category. The relationship between the shape parameters and the narrow, standard, and wide categories can be defined through human observation and subsequent data analysis.

[0194] Additionally or alternatively, the systems and methods described herein may include the use of virtual facet isomorphism maps. A virtual facet isomorphism space can refer to a region that divides the scale space of a diamond cut into areas labeled by graphic isomorphism classes. The isomorphism map can be a two-dimensional projection of the colors in this space encoded by isomorphism type or virtual facet number to create a map of virtual facet possibilities across different scale sets.

[0195] The process for generating a virtual facet isomorphic map may involve scanning the stone and generating a 3D model of it. Alternatively, the 3D model can be created algorithmically. A set of models with different scales (such as crown height, pavilion depth, tabletop dimensions, and shape parameters) can be created. This model can be beam-traced by back-tracing a beam of light passing through the stone using the stone's geometry and the physical properties of refraction and reflection. The space of all virtual facet patterns can then be divided into smaller segments, each representing a unique virtual facet type. For two or three parameter variants, this information can be described as a map with different regions colored according to the isomorphic type, or as a 3D drawing colored according to the isomorphic type.

[0196] A girdle interaction map can visualize which portions of a gemstone's visible field are produced by light rays that interact with the girdle in some way—rays that are either reflected inside the girdle or enter the diamond through it. This map is crucial for understanding where dirt or debris accumulated on the girdle will appear in the diamond's appearance. If the angle of incidence is less than the critical angle given by Snell's law, the light path in the diamond will be reflected like a mirror from the diamond's inner surface. However, if there is dirt or debris on the facets, this can lead to a phenomenon known as hindered total internal reflection, which causes the dirt to suddenly become visible along the light path that would otherwise be reflected. The girdle interaction map records the virtual facets in which girdle dirt might eventually become visible.

[0197] The process for generating the girdle interaction map involves scanning the stone and creating a 3D model of it. Beam tracing can be performed on this model by using the stone's geometry and the physical properties of refraction and reflection to trace the light beams passing through the stone in reverse. Each virtual facet with a light path interacting with the girdle can be highlighted.

[0198] Light entropy mapping diagram ( Figure 18 The virtual facets are created using the concept of light entropy. Virtual facets with adjacent facets that tend to collect light from similar directions are colored as light shadows, while virtual facets with adjacent facets that collect light from different directions are colored as darker shadows, with a continuous color gradient inserted between the two extremes.

[0199] The process for generating the entropy map may include producing a 3D map and performing beam tracing on the model by back-tracing the light beam passing through the stone using the stone's geometry and the physical properties of refraction and reflection. As previously mentioned, the score for each virtual facet can be calculated using the area of ​​the virtual facet and the dot product of the outgoing beam with the outgoing beams of adjacent facets. A continuous color gradient between blue and red can be created, coloring virtual facets with negative scores red and virtual facets with positive scores blue.

[0200] Blazing diffusion map ( Figure 17 This can include a mapping of a virtual hemisphere. Choose an angular radius, such as 2 degrees. Each pixel in the bottom-view of the virtual hemisphere is colored as follows: Take a light source with the selected angular radius and measure the relative area of ​​the convex hull of the illuminated facet (centroid). Color-code each pixel using a linear color gradient from 0 (unilluminated virtual facets) to 1 (illuminated virtual facets expanded as large as possible).

[0201] The process for generating a scintillation diffusion map may include generating a 3D model and performing beam tracing on that model by back-tracing the light beams passing through the stone using the stone's geometry and the physical properties of refraction and reflection. A face-down view of a hemisphere surrounding the diamond is depicted. The user can select the angular radius, in degrees, for the modeling light source. Each pixel in the face-down view is colored as follows: The beams emitted from virtual facets with the selected angular radius centered on that pixel can be viewed. The convex hull of the centroid of these virtual facets can be selected, or alternatively, the convex hull of the virtual facets themselves. The relative area of ​​the convex hull with respect to the total visible area of ​​the diamond can be calculated. Pixels can be color-coded using a linear color gradient from 0 (unilluminated virtual facets) to 1 (illuminated virtual facets expanded as large as possible).

[0202] Alternatively or additionally, instead of plotting the area of ​​the convex hull of the illuminated facets, one can plot the total area, thus giving a thermal map of the degree to which the light source is visible across the surface of the diamond, or one can plot the number of the illuminated virtual facets, thus giving a thermal map of the amount of scintillation as a function of the location of the light source.

