CN109035404A - A kind of human foot model positioning transformations method and system - Google Patents

A kind of human foot model positioning transformations method and system Download PDF

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Publication number
CN109035404A
CN109035404A CN201810604178.5A CN201810604178A CN109035404A CN 109035404 A CN109035404 A CN 109035404A CN 201810604178 A CN201810604178 A CN 201810604178A CN 109035404 A CN109035404 A CN 109035404A
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foot
point
model
line
shoe tree
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谢家欣
林子森
冯梓锋
王浚宇
周知恒
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Dongguan Shite Intelligent Technology Co Ltd
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Dongguan Shite Intelligent Technology Co Ltd
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    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20Finite element generation, e.g. wire-frame surface description, tesselation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T19/00Manipulating 3D models or images for computer graphics
    • G06T19/20Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts

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  • Footwear And Its Accessory, Manufacturing Method And Apparatuses (AREA)

Abstract

The present invention relates to a kind of human foot model positioning transformations method and system, this method comprises: extracting the sole contour line of foot's triangle grid model, identify waist position inside and outside sole;Foot's broadside lines of foot's triangle grid model is extracted, identifies heel position of center line curve and instep position of center line curve;Triangle grid model is moved integrally into adjustment orientation, model coordinate systems are matched with rectangular coordinate system in space, obtain the coordinate value of individual features point;Half sole width followed by width, foot length, instep height, the first toe height and ankle altitude information are obtained by rectangular space coordinate value;To in standard shoe tree number library, by manually selecting with height, shoes money type, gender and regional option, again by the characteristic point characteristic curve data on foot's triangle grid model of automatic identification reconstruct, according to standard foot last carving difference, the highest shoe tree group of user's foot Model Matching degree with reconstruct, the standard shoe tree that system Auto-matching is most adapted to are selected.

Description

A kind of human foot model positioning transformations method and system
Technical field
The present invention relates to shoe last model constructing technology, in particular to a kind of human foot model positioning transformations method and system.
Background technique
People's foot has many characteristics, such as to easily deform and is difficult to remain static, if obtained using contact type measurement equipment The point cloud data for taking foot, the probe of measuring device can squeeze instep in measurement process, allow people's foot shape to deform, making one But also people's pin point cloud that measurement obtains generates some errors while foot receives damage.And it is needed using contact type measurement equipment Very important person's foot is constantly in a certain specific position, and needs to be fixed using equipment on the table, people's foot when measuring It also needs to follow movable workbench, people's foot is difficult to realize these demands, this results in many foot's characteristic parameters and some complexity Curved surface, curve can not be all measured, so that people's foot measurement pointcloud data have very big error.In view of safe and healthy It is required that cannot be hazardous to the human body for measuring the ray of the scanning device of people's pin point cloud, therefore in non-contact measurement Radiographic imaging method and industrial computed tomography imaging method all cannot be used in the measurement of people's pin point cloud.Process of the present invention uses The mode shot when non-contact goes out people's foot model by the image reconstruction shot.
And existing shoe last model Reverse reconstruction file format is mostly point cloud model and blendes together method or facet by boundary The nurbs surface model that characteristic method generates, the model part that these methods obtain can be distorted, and fairness is bad, and there are more superfluous Yu Dian, storage space is big, and data management and analysis difficulty are big, is unfavorable for the real-time processing of model.
Summary of the invention
It is an object of the present invention to which solving prior art foot shoe last model constructs the existing above problem.
To achieve the above object, the present invention provides a kind of human foot model positioning transformations method, this method include execute with Lower step:
The sole contour line for extracting foot's triangle grid model, is become with foot type sole contour line feature existing in database Gesture identifies waist position inside and outside sole;
Foot's broadside lines of foot's triangle grid model is extracted, with foot type broadside lines feature existing in database Trend identifies heel position of center line curve and instep position of center line curve;Triangle grid model is moved integrally and is adjusted Orientation, model coordinate systems are matched with rectangular coordinate system in space, obtain the coordinate value of individual features point;
Half sole width followed by width, foot length, instep height, the first toe height and foot are obtained by rectangular space coordinate value Ankle altitude information;To in standard shoe tree number library, by manually selecting with height, shoes money type, gender and regional option, then by Characteristic point characteristic curve data on foot's triangle grid model of automatic identification reconstruct, according to standard foot last carving difference, select with again The highest shoe tree group of user's foot Model Matching degree of structure, the standard shoe tree that system Auto-matching is most adapted to;
After selection obtains matched standard shoe tree, the alignment of space measurement Data Position need to be carried out to foot last carving model, including adjust Whole foot type heel and shoe tree followed by be aligned, adjustment foot type is integrally evenly distributed in last carving body the right and left, adjustment sole touchdown point with Last carving bottom lands point contact, but the step for during do not change corresponding relationship of the foot type model integrally between each position, with Whole unified rotation translation is transformed to benchmark;
According to the standard shoe tree that matching obtains, and the back height value of selection, to the secondary alignment line of previous step setting With auxiliary rotational circle position, by certain pivot rule carry out profile line segment rotation and translation, and be arranged rotation angle maximum with Minimum limit value;
By the region rotated introversion line segment carry out translation make different zones line segment between original tie point as close as possible to not It is that point of cut-off trims curve with the crosspoint between the inner curve of region, the curve being retained in region, then by each curved section Between be smoothly connected with second order parameter continuity, equally the curved surface in different zones is trimmed and is smoothly connected.
