3D modeling system and method for virtual cutting of gemstone based on geometric topological reorganization

Abstract

This invention discloses a 3D modeling system and method for virtual gemstone cutting based on geometric topology reconstruction. It extracts geometric topological features from the 3D point cloud data and inclusion distribution signals of the rough stone, generating a topology-driven map and a singular region distribution map, and constructing an effective cutting coverage area. It performs optical path refraction distribution analysis to extract the critical angle parameter for total internal reflection, and generates a cutting task allocation strategy through angle interval mapping. The cutting task allocation strategy is decomposed into a core facet sequence and an auxiliary facet sequence. The auxiliary facet sequence is used to form a hot-standby facet node cluster through elastic surface capacity analysis, while the core facet sequence undergoes cutting deviation anomaly monitoring to obtain distortion signals. Based on the distortion signals, curvature correction parameters are extracted and matched with the hot-standby facet node cluster for error compensation to determine the takeover cutting link. A collaborative cutting mesh is generated through seamless connection, and after surface accuracy calibration, virtual cutting 3D modeling instructions are generated, effectively improving the geometric accuracy of the cutting plan and the feasibility assurance capability of the optical path.

Description

Technical Field

[0001] This invention relates to the field of gemstone processing technology, and in particular to a 3D modeling system and method for virtual gemstone cutting based on geometric topology reconstruction. Background Technology

[0002] The cutting quality of rough gemstones directly determines the optical performance and material utilization of the finished product. Rough gemstones often contain unevenly distributed inclusions and geometric fracture zones. The optical axis direction and refractive index characteristics of crystals vary at different locations. These factors combine to make the selection of cutting planes and the determination of facet angles extremely complex. Traditional cutting planning relies heavily on the craftsman's experience, often employing simple polygonization to discretize the rough stone's outer contour into a set of facets in 3D modeling. The resulting 3D mesh model lacks sufficient quantitative description of the surface's fine topology and internal optical properties, making it difficult to optimize facet optical path conditions while avoiding vulnerable areas.

[0003] With the development of 3D scanning and optical inspection technologies, raw stone analysis methods based on point cloud data and transmission signals have been gradually introduced into the field of cutting assistance. However, most existing methods separate geometric analysis and optical analysis, lacking the ability to integrate surface topological features, inclusion distribution, refractive index gradient and cutting deviation dynamic monitoring into a unified mesh planning framework. There is no dynamic correlation between surface description parameters and cutting execution deviation. When the cutting path deviates, the established faceted mesh cannot adaptively adjust the node distribution and curvature parameters. The continuous accumulation of deviation eventually affects the mosaic accuracy and surface continuity of the overall mesh. Summary of the Invention

[0004] This invention discloses a gemstone virtual cutting 3D modeling system and method based on geometric topology reconstruction. It aims to incorporate the surface topology of the rough stone, the spatial distribution of inclusions, the optical properties of the material, and the cutting execution deviation into a unified processing framework. By constructing a topology-driven map, it guides the cutting plane to avoid vulnerable areas. It combines the refractive index gradient and the critical angle parameter of total internal reflection to generate a cutting task allocation strategy with guaranteed optical path feasibility. During the cutting execution process, it monitors deviations in real time and dynamically calls hot standby nodes to complete path compensation, ultimately generating a complete virtual cutting 3D modeling instruction.

[0005] The first aspect of this invention proposes a 3D modeling method for virtual gemstone cutting based on geometric topological reconstruction, comprising the following steps:

[0006] The three-dimensional point cloud data and inclusion distribution signal of the gemstone rough are obtained, and the geometric topological features of the three-dimensional point cloud data and the inclusion distribution signal are extracted to generate a topology-driven map.

[0007] Based on the topology-driven graph, a cutting plane topology recombination is performed to generate a singular region distribution map, and an effective cutting coverage area is constructed based on the constraint avoidance conditions of the singular region distribution map;

[0008] Optical path refraction distribution analysis is performed on the effective cutting coverage area to extract the critical angle parameter of total internal reflection. Based on the critical angle parameter of total internal reflection and the effective cutting coverage area, angle interval mapping is performed to generate a cutting task allocation strategy.

[0009] The cutting task allocation strategy is decomposed into a core facet sequence and an auxiliary facet sequence. Elastic surface capacity analysis is performed on the auxiliary facet sequence to form a hot standby facet node cluster. Cutting deviation anomaly monitoring is performed on the core facet sequence to obtain distortion signals.

[0010] Curvature correction parameters are extracted based on the distortion signal. The curvature correction parameters are matched with the hot standby facet node cluster for error compensation to determine the takeover cutting link. The takeover cutting link is seamlessly connected with the core facet sequence to generate a collaborative cutting mesh. Based on the collaborative cutting mesh, surface accuracy calibration is performed to generate virtual cutting 3D modeling instructions.

[0011] A second aspect of this invention proposes a 3D modeling system for virtual gem cutting based on geometric topology reconstruction, comprising:

[0012] The atlas construction module is used to acquire three-dimensional point cloud data and inclusion distribution signals of gemstone rough, and to extract geometric topological features from the three-dimensional point cloud data and the inclusion distribution signals to generate a topology-driven atlas.

[0013] The singularity avoidance module is used to perform cutting plane topological recombination to generate a singular region distribution map based on the topology-driven map, and to construct an effective cutting coverage area based on the avoidance constraints of the singular region distribution map.

[0014] The strategy generation module is used to perform optical path refraction distribution analysis on the effective cutting coverage area to extract the critical angle parameter of total internal reflection, and generate a cutting task allocation strategy based on the critical angle parameter of total internal reflection and the effective cutting coverage area by performing angle interval mapping.

[0015] The node construction module is used to decompose the cutting task allocation strategy into a core facet sequence and an auxiliary facet sequence, perform elastic surface capacity analysis on the auxiliary facet sequence to form a hot standby facet node cluster, and perform cutting deviation anomaly monitoring on the core facet sequence to obtain distortion signals.

[0016] The instruction output module is used to extract curvature correction parameters based on the distortion signal, perform error compensation matching between the curvature correction parameters and the hot standby facet node cluster to determine the takeover cutting link, seamlessly connect the takeover cutting link with the core facet sequence to generate a collaborative cutting mesh, and perform surface accuracy calibration based on the collaborative cutting mesh to generate virtual cutting 3D modeling instructions.

[0017] The beneficial effects of this invention are reflected in the following points: First, regarding the joint localization problem of the fracture zone and inclusion aggregation area on the surface of the raw stone, the co-localization density of the normal vector consistency analysis results of the three-dimensional point cloud data and the inclusion distribution signal is uniformly quantified into a topological fragility index, generating a topological driving map and generating a singular region distribution map accordingly. Then, an effective cutting coverage area is constructed by avoiding constraints, realizing a complete mapping from the original scanning data to the operable cutting space, so that the determination of the cutting plane has clear geometric and material basis. Second, in the facet angle planning stage, a strong refractive sub-domain is delineated based on the refractive index gradient of the effective cutting coverage area. The material refractive index characteristic values ​​in the main and secondary optical axis directions and the multi-wavelength envelope expansion are combined to generate a set of critical angle candidate parameters. Through total internal reflection condition adaptation and angle interval mapping, the optical feasibility constraints are directly embedded into the cutting task allocation strategy, so that the dihedral angle of each facet is set within the feasible range where the total internal reflection condition is met. Finally, addressing the dynamic deviation problem during the cutting process, the continuous deviation node group of the core facet sequence is identified as a distortion signal. After the curvature correction parameter is decomposed into short-range neighborhood error components and cross-sequence cumulative drift components, error adaptation evaluation is completed in the hot standby facet node cluster and it is gradually fused into a takeover cutting link. It is seamlessly connected with the core facet sequence to form a collaborative cutting mesh. After surface accuracy calibration, virtual cutting 3D modeling instructions are generated, realizing dynamic deviation compensation during the cutting process. Attached Figure Description

[0018] The accompanying drawings illustrate specific examples of the technical solutions described in this invention and, together with the detailed embodiments, form part of the specification, serving to explain the technical solutions, principles, and effects of this invention.

[0019] Figure 1 This is a flowchart illustrating the 3D modeling method for virtual gemstone cutting based on geometric topology reconstruction, as described in this invention.

[0020] Figure 2 This is a structural block diagram of the gemstone virtual cutting 3D modeling system based on geometric topology reconstruction of the present invention. Detailed Implementation

[0021] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0022] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0023] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0024] The technical solutions of the embodiments of this application will be described below.

[0025] like Figure 1 As shown, this embodiment of the invention provides a 3D modeling method for virtual gemstone cutting based on geometric topology reconstruction, including the following steps S110-S150:

[0026] Step S110: Obtain the three-dimensional point cloud data and inclusion distribution signal of the gemstone rough, and extract geometric topological features from the three-dimensional point cloud data and inclusion distribution signal to generate a topology-driven map.

[0027] Specifically, three-dimensional point cloud data and inclusion distribution signals of the rough gemstone were acquired. The sampling point density of the three-dimensional point cloud data reached 120 sampling points per square millimeter, with a coordinate accuracy better than 0.02 mm. This density level is sufficient to resolve the fine curvature structure on the order of 0.1 mm on the surface of the rough stone. The three-dimensional point cloud data was collected by a structured light scanner in six orthogonal directions of the rough stone, generating approximately 200,000 surface points in each direction. The point clouds of adjacent directions were registered using the ICP algorithm and merged into a complete surround point cloud. The registration residual of the point coordinate sequence was controlled within 0.01 mm. The normal vector estimation sequence was calculated by fitting a plane to the neighborhood of each point using principal component analysis. The inclusion distribution signals were acquired using a polarized light transmission detector, covering the wavelength range of 400 nm to 700 nm. The grayscale intensity matrix was recorded pixel by pixel based on the light flux attenuation value of each cross-section. The scanning interval of the cross-section position sequence was set to 0.1 mm. The inclusion type was marked according to the absorption spectrum characteristic region, dividing it into gap-like and point-like types, and appended to the corresponding positions of the grayscale intensity matrix with integer codes. The 3D point cloud data and inclusion distribution signal are spatially matched using calibration plate coordinates. After matching, both share the same Cartesian coordinate system, with a spatial correspondence error of less than 0.03 mm. The grayscale intensity range of the inclusion distribution signal is 0 to 255. Regions with an intensity below 60 correspond to high-absorption inclusion aggregation zones, while regions with an intensity above 210 correspond to transparent structural domains with high crystal clarity.

[0028] In some embodiments, the step of extracting geometric topological features from the three-dimensional point cloud data and the inclusion distribution signal to generate a topology-driven map includes: performing normal vector consistency analysis on the three-dimensional point cloud data to determine normal vector abrupt change regions; performing co-localization analysis on the normal vector abrupt change regions according to the aggregation density of the inclusion distribution signal to generate an inclusion-abrupt change overlap map; performing topological fragility index extraction on the inclusion-abrupt change overlap map to generate a sensitive zone weight distribution map; and using the sensitive zone weight distribution map to generate a topology-driven map.