[0203] Finally, various interactive tools can be used, which allow users to explore the geometry of virtual faceted patterns in relation to light paths.

[0204] Additionally or alternatively, the systems and methods of this paper may include a contrast / sparkle analysis tool, which may be used in any combination or arrangement, having some or all of the following examples. A first example may include displaying a virtual faceted pattern model on a user interface and allowing the user to input a request, such as by clicking on a tile (virtual facet) and selecting a color for the virtual faceted tile, to create a single frame of a flickering movie. This example may also include saving such frames to add to a sequence of over-flickering movies. After selecting x frames, the systems and methods of this paper (e.g., the algorithm) may be used to solve for a unique sequence of lighting configurations in the hemisphere to create the example movie. The virtual movie may be used to display interesting on / off patterns in the virtual faceted pattern tiles. The user interface may be used to create the actual illuminance of the gemstone with an RGB dome, so that the virtual movie can actually be presented to consumers alongside the physical gemstone.

[0205] Figure 14 The example virtual faceted model outputs 1400. Figure 14 In this context, the virtual facet pattern 1402 can be closely related to flickering, where the dense area of ​​small patches exhibits smaller, faster flickering. Furthermore, diagram 1404 can illustrate the virtual facet pattern and virtual facet size. Figure 14 The output can be generated using ray tracing instead of ray tracing. Virtual facets can be determined using various techniques. Area profiles can then be drawn, and the facets can be colored.

[0206] The process for generating a virtual faceted model can include creating a 3D model of the stone and performing ray tracing or beam tracing on the model by back-tracing a beam of light or a set of rays passing through the stone using the stone's geometry and the physical properties of refraction and reflection. Virtual facets can be calculated and displayed. Each virtual facet is colored according to its relative size (small, medium, or large) based on a defined percentage area threshold derived from human observation and classification. The percentage area of ​​each (small, medium, and large) virtual facet can be displayed. A graph indicating the number of virtual facets in each category can be displayed.

[0207] Figure 15 The output for contrast enhancement is shown as 1500. Figure 15 In this context, patterning can correspond to different contrast areas. Furthermore, charts can be used to highlight virtual facets with plateau angles. Figure 15 The output can be generated using ray tracing. Contrast can be calculated based on the proximity of the outgoing ray traced in the vertical reverse direction. Virtual facets within this range can be darkened. The percentage of darkness of the stone can be indicated at the bottom.

[0208] The process for generating contrast enhancement output may include producing a 3D model and performing ray tracing or beam tracing on that 3D model by back-tracing a beam of light or a set of rays passing through the stone using the stone's geometry and the physical properties of refraction and reflection. Virtual facet patterns can be calculated, and the outgoing beam information for each virtual facet can be analyzed. Virtual facets corresponding to high-angle (nearly vertical) incident rays are tinted "very dark," for example, with polar angles between 0 and 7 degrees. Virtual facets further away from the vertical direction (e.g., 7 to 15 degrees) can be tinted dark. Virtual facets within 45 degrees of the vertical direction are tinted slightly darker. Other virtual facets may be left untinted.

[0209] Additionally or alternatively, the systems and methods described herein may include an interactive, web-based encyclopedia of diamond cutting. This encyclopedia could be generated using a unique enumeration algorithm that allows for the efficient creation of comprehensive and detailed resources on diamond cutting. This could include interactive tools providing a variety of insights into diamond cutting. The encyclopedia described herein could provide textual or visual representations of the metrics derived herein for each type of diamond cut. For example, the encyclopedia could show virtual facet patterns, contrast performance, angular spectrum output, light return, light scintillation, etc., of a diamond.

[0210] In these examples, various methods can be used to generate pages corresponding to each diamond design through algorithms. Information from the charts, maps, and analyses listed above can be included for each cut. Information and research on the most common diamond designs can be added. Users can change the diamond proportions and obtain calculated charts, maps, and data based on these changes.

[0211] Multiple ideal 3D models of diamonds are created using an enumeration algorithm. These models are then optimized using metrics such as light return, contrast enhancement, and light entropy. This optimization can be automated using linear approximation constrained optimization (COBYLA), genetic algorithms, or other machine learning techniques, or it can be accomplished through manual tuning and analysis. The page is populated with these diamond models and can display visualizations of the diamond's performance as illustrated in this article.

[0212] Implementation Examples The current embodiments can be implemented using a combination of hardware and software components. The hardware components include scanning equipment and a computer, while the software components consist of ray / beam tracing and analysis software. It is proposed that the interactive encyclopedia be hosted on a distributed network platform.