Preferably for the human foot model after realignment, the long i.e. line segment A1B length of foot is being intercepted respectively along positive direction of the x-axis 25% and 68% point be set as point F1, F2, then choose that the long point abscissa of 68% foot increases 15mm and abscissa reduces 20mm's respectively Two o'clock is set to point F3, F4, draws a secondary alignment perpendicular to x-axis respectively in tri- data points of F1F3F4 of interception Line and the auxiliary rotational circle for being parallel to xz plane, and in auxiliary line position respectively by foot's triangle grid model, sole contour line Be divided into four parts with foot broadside lines, by the step for the contour line that obtains and foot's triangle grid model by different parts Form four groups, the auxiliary line of same position and auxiliary circle formed into a group, the step for secondary alignment line and z Axis is parallel and intersects with x-axis, assists the intersection point of the center of circle of rotational circle co-located secondary alignment line and x-axis.
Preferably, first by region 1 using point F3 as rotary middle point auxiliary rotational circle on rotated counterclockwise by angle α (degree),α∈[2,8];
Then region 3 is rotated clockwise into angle beta (degree) on auxiliary rotational circle using point F4 as rotary middle point,
Then by region 4 using point F2 as rotary middle point auxiliary rotational circle on rotated counterclockwise by angle γ (degree),
On the other hand, the present invention provides a kind of human foot model positioning transformations system, which includes:
First extraction unit, for extracting the sole contour line of foot's triangle grid model, with foot type existing in database Sole contour line characteristic trend identifies waist position inside and outside sole;
Second proposes member, for extracting foot's broadside lines of foot's triangle grid model, with existing in database Foot type broadside lines characteristic trend identifies heel position of center line curve and instep position of center line curve;By the triangulation network Lattice model moves integrally adjustment orientation, and model coordinate systems are matched with rectangular coordinate system in space, obtains the coordinate value of individual features point;
Matching unit, for obtaining half sole width followed by width, foot length, instep height, first by rectangular space coordinate value Toe height and ankle altitude information;To in standard shoe tree number library, by manually selecting with height, shoes money type, gender and Regional option, then by the characteristic point characteristic curve data on foot's triangle grid model of automatic identification reconstruct, according to standard foot last carving Difference selectes the highest shoe tree group of user's foot Model Matching degree with reconstruct, the standard shoe tree that system Auto-matching is most adapted to;
Adjustment unit after obtaining matched standard shoe tree for selection, need to carry out space measurement data bit to foot last carving model It sets alignment, including adjustment foot type heel and shoe tree followed by is aligned, adjustment foot type is integrally evenly distributed in last carving body the right and left, adjustment Sole touchdown point and last carving bottom land point contact, but the step for during do not change foot type model integrally between each position Corresponding relationship is transformed to benchmark with whole unified rotation translation;
Rotary unit, the standard shoe tree for being obtained according to matching, and the back height value of selection, are arranged previous step Secondary alignment line and auxiliary rotational circle position by certain pivot rule progress profile line segment rotation and translation and rotation is set The minimum and maximum limit value of angle;
Processing unit makes original tie point between different zones line segment for the region rotated introversion line segment to be carried out translation As close as possible to, curve is trimmed using the crosspoint between different zones inner curve as point of cut-off, the curve being retained in region, It will be smoothly connected again between each curved section with second order parameter continuity, the curved surface in different zones be equally subjected to trimming peace Slip.
Detailed description of the invention
Fig. 1 is that a kind of foot's shoe last model provided in an embodiment of the present invention constructs system structure diagram;
Fig. 2 is the image reconstruction system workflow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system;
Fig. 3 is that the reconstruct foot point cloud model processing system workflow of the building system of foot's shoe last model shown in Fig. 1 is shown It is intended to;
Fig. 4 is the processing of reconstruct foot triangle grid model and characteristic point ginseng that foot's shoe last model shown in Fig. 1 constructs system Number automatically extracts and labeling system workflow schematic diagram;
Fig. 5 is the human foot model positioning transformations working-flow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system;
Fig. 6 is foot's characteristic parameter driving standard shoe tree anamorphotic system work that foot's shoe last model shown in Fig. 1 constructs system Make flow diagram;
Fig. 7 is the reconstruct shoe last model detection system workflow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system;
Fig. 8 is the reconstruct shoe last model output system workflow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system;
Fig. 9 is the personal shoe tree data base management system workflow signal that foot's shoe last model shown in Fig. 1 constructs system Figure;
Figure 10 is that foot's shoe last model shown in Fig. 1 constructs the shoe tree database sharing of system and management system workflow is shown It is intended to;
Figure 11 (a)-Figure 11 (c) is foot's feature line feature point schematic diagram;
Figure 12 (a)-Figure 12 (b) is shoe tree characteristic curve schematic diagram.