[0029] Normal vector consistency analysis was performed on 3D point cloud data to identify regions of abrupt changes in normal vectors. In the normal vector estimation sequence of 3D point cloud data, continuous point groups with deflection angles exceeding 12° form directional faults with their neighboring point groups. This discontinuity directly corresponds to the location of geometric fracture zones on the surface of the raw stone. Normal vector consistency analysis is based on the normal vector estimation sequence of the 3D point cloud data. Within the neighborhood of each point (the neighborhood radius is set to 5 times the point spacing), the angular dispersion of the normal vector direction is statistically analyzed. The dispersion is quantified by the mean of the angles between all normal vector pairs within the neighborhood. The point coordinate sequence of the 3D point cloud data is used to determine the neighborhood range of each point. If the number of valid points within the neighborhood is less than 10, the consistency score of that point is not included in the statistics. Points with consistency scores below a threshold (set to 8°) are marked as inconsistent points. Continuously distributed inconsistent point groups in the 3D point cloud data are clustered using DBSCAN to form regions of abrupt changes in normal vectors. The clustering parameters are set to a minimum of 50 points and a neighborhood distance of 0.3 mm. The bandwidth of the boundary coordinate sequence of the mutation region of the normal vector mutation along the edge of the raw stone is usually 0.5mm to 2mm. The normal vector deflection amplitude of the mutation region of the normal vector mutation is characterized by the difference between the maximum angle and the mean angle in the region. The regional clustering characteristics of the mutation region of the normal vector mutation are quantified by the ratio of the density of core points to the density of edge points in each cluster. When the point density is insufficient, the boundary error can reach 0.5mm.

[0030] Co-localization analysis is performed on the abrupt change region of the normal vector based on the aggregation density of the inclusion distribution signal to generate an inclusion-abrupt change overlap map. The co-localization analysis projects the coordinate sequence of the abrupt change boundary of the normal vector abrupt change region onto a coordinate grid defined by the cross-sectional position sequence of the inclusion distribution signal. The coordinate projection uses the nearest neighbor interpolation method, with an interpolation accuracy equal to the cross-sectional spacing of 0.1 mm. Local statistical analysis is performed on the gray-level intensity matrix of the inclusion distribution signal within the spatial range covered by the abrupt change region of the normal vector. The aggregation density of the inclusion distribution signal is quantified by the inverse mapping of the local mean of the gray-level intensity matrix. Locations with a gray-level mean below 80 have high aggregation density, corresponding to high inclusion aggregation areas. The inclusion-mutation overlap map uses a 0.2mm × 0.2mm spatial grid as the basic unit. The overlap density matrix element of each grid in the inclusion-mutation overlap map is calculated according to the following formula: Overlap density value = Region clustering feature × Local mean of gray intensity matrix × Co-location intensity coefficient × (Normal vector deflection amplitude / Maximum normal vector deflection amplitude), where all factors are dimensionless values. The co-location intensity coefficient is determined according to the inclusion type label, taking 1.5 for fissure types and 1.0 for point types. The normal vector deflection amplitude is normalized to the range of 0 to 1 by dividing by the maximum deflection amplitude within the region. The coverage area ratio of the inclusion-mutation overlap map is characterized by the proportion of the mutation boundary point in each grid to the total area of ​​the grid. When the coverage area ratio exceeds 0.6, the grid is marked as a highly overlapping unit.

[0031] A topological fragility index was extracted from the inclusion-mutation overlap map to generate a sensitive zone weight distribution map. The overlap density values ​​in the inclusion-mutation overlap map exhibit a chain-like connected distribution. Regions with high overlap density values ​​connect to form band-like structures extending along the original stone texture. This morphology constitutes the core geometric basis for the topological fragility index extraction. The topological fragility index is calculated based on the overlap density value matrix of the inclusion-mutation overlap map, using a 1mm×1mm sliding window to scan grid by grid, extracting the gradient magnitude and direction of the overlap density values ​​within each window. The coverage area of ​​the inclusion-mutation overlap map is 30% higher than the baseline value for highly overlapping units exceeding 0.6 in the topological fragility index calculation, ensuring that regions with both geometrically and in terms of inclusion concentration receive higher fragility ratings. The sensitive zone weight distribution map is based on the grid system of the inclusion-mutation overlap map. The topological fragility index of each grid is normalized to the 0-1 interval and then mapped to a weight value sequence. Normalization uses max-min linear scaling. When the difference in overlap density between adjacent grates in the inclusion-mutation overlap map exceeds 0.3, the boundary between the two grates is marked as a sensitive zone boundary in the sensitive zone weight distribution map. The coordinates of the sensitive zone nodes are taken as the spatial coordinates of each marked point on this boundary. The vulnerability index level of the sensitive zone weight distribution map is divided according to the weight value range: 0 to 0.3 is marked as low vulnerability level, 0.3 to 0.6 is medium vulnerability level, and 0.6 to 1.0 is high vulnerability level. The level is encoded as an integer and appended to each grate record for subsequent loop construction to read the node priority.

[0032] A topology-driven graph is generated using a sensitive zone weight distribution map. In the sensitive zone weight distribution map, grids with weight values ​​higher than 0.75 are concentrated in the three main facet intersection areas of the rough stone, accounting for approximately 8%, 6%, and 5% of the total surface area, respectively. This concentration determines the orientation of the main path of the topology-driven graph. The topology-driven graph is constructed by extracting grids with weight values ​​greater than 0.5 from the weight value sequence of the sensitive zone weight distribution map. The corresponding sensitive zone node coordinates are used as candidate nodes, typically accounting for 20% to 35% of the total grids. Sensitive zone node coordinates are connected according to spatial proximity, prioritizing connections between adjacent nodes with weight value differences less than 0.1 to form an initial node chain. This initial node chain is then optimized using Dijkstra's shortest path algorithm to generate the graph skeleton. The node priority weights in the topology-driven graph are directly taken from the vulnerability index level markers of the sensitive zone weight distribution map: high vulnerability level corresponds to a node priority weight of 1.0, medium vulnerability level to 0.6, and low vulnerability level to 0.3. The weight value sequence of the sensitive zone weight distribution map is used to verify coverage integrity after the initial construction of the topology-driven map. Grids with weight values ​​greater than 0.8 that are not included in the map nodes are added through supplementary insertion operations. The path connectivity identifier between each pair of adjacent nodes in the topology-driven map records the connection type: direct connectivity is when the distance between adjacent grids is less than 0.3 mm, bridging connectivity is when the distance is between 0.3 mm and 1.0 mm, and bridging connectivity locations are marked as potential segmentation risk points.

[0033] Step S120: Based on the topology-driven graph, perform topological recombination of the cutting plane to generate a singular region distribution map, and construct an effective cutting coverage area based on the constraint avoidance conditions of the singular region distribution map.

[0034] In some embodiments, the step of generating a singular region distribution map by performing topological recombination of the cutting plane based on the topology-driven map includes: performing topological recombination on the cutting plane based on the topology-driven map to generate a set of boundary curvature gradients for each singular region; back-mapping the maximum gradient direction of each singular region in the set of boundary curvature gradients to the cutting plane to generate a set of candidate boundaries; verifying the consistency of the candidate boundaries with the spatial coverage of the set of boundary curvature gradients to determine a valid boundary sequence; and generating a singular region distribution map according to the valid boundary sequence.

[0035] The cutting plane is topologically reorganized based on the topology-driven graph to generate a boundary curvature gradient set. The cutting plane is determined by the spatial orientation of the main path of the topology-driven graph, with the geometric center of the high-priority node cluster area as the origin of the normal vector, and the plane perpendicular to the overall extension direction of the graph skeleton as the initial orientation of the cutting plane. The grid resolution of the cutting plane coordinates is set to 0.1 mm. The curvature gradient magnitude of the local region of the cutting plane corresponding to nodes with a priority weight of 0.9 in the topology-driven graph can reach 3.2 rad / mm, far exceeding the 0.8 rad / mm of the low-priority node region. This difference directly defines the spatial range of the high-gradient partition of the boundary curvature gradient set. The coordinates of the sensitive zone nodes in the topology-driven graph serve as spatial anchor points for the topology reorganization of the cutting plane. Curvature analysis is performed centered on each anchor point, with the analysis window radius set to 1.5 mm. The cutting plane topology reorganization projects the bridging connections marked by the path connectivity identifiers in the topology-driven graph onto the cutting plane. The curvature gradients within a 0.8mm radius of the projected locations are calculated separately and recorded as independent components in the gradient magnitude sequence of the boundary curvature gradient set. These components are preferentially used as inflection point sources during the generation of the boundary candidate set for inverse mapping. The gradient magnitude sequence of the boundary curvature gradient set is obtained by finite difference estimation of the normal curvature at the boundaries of each singular region on the cutting plane, with a difference step size set to 0.1mm to match the coordinate accuracy of the original point cloud. The node priority weights of the topology-driven graph modulate the gradient magnitude sequence of the boundary curvature gradient set. The gradient magnitudes of high-priority node regions are multiplied by a magnification factor of 1.3 after calculation to highlight the curvature characteristics of vulnerable zones. The maximum gradient direction of the boundary curvature gradient set is represented by the spatial vector corresponding to the maximum gradient magnitude at the boundaries of each singular region, described in Euler angles with an angular resolution of 0.5°. The spatial coverage of the boundary curvature gradient set records the bounding rectangle coordinates of each singular region on the cutting plane, defined by the coordinates of the four vertices, with an accuracy consistent with the 0.1mm resolution of the cutting plane coordinate grid.

[0036] The maximum gradient direction of each singular region in the boundary curvature gradient set is back-mapped onto the cutting plane to generate a candidate set of boundary lines. Compared to the low gradient region with an amplitude of 0.8 rad / mm, the high gradient segment (3.2 rad / mm) in the boundary curvature gradient set has a maximum gradient direction that deviates by more than 25° from the inward tilt of the maximum gradient direction towards the cutting plane. This deviation causes a significant deflection of the back-mapped path on the cutting plane. The generation of the candidate set of boundary lines uses the maximum gradient direction of the boundary curvature gradient set as input. The maximum gradient direction vector of each singular region is inverted and projected onto the coordinate system of the cutting plane. The lines connecting the projection points form the initial candidate boundary lines. The local peak positions of the gradient amplitude sequence of the boundary curvature gradient set determine the distribution of the inflection points of each candidate line in the candidate set. The direction of the inflection points is based on the intersection of the normal plane of the maximum gradient direction and the cutting plane. The confidence score of each candidate line in the candidate set of boundary lines is calculated by normalizing the mean of the corresponding gradient amplitude sequence of the boundary curvature gradient set. The higher the gradient mean, the higher the confidence score, with a score range of 0 to 1. If the angle between the maximum gradient direction of the boundary curvature gradient set and the normal vector of the cutting plane exceeds 85°, the corresponding candidate line in the boundary candidate set is marked as a low-reliability candidate line, and the confidence score is automatically reduced by 0.3. If the score is lower than 0 after the reduction, it is recorded as 0, ensuring that the confidence score always remains within the range of 0 to 1. The coordinate sequence of the candidate boundary lines in the boundary candidate set is described by the two-dimensional coordinate system of the cutting plane. Each candidate line contains no less than 10 inflection point coordinates, and the distance between adjacent inflection points does not exceed 0.5 mm.