[0213] In a first example embodiment, a method for analyzing the appearance of a diamond is provided. This method may include obtaining a 3D model file from a stone scan or another scan that is virtually created. The diamond scan (e.g., a real diamond or a virtual representation of a diamond) can be generated by a scanning device. The model can be generated from the output of the diamond scan using analytical techniques. The virtual scan can be obtained using scanning hardware or other 3D modeling or gen-cutting software.

[0214] The method may also include performing ray or beam tracing analysis on the stone to calculate virtual facet patterns and outgoing beam information. The method may also include calculating metrics such as light return, flicker probability, and contrast salience. Figure 9Any one of the following: virtual facet area distribution, virtual facet depth distribution, contour characteristics, weight ratio, symmetry fraction, graphic isomorphism class of virtual facet pattern, Hausdorff distance between virtual facet pattern and specified graphic, and / or graphic edit distance between virtual facet pattern and specified graphic.

[0215] Once this set of metrics is calculated, it can be included in various outputs, such as consumer-facing reports or used to populate pages in a diamond encyclopedia. These metrics can also be used in studies to optimize cut designs.

[0216] In some instances, these metrics are included in customer-facing diamond reports. In other instances, the method involves generating content for a diamond encyclopedia.

[0217] Additionally or alternatively, the systems and methods described herein may include representations of diamond appearance, which may include any of virtual facet patterns and have details such as coloring by virtual facet area, coloring by beam depth, edge coloring by type, coloring by contrast, ASET and variant coloring, as well as symmetry maps, profile assessments, angular spectrum diagrams, isomorphic maps, outgoing beam diagrams, interactive light path and light source visualizers, and contrast / scintillation demonstration tools.

[0218] Additionally or alternatively, the systems and methods described herein may include a physical device that surrounds a diamond with a hemisphere of light source, the hemisphere being programmed to reproduce a selected pattern or pattern sequence (movie).

[0219] Additionally or alternatively, the systems and methods described herein may include methods for generating an interactive, web-based encyclopedia of diamond cutting. These methods may include automatically generating a list of facet arrangements of a certain complexity using an enumeration algorithm. The methods may also include automatically populating a set of best-guess proportions and displaying charts and interactive content. Furthermore, the methods may include creating an interface for users to adjust the proportion set and display newly calculated charts.

[0220] Additionally or alternatively, the systems and methods described herein may include supplementing automatically generated content with manually created content for the most popular diamond shapes, including cutting guidelines for achieving desired properties. Additionally or alternatively, the systems and methods described herein may include an interactive, web-based diamond cutting encyclopedia, which may be generated using any of the methods described herein.

[0221] Network Example exist Figure 19 Examples of networked computing arrangements that can be utilized in this paper are shown. Figure 19In this context, a computer 1902, used to process images from a camera, can generate data including pixel data of the captured images. The computer 1902 can be any number or combination of computers of various types, such as those contained within the camera itself, the light source itself, and / or another computer arrangement communicating with the camera and / or light-generating components (and in some examples, stage motors and / or camera lens motors), including but not limited to laptop computers, desktop computers, tablet computers, tablet phones, smartphones, or any other devices for processing and transmitting digitized data. Such a computer 1902 can be used to control a camera 1980 and / or a light-generating device 1990 as described herein. Figure 19 The document describes computer 1902, as well as additional or alternative examples.

[0222] Return to Figure 19 Computer resources for any aspect of the system can reside on network 1920 in a networked or distributed format. Furthermore, data captured from any computer 1902 for pixelated images can be transferred to backend computer 1930 and associated data storage device 1932 for storage and analysis. In some examples, the transfer can be wireless 1910 via cellular or WiFi transmission using associated routers and hubs. In some examples, the transfer can be via a wired connection 1912. In some examples, the transfer can be via a network such as the Internet 1920 to backend server computer 1930 and associated data storage device 1932. At backend server computer 1930 and associated data storage device 1932, pixelated image data can be stored, analyzed, compared with previously stored image data to create models or analyses as described herein, or any other type of image data analysis. In some examples, the storage, analysis, and / or processing of image data can be performed at the computer 1902 involved in the original image capture. In some examples, data storage, analysis, and / or processing can be partitioned between local computer 1902 and backend computing system 1930. Networked computer resource 1930 can allow for the use of more data processing power than is otherwise available at local computer 1902. In this way, the processing and / or storage of image data can be offloaded to computing resources available on the network. In some examples, networked computer resource 1930 may be a virtual machine within a cloud infrastructure. In some examples, networked computer resource 1930 may be distributed across many computing resources via a cloud infrastructure. The example of a single computer server 1930 is not intended to limit and is merely one example of computing resources that can be utilized by the systems and methods described herein.