Specific embodiment
After embodiments of the present invention are described in detail by way of example below in conjunction with attached drawing, of the invention its His features, characteristics, and advantages will be more obvious.
Fig. 1 is that a kind of foot's shoe last model provided in an embodiment of the present invention constructs system schematic.As shown in Fig. 1, this is System includes follow shot equipment, processing server, image reconstruction system, reconstruct foot's point cloud model processing system, reconstruct foot Triangle grid model processing and characteristic point parameter automatically extract simultaneously labeling system, human foot model positioning transformations system, shoe tree data Library building and management system, foot's characteristic parameter driving standard shoe tree anamorphotic system, reconstruct shoe last model detection system, personal shoes Last carving data base management system and reconstruct shoe last model output system.
Fig. 2 is the image reconstruction system workflow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system.Such as Fig. 2 institute Show, image reconstruction system workflow setting are as follows:
People places object of reference when level is stood, on foot side, and foot is contacted object of reference, is placed on object of reference naturally, Using follow shot equipment around foot shoot one group of two dimensional image or around foot shoot one section of complete video as far as possible every Change angle is between 10 degree to 45 degree within one second.It is required that mobile device shoots pixel in 200pdi or more.Mobile device passes through net Network will shoot gained image graphic and upload to processing server.It is generally difficult to obtain whole foot's letters by a sub-picture Breath, needs to obtain the image at each position of people's foot, then whole people's foot 3D point cloud number is obtained after being merged by registration algorithm According to.
Gray processing processing is carried out for the image of upload, the specific steps are color is divided into R, tri- Color Channels of G, B are right In different colorations, brightness, the pixel of saturation degree indicates white brightness with Y, calculates the brightness value of each pixel, makes brightness Value and its R, G, B value is corresponding, obtains gray level image.And gray processing processing is equally carried out for video, a frame was taken every one second Image is as reconstruction model reference picture.
The pixel value for belonging to background parts is zeroed by the threshold value that people's foot and background can be reasonably distinguished by setting (or being maximized) retains the pixel value for belonging to people's foot part.Multiple scale detecting angle point technology is used based on gray level image, quickly It extracts characteristics of image angle point and finds corresponding relationship in the image of the overlapping of Same Scene, and different images are carried out by reference Scaling on the basis of object size.
First by forming image resolution pyramid, to determine the characteristic point in each image for changing resolution ratio. It is denoised with SIFT algorithm smoothed image, gray level image is used to the N-dimensional space normal distribution equation of Gaussian blurring function:Wherein σ indicates Image Smoothness, that is, normal distyribution function standard deviation, as σ is incremented by, resolution ratio Successively decrease, r is blur radius, and blur radius refers to template elements to the distance of template center.By Gaussian blurring function G(x,y,δ)With Original image I(x,y)The scale-space representation formula of the image: L is obtained using convolution algorithm(x,y,δ)=G(x,y,δ)*I(x,y).Image is done The Gaussian Blur of different scale, the method that resolution ratio successively reduces down-sampled i.e. are sampled smoothed image, building Gauss gold Word tower and difference of Gaussian pyramid determine the position for indicating image Harris corner characteristics in pyramidal each layer.
By finding the position of each corner characteristics, the angle intensity is shown, according to angle intensity and predetermined minimum intensity threshold pair Than, point is deleted, retest determines whether sum is more than maximum permissible value, if being more than, increases radius and repetitive process again, Alternately, until Angle Position number equals or falls below maximum permissible value.
By using the method for blur gradients, each corner characteristics distribution orientation is given.First angle point is detected under large scale, Then real characteristic angle point relatively precisely determine under smaller scale.
Because Gaussian kernel is unique linear kernel, that is to say, that other will not be introduced by, which being obscured using Gauss collecting image, makes an uproar Sound, therefore selected Gaussian kernel just to construct the scale of image.Harris angle point operator is turned with the first derivative of Gaussian kernel Become scale space operator, for scale space operator to the analysis of image not by image grayscale level, the influence of contrast variation is full Sufficient translation invariance, scale invariability, Euclid's invariance, the characteristics such as affine-invariant features.
For the more position of precise positioning characteristic point and scale, redundancy is removed by being fitted the method for three-dimensional quadratic function Characteristic point and unstable skirt response point improve noise resisting ability to enhance matching stability.