[0037] The candidate boundary line set is validated for consistency with the spatial coverage of the boundary curvature gradient set to determine the effective boundary line sequence. Candidate lines with a confidence score of 0.85 and those with a score of 0.4 have different inflection point densities within the spatial coverage of the boundary curvature gradient set: 8 per millimeter for the former and 3 per millimeter for the latter. This density difference forms the core criterion for selecting effective boundary line sequences. The consistency validation involves checking the overlap between each candidate boundary line coordinate sequence and the spatial coverage of the boundary curvature gradient set. The criterion is whether each inflection point falls within the bounding rectangle of the coverage area. The validation results of the spatial coverage of the boundary curvature gradient set for each candidate line are quantified by the consistency ratio, which is the ratio of the number of candidate line inflections falling within the coverage area to the total number of inflections on the candidate line. Candidate lines with a consistency ratio exceeding 0.7 and a confidence score exceeding 0.6 are included in the effective boundary line sequence; both conditions must be met simultaneously to exclude misjudgments caused by accidental coverage. The weights of each segment in the effective boundary line sequence are weighted and corrected by the gradient magnitude sequence of the boundary curvature gradient set. The weights of segments corresponding to high gradient regions are multiplied by an amplification factor of 1.2 to increase the ranking priority of high gradient boundaries. Each segment in the effective boundary line sequence is accompanied by a consistency score, calculated using the formula S = 0.6 × R + 0.4 × C, where S is the consistency score, R is the consistency ratio, and C is the confidence score. The effective boundary line sequence is ultimately stored in descending order of consistency score. The weights of each segment are transferred along with the consistency score to the risk level assessment of the corresponding region on the singular region distribution map. The risk level of the region corresponding to a high-weight segment is increased by one level based on the consistency score.

[0038] A singular region distribution map is generated based on the effective boundary line sequence. Line segments with a similarity score higher than 0.8 in the effective boundary line sequence exhibit a radial spatial distribution on the cutting plane. The center of this radial distribution overlaps with the high-priority node cluster area of ​​the topology-driven map within 0.3 mm, and this morphological consistency verifies the geometric consistency of the boundary line extraction. The singular region distribution map is generated using the coordinates of the effective boundary line sequence as boundaries. The cutting plane is directly divided into several closed regions according to the enclosing relationship of the effective boundary line sequence. The boundaries of each closed region are determined by the coordinates of the effective boundary line sequence, and the centroid coordinates of each closed region serve as region index nodes for subsequent risk level assessment and spatial positioning of constraint conditions. The similarity score of the effective boundary line sequence is passed to the risk level assessment of each closed region in the singular region distribution map. The higher the similarity score of the corresponding boundary, the more certain the singularity of the region, and the higher the risk level. In the singular region distribution map, the boundary coordinates of each singular region directly inherit the coordinates of the effective boundary line sequence, maintaining an accuracy of 0.1 mm. The region area is calculated using the Shoelace formula: A = (1 / 2)|Σ(x_i·y_{i+1}−x_{i+1}·y_i)|, where (x_i, y_i) are the two-dimensional coordinates of the cutting plane at the i-th boundary inflection point. The summation iterates through all n inflection points, with the subscript n+1 set to 1. Regions corresponding to line segments with a similarity score below 0.5 in the effective boundary line sequence are marked as uncertain regions in the singular region distribution map. The avoidance constraints of the singular region distribution map classify them into the optional avoidance range rather than the mandatory avoidance range. The avoidance constraints of the singular region distribution map use the risk level of each region as the core criterion. Regions with a risk level higher than the medium risk threshold (corresponding to a similarity score of 0.6) generate mandatory avoidance constraints, while those below the threshold generate suggested avoidance constraints. The two types of constraints are stored as Boolean flags in the constraint record of the singular region distribution map.

[0039] An effective cutting coverage region is constructed based on the avoidance constraints of the singular region distribution map. The mandatory avoidance constraint coverage area in the singular region distribution map accounts for 18% of the total area of ​​the cutting plane, the suggested avoidance constraint coverage area accounts for 12%, and the remaining 70% constitutes the candidate space for the effective cutting coverage region. This area ratio indicates that the cutting plane still has sufficient effective operational conditions. The construction of the effective cutting coverage region starts from the boundary coordinates of the mandatory avoidance region in the avoidance constraints of the singular region distribution map, shrinking inward by 0.5mm to generate an extended avoidance boundary. The effective cutting coverage region is the remaining space after subtracting the area enclosed by the extended avoidance boundary from the total area of ​​the cutting plane. The effective contour retains the original geometry without convexification to fully preserve the non-convex effective area. The boundary coordinates of each singular region in the singular region distribution map are used to refine the coverage region boundary after the effective cutting coverage region contour is determined, eliminating local overlap with the singular region boundary. The refinement resolution is 0.1mm. After the candidate space of the effective cut coverage area is refined with contours, connectivity is checked. Isolated sub-regions with an area less than 5 mm² are removed from the effective cut coverage area to ensure that each coverage sub-region has a practically operable minimum geometric size. Suggested avoidance constraint regions from the singular region distribution map are retained in the effective cut coverage area with low priority markings. Low-priority regions are only enabled when the capacity of high-priority regions is insufficient. The refractive index partitioning of the effective cut coverage area is generated by overlaying the risk level of the singular region distribution map with the gemstone material refractive a priori distribution. The gemstone material refractive a priori distribution is preloaded based on a gemstone type standard database, using the nominal refractive index value and gradient direction at each spatial coordinate as basic fields. After alignment with the coordinate system of the effective cut coverage area, it participates in the overlay. Regions with low risk levels correspond to uniform refractive index partitions, while high refractive index gradient regions are stored in the effective cut coverage area with independent partition markings. The refractive index gradient feature values ​​of each partition are recorded in the partitioning field of the effective cut coverage area with a precision of 0.01 units.

[0040] Step S130: Perform optical path refraction distribution analysis on the effective cutting coverage area to extract the critical angle parameter of total internal reflection, and generate a cutting task allocation strategy based on the critical angle parameter of total internal reflection combined with the effective cutting coverage area by angle interval mapping.

[0041] In some embodiments, the step of performing optical path refraction distribution analysis on the effective cut coverage area to extract the critical angle parameters for total internal reflection includes: dividing the effective cut coverage area into strong refractive sub-domains according to the refractive index gradient and extracting the facet normal vector distribution; extracting material refractive index feature values ​​from the strong refractive sub-domains to generate a set of candidate critical angle parameters; performing total internal reflection conditional adaptation between the candidate critical angle parameters and the facet normal vector distribution to generate a critical angle matrix; and selecting feasible angular domains based on the critical angle matrix to extract the critical angle parameters for total internal reflection.

[0042] Strong refractive subdomains are determined by dividing the effective cut coverage area according to the refractive index gradient, and the distribution of facet normal vectors is extracted. In the refractive index partition field of the effective cut coverage area, the gradient feature value of the waist annular zone reaches 0.08 / mm, which is about four times that of the crown plateau region (0.02 / mm). This difference in gradient distribution directly defines the main spatial range of the strong refractive subdomain. The effective cut coverage area is divided with a threshold of 0.05 / mm. Partitions with gradient feature values ​​exceeding the threshold are merged into strong refractive subdomains. The spatial boundary coordinates of the strong refractive subdomains inherit the coordinate resolution of 0.1mm of the effective cut coverage area. The proportion of the area of ​​the strong refractive subdomain to the total area of ​​the effective cut coverage area is recorded in the strong refractive subdomain field. This proportion is used as a global reference benchmark for weighting the confidence of each node when generating the critical angle candidate parameter set. A higher area proportion indicates a wider coverage of strong refractive features, and the confidence benchmark value of each node is increased by 0.05 accordingly. The risk level field of the effective cut coverage area is used as an auxiliary criterion. Partitions with high risk levels and gradients exceeding the threshold are preferentially assigned to the strong refractive subdomain, while partitions with gradients below the threshold are marked as weak refractive background domains and are not included in the strong refractive subdomain. The facet normal vector distribution is established point by point on the grid nodes of the strong refractive subdomain with a sampling interval of 0.2mm. The normal vector is recorded in unit vector form with an azimuth angle accuracy of 0.5°. In the facet normal vector distribution, point groups with a node azimuth angle standard deviation of less than 3° are marked as convergence regions, and those exceeding 3° are marked as divergence regions. The division results of convergence and divergence regions are appended to the node records of the facet normal vector distribution, providing a direct basis for the subsequent assignment of the reliability of the critical angle matrix. The total number of effective nodes in the facet normal vector distribution corresponds one-to-one with the number of sampling nodes in the strong refractive subdomain.

[0043] For example, the step of extracting material refractive index feature values ​​from the strongly refractive subdomain to generate a critical angle candidate parameter set includes: dividing the strongly refractive subdomain into a principal optical axis direction domain and a secondary optical axis direction domain according to the optical axis direction; extracting material refractive index feature values ​​from the principal optical axis direction domain and the secondary optical axis direction domain respectively to generate a biaxial critical angle difference diversity; performing multi-wavelength envelope expansion on the biaxial critical angle difference diversity to determine the critical angle constraint interval; and generating a critical angle candidate parameter set based on the critical angle constraint interval.

[0044] The strong refractive subdomain is divided into a principal optical axis direction domain and a secondary optical axis direction domain according to the optical axis direction. The optical axis deflection angle within the strong refractive subdomain was measured to be 28° in a gemstone sample. This deflection causes an asymmetrical distribution of birefringence intensity in different directions. Merging the principal and secondary optical axis direction domains would lead to an accumulated critical angle estimation deviation exceeding 0.4°; therefore, the two domains must be demarcated independently. The optical axis azimuth angle of the strong refractive subdomain is obtained by performing principal component analysis on the refractive index gradient directions of each partition. The first principal component direction is defined as the principal optical axis direction, and the second principal component direction is defined as the secondary optical axis direction. The angle between the two directions is usually close to 90°, but due to crystal anisotropy, there is a deviation of 2° to 5°. This deviation directly affects the boundary position for determining the direction assignment. In the strong refractive subdomain, the orientation of each node is determined based on its angle with the principal optical axis. Nodes with an angle less than 45° are assigned to the principal optical axis orientation domain, while those with an angle greater than 45° are assigned to the secondary optical axis orientation domain. Nodes whose angle falls exactly within a ±1° window of 45° are further identified using the consistency of the local orientation of the gradient field as an auxiliary criterion. The two domains are merged to cover all valid nodes in the strong refractive subdomain without overlap. The number of nodes covered by the principal optical axis orientation domain typically accounts for 55% to 65% of the total number of nodes in the strong refractive subdomain. This proportion reflects the degree of alignment between the orientation of the gemstone crystal's optical axis and the geometric principal axis of the rough stone. The node coordinate sequence of the principal optical axis orientation domain is obtained from the strong refractive subdomain by filtering according to the orientation identifier. The secondary optical axis orientation domain covers the remaining nodes, and each node is uniquely assigned to either the principal optical axis orientation domain or the secondary optical axis orientation domain through its orientation domain identifier.