[0223] Example computer devices As described, any number of computing devices can be incorporated into or connected to the various component parts of the system described herein. For example, camera systems may include their own computing systems, lighting systems may include their own computing systems, and these computing systems can be used to collect, store, and analyze data from camera images. Such systems can be local and integrated with this document and... Figure 19 The systems described herein are directly connected. In some examples, some computing resources may be networked or communicate via a network, so that they are not necessarily co-located with the optical systems described herein. In any case, any computing system used herein may include component parts (such as...) Figure 20 (The component part described in the document).

[0224] Figure 20 An example computing device 2000 that can be used in the systems and methods described herein is shown. In the example computer 2000, a CPU or processor 2010 communicates with a user interface 2014 via a bus or other communication 2012. The user interface includes example input devices such as a keyboard, mouse, touchscreen, buttons, joystick, or one or more other user input devices. The user interface 2014 also includes a display device 2018, such as a screen. Figure 20 The computing device 2000 shown also includes a network interface 2020 for communicating with the CPU 2020 and other components. The network interface 2020 allows the computing device 2000 to communicate with other computers, databases, networks, user equipment, or any other computing-capable device. In some examples, the communication method may be via WiFi, cellular, Bluetooth Low Energy, wired communication, or any other type of communication. In some examples, the example computing device 2000 includes a peripheral device 2024 that also communicates with the processor 2010. In some examples, the peripheral device includes an antenna 2026 for communication. In some examples, the peripheral device 2024 may include a camera assembly 2028. In some example computing devices 2000, a memory 2022 communicates with the processor 2010. In some examples, the memory 2022 may include instructions for executing software, such as an operating system 2032, a network communication module 2034, other instructions 2036, an application program 2038, an application program for digitizing images 2040, an application program for processing image pixels 2042, a data storage device 2058, data (such as data tables) 2060, transaction logs 2062, sample data 2064, encrypted data 2070, or any other type of data.

[0225] in conclusion As disclosed herein, features consistent with these embodiments can be implemented via computer hardware, software, and / or firmware. For example, the systems and methods disclosed herein can be embodied in various forms, including, for example, data processors (such as computers, which also include databases, digital electronic circuits, firmware, software, computer networks, servers, or combinations thereof). Furthermore, while some of the disclosed embodiments describe specific hardware components, systems and methods consistent with the inventives herein can be implemented with any combination of hardware, software, and / or firmware. Moreover, the foregoing features and other aspects and principles of the inventives herein can be implemented in a variety of environments. Such environments and related applications can be specifically constructed to perform various routines, processes, and / or operations according to the embodiments, or they may include general-purpose computers or computing platforms that are selectively activated or reconfigured by code to provide necessary functionality. The processes disclosed herein are not inherently associated with any particular computer, network, architecture, environment, or other device and can be implemented through appropriate combinations of hardware, software, and / or firmware. For example, various general-purpose machines can be used with programs written according to the teachings of the embodiments, or it may be more convenient to construct specialized devices or systems to perform the required methods and techniques.

[0226] Some aspects of the methods and systems described herein, such as logic, can be implemented as functions programmable into any of a variety of circuit systems, including programmable logic devices (PLDs), such as field-programmable gate arrays (FPGAs), programmable array logic (PAL) devices, electrically programmable logic and memory devices, and standard cell-based devices, as well as application-specific integrated circuits (ASICs). Other possibilities for implementing some aspects include memory devices, microcontrollers with memory (such as EEPROMs), embedded microprocessors, firmware, software, etc. Furthermore, some aspects can be embodied in microprocessors with software-based circuit simulation, discrete logic (timing and combinational), custom devices, fuzzy (neural) logic, quantum devices, and any hybrid of the above device types. The underlying device technologies can be provided in various component types, such as metal-oxide-semiconductor field-effect transistor (MOSFET) technology such as complementary metal-oxide-semiconductor (CMOS), bipolar technology such as emitter-coupled logic (ECL), polymer technologies (e.g., silicon conjugated polymers and metal conjugated polymer-metal structures), hybrid analog and digital, etc.