It carries out curve fitting to scale space difference of Gaussian function, original position is obtained plus the offset and scale of fitting Obtain the exact position of characteristic point.Wherein fitting function are as follows:It asks It leads and functional equation is allowed to be equal to 0, obtain extreme point deviation amount expression formula are as follows:Corresponding extreme point expression formula are as follows:When extreme point deviation amountWhen, current signature point position must be changed, in a new location repeatedly Interpolation, if beyond the number of iterations set or exceeding image boundary range, deletes the point until convergence.While in order to avoid D(x)Functional value is too small and wild effect caused by by noise jamming, | D(x)|≤0.03 extreme value point deletion.
After obtaining characteristic point position, local principal curvatures is acquired by Hessian matrix (Hessian matrix), it is assumed that Hessian Matrix expression are as follows:The sum of diagonal of a matrix is Tr(H)Its expression formula are as follows: Tr(H)=Dxx+Dyy=alpha+beta, The determinant of matrix H is Det(H), expression formula Det(H)=DxxDyy-(Dxy)2=α β.Curvature threshold is set as γ, is passed through JudgementIt is whether true, if set up if retain marginal point, otherwise delete, with this judge principal curvatures whether Under the threshold value of setting.KD-tree algorithm acceleration search is used in the process.
The Sobel operator for reusing Canny edge detection algorithm calculates the difference Gx of gradient calculating both horizontally and vertically And Gy, calculate gradient-norm and direction:θ=atan2 (Gy,Gx), gradient angle, θ ∈ [- π, π], by its approximation To four direction, level is respectively represented, vertical and two diagonals (0 °, 45 °, 90 °, 135 °).It can be with ± i π/8 (i =1,3,5,7) divide, fall in the gradient angle in each region to a particular value, represent one of four direction.
The gradient edge more than one pixel usually drawn is wide, but multiple pixels are wide.Therefore gradient map as is also It is very fuzzy.In order to meet only one accurate point width of edge, edge is refined using non-maximum value suppressing method, helps to protect It stays local maxima gradient and inhibits every other gradient value, only remain position most sharp keen in change of gradient.Algorithm is as follows:
Compare the gradient intensity of current point and the gradient intensity of positive and negative gradient direction point.If the gradient intensity of current point and It is maximum that the gradient intensity of other equidirectional points, which compares, retains its value.Otherwise inhibit, that is, be set as 0.
Front we gradient direction approximation to level, vertical and two diagonal line four directions, so each pixel root It is compared according to itself direction in one of this four direction, decides whether to retain.
Canny algorithm application bivalve value, i.e. a high threshold values and a low valve valve distinguish edge pixel.If edge picture Vegetarian refreshments gradient value is greater than high threshold values, then is considered as strong edge point.If edge gradient value is less than high threshold values, it is greater than low valve valve, Then it is labeled as weak marginal point.Point less than low valve valve is then suppressed.
The 8 connection field pixels for checking a weak marginal point with hysteresis bounds track algorithm again, as long as there is strong edge point to deposit , then this weak marginal point be considered as really edge remain.
The weak edge of all connections is searched for depth-priority-searching method, if one connection weak edge any one point and The connection of strong edge point, then retain this weak edge, otherwise inhibit this weak edge.
After obtained edge contour, the stabilising direction of partial structurtes is sought using the resulting image gradient of previous step, is used The gradient-norm of pixel and direction in cake chart statistics field are segmented by 10 degree, and the maximum region direction of cake chart represents feature The principal direction of point, in order to enhance matched robustness, Retention area region is greater than the auxiliary direction of conduct of principal direction 80%.Spy Sign point copies as the characteristic point of segmentation, and direction value is assigned to the characteristic point after duplication respectively.Finally to discrete gradient side Interpolation fitting processing is carried out to histogram, acquires more accurately deflection angle value.
Each characteristic point establishes a descriptor, with one group of vector description, describes sub- use in characteristic point scale space The gradient information in 8 directions calculated in 4*4 window, total 4*4*8=128 dimensional vector characterization.The size of each subregion and spy Identical when sign point direction distribution, i.e., there is N_otc pixel in each region, then distributes the square that side length is N_otc for each subregion Shape region is sampled.Bilinear interpolation is used again, is determined and is calculated the required image-region of description, reference axis is rotated to be The direction of characteristic point to ensure rotational invariance, then the sampled point in field is assigned in corresponding subregion, by subregion Interior gradient value is assigned on 8 directions, calculates its weight, then interpolation calculation 8 direction gradients of each seed point.Finally carry out Normalized counts 128 dimension SIFT local descriptions of each characteristic point, the as feature vector of characteristic point.
