A personalized nail outer surface generation method based on three-dimensional pose deformation
By using a three-dimensional posture deformation algorithm, the key geometric features of the nail are automatically identified and corrected, solving the problem of non-adherence in the generation of the outer surface of the nail in existing technologies. This achieves high-precision and automated generation of the outer surface of the nail, improving the wearing comfort and production efficiency of phototherapy nails.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUXI YABOSHI MEDICAL TECHNOLOGY CO LTD
- Filing Date
- 2026-06-03
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies struggle to generate models that closely fit the wearer's nail surface under automated conditions, resulting in decreased wearing comfort and aesthetic quality of gel nails, as well as low production efficiency.
A three-dimensional posture deformation-based method is adopted. Through multi-stage posture correction and scale deformation algorithms, key geometric features are automatically identified from the wearer's fingernail point cloud data to generate an outer surface model that closely matches the wearer's real fingernail. This includes steps such as rotation, translation, non-uniform scaling, width direction deformation, and centerline constraint.
It achieves high-precision generation of personalized nail surfaces, improves the fit and wearing comfort of UV-cured nails, reduces production costs, and enhances automated manufacturing efficiency.
Smart Images
Figure CN122492942A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of three-dimensional digital modeling and personalized manufacturing technology, and in particular to a method for generating personalized nail outer surfaces based on three-dimensional posture deformation. Background Technology
[0002] With the widespread adoption of 3D scanning and digital modeling technologies, the demand for personalized manicures and gel nails is growing. Traditional customization processes typically rely on standard templates or experience-based modeling, followed by manual adjustments by designers to achieve a perfect fit. While this method can visually achieve some individual differences, the overall fit is poor, automation is low, and it depends heavily on the operator's experience. Because different users' nails vary significantly in vertical and horizontal arcs, root shape, and thickness distribution, standard templates often fail to simultaneously meet the requirements of comfort and stability. This often results in issues such as lifting, tightness, and hollowness after application, affecting both aesthetics and durability.
[0003] In existing technologies, some methods attempt to scale and rotate standard nail models using 3D scan data to improve fit. However, most of these methods are based on global rigid body transformations or simple linear deformations, failing to accurately reflect the complex surface features of individual nails. When the scan data exhibits pose offset, conventional Iterative Closest Point (ICP) registration methods are easily affected by local symmetry, leading to incorrect outer surface orientation or local misalignment. Even with correct scaling, achieving overall surface alignment remains difficult. Furthermore, traditional deformation control methods typically only adjust scale in a single direction, lacking coordinated constraints on width, height, end transitions, and midline balance, easily resulting in imbalanced proportions or uneven thickness. Empirical scaling or manual adjustments cannot accurately reflect the true 3D shape of the wearer's nails. Due to the nonlinear curvature of the nail surface in both longitudinal and transverse directions, and significant differences in pose, curvature, and proportions between individuals, existing methods struggle to achieve stable and automatic 3D matching under pose error conditions. Meanwhile, when there is noise or pose deviation in the nail point cloud, traditional algorithms often suffer from problems such as alignment drift, scaling imbalance and shape distortion, resulting in the generated outer surface model not fitting the real nail, affecting the wearing comfort and appearance quality of photogel nails.
[0004] For the reasons mentioned above, existing technologies struggle to accurately generate the outer surface of individual nails under automated conditions. This is especially true in the manufacturing of gel nails, where the outer surface morphology not only affects the appearance but also directly determines the precision of subsequent processes such as inner surface generation, thickness control, and printing / curing. The reliance on manual labor and geometric errors in existing processes reduce production efficiency and increase rework costs. Summary of the Invention
[0005] The purpose of this invention is to provide a method for generating a personalized nail outer surface based on three-dimensional posture deformation. This method can automatically identify key geometric features from the wearer's nail point cloud data and generate an outer surface model that closely matches the wearer's real nail through multi-stage posture correction and scale deformation algorithms.
[0006] To achieve the above objectives, this invention provides a method for generating a personalized nail outer surface based on three-dimensional pose deformation, the specific steps of which are as follows: Step S1: Obtain the 3D point cloud set of the wearer's fingernails, perform data preprocessing, and project the preprocessed 3D point cloud set onto a plane to obtain the projection set; Step S2: Calculate the longitudinal curvature angle of the nail using the projection set; Step S3: The standard nail model is initially aligned with the nail's posture based on the longitudinal curvature angle of the nail; Step S4: Perform composite posture deformation on the initially aligned model to obtain a personalized outer surface model.