[0045] Material refractive index feature values ​​were extracted from the principal optical axis and secondary optical axis directions to generate biaxial critical angle difference diversity. The measured average refractive index in the principal optical axis direction was 1.762, and in the secondary optical axis direction it was 1.770. The difference of 0.008 corresponds to an angular deviation of approximately 0.2° at the critical angle level. The difference amplitude benchmark of the biaxial critical angle difference diversity was thus determined. Although the absolute value of this difference is small, under the cutting accuracy requirement of only 0.5° for the facet angle of the original stone pavilion, the systematic deviation of 0.2° accounts for 40% of the total tolerance and cannot be ignored. The material refractive index characteristic values ​​of each node in the main optical axis direction domain are estimated by integrating the local refractive index gradient field along the optical axis direction. The integration step size is set to 0.05 mm. The secondary optical axis direction domain is acquired in the same way. The integration path is orthogonal to the main optical axis direction. The integration starting point is taken as the projected coordinates of each node on the boundary of the strong refractive sub-domain to ensure that the spatial reference of the integration path of the two domains is consistent. If the integration starting point reference of the two domains is inconsistent, the differential amplitude will introduce additional spatial offset error. Two sets of refractive index eigenvalues ​​constitute the principal and secondary axis components of the biaxial critical angle difference set, respectively. The critical angle corresponding to each node is calculated by the formula θ_c=arcsin(1 / n), where θ_c is the critical angle for total internal reflection, and n is the material refractive index eigenvalue at that node. Locations in the difference set where the refractive index difference between the principal and secondary axis component nodes exceeds 0.015 are marked as strongly anisotropic nodes. This marking is used to identify high-difference segments that need to be processed separately when expanding the critical angle constraint interval. Locations where the refractive index difference is less than 0.003 are marked as weakly anisotropic nodes. The difference amplitude of weakly anisotropic nodes in the biaxial critical angle difference set is close to zero, and they can be merged into a single-axis approximation during the subsequent expansion of the critical angle constraint interval to reduce computational load. The biaxial critical angle difference set uses node coordinates as an index. Each record contains a direction domain identifier, material refractive index eigenvalue, corresponding critical angle value, and anisotropic marker. The total number of valid records in the difference set is equal to the sum of the nodes in the principal optical axis direction domain and the secondary optical axis direction domain.

[0046] Multi-wavelength envelope expansion is performed on the biaxial critical angle difference diversity to determine the critical angle constraint interval. The critical angle of the principal axis field of the biaxial critical angle difference diversity is 34.6° at a reference wavelength of 550nm. At 400nm, the dispersive refractive index increases to 1.785, and the critical angle narrows to 34.0°. This 0.6° narrowing constitutes the main source of the dispersion boundary of the critical angle constraint interval. The dispersion amplitude of the secondary axis field is slightly smaller within the same wavelength range, and the difference in dispersion amplitude between the principal and secondary axes typically does not exceed 0.1°. Multi-wavelength envelope expansion uses each node of the biaxial critical angle difference diversity as the processing unit, expanding to seven wavelength nodes in a 50nm step size within the range of 400nm to 700nm. The change in refractive index with wavelength is estimated using the Cauchy dispersion formula n(λ) = A + B / λ², where n(λ) is the refractive index at wavelength λ, A is the basic refractive index coefficient, and B is the dispersion coefficient, both taken as prior material values. The critical angle value corresponding to each wavelength forms a seven-point wavelength response sequence for that node. The critical angle constraint interval is taken as the minimum and maximum values ​​of the 7-point response sequence of each node, recorded in the format [θ_min, θ_max], with an angular resolution of 0.1° and an interval width typically between 0.5° and 1.2°. The principal axis component and the secondary axis component each form their own constraint interval. Their intersection is the conservative estimation interval, and their union is the relaxed estimation interval. When expanding the envelope, the strongly anisotropic nodes of the dual-axis critical angle difference diversity simultaneously refer to the outer envelope range of both the principal and secondary axis response sequences to take a wider [θ_min, θ_max] interval to prevent the single-axis estimation from missing extreme values. Nodes with a width exceeding 1.0° are marked as dispersion-sensitive nodes.

[0047] A candidate set of critical angle parameters is generated based on the critical angle constraint interval. Dispersion-sensitive nodes account for approximately 22% of all nodes within the critical angle constraint interval. The candidate set must employ a tolerance strategy for these records to address the critical angle shift caused by light source wavelength drift during actual cutting. The candidate set uses the midpoint of each node within the critical angle constraint interval as the representative value for the candidate critical angle, with an error tolerance of half the interval width. When the interval ends are asymmetrical, the geometric midpoint, rather than the weighted midpoint, is used as the representative value to avoid introducing a systematic bias towards a particular wavelength. The error tolerance for dispersion-sensitive nodes in the candidate set is further extended by 0.15°. This extension is estimated based on the maximum critical angle shift caused by the material's prior dispersion coefficient within the range of 400nm to 700nm. The error tolerance for non-sensitive nodes in the candidate set remains at half the original interval width. In the critical angle constraint interval, the representative value of the candidate critical angle for strongly anisotropic nodes is taken as the midpoint of the intersection of the two constraint intervals of the primary and secondary axes. If the intersection is empty, the average of the midpoints of the two intervals is taken, and the confidence of the node is forcibly reduced to a low level. If the number of nodes whose confidence is forcibly reduced exceeds 10% of all nodes, the primary and secondary axis direction domain division results must be backtracked to check whether there is a systematic bias in the optical axis azimuth angle estimation. Nodes with a critical angle constraint interval width of less than 0.5° are marked with high confidence, 0.5° to 1.0° as medium confidence, and more than 1.0° as low confidence. The candidate values ​​of low-confidence nodes are additionally superimposed with a conservative bias of 0.1° during the adaptation calculation to reduce the risk of misjudgment. The total number of valid records in the critical angle candidate parameter set is equal to the number of valid nodes in the critical angle constraint interval.

[0048] The critical angle matrix is ​​generated by adapting the candidate parameter set of critical angles to the facet normal vector distribution under total internal reflection conditions. The total internal reflection condition adaptation uses the candidate critical angle values ​​of each node in the candidate parameter set as a comparison benchmark. The angle between the normal vector at the corresponding coordinate of the facet normal vector distribution and the incident direction is calculated as the actual incident angle θ_i. The relationship between θ_i and the candidate critical angle values ​​is used to determine whether the total internal reflection condition is met. The determination results are divided into three categories: satisfied, not satisfied, and critical. Nodes whose |θ_i−θ_c| is less than the error tolerance are classified into the critical category. Critical category nodes must be given additional conservative treatment when screening the feasible interval of the dihedral angle. The critical angle matrix is ​​based on the node coordinate index of the facet normal vector distribution. Each element records the candidate critical angle value, the actual incident angle θ_i, the fit judgment category, and the confidence coefficient. The confidence coefficient of the convergence zone node is set to 1.0, and the confidence coefficient of the divergence zone node is calculated by the formula min(1.0, 3° / azimuth standard deviation). Nodes with a confidence coefficient lower than 0.5 after reduction are marked with a low confidence mark in the critical angle matrix. Low confidence nodes do not participate in the mean statistics when screening the feasible angle region, but are retained in the matrix for the purpose of checking the coverage integrity. The total number of effective elements in the critical angle matrix is ​​equal to the number of nodes jointly covered by the critical angle candidate parameter set and the facet normal vector distribution.

[0049] The feasible angular region is selected based on the critical angle matrix to extract the critical angle parameters for total internal reflection. Nodes in the critical angle matrix that meet the fitness criteria account for 83% of the principal axis region and only 61% of the secondary axis region. The critical angle parameters for total internal reflection must be counted separately along the principal and secondary axes and cannot be combined. The feasible angular region is based on nodes in the critical angle matrix that meet the fitness criteria and have a confidence coefficient of not less than 0.8. After removing isolated sub-regions with an area less than 2 mm² through spatial connectivity testing, a feasible region node set is formed. The mean of the candidate critical angle values ​​within the feasible region node set is the representative value of the total internal reflection critical angle parameter. The standard deviation is recorded simultaneously as a dispersion index. Feasible region node sets with a standard deviation exceeding 0.3° must be further partitioned by spatial location and statistically analyzed separately to identify whether there is a bimodal distribution of critical angles caused by refractive index gradient boundaries within the feasible region. When a bimodal distribution is identified, the feasible region is split into two independent sub-regions according to the refractive index gradient boundary line. The mean and standard deviation of the critical angles of each sub-region are statistically analyzed to generate two sets of corresponding total internal reflection critical angle parameters, which are then passed to the subsequent angle interval mapping. Each set of parameters carries an axial partition identifier to distinguish its spatial range. The primary axis and secondary axis nodes are statistically analyzed separately to generate the primary axis total internal reflection critical angle parameters and the secondary axis total internal reflection critical angle parameters. Nodes determined to be "critical" are not included in the mean statistics, and their coordinates and critical angle values ​​are additionally recorded in the form of boundary nodes. The total internal reflection critical angle parameters consist of four items: the mean of the primary axis critical angle, the mean of the secondary axis critical angle, the biaxial difference value, and the error tolerance statistics.

[0050] In some embodiments, the step of generating a cutting task allocation strategy by mapping angle intervals based on the total internal reflection critical angle parameter and the effective cutting coverage area includes: generating a feasible dihedral angle interval by mapping angle intervals based on the total internal reflection critical angle parameter; jointly filtering the feasible dihedral angle interval and the effective cutting coverage area to determine a faceted link set; prioritizing the faceted link set to generate a cutting task hierarchical distribution; and generating a cutting task allocation strategy based on the cutting task hierarchical distribution.

[0051] Angle interval mapping is performed based on the critical angle parameter of total internal reflection to generate feasible intervals for dihedral angles. The principal axis mean of the critical angle parameter of total internal reflection (34.6°) differs from the secondary axis mean of 34.4° by 0.2°. This difference must be expanded into independent tolerance zones in the angle interval mapping to cover the respective cutting angle jitter ranges in the principal and secondary axis directions. If the two axes are merged into a single tolerance zone, it will result in a systematic underestimation of 0.2° in the secondary axis direction. The angle interval mapping uses the principal axis mean and secondary axis mean of the critical angle parameter of total internal reflection as reference points, and expands to both sides by an error tolerance Δ to form the principal axis candidate interval [θ_c(principal)−Δ,θ_c(principal)+Δ] and the secondary axis candidate interval [θ_c(secondary)−Δ,θ_c(secondary)+Δ]. The intersection of the two intervals is defined as the dual-axis common feasible zone, and the width of the common feasible zone directly reflects the compatibility of the principal and secondary axis parameters. The feasible interval for dihedral angles uses the biaxial common feasible zone as its core interval, with an additional 0.3° safety margin at each end. The margin value is determined based on the angular dispersion of the critical nodes in the boundary nodes of the total internal reflection critical angle parameter. Low-confidence records with an error tolerance exceeding 0.15° in the total internal reflection critical angle parameter are processed separately in the feasible interval for dihedral angles using a tolerance limit identifier. The interval width of the tolerance limit partition is narrowed by 0.1° compared to the standard partition to compensate for parameter uncertainty. Each record in the feasible interval for dihedral angles includes a lower bound angle, an upper bound angle, an interval width, and an axial partition identifier, with an angle value accuracy of 0.1°.