Euclidean distance by describing son between two characteristic points of searching is closer to, and the Euclidean between other feature point descriptions Apart from farther away characteristic point between as the candidate feature matching pair two images.By each characteristic point matched in obtained image Coordinate is indicated with homogeneous coordinates, and homogeneous coordinates are standardized expression.
x1,x2∈R3xn, n is pairing sum, x1,x2For matching a pair of of in two images Point.Standardize x1,x2Homogeneous coordinates after:Wherein uxjAnd uyjRespectively indicate xij, yijAverage value, δxjAnd δyjRespectively indicate xij, yijStandard deviation.It is obtained again by homogeneous coordinates here Secondary coordinates matrix quantificational expression:
Wherein abcdrfghi indicates that rotation and scaling matrix, lmn indicate translation square Battle array, pqr indicate that projection matrix, s indicate overall conversion matrix.Obtain x1,x2Two shape Interactive matrix, expression formula are as follows:Calculated by calculating and comparing Euclidean distance two shape Interactive matrix by column between difference, And arrange the Euclidean distance between each column vector by descending descending, threshold value point of cut-off is set, Euclidean distance value is greater than The matching of point value is truncated to deletion in threshold value, leaves correctly matching pair.
For three-dimensional point cloud model, indicatrix extraction process is exactly that the data point on model is analyzed and counted It calculates, finds out characteristic point therein, and connect and compose smooth features curve, uneven, shortage topology between point is issued for data point The point cloud data of link information carries out Gauss Discrete Mapping to each point in point cloud data with discrete Gauss Map method, Mapping point is subjected to the coagulation type hierarchical clustering based on distance with K-meam algorithm, cluster result and curvature are analyzed, And selected with parameter of the adaptive iterative process to algorithm, optimal feature point set is obtained, the identification feature comprising before The sharp mutable site characteristic point being difficult in point step.Then use the characteristic curve based on PCA principal component analytical method raw Long algorithm, characteristic point is connected, and obtains the characteristic curve of fairing.PCA Principal Component Analysis Algorithm is finally used, to the data obtained sample Dimensionality reduction compression is carried out, storage memory is reduced.
Fig. 3 is that the reconstruct foot point cloud model processing system workflow of the building system of foot's shoe last model shown in Fig. 1 is shown It is intended to.As shown in figure 3, reconstruct foot's point cloud model processing system workflow are as follows:
By obtaining having compared with precise positioning, direction, feature vector, the point of descriptor by two-dimensional images matching reconstruct Cloud threedimensional model.But it generally can not be directly as people's foot 3D model data, at this time by the 3D point cloud data that picture reconstruction obtains Obtained point cloud model cannot be directly used to parameter extraction and reconstructed surface, need to carry out some pretreatments also to reduce model not Foot.
Since the 3D point cloud data of acquisition are inevitable that noise (i.e. outlier) exists, simultaneously because human body Between block and will appear cavity, in addition the flatness of point cloud data is also poor.It needs to simplify point cloud model, and is removed Discrete point, the processing of smooth and holes filling.
Fragment first is carried out to point cloud model with the method for spatial level subdivision, one is calculated for each fragment and simplifies expression, The point cloud model being simplified.
With string high differentiation, the front and back two o'clock of connecting detection point, the distance of technology intermediate data points to string, by this distance It is compared with the franchise value being given to, is then abnormal point if more than franchise value, is deleted, so that density height in point cloud model is removed, The noise in the biggish place of Curvature varying.Weighted median filtering method is used again, eliminates burr, smoothing model.
By calculating the uniform hole boundary of length of each edge, if it exceeds 2 times of equalization points are away from then taking its midpoint to be added to In hole boundary.Unified boundary direction, hole boundary is all unified for counterclockwise.Inner and outer boundary is judged, to outer boundary Profile carries out judgement removal.The concavity and convexity for being closed each vertex in hole boundary is different, and angle calcu-lation mode is different, each according to calculating Filling point coordinate is calculated in the size of angle, and the illegal judgement point fallen in outside perforated is removed, can be obtained Filling point coordinate.The iterative cycles process, until new filling point cannot be calculated, then holes filling terminates.
Fig. 4 is the processing of reconstruct foot triangle grid model and characteristic point ginseng that foot's shoe last model shown in Fig. 1 constructs system Number automatically extracts and labeling system.As shown in figure 4, the processing of reconstruct foot's triangle grid model and characteristic point parameter automatically extract simultaneously Labeling system workflow are as follows:
To treated, point cloud model uses Waston algorithm to carry out triangulation and optimization, by point cloud model triangle gridding Change, increases the topological relation between a cloud, especially in deformation process, triangle mesh model while retaining point cloud data again It has great advantages.Three-dimensional grid sequence compaction is carried out with the deformation of surface technology based on thin plate spline again, passes through MC algorithm Carry out three-dimensionalreconstruction.MC algorithm uses the tri patch of triangle band connection dispersion, reduces EMS memory occupation;Using reduction tri patch Quantity, reduce time and space complexity;Discrete noise region is filtered using connectivity detection, removes impurity;Finally examine Hole is measured, and by filling-up hole to model process of refinement.