[0227] It should also be noted that the various logic and / or functions disclosed herein can be enabled using any number of combinations of hardware, firmware, and / or data and / or instructions embodied in various machine-readable or computer-readable media, depending on their behavior, register passing, logic components, and / or other characteristics. Computer-readable media that can embody such formatted data and / or instructions include, but are not limited to, various forms of non-volatile storage media (e.g., optical, magnetic, or semiconductor storage media) and carrier waves that can be used to transmit such formatted data and / or instructions via wireless, optical, or wired signal media or any combination thereof. Examples of transmitting such formatted data and / or instructions via carrier waves include, but are not limited to, transmission (upload, download, email, etc.) over the Internet and / or other computer networks via one or more data transmission protocols (e.g., HTTP, FTP, SMTP, etc.).

[0228] Unless the context explicitly requires otherwise, throughout the specification and claims, the terms “comprising,” “including,” etc., shall be interpreted as inclusive, contrary to their meanings of exclusivity or exhaustiveness; that is, in the sense of “including but not limited to.” Use of singular or plural terms shall also include the plural or singular, respectively. Furthermore, the terms “in this document,” “in the following,” “above,” “below,” and similar terms refer to this application as a whole, and not to any particular part of this application. When the term “or” is used in a list referring to two or more items, the term encompasses all of the following interpretations: any one item in the list, all items in the list, and any combination of items in the list.

[0229] Although certain currently preferred embodiments of the embodiments have been specifically described herein, it will be apparent to those skilled in the art to which these descriptions pertain that variations and modifications can be made to the various embodiments shown and described herein without departing from the spirit and scope of the embodiments. Therefore, the embodiments are intended to be limited only to the extent required by applicable legal rules.

[0230] This embodiment can be embodied in the form of methods and apparatus for practicing these methods. This embodiment can also be embodied in the form of program code embodied in a tangible medium (such as a floppy disk, CD-ROM, hard disk, or any other machine-readable storage medium), wherein when the program code is loaded onto and executed by a machine such as a computer, the machine becomes an apparatus for practicing the embodiment. This embodiment can also be in the form of program code, for example, whether stored in a storage medium, loaded onto a machine and / or executed by a machine, or transmitted via some transmission medium (such as via electrical wiring or cable, via optical fiber, or via electromagnetic radiation), wherein when the program code is loaded onto and executed by a machine such as a computer, the machine becomes an apparatus for practicing the embodiment. When implemented on a general-purpose processor, the program code segment is combined with the processor to provide a unique device similar to the operation of a specific logic circuit.

[0231] The software is stored in a machine-readable medium that can take many forms, including but not limited to tangible storage media, carrier media, or physical transmission media. Non-volatile storage media include, for example, optical discs or disks, any storage device such as any computer(s). Volatile storage media include dynamic memory, such as the main memory of such a computer platform. Tangible transmission media include: coaxial cables; copper wires and optical fibers, including wires that form a bus within a computer system. Carrier transmission media can take the form of electrical or electromagnetic signals, or sound or light waves (such as those generated during radio frequency (RF) and infrared (IR) data communications). Therefore, common forms of computer-readable media include, for example: disks (e.g., hard disks, floppy disks, retractable disks) or any other magnetic media, CD-ROMs, DVDs or DVD-ROMs, any other optical media, any other physical storage media, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips, carriers that transport data or instructions, cables or links that transport such carriers, or any other medium from which a computer can read programming code and / or data. Many such forms of computer-readable media may involve loading one or more sequences of one or more instructions into a processor for execution.

[0232] For purposes of explanation, the foregoing description has been given with reference to specific embodiments. However, the illustrative discussion above is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. In view of the foregoing teachings, many modifications and variations are possible. Some embodiments were chosen and described in order to best explain the principles of the embodiments and their practical application, thereby enabling others skilled in the art to best utilize the various embodiments with various modifications suitable for the particular intended use.

Claims

1. A method for generating a virtual faceted model of a gemstone, the method comprising: Receive data about the scanned gemstone at a computer equipped with a processor and memory; The computer generates a 3D gem model using the received scanned gem data; The computer receives user input regarding the selection of a lighting environment related to the colors of the 3D model and an ideal hemisphere surrounding the virtual model. The computer uses the outgoing beam data from the 3D model file, along with ray tracing analysis of the 3D model and user-input lighting environment selection, to determine the facet color and illuminance; and The computer causes virtual facet illumination or facet color to be displayed on a user interface showing the 3D model.

2. The method according to claim 1, wherein the lighting environment selection is at least one of a single or multiple colored or white light sources, or an arbitrary allocation of light intensity.