[0052] A joint screening process is used to determine the faceted link set based on the feasible dihedral interval and the effective cut coverage area. The tolerance zone of the feasible dihedral interval has approximately 35% spatial overlap with the low-priority marked area of ​​the effective cut coverage area. This dual-constraint area must simultaneously meet both angular and spatial constraints, making it the most stringent segment in the joint screening. The proportion of candidate links ultimately included in the faceted link set within this segment is typically less than 50% of other areas at the same level. Candidate faceted links are generated based on the spatial contour coordinates of each partition within the effective cut coverage area. Links are formed by connecting adjacent grid nodes within each partition in order of spatial proximity. Each candidate faceted link contains at least 5 nodes, with the node spacing not exceeding three times the coordinate resolution of the effective cut coverage area. The joint screening uses the upper and lower bounds of the angles of each partition in the feasible dihedral interval as angular constraints, and the contour coordinates and Boolean identifiers of the constraint records of each partition in the effective cut coverage area as spatial constraints. The feasibility of all candidate faceted links within the coverage area of ​​the strong refraction subdomain is verified one by one. Forced avoidance constraints within the effective cut coverage area are directly excluded during joint screening. The coordinates of each inflection point of a candidate link must fall within the effective contour of the effective cut coverage area to pass spatial verification. The dihedral angle feasible interval is used to verify the actual dihedral angle nodes at each facet node of each candidate link. Candidate links with at least 90% compliant angle nodes are included in the faceted link set. The partition priority marker of the effective cut coverage area is passed to the priority field of each link in the faceted link set. Each link record includes a node coordinate sequence, a dihedral angle measured value sequence, and a spatial feasibility identifier.

[0053] Priority is assigned to the faceted link set to generate a hierarchical distribution of cutting tasks. The priority field of each link in the faceted link set inherits from the effective cutting coverage area partition marker. However, a single inheritance cannot distinguish the angle matching quality of different links within the same partition. Directly sorting by inherited values ​​would result in links with vastly different angle compliance ratios within the same partition receiving the same priority, causing the execution order to deviate from actual geometric conditions. Therefore, it is necessary to overlay angle compliance ratio and spatial continuity scores and re-calibrate. The comprehensive score of the hierarchical distribution of cutting tasks is calculated using the formula G = 0.4 × P + 0.35 × Q + 0.25 × K, where G is the comprehensive score, P is the partition priority weight, Q is the proportion of angle-compliant nodes, and K is the link spatial continuity score. All three are normalized to the 0-1 range. The comprehensive score of the hierarchical distribution of cutting tasks is normalized to the 0-1 range, with the highest comprehensive score within the faceted link set as the benchmark, ensuring that the hierarchical distribution of cutting tasks fully utilizes the 0-1 range and does not concentrate on a narrow segment. If the difference in the comprehensive score of multiple links within the same partition is less than 0.05 after calculation, the link with more nodes is given priority. If the number of nodes is the same, the link spatial continuity score is used as the deciding factor to avoid unstable ranking results due to tied comprehensive scores. The hierarchical distribution of the cutting task divides each link in the faceted link set into three levels according to its comprehensive score: scores above 0.7 are assigned to Level 1 (priority execution), scores between 0.4 and 0.7 are assigned to Level 2 (regular execution), and scores below 0.4 are assigned to Level 3 (backup execution). Typically, Level 1 accounts for 15% to 25%, Level 2 accounts for 50% to 60%, and Level 3 accounts for the remainder. The hierarchical distribution results of the cutting task are recorded together with the comprehensive score and level identifier of each link. The spatial distribution range of the link nodes in each level is recorded by the bounding rectangle. The spatial overlap ratio between the bounding rectangles of Level 1 and Level 2 links is usually no more than 20%. If the overlap ratio is too high, the reasonableness of the partition priority weight setting must be reviewed.

[0054] A cutting task allocation strategy is generated based on the hierarchical distribution of cutting tasks. In a certain gemstone sample, the first-level links of the cutting task hierarchy are concentrated in the pavilion region, covering approximately 80% of the total pavilion facet area. This concentration creates a clear circular progression structure in the main execution sequence of the cutting task allocation strategy, with smooth angular transitions between adjacent first-level links and minimal backlash. The cutting task allocation strategy uses the hierarchy identifier of the cutting task distribution as the sorting key. Within the same hierarchy, links are arranged according to the spatial position of their node coordinate sequences. When the spatial distance between adjacent links is less than 0.5 mm, they are preferentially arranged consecutively to reduce backlash. When the distance exceeds 1.5 mm, a transition node is inserted between the two links to maintain the geometric continuity of the toolpath. The node coordinate sequences and measured dihedral angle sequences of each link in the cutting task hierarchy are converted into toolpath parameters in the cutting task allocation strategy. These path parameters include the approach angle, cutting direction vector, and cutting depth. The approach angle directly references the measured dihedral angle values ​​of each link. The three-level links in the cutting task hierarchy are marked as conditionally enabled in the cutting task allocation strategy. They are only enabled when the spatial coverage is insufficient after the first and second level links have been executed. Before enabling, the angle compliance must be re-verified. The cutting task allocation strategy outputs a list of link execution order as the main body. The list entries correspond one-to-one with each link in the cutting task hierarchy. Each entry contains toolpath parameters, hierarchy identifier, and conditionally enabled identifier. The outer rectangle coordinates of the cutting task hierarchy are added to the cutting task allocation strategy as the basis for verifying the coverage integrity.

[0055] Step S140: Decompose the cutting task allocation strategy into core facet sequence and auxiliary facet sequence. Perform elastic surface capacity analysis on the auxiliary facet sequence to form a hot standby facet node cluster. Perform cutting deviation anomaly monitoring on the core facet sequence to obtain distortion signal.

[0056] Specifically, the cutting task allocation strategy is broken down into a core facet sequence and an auxiliary facet sequence. In the link execution order list of the cutting task allocation strategy, the first-level link entries correspond to the main facet positions of the circular propulsion structure of the pavilion section of the raw stone. These positions have the tightest toolpath parameter constraints, the smallest angle tolerance, and the facet geometry has the most direct impact on the final firing effect, constituting the main source of the core facet sequence. The cutting task allocation strategy is decomposed according to hierarchical identifiers. All first-level links are assigned to the core facet sequence, all third-level links are assigned to the auxiliary facet sequence, and second-level links are further judged based on the axial partition identifier of the feasible dihedral angle interval: second-level links whose axial partition belongs to the main axis and whose angle compliance nodes account for more than 95% are assigned to the core facet sequence, and the remaining second-level links are assigned to the auxiliary facet sequence. The core facet sequence carries approximately 40% to 50% of the link entries of the cutting task allocation strategy. The geometric positions are concentrated in the intersection area of ​​the pavilion and waist. The angle connection relationship between the facets in this area has a significant impact on the total internal reflection condition, and any deviation at any node may be transmitted to adjacent nodes along the link. The auxiliary facet sequence carries the allowance entries, has a relatively dispersed geometric distribution, and its node angle tolerance is relatively loose, providing the geometric conditions to accept the deviation compensation of the core facet sequence. The core facet sequence and the auxiliary facet sequence each retain the toolpath parameters, level identifiers, and condition activation identifiers of the cutting task allocation strategy. After decomposition, the node coordinates of the two sequences do not overlap, and the merged sequence covers the entire spatial range of the cutting task allocation strategy.

[0057] In some embodiments, the step of performing elastic surface capacity analysis on the auxiliary facet sequence to form a hot-standby facet node cluster includes: hierarchically dividing the auxiliary facet sequence according to curvature gradient to generate a high-capacity facet layer and a low-capacity facet layer; performing elastic surface capacity aggregation analysis on the high-capacity facet layer and the low-capacity facet layer to generate a capacity distribution matrix; performing optical path compatibility screening on the capacity distribution matrix to generate a compatible node set; and using the compatible node set to form a hot-standby facet node cluster.

[0058] The auxiliary facet sequence is hierarchically divided according to curvature gradient to generate high-capacity and low-capacity facet layers. The curvature gradient value of each node in the auxiliary facet sequence is obtained by mapping the node coordinates to the surface curvature field of the rough stone established by the 3D point cloud data, and extracting the normal curvature gradient magnitude within a 0.5 mm radius neighborhood centered on each node coordinate. The unit of curvature gradient value is rad / mm. This operation reuses the normal vector estimation sequence and point coordinate sequence of the 3D point cloud data in S110. The curvature gradient value at a certain node in the auxiliary facet sequence reaches 1.8 rad / mm, while at another node in the same sequence it is only 0.4 rad / mm. The difference in geometric adaptability between the high and low gradients is significant. The high gradient node can bear a larger angle adjustment margin, and the surface shape changes more flexibly in response to the direction of external force. This difference constitutes the core basis for hierarchical division. The auxiliary facet sequence uses 1.0 rad / mm as the dividing threshold. Nodes with curvature gradient values ​​exceeding the threshold are assigned to the high-capacity facet layer, while those below the threshold are assigned to the low-capacity facet layer. Nodes within ±0.1 rad / mm of the threshold are assigned a second time using the mean curvature gradient in their neighborhood as an auxiliary criterion, avoiding frequent cross-layer assignments for boundary nodes due to small gradient fluctuations. The geometric adaptation margin of nodes in the high-capacity facet layer is quantified by the difference between the curvature gradient value and the threshold of 1.0 rad / mm. The larger the difference, the wider the adjustment space that the node can contribute in the elastic surface capacity aggregation analysis. The adaptation margin of nodes in the low-capacity facet layer is correspondingly narrower, and their weight in the aggregation analysis is lower. The spatial distribution of nodes in the two layers in the auxiliary facet sequence exhibits obvious banded partitioning characteristics. Nodes in the high-capacity facet layer are mainly clustered in the angular transition zones with drastic curvature changes, while nodes in the low-capacity facet layer are distributed in the flat areas of the surface. High-capacity facet layers typically cover 35% to 45% of the total number of nodes in the auxiliary facet sequence, while low-capacity facet layers cover the remaining nodes. Each of the two layers retains the node coordinate sequence and the measured dihedral angle sequence of the auxiliary facet sequence, and a layer identifier is attached to each node.

[0059] Capacity aggregation analysis of elastic surfaces was performed using high-capacity and low-capacity faceted layers to generate a capacity distribution matrix. In the high-capacity faceted layer, the node clusters within a 30° range below the waist have an average geometric fit margin of 0.7 rad / mm, while the node clusters in the same region of the low-capacity faceted layer have a margin of only 0.2 rad / mm. This spatial difference in margin determines that the high-value areas of the capacity distribution matrix are mainly distributed below the waist, while the cap plateau region, constrained by the flatness of the surface, generally exhibits lower capacity aggregation values. The elastic surface capacity aggregation analysis uses a 0.5mm×0.5mm spatial grid as the basic unit. It traverses all nodes in the high-capacity faceted layer and the low-capacity faceted layer that fall into the same grid. The geometric adaptation margin of each node is weighted and accumulated according to the formula V=0.7×ΣM_h+0.3×ΣM_l to obtain the capacity aggregation value of the grid, where V is the capacity aggregation value, M_h is the geometric adaptation margin of each node in the high-capacity faceted layer that falls into the grid, and M_l is the geometric adaptation margin of each node in the low-capacity faceted layer. The summation is performed on all nodes in each layer within the grid. The weight ratio is set based on the fact that the nodes in the high-capacity faceted layer bear the main adjustment in angle compensation, while the nodes in the low-capacity faceted layer only perform auxiliary correction. The capacity distribution matrix uses the capacity aggregation value of each grid as its element. The matrix coordinate index is consistent with the node coordinate system of the auxiliary facet sequence, with a resolution of 0.5 mm. When the number of nodes in the high-capacity facet layer within a grid is zero, the capacity aggregation value of that grid is contributed only by the low-capacity facet layer. The corresponding grid element in the capacity distribution matrix is ​​marked as a low-capacity identifier. In the capacity distribution matrix, grids with aggregation values ​​exceeding 1.2 rad / mm are marked as high-capacity regions, those between 0.5 rad / mm and 1.2 rad / mm are medium-capacity regions, and those below 0.5 rad / mm are low-capacity regions. The spatial distribution of these three types of regions directly reflects the overall elastic bearing structure of the auxiliary facet sequence in the capacity distribution matrix.