Fig. 5 is the human foot model positioning transformations working-flow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system. As shown in figure 5, human foot model positioning transformations working-flow are as follows:
Obtain the model that the non-fluidity triangle gridding of foot is constituted, but the acquisition of the non-fluidity triangle grid model of foot type It is the two-dimentional foot type image reconstruction gained original based on stereoscopic vision, the standard shoe tree in human foot model and shoe tree database is all Defined in respective local coordinate, coordinate origin, change in coordinate axis direction is different, and spatial position is entanglement, copes with foot Model carries out orientation adjustment according to the shoe last model space coordinate benchmark of system, adapts it to this process identifying system.Figure 11 (a)-Figure 11 (c) is foot's feature line feature point schematic diagram, specific implementation step are as follows: extracts the foot of foot's triangle grid model Return pulley profile identifies waist position inside and outside sole with foot type sole contour line characteristic trend existing in database, inside and outside sole position Waist most salient point is respectively C1C2, and waist most salient point is respectively B1B2 inside and outside heel region followed by peripheral point is B, half sole first Toe endpoint is A, is then sequentially connected AC1B1BB2C2, forms complete closed curve, the as preliminary contour line of sole.Then It is separately connected C1C2, B1B2, B point makees straight line excessively and line segment B1B2 intersects at point D1, adjustment BD1 and line segment B1B2 corner dimension, Make 96 degree of angle B1D1B, extend BD1 and intersect at point D2 with line segment C1C2,.It crosses half sole the first toe terminal A and is line segment BD2 and prolong The vertical line of long line simultaneously meets at point A1, then line segment A1B is sole center line, and the Euclidean distance between point A1 and point B is sole Length.Foot's broadside lines of foot's triangle grid model is similarly extracted, it is special with foot type broadside lines existing in database Sign trend, identification heel position of center line curve are l1, and instep position of center line curve is l2, are sequentially connected curve l1A1Bl2.Make point B as coordinate origin, line segment A1B is in x-axis principal direction, curve l1l and the line segment A1B curve connecting and xz Plane is parallel, and line segment B1B2 and line segment C1C2 are parallel with x/y plane, and triangle grid model is moved integrally adjustment orientation, model Coordinate system is matched with rectangular coordinate system in space, obtains the coordinate value of individual features point.
Half sole width C 1C2 followed by width B1B2M, the long A1B of foot, the instep height (midpoint l2 z are obtained by spatial value Coordinate value), the first toe height, the data such as ankle height.Thus in standard shoe tree number library, by manually selecting with height, shoes Money type (sport footwear, playshoes, high-heeled shoes, sandals etc.), gender, the options such as area, then the foot three reconstructed by automatic identification Characteristic point characteristic curve data on the grid model of angle select user's foot Model Matching degree with reconstruct according to standard foot last carving difference Highest shoe tree group, the standard shoe tree that system Auto-matching is most adapted to.Because completely the same shoe tree is not with foot type size The shoe tree of the most comfortable interferes proper motion in order to avoid shoes are tightly attached to people's foot, needs to reserve some surpluses of putting in shoes with after Tolerance, general last carving enclose=bottoms-feel difference.Exist only between foot and shoe tree and puts surplus and dimension difference, it could preferably It locks foot and does not have extruding sense of discomfort again.
After selection obtains matched standard shoe tree, although human foot model has pressed shoe tree spatial coordinate system in step before Orientation adjustment is carried out, but there are still spatial position dislocation in local location, need to carry out space measurement Data Position to foot last carving model Alignment, including adjustment foot type heel and shoe tree followed by be aligned, adjustment foot type is integrally evenly distributed in last carving body the right and left, adjustment foot Bottom touchdown point and last carving bottom land point contact, but the step for during do not change pair of the foot type model integrally between each position It should be related to, benchmark is transformed to whole unified rotation translation.
For the human foot model after realignment, the long i.e. line segment A1B length of foot is being intercepted respectively along positive direction of the x-axis (with millimeter For unit) 25% and 68% point be set as point F1, F2, then choose that the long point abscissa of 68% foot increases 15mm and abscissa is reduced respectively The two o'clock of 20mm is set to point F3, F4, draws one respectively perpendicular to the auxiliary of x-axis in tri- data points of F1F3F4 of interception Alignment line and the auxiliary rotational circle for being parallel to xz plane are helped, and in auxiliary line position respectively by foot's triangle grid model, sole Contour line and foot broadside lines are divided into four parts, by the step for the contour line that obtains and foot's triangle grid model by not Form four groups with position, the auxiliary line of same position and auxiliary circle formed into a group, the step for secondary alignment Line is parallel with z-axis and intersects with x-axis, assists the intersection point of the center of circle of rotational circle co-located secondary alignment line and x-axis.