[0007] Preferably, in step S1, the three-dimensional point cloud set is ,in, For the first The 3D point cloud coordinates of each point are obtained. Data preprocessing includes filtering, smoothing, and standardization. The resulting point cloud set is... ,Will Projecting onto the XZ plane, we obtain the projection set as follows: ,in, These are the projected coordinates.
[0008] Preferably, in step S2, the formula for calculating the longitudinal curvature angle of the nail is as follows: ; in, The longitudinal curvature angle of the nail is used as a reference for subsequent posture alignment. These are the Z-axis projection coordinates of the vertex and tail point, respectively. These are the X-axis projection coordinates of the vertex and tail point, respectively; Calculate the median of the data points within the set maximum value range along the Z-axis; the point corresponding to the median is the vertex. The calculation formula is as follows: ; in: A set of points that satisfy the threshold condition for the maximum value in the Z-axis direction; This represents the maximum value of the point cloud along the Z-axis. The preset height threshold; This is a median function.
[0009] Calculate the median of the data points within a set minimum range along the X-axis. The point corresponding to the median along the X-axis is the tail point. The calculation formula is as follows: ; ; in: A set of points that satisfy the minimum threshold condition in the X-axis direction; This represents the minimum value of the point cloud along the X-axis. This is a preset threshold for the tail region.
[0010] Preferably, step S3 is as follows: Step S31: Place the standard nail model Import a unified coordinate system. For the first A standard nail coordinate; Step S32: Calculate the difference in longitudinal curvature angle between the actual nail point cloud and the standard nail model. The calculation formula is as follows: ; in: The longitudinal curvature of the actual fingernail dot cloud; The longitudinal curvature of a standard nail model.
[0011] The rotation matrix around the Y-axis is obtained based on the longitudinal curvature angle of the nail. as follows: ; Step S33: Rotate and correct the vertices of the standard nail model so that the bending direction of the standard nail model is consistent with the longitudinal bending arc angle of the actual nail; the calculation formula for the rotated model points is as follows: ; in: Standard nail model points; These are the model points after rotation correction.
[0012] Step S34: Perform translation correction on the rotated model so that the tail point of the actual nail coincides with the tail point of the rotated model, and the translation vector... The calculation formula is as follows: ; in, and These are the actual nail tail point and the tail point of the rotated model, respectively.
[0013] Preferably, in step S4, the composite attitude deformation includes non-uniform scaling, width direction deformation, and centerline constraint.
[0014] Preferably, the non-uniform scaling process is as follows: the model with initial posture alignment is non-uniformly scaled to match the overall size of the wearer's nails; The envelope width and height of the statistical point cloud data in the Y-axis and Z-axis directions are calculated using the following formulas: ; ; in, and These represent the envelope width and height in the Y-axis and Z-axis directions, respectively. and These represent the maximum and minimum values along the Y-axis, respectively. and These are the maximum and minimum values along the Z-axis, respectively. The scaling factor is calculated using the following formula: ; ; in, and These are the scaling factors in the Y-axis and Z-axis directions, respectively. and These represent the envelope width and height of the corresponding model in the Y-axis and Z-axis directions, respectively. The model with initial orientation alignment is non-uniformly scaled based on scaling factors in the Y-axis and Z-axis directions.
[0015] Preferably, the specific process of width direction deformation is as follows: width direction deformation is used to improve the adaptability to different nail types; The width center is determined using the following formula: ; in: This represents the coordinate value of the center of the model width along the Y-axis. is the point set of the standard nail model; max and min represent the maximum and minimum value functions, respectively.
[0016] A symmetrical outward expansion is applied with the width center as the reference. The deformation constraint function for the symmetrical outward expansion in the width direction is as follows: ; in, For the expanded first The coordinate values in the Y-axis direction. This is an expansion ratio. It allows the model to better adapt to different A-type shapes (flat, curved, etc.).