[0060] A compatible node set is generated by optical path compatibility screening of the capacity distribution matrix. The high-capacity grates in the capacity distribution matrix are located in the pavilion ring area. Nodes in this region are concentrated in the principal axis partition within the dihedral feasible interval of the cutting task allocation strategy, exhibiting the highest overlap between geometric capacity and optical path constraints. Optical path compatibility screening is first performed in this region. The screening uses the center coordinates of each grates in the capacity distribution matrix as a reference, extracting the normal vectors of the facet normal vector distribution at those coordinates. For grates falling within the coverage area of ​​the strong refractive subdomain, the normal vectors of the corresponding nodes are directly extracted. For grates outside the coverage area of ​​the strong refractive subdomain, the estimated normal vector values ​​are extrapolated from the boundary nodes of the facet normal vector distribution using the nearest neighbor interpolation method. The effective extrapolation radius does not exceed 0.5 mm; grates exceeding this range are directly marked as incompatible and skipped from subsequent matching. The incident angle is matched between the normal vector and the mean critical angle of the principal and secondary axes given by the critical angle parameter of total internal reflection. Grids with incident angle deviations within the feasible range of the dihedral angle are determined to be optically compatible. Grids with deviations exceeding the feasible range of the dihedral angle but falling within the tolerance limit are marked as conditionally compatible. The remaining grids are determined to be incompatible and excluded from the screening results. For low-capacity grids in the capacity distribution matrix, an additional requirement is that the incident angle deviation does not exceed 60% of the width of the feasible range of the dihedral angle to avoid optical path mismatch caused by insufficient angle adjustment margin for low-capacity nodes. The compatible node set includes all nodes corresponding to grids that are determined to be optically compatible and conditionally compatible. Conditionally compatible nodes are distinguished by conditional identifiers in the compatible node set. The number of effective nodes in the compatible node set usually accounts for 60% to 75% of the total number of grids in the capacity distribution matrix.

[0061] A hot-standby faceted node cluster is constructed using a set of compatible nodes. The spatial density of optical path compatible nodes in the pavilion ring area reaches 3.2 per square millimeter, while conditionally compatible nodes are mainly distributed in the waist transition area. These two types of nodes are spatially arranged in concentric bands, forming a two-layer topological structure for the hot-standby faceted node cluster. The inner core area is geometrically adjacent to the core faceted sequence, providing the spatial conditions for rapid takeover. The hot-standby faceted node cluster uses optical path compatible nodes from the compatible node set as core nodes and conditionally compatible nodes as peripheral nodes. Based on spatial proximity, the core and peripheral nodes are organized into several local clusters. The distance between adjacent nodes within a cluster does not exceed 1.0 mm; if the distance exceeds 1.0 mm, the two nodes are not grouped into the same cluster to ensure a smooth path transition during takeover cutting within the same local cluster. The center coordinates of each local cluster are taken as the spatial average of the coordinates of the core node within the cluster, and the cluster radius is taken as the distance from the center coordinates to the farthest peripheral node. Local clusters with fewer than 3 nodes are removed from the hot-standby faceted node cluster to ensure that each hot-standby location has practical replacement capability. In the hot standby faceted node cluster, the hot standby priority of the core node is higher than that of the peripheral nodes. The capacity aggregation value of the compatible node set of the core node and the optical path compatibility identifier are synchronously attached to each node. The peripheral nodes are marked with conditional compatibility identifiers. The spatial coverage of the hot standby faceted node cluster is represented by the union of the outer rectangles of each local cluster. The coverage overlaps with the spatial distribution of the core faceted sequence by no less than 30%, ensuring that the takeover and cut-off links have the possibility of geometric continuity.

[0062] Anomaly monitoring of cutting deviation is implemented to acquire distortion signals for the core facet sequence. During the execution of the core facet sequence, the measured dihedral angle at a certain facet node deviates from the preset value of the path parameter by 0.8°, exceeding 40% of the width of the feasible dihedral angle interval. This magnitude of deviation directly affects the establishment of total internal reflection conditions in angle-sensitive sections. If not captured in time, the deviation will be chained along adjacent nodes of the core facet sequence, potentially causing geometric failure of the entire chain when accumulated to subsequent nodes. The cutting deviation anomaly monitoring is a real-time capture mechanism designed to address this propagation risk. The cutting deviation anomaly monitoring uses the preset feed angle in the tool path parameters of each node in the core facet sequence as the reference value. During the cutting execution, the measured dihedral angle is collected node by node, and the difference between the measured value and the reference value is defined as the node deviation. Nodes with an absolute deviation value exceeding 0.5° are marked as abnormal. The 0.5° threshold corresponds to 25% of the standard partition width of the feasible dihedral angle interval. Below this proportion, the deviation can be naturally absorbed by the facet curvature without affecting the optical path conditions. When three or more consecutive adjacent nodes in the core facet sequence trigger anomaly markers, the deviation sequence of that node group is determined to be a distortion signal. The amplitude of the distortion signal is taken as the average of the deviations of the node group, the direction is taken as the direction of the principal component of the deviation sequence, and the spatial position is taken as the geometric center of the node group coordinates. The lower limit for the number of consecutive nodes is set to 3 because the common deviation of two adjacent nodes cannot statistically exclude the interference of random measurement errors. Anomaly markers triggered by a single isolated node do not constitute a distortion signal and are only recorded as occasional noise points. Occasional noise points are retained in the monitoring record of the core facet sequence but do not trigger the takeover process. Once a consecutive node group is determined to be a distortion signal, the current execution of the link where the node group is located is immediately stopped. The amplitude, direction, and spatial position of the distortion signal constitute a complete description of the distortion signal, which is used for curvature correction parameter extraction.

[0063] Step S150: Extract curvature correction parameters based on the distortion signal, match the curvature correction parameters with the hot standby facet node cluster for error compensation to determine the takeover cutting link, seamlessly connect the takeover cutting link with the core facet sequence to generate a collaborative cutting mesh, and perform surface accuracy calibration based on the collaborative cutting mesh to generate virtual cutting 3D modeling instructions.

[0064] Specifically, curvature correction parameters are extracted based on the distortion signal. The amplitude of the distortion signal in a gemstone sample is recorded as 0.8°, with its direction biased towards the inner side of the pavilion's angular band. This directional bias indicates that the deviation originates from the continuous interference of abrupt curvature changes in the angular band on the tool path, rather than random measurement error. Therefore, the extraction of curvature correction parameters must prioritize this direction. The amplitude and spatial location of the distortion signal pinpoint the specific node group in the core facet sequence where geometrical offset occurs. Centered on the spatial location of this node group, the local curvature distribution of the gemstone surface is extracted within a radius of 2.0 mm. The local curvature distribution is described by the principal curvature κ_1 and the secondary curvature κ_2, and the difference between them, κ_1−κ_2, reflects the anisotropy intensity of the surface at that location. When the angle between the direction of the distortion signal and the principal curvature direction of the local curvature distribution exceeds 30°, the judgment deviation is caused by the mismatch between the cutting direction and the principal curvature direction. The correction vector of the curvature correction parameter is offset in the opposite direction along the principal curvature direction, and the offset amount is calculated as 1.2 times the amplitude of the distortion signal. When the angle does not exceed 30°, the judgment deviation is caused by the local curvature amplitude exceeding the preset range of the tool path parameters. The correction amplitude of the curvature correction parameter is directly taken as the amplitude of the distortion signal. The curvature correction parameter is completely described by three items: correction vector, correction amplitude, and effective spatial range. The effective spatial range is a circular area with the spatial position of the distortion signal as the center and 1.5 times the geometric radius of the distortion signal node group as the radius. The effective spatial range of the curvature correction parameter has a spatial overlap of no less than 25% with the coverage of the hot standby facet node cluster to ensure that the correction parameter can find an effective corresponding compensation position in the hot standby node.

[0065] In some embodiments, the step of performing error compensation matching between the curvature correction parameter and the hot standby faceted node cluster to determine the takeover cut-off link includes: decomposing the curvature correction parameter into short-range neighborhood error components and cross-sequence cumulative drift components; performing surface similarity screening in the hot standby faceted node cluster based on the short-range neighborhood error components to form a candidate takeover node set; performing error adaptation evaluation on the candidate takeover node set based on the cross-sequence cumulative drift components to determine the takeover priority sequence; and fusing the candidate takeover node set step by step according to the takeover priority sequence to determine the takeover cut-off link.

[0066] The curvature correction parameter is decomposed into short-range neighborhood error components and cross-sequence cumulative drift components. The 0.8° correction amplitude of the curvature correction parameter manifests as a gradual accumulation of 0.15° between adjacent nodes within a local segment with a node spacing of 0.3mm in the core facet sequence. However, over longer distances spanning more than three nodes, it exhibits a systematic drift along the overall path. These two error forms differ fundamentally in their compensation strategies and must be processed separately after decomposition. The short-range neighborhood error component extracts the difference in correction vectors between adjacent node pairs within the curvature correction parameter's effective range. The mean of these differences serves as the short-range component amplitude, and the direction is taken as the principal component direction of the difference sequence. The short-range neighborhood error component describes the minute angular jumps caused by local surface irregularities between nodes. The cross-sequence cumulative drift component is characterized by the slope of the linear fit of the correction vectors of all nodes within the curvature correction parameter's effective range. The slope direction corresponds to the spatial direction of the drift, and the slope amplitude corresponds to the drift rate per millimeter. The cross-sequence cumulative drift component reflects the systematic angular offset trend of the toolpath over a longer distance. The sum of the magnitudes of the short-range neighborhood error component and the cross-sequence cumulative drift component deviates from the original correction magnitude of the curvature correction parameter by no more than 5%, thus verifying the completeness of the decomposition results. If the deviation exceeds 5%, the linear fitting range is readjusted and the decomposition is repeated until the sum of the two components converges to the allowable range.

[0067] In the hot-standby faceted node cluster, candidate takeover node sets are formed by surface similarity screening based on short-range neighborhood error components. The amplitude of the short-range neighborhood error component is 0.15° / node spacing. The node clusters in the core node region of the hot-standby faceted node cluster whose local curvature change rate is closest to this component amplitude are concentrated in the inner waist ring, which becomes the priority search space for surface similarity screening. Surface similarity screening uses the amplitude and direction of the short-range neighborhood error component as matching targets. It traverses all core nodes in the hot-standby faceted node cluster and calculates the absolute difference between the curvature change rate in the neighborhood of each core node and the amplitude of the short-range neighborhood error component. Nodes with a difference less than 0.05° / mm are marked as highly similar nodes, nodes with a difference between 0.05° / mm and 0.15° / mm are marked as moderately similar nodes, and nodes with a difference greater than 0.15° / mm are excluded. The direction of the short-range neighborhood error component is used for secondary screening of highly similar nodes. Highly similar nodes whose local principal curvature direction and the direction of the short-range neighborhood error component are at an angle of no more than 20° are retained, while those exceeding 20° are downgraded to medium-similar nodes. The direction consistency constraint ensures that the surface orientation of each node in the candidate takeover node set matches the geometric shape of the distortion signal source segment, rather than just having similar amplitudes. The peripheral condition-compatible nodes of the hot standby faceted node cluster are processed according to the standard for medium-similar nodes in the surface similarity screening. After passing the screening, they are included in the candidate takeover node set with conditional candidate identifiers. The number of effective nodes in the candidate takeover node set typically accounts for 45% to 60% of the total number of nodes in the hot standby faceted node cluster. Highly similar nodes and medium-similar nodes in the candidate takeover node set are stored hierarchically according to their identifiers.