According to the standard shoe tree that matching obtains, and the back height value (in inches) of selection, previous step is set The secondary alignment line set and auxiliary rotational circle position, carry out profile line segment rotation and translation by certain pivot rule, and rotation is arranged The minimum and maximum limit value of gyration.Being located at F3 point rotation angle is α, is β in F4 point rotation angle, rotates angle in F1 point For γ, F3 is region 1 along positive direction of the x-axis curved portion, and F3 is region 2 along positive direction of the x-axis intersection along negative direction of the x-axis and F4, F1 is region 3 along positive direction of the x-axis intersection along negative direction of the x-axis and F1, and F1 is region 4 along negative direction of the x-axis part.First by region 1 using point F3 as rotary middle point auxiliary rotational circle on rotated counterclockwise by angle α (degree), α∈[2,8].Then region 3 is rotated clockwise into angle beta (degree) on auxiliary rotational circle using point F4 as rotary middle point,
Then by region 4 using point F2 as rotary middle point auxiliary rotational circle on rotated counterclockwise by angle γ (degree),
The region rotated is turned inward into line segment Carry out translation make different zones line segment between original tie point as close as possible to using the crosspoint between different zones inner curve as point of cut-off Curve is trimmed, the curve being retained in region, then will be smoothly connected between each curved section with second order parameter continuity, Similarly the curved surface in different zones is trimmed and is smoothly connected.
Fig. 6 is foot's characteristic parameter driving standard shoe tree anamorphotic system work that foot's shoe last model shown in Fig. 1 constructs system Make flow diagram.As shown in fig. 6, foot's characteristic parameter drives standard shoe tree anamorphotic system workflow are as follows:
Horizontal standing human foot model is converted into band with high human foot model, and obtains band with the profile of high human foot model Curve.Purpose for human foot model deformation is primarily to make foot type and shoe tree camber ratio more consistent, convenient for foot last carving model Analysis of Human Comfort and data inspection correction, while the exposed human foot model laid flat being allowed to be adjusted to closer to making when wearing shoes Type radian.
Each position degree of enclosing line is imported, band is utilized into minimum two with the contour curve of high human foot model and standard shoe last model Multiplication and conventional method matched curve, using the contour line of human foot model as the contour line parameter of benchmark adjustment criteria last carving model, One circle contour line is divided into 360 points, wherein closing on 3 points of polar radius by parameter spacing between comparative silhouette line and degree of enclosing line It is respectively as follows: ρi+1ii-1, intermediate polar radius value is
If ρiCorresponding polar radius is ρ after fairingi, the triangular apex obtained after fairing is ρ, with minimizing energy method public affairs Formula combination polar radius value seeks the polar radius point after Fair Fitting:Wherein θ In the triangle constituted for 3 points, while meeting least square method:Utilize weight factor Controlling curve fairness and Approximation with human foot model parameter, generate final shoe tree control line.
Last surface is generated according to the new shoe tree control line of generation, it will system mouth line and last carving using back arc line and last carving lineback Return pulley profile is divided into two parts respectively, by adjacent contours connection, forms three four borderline regions.It imports in previous step and adjusts Whole good new degree of enclosing line, is trimmed to three parts for each position degree of enclosing line last carving return pulley profile and last carving lineback.Last carving bottom is used first Contour line and last carving bottom point degree of enclosing line, constitute the last carving bottom surface for having the direction z radian.System mouth line and last carving lineback intersection are chosen again Degree of enclosing line last carving return pulley profile is divided into two parts, then by last carving lineback, back arc line, last carving return pulley profile, system mouth line and should The adjacent contours connection of position degree of enclosing line forms five four borderline regions.Then using in curved surface of last region boundary line and enclose It spends line and constitutes various pieces curved surface.
Connection based on surface boundary continuity and fairness is carried out to the curved surface that above-mentioned steps obtain, makes adjacent curved surface side Boundary line all has same points and order, and adjacent curved surface is made to meet second order continuity in boundary, and singular point or extra is not present Inflection point, Curvature varying is smaller between curved surface.Make to be mutually linked between curved surface simultaneously, the curvature portion of extension is repaired along intersecting lens It cuts.Curved surface ideal not enough for fairing effect, by regulate and control curved surface control point, make control point correspond and uniformly Distribution, and then the more fairing of the curved surface of last of each region is stitched together.Resulting each position curved-surface structure line is parameterized Mode stores, and convenient artificial change is corrected while reducing calculation amount caused by adjustment next time local curve.
The closing that the curved surface being smoothly connected and last carving bottom surface and system mouth face are stitched into a hypostazation is whole, thus obtains Shoe last model based on foot's picture reconstruction model, and the shoe tree master pattern for adjusting, can be according to choosing different shoes Class, shoes money, by the parameter corresponding relationship between different type standard shoe tree, carry out corresponding tune with height on the shoe last model of reconstruct It is whole.Change for different shoe last styles can recognize the shoe last and last carving status secant profile, generally toe of script shoe last model Degree of enclosing line divides shoe last model, then identifies that target shoe last model boundary connects contour line, by the last carving body model and target after segmentation Shoe last model carries out elastic deformation connection, removes seam using three-dimensional smoothing algorithm, is smoothly connected.The curved surface that will be smoothly connected The closing for being stitched into a hypostazation with last carving bottom surface and system mouth face is whole, to obtain the customized shoe-last mould of different shoe last styles Type.