[0017] Preferably, the specific process of centerline constraint is as follows: centerline constraint is used to ensure that the model and the point cloud data are aligned in direction; The midpoints of the left and right boundaries of the point cloud data are calculated based on the XY plane cross-section to obtain the set of point cloud centerlines. Based on the midpoints of the left and right boundaries of the model data calculated from the XY plane cross-section, the set of model centerlines is obtained. ; The formula for calculating the difference in the midline is as follows: ; ; in, and These represent the positional differences between the point cloud centerline and the model centerline along the X-axis and Y-axis, respectively. It is a function of average value. and These are the sets of X-axis coordinates and Y-axis coordinates of the point cloud centerline, respectively. and These are the sets of X-axis and Y-axis coordinates of the lines in the model, respectively. and A global translation is performed so that the centerline of the point cloud coincides with the centerline of the model. Global translation correction is then applied to the model based on the average offset of the centerline. The formula for calculating the model points after translation is as follows: ; in: For model points; These are the model points after centerline correction.
[0018] Preferably, the curvature between the actual point cloud data is obtained. When the curvature is greater than the set value, the model centerline and the point cloud centerline are segmented, and the segmented calculation and translation are performed.
[0019] Therefore, the present invention employs the aforementioned method for generating personalized nail outer surfaces based on three-dimensional posture deformation, which has the following beneficial effects: rotation and translation are performed during initial posture alignment, and non-uniform scaling, width-direction deformation, and midline constraints are applied during composite posture deformation, achieving multi-stage posture deformation. Through multi-stage posture correction and deformation control, the model and the wearer's nail maintain consistency in spatial direction. Its tail vertex arc angle recognition and midline constraint alignment algorithm can automatically determine the direction and curvature trend of the nail under different scanning postures, effectively avoiding the angle drift and matching error problems caused by symmetry in traditional registration algorithms. By introducing a width and height scaling mechanism based on point cloud envelope, the proportional relationship of the standard model can be adaptively adjusted, achieving individualized matching while maintaining the natural overall curvature. This deformation algorithm adopts central symmetric expansion in the width direction and combines curvature correction in the height direction, thereby automatically generating a coordinated outer surface for different nail types (flat, curved, wide and short, etc.). Compared with existing manual adjustment methods, the present invention has higher geometric consistency and repeatability. The alignment, rotation, and scaling parameters calculated by the algorithm are automatically determined by the model's own geometric features, requiring no manual intervention and independent of the initial pose. Therefore, even if the input nail point cloud has local defects or scanning errors, stable registration results can still be obtained through global morphological constraints. This results in a personalized outer surface model that highly matches the wearer's nail geometry. This model retains the structural continuity of the standard model and closely matches the actual nail in key dimensions such as longitudinal arc, transverse arc, width, and height, providing accurate and automated basic data support for subsequent inner surface thickness generation, thickness field construction, and 3D printing.
[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0021] Figure 1 This is a flowchart of a method for generating a personalized nail outer surface based on three-dimensional posture deformation according to the present invention. Figure 2 This is a schematic diagram of the projection of the preprocessed 3D point cloud set of the present invention onto the XZ plane; Figure 3 This is a schematic diagram illustrating the posture correction of the standard nail model of this invention with the nail point cloud of the wearer; Figure 4 This is a schematic diagram of the scale matching and outward deformation of the present invention. (a) is a diagram of the model deformation process; (b) is an actual fingernail. Figure 5 This is a diagram illustrating the line constraint alignment process in this invention. Figure 6 A three-dimensional view of the personalized nail outer surface model produced by this invention; Figure 7This is a side view of the personalized nail outer surface model produced by this invention; Figure 8 This is a diagram showing the effect of fitting the personalized nail outer surface model produced by this invention with the original nail dot cloud. Detailed Implementation
[0022] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0023] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0024] like Figure 1 As shown, a method for generating a personalized nail outer surface based on three-dimensional pose deformation is described, with the following specific steps: Step S1: Obtain a 3D point cloud set of the wearer's fingernails. Use a 3D scanning device to acquire the raw point cloud data of the wearer's fingernails and perform data preprocessing. By calculating the boundary range and normal distribution of the point cloud, the coordinate system is standardized so that the fingernail tip is aligned along the negative X direction, the width along the Y direction, and the height along the Z direction, providing a unified reference for subsequent calculations. Project the preprocessed 3D point cloud set onto a plane to obtain the projected set. The 3D point cloud set is... ,in, For the first The 3D point cloud coordinates of [number] points were obtained. Data preprocessing included filtering and smoothing. The processed point cloud set is [details]. ,Will Projecting onto the XZ plane, we obtain the projection set as follows: ,in, These are the projected coordinates.