[0068] For example, the step of determining the takeover priority sequence by performing error adaptation evaluation on the candidate takeover node set based on the cross-sequence cumulative drift component includes: performing offset quantization on the surface geometric parameters of the candidate takeover node set and the cross-sequence cumulative drift component to generate an error coverage score sequence; performing interval segmentation calibration on the error coverage score sequence to generate a rating distribution map; extracting the adaptation surplus of each node in the candidate takeover node set from the rating distribution map; and determining the takeover priority sequence based on the distribution intensity of the adaptation surplus.

[0069] The surface geometry parameters of the candidate takeover node set are offset-quantized with the cross-sequence cumulative drift component to generate an error coverage scoring sequence. The drift rate of the cross-sequence cumulative drift component is 0.12° per millimeter, while the surface curvature of a highly similar node in the candidate takeover node set changes at a rate of only 0.04° per millimeter along the drift direction. The difference of 0.08° / mm means that if this node undertakes the takeover task, it needs to absorb approximately 0.12° of cumulative deviation within a 1.5mm path. Whether its geometric margin is sufficient needs to be verified by offset quantization. Offset quantization uses the surface curvature and tangent curvature of each node in the candidate takeover node set as geometric parameters. It projects the drift direction of the cross-sequence cumulative drift component onto the tangent plane of each node and calculates the maximum angular offset that the surface geometric parameters can compensate for in the projection direction. The ratio of this maximum offset to the drift rate of the cross-sequence cumulative drift component is defined as the error coverage rate of that node, calculated as CR = D_max / v_drift, where CR is the error coverage rate, D_max is the maximum angular offset that the surface geometric parameters can compensate for in the projection direction, and v_drift is the drift rate, in ° / mm. The error coverage rate scoring sequence is arranged after normalizing the error coverage rate of each node. Normalization is based on the maximum error coverage rate within the candidate takeover node set, with the normalization result falling between 0 and 1. Nodes with a coverage rate below 0.3 are marked as under-covered in the error coverage rate scoring sequence. This mark is directly mapped to a low rating when generating the rating distribution map. The number of valid records in the error coverage rate scoring sequence is equal to the number of valid nodes in the candidate takeover node set.

[0070] An interval segmentation and calibration of the error coverage score sequence was performed to generate a rating distribution map. Nodes with scores higher than 0.75 in the error coverage score sequence were concentrated in the inner lumbar annular region, while nodes with scores lower than 0.3 were mainly distributed at the crown edge. The spatial separation of the nodes at both ends resulted in a clear spatial gradient in the rating distribution map, with a transition band of approximately 1.5 mm wide between the high-rated and low-rated regions. The rating distribution map was segmented based on the score value of the error coverage score sequence. Scores higher than 0.7 were calibrated as Level 1 adaptation, 0.4 to 0.7 as Level 2 adaptation, and lower than 0.4 as Level 3 adaptation. The three levels were appended to each node of the rating distribution map with integer codes. In the error coverage score sequence, spatially adjacent nodes belonging to the same Level 1 adaptation are merged into an adaptation connectivity region in the rating distribution map. Isolated Level 1 regions with a connectivity region area of ​​less than 1.5 mm² are downgraded to Level 2 adaptation to eliminate the interference of isolated high-scoring nodes on the spatial continuity of the takeover path. The priority of the insufficient coverage mark is higher than the isolation region downgrade rule. When a node triggers both rules simultaneously, the insufficient coverage mark takes precedence, and it is directly classified into Level 3 adaptation. The mean error coverage score, number of nodes, and spatial range of each level of adaptation nodes in the rating distribution map are recorded as statistical fields. The mean error coverage score of Level 1 adaptation nodes is usually between 0.78 and 0.85, while the mean of Level 3 adaptation nodes is generally below 0.35. The difference between the two means forms the quantitative basis for the differentiated ranking of the takeover priority sequence.

[0071] The adaptation margin of each node in the candidate takeover node set is extracted from the rating distribution map. In the rating distribution map, the error coverage score of a node in the first-level adaptation region is 0.82, corresponding to a maximum compensable angular offset of 0.68°. The deviation introduced by the cross-sequence cumulative drift component within the takeover path of this node is 0.51°. The difference between the two, 0.17°, is the adaptation margin of this node. A positive margin indicates that the node still retains a certain geometric redundancy after undertaking the takeover task. The adaptation margin is calculated using the formula M = D_max − v_drift × L, where M is the adaptation margin, D_max is the maximum compensable angular offset, v_drift is the drift rate, and L is the takeover path, where L is the Euclidean distance from the node to the spatial location of the distorted signal. Nodes with negative adaptation surplus in the candidate takeover node set indicate that their geometric surplus is insufficient to cover the cumulative drift component across sequences. These nodes are marked as insufficient in the rating distribution map. Nodes with insufficient surplus do not enter the takeover priority sequence but are retained in the candidate takeover node set for emergency use when all nodes with sufficient surplus are exhausted. The distribution of adaptation surplus is non-uniform across the rating regions of the rating distribution map. The surplus in the first-level adaptation region is typically between 0.1° and 0.3°, while that in the second-level adaptation region is between 0° and 0.15°. This distribution characteristic means that the ranking of the takeover priority sequence cannot rely solely on ratings and must be further refined by considering the intensity of the surplus distribution.

[0072] The takeover priority sequence is determined based on the distribution intensity of the adaptation surplus. In the rating distribution map, nodes with adaptation surpluses exceeding 0.15° within the first-level adaptation connectivity region exhibit high spatial concentration, forming a surplus intensity peak region. Nodes corresponding to this peak region can both cover cross-sequence cumulative drift components and maintain sufficient redundancy during takeover cutting, thus having the highest takeover priority. The takeover priority sequence uses the distribution intensity of the adaptation surplus as the primary sorting key and the rating calibration result of the rating distribution map as the secondary sorting key. The takeover order of each node is determined by combining these two keys. Relying solely on the rating while ignoring the distribution intensity of the surplus can lead to some highly rated but low-concentration nodes being incorrectly placed at the top, creating a risk of insufficient compensation in local segments of the takeover path. Distribution intensity is characterized by the ratio of each node's adaptation surplus to the average adaptation surplus of all nodes in its spatial neighborhood (neighborhood radius 1.0 mm). Nodes with a ratio exceeding 1.3 are classified as high-intensity nodes, those between 0.8 and 1.3 as medium-intensity nodes, and those below 0.8 as low-intensity nodes. High-intensity nodes have higher takeover priority than medium-intensity and low-intensity nodes within the same rating. Nodes within the same intensity level are further subdivided into a third sorting order based on error coverage scores. The takeover priority sequence arranges all non-negative surplus nodes in the candidate takeover node set according to the above rules. The sorting results are labeled with priority numbers from high to low. If multiple nodes exist within the same priority, the final sorting is based on the distance from the node to the spatial location of the distortion signal, from closest to farthest. The closer the spatial distance, the smoother the takeover path transition and the easier it is to ensure the continuity of the path tangent direction. The number of effective nodes in the takeover priority sequence is equal to the total number of nodes with non-negative adaptation surplus in the candidate takeover node set.

[0073] The candidate takeover node set is fused step-by-step according to the takeover priority sequence to determine the takeover cut-off link. The highest priority node in the takeover priority sequence is located in the inner waist ring zone, with an adaptation margin of 0.22° and a spatial distance of 1.2mm from the distorted signal. The path extending from this node to the core faceted sequence deviation node group has the dual advantages of the shortest spatial span and the highest geometric redundancy. Step-by-step fusion starts from the node with the highest takeover priority sequence number and successively includes the next highest priority nodes. After each node is included from the takeover priority sequence, the cross-sequence cumulative drift component compensation amount covered by the current fused link is recalculated. When the cumulative compensation amount reaches 90% of the total amplitude of the cross-sequence cumulative drift component, the takeover priority sequence fusion terminates, and the current link is designated as the takeover cut-off link. Conditionally compatible nodes in the candidate takeover node set are only activated during the step-by-step fusion process when all nodes with sufficient margin have been included but the 90% compensation threshold still cannot be reached. After the conditionally compatible nodes are activated, a conservative compensation margin of 0.05° must be added to compensate for the deviation risk caused by the uncertainty of their optical path compatibility. The node coordinate sequence of the takeover and cut link is inherited from the candidate takeover node set. The link geometry is arranged in the order of the spatial position of the included nodes. When the distance between adjacent nodes exceeds 1.0 mm, interpolation nodes are inserted to maintain the geometric continuity of the path. The surface parameters of the interpolation nodes are taken as the linear interpolation values ​​of the corresponding parameters of the two end nodes. The takeover and cut link is finally fully described by three items: node coordinate sequence, adaptation margin of each node, and path compensation amount.

[0074] The takeover cut link and the core facet sequence are seamlessly connected to generate a collaborative cut mesh. The spatial distance between the coordinates of the starting node of the takeover cut link and the coordinates of the end node of the distortion signal node group of the core facet sequence is 0.9 mm, which is less than the bridging connectivity threshold of 1.0 mm. The two can be directly connected without inserting additional transition nodes. This geometric condition provides a favorable basis for seamless connection. Seamless connection uses the starting node of the takeover cut link and the end node of the distortion signal node group of the core facet sequence as the junction point. At the junction point, the tangent directions of the paths on both sides are verified for first-order continuity. If the angle between the tangents on both sides does not exceed 5°, it is judged as geometrically continuous and directly merged; if the angle exceeds 5°, three nodes are taken on each side of the junction point to form a transition segment. Cubic spline interpolation is performed on the path of the transition segment to eliminate abrupt changes in direction. After interpolation, the angle between the tangents at the junction point must converge to within 3°. The normal execution segment before the distortion signal node group and the takeover cutting link after the distortion signal node group together constitute the backbone path of the collaborative cutting mesh. The mesh nodes of the collaborative cutting mesh are filled by the backbone path nodes and the low-capacity facet layer nodes that have not been called in the auxiliary facet sequences on both sides. The mesh resolution is based on a spacing of 0.3 mm. When the node spacing exceeds 0.3 mm, interpolation nodes are added. The coverage of the collaborative cutting mesh must completely include the original spatial range of the core facet sequence. If there is a coverage gap, the gap position is filled by the adjacent nodes from the hot standby facet node cluster.