3. The method of claim 1, further comprising the computer causing an animation of the virtual facet illuminance or facet color based on a programmed lighting environment sequence.

4. The method of claim 3, wherein the programmed lighting environment sequence comprises at least one of a model of a moving light source or a model of a shading ring that moves concentrically away from the hemispherical poles of the model.

5. The method of claim 1, wherein the lighting environment selection models the total illuminance of a hemisphere surrounding the gem model, with selected darkened portions to model occlusion and contrast.

6. The method of claim 1, further comprising using the computer to analyze the contrast of virtual facets in the 3D model using a model of the emitted beam data.

7. A system for reproducing a target virtual facet in a real gemstone, comprising: processor; as well as A memory having instructions that, when executed by the processor, cause the processor to perform steps including the following: Obtain data related to the scanned gemstone; Generate 3D gem models using the obtained scanned gem data; The virtual facet pattern and the first outgoing beam data are determined based on the ray tracing or beam tracing analysis of the 3D gem model and the input viewing direction. as well as This causes the determined virtual facet pattern to be displayed on a user interface that shows the 3D model and the determined virtual facet pattern.

8. The system of claim 7, wherein the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing facet depth information.

9. The system of claim 7, wherein the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing the actual virtual facet size from the 3D model.

10. The system of claim 7, wherein the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing the angle at which light is drawn from the virtual facets of the 3D model.

11. The system of claim 7, wherein the step further includes displaying virtual faceted details on the user interface.

12. The system of claim 11, wherein the virtual facet details include at least one of the following: virtual facets colored according to area, virtual facets colored according to beam depth, virtual facet edges colored according to type, or virtual facets colored according to waist-edge interaction.

13. The system of claim 7, wherein the step further comprises: A set of metrics is calculated based on the determined virtual facet pattern and the determined first outgoing beam data. The set of metrics includes at least one of the following: light return, scintillation probability, virtual facet area distribution, virtual facet depth distribution, light entropy, scintillation diffusion, graphic isomorphism class of the virtual facet pattern, Hausdorff distance from the virtual facet pattern to the specified graphic, or graphic edit distance from the virtual facet pattern to the specified graphic.

14. The system of claim 13, further comprising: Multiple simplified diagrams of virtual facet patterns are generated using a computed metric by using an enumeration algorithm to generate a list of facet arrangements according to complexity. Determine the optimal ratio prediction set; A diagram that displays multiple simplified diagrams of the virtual faceted pattern; as well as Receive an instruction to adjust the scale set of the virtual facet pattern, and cause a chart to be displayed based on the received instruction.

15. A computer-implemented method for generating a virtual faceted model of a gemstone, the method comprising: Receive data about the scanned gemstone; Generate 3D gem models using the received scanned gem data; The virtual facet pattern and the first outgoing beam data are determined based on the ray tracing or beam tracing analysis of the 3D gem model and the input viewing direction. as well as This causes the determined virtual facet pattern and virtual facet details to be displayed on the user interface that shows the 3D model and the determined virtual facet pattern.

16. The computer-implemented method of claim 15, wherein the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing facet depth information or by utilizing the actual virtual facet size from the 3D model.

17. The computer-implemented method of claim 15, wherein the determined virtual facet pattern is aligned with a selected visual perception angle by utilizing the angle from which light is drawn from the virtual facets of the 3D model.

18. The computer-implemented method of claim 15, wherein the facet details include at least one of the following: virtual facets colored according to area, virtual facets colored according to beam depth, virtual facet edges colored according to type, or virtual facets colored according to waist-edge interaction.

19. The computer-implemented method of claim 15, further comprising the computer calculating a set of metrics based on the determined virtual facet pattern and the determined first outgoing beam data, the set of metrics including at least one of the following: light return, scintillation probability, virtual facet area distribution, virtual facet depth distribution, light entropy, scintillation diffusion, graphic isomorphism class of the virtual facet pattern, Hausdorff distance from the virtual facet pattern to a specified graphic, or graphic edit distance from the virtual facet pattern to a specified graphic.

20. The computer-implemented method according to claim 19, further comprising: Multiple simplified diagrams of virtual facet patterns are generated using a computed metric by using an enumeration algorithm to generate a list of facet arrangements according to complexity. Determine the optimal ratio prediction set; A diagram that displays multiple simplified diagrams of the virtual faceted pattern; Receive instructions to adjust the scale set of the virtual facet pattern; as well as This allows the display of charts based on the received instructions.

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