[0025] Step S2: Calculate the longitudinal curvature angle of the nail using the projection set. For example... Figure 2 As shown, the formula for calculating the longitudinal curvature angle of a nail is as follows: ; in, The longitudinal curvature angle of the nail is used as a reference for subsequent posture alignment. These are the Z-axis projection coordinates of the vertex and tail point, respectively. These are the X-axis projection coordinates of the vertex and tail point, respectively.
[0026] By setting thresholds for the X-axis and Z-axis directions, a set of points in the corresponding region is selected. The median of the data points near the maximum value in the Z-axis direction is calculated, and the point corresponding to the median is the vertex. The calculation formula is as follows: ; in: A set of points that satisfy the threshold condition for the maximum value in the Z-axis direction; This represents the maximum value of the point cloud along the Z-axis. The preset height threshold; This is a median function.
[0027] Calculate the median of the data points near the minimum value along the X-axis. The point corresponding to the median along the X-axis is the tail point. The calculation formula is as follows: ; ; in: A set of points that satisfy the minimum threshold condition in the X-axis direction; This represents the minimum value of the point cloud along the X-axis. This is a preset threshold for the tail region.
[0028] Based on the spatial coordinate difference between the tail point and the vertex, the longitudinal arc angle of the nail is calculated, and this arc angle is used as a reference value for model rotation correction.
[0029] Step S3: The standard nail model is initially aligned with the nail's posture based on the longitudinal curvature angle of the nail.
[0030] like Figure 3 As shown, step S31: Using a standard nail model Import a unified coordinate system. For the first A standard nail coordinate.
[0031] Step S32: Calculate the difference in longitudinal curvature angle between the actual nail point cloud and the standard nail model. The calculation formula is as follows: ; in: The longitudinal curvature of the actual fingernail dot cloud; The longitudinal curvature of a standard nail model.
[0032] The rotation matrix around the Y-axis is obtained based on the longitudinal curvature angle of the nail. as follows: ; Step S33: Rotate and correct the vertices of the standard nail model so that the bending direction of the standard nail model is consistent with the longitudinal bending arc angle of the actual nail. The calculation formula for the rotated model points is as follows: ; in: Standard nail model points; These are the model points after rotation correction.
[0033] Step S34: Perform translation correction on the rotated model so that the tail point of the actual nail coincides with the tail point of the rotated model, and the translation vector... The calculation formula is as follows: ; in, and These are the actual fingernail tail point and the tail point of the rotated model, respectively. By translating, their tail points are made to coincide with the tail point of the wearer's fingernail dot cloud, thus achieving preliminary posture alignment in three-dimensional space.
[0034] Step S4: Perform composite attitude deformation on the initially aligned model to obtain a personalized outer surface model. Composite attitude deformation includes non-uniform scaling, width direction deformation, and centerline constraint.
[0035] like Figure 4 As shown, the specific process of non-uniform scaling is as follows: Non-uniform scaling is performed on the model whose posture is initially aligned to achieve matching of the overall size of the wearer's nails.
[0036] The envelope width and height of the statistical point cloud data in the Y-axis and Z-axis directions are calculated using the following formulas: ; ; in, and These represent the envelope width and height in the Y-axis and Z-axis directions, respectively. and These represent the maximum and minimum values along the Y-axis, respectively. and These are the maximum and minimum values along the Z-axis, respectively.
[0037] The scaling factor is calculated using the following formula: ; ; in, and These are the scaling factors in the Y-axis and Z-axis directions, respectively. and These represent the envelope width and height of the corresponding model in the Y-axis and Z-axis directions, respectively. The model with initial pose alignment is then non-uniformly scaled according to scaling factors in the Y-axis and Z-axis directions. The standard model is scaled proportionally to match the actual size of the wearer's nails.
[0038] The specific process of width-direction deformation is as follows: Width-direction deformation is used to improve adaptability to different nail types. The width center is determined using the following formula: ; in: This represents the coordinate value of the center of the model width along the Y-axis. is the point set of the standard nail model; max and min represent the maximum and minimum value functions, respectively.
[0039] A symmetrical outward expansion is applied with the width center as the reference. The deformation constraint function for the symmetrical outward expansion in the width direction is as follows: ; in, For the expanded first The coordinate values in the Y-axis direction. The expansion ratio is set to improve the model's adaptability to different armor types (flat, curved, etc.). In the width direction, the model expands symmetrically outwards from its centerline. The expansion ratio can be set according to different armor types; for example, the expansion coefficient for flat armor is 1.15, and for curved armor it is 1.20, thus achieving natural curvature compensation.