[0075] Virtual cutting 3D modeling commands are generated based on surface accuracy calibration using a collaborative cutting mesh. The collaborative cutting mesh for a specific gemstone sample contains 1240 effective mesh nodes, with 62% being main path nodes and 38% being auxiliary fill nodes. The surface geometry parameters at the main path nodes are directly inherited from the connecting cutting links and core facet sequences. The parameters at the auxiliary fill nodes must be calibrated for surface accuracy before being included in the modeling commands. Surface accuracy calibration uses the normal vectors of each node in the collaborative cutting mesh as the calibration object, controlling the angle between the normal vectors of adjacent nodes to within 2°. For adjacent node pairs exceeding 2°, the normal vectors of the two nodes are adjusted by taking a weighted average, with weights allocated according to the size of the adaptation margin of each node. Nodes with larger margins have higher weights and smaller normal vector corrections to preserve geometric margins. After the collaborative cutting mesh is calibrated for surface accuracy, the normal vector sequence, coordinate sequence, and curvature correction parameter correction vector of each node together constitute the geometric input of the virtual cutting 3D modeling command. The modeling command is generated node by node with the smallest unit. Each node corresponds to one modeling command. The command content includes four parameters: the three-dimensional coordinates of the node, the normal vector direction, the feed angle, and the cutting depth. The feed angle directly inherits the measured dihedral angle value of the main path node of the collaborative cutting mesh or the interpolated angle of the auxiliary filling node. The virtual cutting 3D modeling command is output according to the spatial arrangement order of the collaborative cutting mesh nodes. The main path node command is output first, and the auxiliary filling node command follows in spatial position order. The entire command set covers the complete spatial range of the collaborative cutting mesh. The geometric coverage integrity of the command set is verified by the absence of gaps in the nodes within the outer rectangle of the collaborative cutting mesh.

[0076] In order to implement the gemstone virtual cutting 3D modeling method based on geometric topology reconstruction corresponding to the above method embodiments, so as to achieve the corresponding functions and technical effects. Figure 2 A structural block diagram of a gemstone virtual cutting 3D modeling system 200 based on geometric topology reconstruction according to an embodiment of this application is shown. For ease of explanation, only the parts relevant to this embodiment are shown. The gemstone virtual cutting 3D modeling system 200 based on geometric topology reconstruction according to an embodiment of this application includes:

[0077] The map construction module 201 is used to acquire three-dimensional point cloud data and inclusion distribution signals of gemstone rough, and to extract geometric topological features from the three-dimensional point cloud data and the inclusion distribution signals to generate a topology-driven map.

[0078] The singularity avoidance module 202 is used to perform cutting plane topological recombination to generate a singular region distribution map based on the topology-driven map, and to construct an effective cutting coverage area based on the avoidance constraints of the singular region distribution map.

[0079] The strategy generation module 203 is used to perform optical path refraction distribution analysis on the effective cutting coverage area to extract the critical angle parameter of total internal reflection, and generate a cutting task allocation strategy based on the critical angle parameter of total internal reflection and the effective cutting coverage area by performing angle interval mapping.

[0080] The node construction module 204 is used to decompose the cutting task allocation strategy into a core facet sequence and an auxiliary facet sequence, perform elastic surface capacity analysis on the auxiliary facet sequence to form a hot standby facet node cluster, and perform cutting deviation anomaly monitoring on the core facet sequence to obtain distortion signals.

[0081] The instruction output module 205 is used to extract curvature correction parameters based on the distortion signal, perform error compensation matching between the curvature correction parameters and the hot standby facet node cluster to determine the takeover cutting link, seamlessly connect the takeover cutting link with the core facet sequence to generate a collaborative cutting mesh, and perform surface accuracy calibration based on the collaborative cutting mesh to generate a virtual cutting 3D modeling instruction.

[0082] The aforementioned gemstone virtual cutting 3D modeling system 200 based on geometric topology reconstruction can implement the gemstone virtual cutting 3D modeling method based on geometric topology reconstruction described in the above method embodiments. The options in the above method embodiments are also applicable to this embodiment, and will not be detailed here. The remaining content of this application's embodiments can be referred to the content of the above method embodiments, and will not be repeated in this embodiment.

[0083] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

Claims

1. A 3D modeling method for virtual gemstone cutting based on geometric topological reconstruction, characterized in that, include: The three-dimensional point cloud data and inclusion distribution signal of the gemstone rough are obtained, and the geometric topological features of the three-dimensional point cloud data and the inclusion distribution signal are extracted to generate a topology-driven map. Based on the topology-driven graph, a cutting plane topology recombination is performed to generate a singular region distribution map, and an effective cutting coverage area is constructed based on the constraint avoidance conditions of the singular region distribution map; Optical path refraction distribution analysis is performed on the effective cutting coverage area to extract the critical angle parameter of total internal reflection. Based on the critical angle parameter of total internal reflection and the effective cutting coverage area, angle interval mapping is performed to generate a cutting task allocation strategy. The cutting task allocation strategy is decomposed into a core facet sequence and an auxiliary facet sequence. Elastic surface capacity analysis is performed on the auxiliary facet sequence to form a hot standby facet node cluster. Cutting deviation anomaly monitoring is performed on the core facet sequence to obtain distortion signals. Curvature correction parameters are extracted based on the distortion signal. The curvature correction parameters are matched with the hot standby facet node cluster for error compensation to determine the takeover cutting link. The takeover cutting link is seamlessly connected with the core facet sequence to generate a collaborative cutting mesh. Based on the collaborative cutting mesh, surface accuracy calibration is performed to generate virtual cutting 3D modeling instructions.

2. The method according to claim 1, characterized in that, The step of extracting geometric topological features from the three-dimensional point cloud data and the inclusion distribution signal to generate a topology-driven map includes: Perform normal vector consistency analysis on the three-dimensional point cloud data to determine the regions of abrupt changes in normal vectors; The colocalization analysis of the normal vector mutation region according to the aggregation density of the inclusion distribution signal generates an inclusion-mutation overlap map; The inclusion-mutation overlap map is subjected to topological fragility index extraction to generate a sensitive zone weight distribution map; The topology-driven map is generated using the sensitive band weight distribution map.

3. The method according to claim 1, characterized in that, The step of generating a singular region distribution map by cutting the plane topology and reorganizing it according to the topology-driven map includes: Based on the topology-driven map, the cutting plane is subjected to topological recombination processing to generate the boundary curvature gradient set of each singular region; The maximum gradient direction of each singular region in the boundary curvature gradient set is back-mapped to the cutting plane to generate a candidate set of boundary lines. The valid boundary line sequence is determined by verifying the consistency of the candidate boundary line set with the spatial coverage of the boundary curvature gradient set. A distribution map of singular regions is generated based on the effective boundary line sequence.

4. The method according to claim 1, characterized in that, The step of performing optical path refraction distribution analysis on the effective cut coverage area to extract the critical angle parameter of total internal reflection includes: The effective cut coverage area is divided into strong refractive sub-domains according to the refractive index gradient, and the distribution of facet normal vectors is extracted; Extract material refractive index feature values ​​from the strong refractive subdomain to generate a set of candidate parameters for the critical angle; The critical angle candidate parameter set is adapted to the facet normal vector distribution by total internal reflection condition to generate the critical angle matrix. Based on the critical angle matrix, the feasible region of angles is selected to extract the critical angle parameters for total internal reflection.

5. The method according to claim 1, characterized in that, The method for generating a cutting task allocation strategy based on the total internal reflection critical angle parameter combined with the effective cutting coverage area through angle interval mapping includes: Based on the total internal reflection critical angle parameter, an angle interval mapping is performed to generate a feasible interval for dihedral angles; The faceted link set is determined by jointly screening the feasible interval of the dihedral angle and the effective cutting coverage area; Priority is assigned to the faceted link set to generate a hierarchical distribution of the cutting tasks; A cutting task allocation strategy is generated based on the hierarchical distribution of the cutting tasks.

6. The method according to claim 1, characterized in that, The process of performing elastic surface capacity analysis on the auxiliary facet sequence to construct a hot-standby facet node cluster includes: The auxiliary facet sequence is hierarchically divided according to the curvature gradient to generate a high-capacity facet layer and a low-capacity facet layer; Based on the high-capacity faceted layer and the low-capacity faceted layer, an elastic surface capacity aggregation analysis is performed to generate a capacity distribution matrix; The capacity distribution matrix is ​​subjected to optical path compatibility screening to generate a set of compatible nodes; The compatible node set is used to construct a hot-standby faceted node cluster.

7. The method according to claim 1, characterized in that, The step of performing error compensation matching between the curvature correction parameters and the hot standby faceted node cluster to determine the takeover and cut-off link includes: The curvature correction parameter is decomposed into a short-range neighborhood error component and a cross-sequence cumulative drift component; In the hot standby faceted node cluster, a candidate takeover node set is formed by surface similarity screening based on the short-range neighborhood error components. The candidate takeover node set is evaluated for error adaptation based on the cross-sequence cumulative drift component to determine the takeover priority sequence; The candidate takeover node set is merged step by step according to the takeover priority sequence to determine the takeover and cut-off link.

8. The method according to claim 4, characterized in that, The step of extracting material refractive index feature values ​​from the strongly refractive subdomain to generate a candidate parameter set for the critical angle includes: The strong refractive subdomain is divided into a primary optical axis direction domain and a secondary optical axis direction domain according to the optical axis direction; Material refractive index feature values ​​are extracted from the principal optical axis direction domain and the secondary optical axis direction domain respectively to generate biaxial critical angle difference diversity; Multi-wavelength envelope expansion is performed on the biaxial critical angle difference diversity to determine the critical angle constraint interval; A set of candidate parameters for critical angles is generated based on the critical angle constraint interval.

9. The method according to claim 7, characterized in that, The step of determining the takeover priority sequence by performing error adaptation evaluation on the candidate takeover node set based on the cross-sequence cumulative drift component includes: The surface geometry parameters of the candidate takeover node set are offset-quantized with the cross-sequence cumulative drift components to generate an error coverage score sequence; The error coverage score sequence is segmented into intervals and labeled to generate a rating distribution map; Extract the adaptation surplus of each node in the candidate takeover node set from the rating distribution map; The takeover priority sequence is determined based on the distribution intensity of the adaptation surplus.

10. A 3D modeling system for virtual gemstone cutting based on geometric topological reconstruction, characterized in that, include: The atlas construction module is used to acquire three-dimensional point cloud data and inclusion distribution signals of gemstone rough, and to extract geometric topological features from the three-dimensional point cloud data and the inclusion distribution signals to generate a topology-driven atlas. The singularity avoidance module is used to perform cutting plane topological recombination to generate a singular region distribution map based on the topology-driven map, and to construct an effective cutting coverage area based on the avoidance constraints of the singular region distribution map. The strategy generation module is used to perform optical path refraction distribution analysis on the effective cutting coverage area to extract the critical angle parameter of total internal reflection, and generate a cutting task allocation strategy based on the critical angle parameter of total internal reflection and the effective cutting coverage area by performing angle interval mapping. The node construction module is used to decompose the cutting task allocation strategy into a core facet sequence and an auxiliary facet sequence, perform elastic surface capacity analysis on the auxiliary facet sequence to form a hot standby facet node cluster, and perform cutting deviation anomaly monitoring on the core facet sequence to obtain distortion signals. The instruction output module is used to extract curvature correction parameters based on the distortion signal, perform error compensation matching between the curvature correction parameters and the hot standby facet node cluster to determine the takeover cutting link, seamlessly connect the takeover cutting link with the core facet sequence to generate a collaborative cutting mesh, and perform surface accuracy calibration based on the collaborative cutting mesh to generate virtual cutting 3D modeling instructions.

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