[0040] like Figure 5 As shown, the specific process of centerline constraint is as follows: Centerline constraint is used to ensure that the model and the point cloud data are aligned in direction.
[0041] The midpoints of the left and right boundary points of the fingernail point cloud are extracted to form the centerline. The average offset between the model centerline and the point cloud centerline is calculated. Based on the XY plane cross-section, the midpoints of the left and right boundaries of the point cloud data are calculated to obtain the set of point cloud centerlines. Based on the midpoints of the left and right boundaries of the model data calculated from the XY plane cross-section, the set of model centerlines is obtained. ; The formula for calculating the difference in the midline is as follows: ; ; in, and These represent the positional differences between the point cloud centerline and the model centerline along the X-axis and Y-axis, respectively. It is a function of average value. and These are the sets of X-axis coordinates and Y-axis coordinates of the point cloud centerline, respectively. and These are the sets of X-axis and Y-axis coordinates of the lines in the model, respectively. and A global translation is performed to align the centerline of the point cloud with the centerline of the model. Translation corrections are then applied to the model to ensure the two centerlines coincide in the XY plane. This guarantees the symmetry and stable fit between the outer surface model and the real fingernail in the planar direction.
[0042] The output personalized external surface model is as follows Figure 6 , Figure 7 as well as Figure 8 As shown, the data can be saved in common 3D formats such as PLY, STL, or OBJ, providing a precise geometric basis for subsequent inner surface generation, thickness control, and edge sealing modeling. The generated outer surface model is consistent with the original fingernail point cloud in terms of curvature, width, and upward height, significantly improving the fitting accuracy.
[0043] For the nail tip area, a higher sampling density can be used to improve the accuracy of posture judgment; for nails with large curvature, segmented calculation of midline constraints can be added to prevent local misalignment. In practical applications, the algorithm of this embodiment can run in real time on a regular computer or 3D modeling system, and the generated outer surface model can be directly input into a 3D printer or photopolymerization system for personalized nail tip manufacturing. The technical solution of this embodiment can be directly connected with the subsequent inner surface generation, thickness control, and edge sealing modeling processes to form a complete personalized nail tip digital manufacturing chain. The outer surface model generated by this method has a precise structure and controllable parameters, which not only improves the fit and comfort of customized photopolymer nails, but also significantly enhances the automation level and production efficiency of digital design and 3D printing manufacturing.
[0044] In summary, this embodiment achieves the automatic generation of personalized nail outer surfaces through multi-level geometric control, including posture recognition, arc angle correction, dimensional deformation, and midline constraints. It boasts high precision, high efficiency, and good versatility. With advantages such as high precision, high stability, automatic execution, and scalable applications, it can provide a reliable geometric modeling foundation for personalized phototherapy nails, artificial nails, and related beauty products, and has broad application prospects in fields such as digital nail manufacturing, personalized medical assistance, and customized consumer product design.
[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A method for generating personalized nail outer surface based on three-dimensional pose deformation, characterized in that, The specific steps are as follows: Step S1: Obtain the 3D point cloud set of the wearer's fingernails, perform data preprocessing, and project the preprocessed 3D point cloud set onto a plane to obtain the projection set; Step S2: Calculate the longitudinal curvature angle of the nail using the projection set; Step S3: The standard nail model is initially aligned with the nail's posture based on the longitudinal curvature angle of the nail; Step S4: Perform composite posture deformation on the initially aligned model to obtain a personalized outer surface model.
2. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 1, characterized in that: In step S1, the three-dimensional point cloud set is ,in, For the first The 3D point cloud coordinates of each point are obtained. Data preprocessing includes filtering, smoothing, and standardization. The resulting point cloud set is... ,Will Projecting onto the XZ plane, we obtain the projection set as follows: ,in, These are the projected coordinates.
3. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 2, characterized in that: In step S2, the formula for calculating the longitudinal curvature angle of the nail is as follows: ； in, The longitudinal curvature of the nail. These are the Z-axis projection coordinates of the vertex and tail point, respectively. These are the X-axis projection coordinates of the vertex and tail point, respectively; Calculate the median of the data points within the set maximum value range along the Z-axis; the point corresponding to the median is the vertex. The calculation formula is as follows: ； ； in, A set of points that satisfy the threshold condition for the maximum value in the Z-axis direction; This represents the maximum value of the point cloud along the Z-axis. The preset height threshold; It is a median function. The maximum value in the Z-axis direction; Calculate the median of the data points within a set minimum range along the X-axis. The point corresponding to the median along the X-axis is the tail point. The calculation formula is as follows: ； ； in: A set of points that satisfy the minimum threshold condition in the X-axis direction; This represents the minimum value of the point cloud along the X-axis. This is a preset threshold for the tail region.
4. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 3, characterized in that, Step S3 is as follows: Step S31: Place the standard nail model Import a unified coordinate system. For the first A standard nail coordinate; Step S32: Calculate the difference in longitudinal curvature angle between the actual nail point cloud and the standard nail model. The calculation formula is as follows: ； in: The longitudinal curvature of the actual fingernail dot cloud; The longitudinal curvature angle of a standard nail model is given; based on the longitudinal curvature angle of the nail, the rotation matrix about the Y-axis is obtained. as follows: ； Step S33: Rotate and correct the vertices of the standard nail model so that the bending direction of the standard nail model is consistent with the longitudinal bending arc angle of the actual nail. The calculation formula for the rotated model points is as follows: ； in: Standard nail model points; These are the model points after rotation correction; Step S34: Perform translation correction on the rotated model so that the actual nail tail point coincides with the tail point of the rotated model, and the translation vector... The calculation formula is as follows: ； in, and These are the actual nail tail point and the tail point of the rotated model, respectively.
5. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 4, characterized in that: In step S4, the composite attitude deformation includes non-uniform scaling, width direction deformation, and centerline constraint.
6. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 5, characterized in that: The specific process of non-uniform scaling is as follows: Non-uniform scaling is performed on the model that has been initially aligned in posture to achieve matching of the overall size of the wearer's nails; The envelope width and height of the statistical point cloud data in the Y-axis and Z-axis directions are calculated using the following formulas: ； ； in, and These represent the envelope width and height in the Y-axis and Z-axis directions, respectively. and These represent the maximum and minimum values along the Y-axis, respectively. and These are the maximum and minimum values along the Z-axis, respectively. The scaling factor is calculated using the following formula: ； ； in, and These are the scaling factors in the Y-axis and Z-axis directions, respectively. and These represent the envelope width and height of the corresponding model in the Y-axis and Z-axis directions, respectively. The model with initial orientation alignment is non-uniformly scaled based on scaling factors in the Y-axis and Z-axis directions.
7. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 5, characterized in that: The specific process of width-direction deformation is as follows: Width-direction deformation is used to improve the adaptability to different nail types; The width center is determined using the following formula: ； in: This represents the coordinate value of the center of the model width along the Y-axis. The standard nail model point set; max and min represent the maximum and minimum value functions, respectively; A symmetrical outward expansion is applied with the width center as the reference. The deformation constraint function for the symmetrical outward expansion in the width direction is as follows: ； in, For the expanded first The coordinate values in the Y-axis direction. This represents the expansion ratio.
8. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 5, characterized in that: The specific process of centerline constraint is as follows: Centerline constraint is used to ensure that the model and point cloud data are aligned in direction; The midpoints of the left and right boundaries of the point cloud data are calculated based on the XY plane cross-section to obtain the set of point cloud centerlines. Based on the midpoints of the left and right boundaries of the model data calculated from the XY plane cross-section, the set of model centerlines is obtained. ; The formula for calculating the difference in the midline is as follows: ； ； in, and These represent the positional differences between the point cloud centerline and the model centerline along the X-axis and Y-axis, respectively. It is a function of average value. and These are the sets of X-axis coordinates and Y-axis coordinates of the point cloud centerline, respectively. and These are the sets of X-axis coordinates and Y-axis coordinates of the lines in the model, respectively. The model is subjected to overall translation correction based on the average offset of the centerline. The calculation formula for the translated model points is as follows: ； in: For model points; These are the model points after centerline correction.
9. The method for generating a personalized nail outer surface based on three-dimensional posture deformation according to claim 8, characterized in that: The curvature between the actual point cloud data is obtained. When the curvature is greater than the set value, the model centerline and the point cloud centerline are segmented, and the segments are calculated and translated.