Fig. 7 is the reconstruct shoe last model detection system workflow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system. As shown in fig. 7, reconstruct shoe last model detection system workflow are as follows:
Calculating human foot model measures the distance and angle between the shoe last model corresponding points of building, and maximum detecting distance is arranged, Maximum angle is compared the distance obtained and angle is calculated with the allowable error value of setting, and measurement obtains maximum positive normal Deviation and maximum negative Norma l deviation, evaluate local error distribution consistency degree, if the maximum value being calculated is than the permission of setting It is worth small, shows that shoe tree generated meets the requirements, otherwise just needs to modify to the shoe tree of generation, be met the requirements until generating Shoe tree.
Category of model integration is loaded into master pattern library and is stored in personal shoe tree database, the pipe based on shoe tree database Reason mode and data analysis, timely update and safeguard personal shoe tree database, and can be by different brands in shoe tree database Different model shoes money shoe last model parameter is analyzed with the collocation degree of personal similar shoes money shoe last model parameter, obtains comfort level Report, is shown by interactive interface, is facilitated user to choose the shoes being more comfortably more suitable for and is carried out.
Fig. 8 is the reconstruct shoe last model output system workflow schematic diagram that foot's shoe last model shown in Fig. 1 constructs system. As shown in figure 8, reconstruct shoe last model output system workflow are as follows:
The foot type shoe last model completed for building can be converted directly into non-fluidity grid model format, utilize 3 D-printing Machine carries out rapid shaping.Thimble can also be added in shoe last and last carving heel point position by system, and model group is combined into entity, Numerical Control Simulation processing is carried out, is exported to meet the file format of CAM processing and obtaining NC numerical control code.It can also be by extracting model wheel Profile obtains the contour line in three-view diagram direction, and output printing or laser engraving are shoe tree snap-gauge and cardboard, for model check and correction.
Fig. 9 is the personal shoe tree data base management system workflow signal that foot's shoe last model shown in Fig. 1 constructs system Figure.As shown in figure 9, personal shoe tree data base management system workflow are as follows:
Maintenance for personal shoe tree database, main method are as follows: file parameters maintenance is carried out to existing model, on basis When foot's reconstruction model and constant basic shoe last model, increases or modification model parameter updates existing according to Rational Parameters analysis There is model parameter, cancels that original model is old or wrong parameter.It can be carried out by combination decision tree algorithm in filtration parameter Feature selecting and direction selection, filtering are cancelled model parameter, are no longer stored in individual subscriber shoe tree database.Group is used simultaneously Decision Tree algorithms are closed, many huge trees are generated to objective attribute target attribute parameter, then basis finds the statistical result of each attribute The biggish character subset of information content.If the character subset of some often changes, and some character subset difference in change Be worth very little, then using the character subset infrequently changed as fixed character, more multioperation when increasing every time or modifying model parameter The character subset group often changed is left in space for, reduces the operational analysis time.
Figure 10 is that foot's shoe last model shown in Fig. 1 constructs the shoe tree database sharing of system and management system workflow is shown It is intended to.As shown in Figure 10, shoe tree database sharing and management system workflow are as follows:
Building and management for shoe tree database construct shoe tree data base administration by way of parametrization management System.Figure 12 (a)-Figure 12 (b) is shoe tree characteristic curve schematic diagram, construction method are as follows: by manually selecting with height, shoes money type (sport footwear, playshoes, high-heeled shoes, sandals etc.), gender, the options such as area, then the foot's triangle gridding reconstructed by automatic identification Characteristic point characteristic curve data (substantially degree of enclosing, the data such as foot length) on model, the standard shoe tree that system Auto-matching is most adapted to.
The wherein foundation of shoe last model database is managed in a manner of race's table, and uses combination decision tree algorithm (Random Forests) carries out feature selecting and constructs effective classifier, by the shoe last with same or similar structure style With different footwear standard shoe last models, general shoe tree position is established as male parent, then each parameter is controlled on its basis System, which generates, derives from type shoe tree, and classification integration is loaded into master pattern library.
The mode in standard shoe tree model data source has: 1. pairs of existing shoes type demands are arranged and are divided, by different regions The last size standard of country is by Data Integration, and according to each positional parameter data are manually entered, it is reasonable that system calculates data automatically Property, corresponding professional parameter is calculated automatically, generates shoe tree in the automatic Parametric modeling procedure algorithm of internal system Nurbs surface model, dimensioning, detection model is normative, obtains the calculating analysis report of Model Matching, category of model integration It is loaded into master pattern library;2. picture reconstruction material object shoe tree mode, obtains shoe tree point cloud model, pre-processes and extract feature point feature Line) key parameter is obtained, it is automatic to calculate data reasonability, it is generated in the automatic Parametric modeling procedure algorithm of internal system Shoe tree nurbs surface model, dimensioning, detection model is normative, obtains the calculating analysis report of Model Matching, category of model Integration is loaded into master pattern library;3. shooting people foot image, foot's point cloud model is obtained from image reconstruction, point cloud model is converted For triangle grid model, characteristic point characteristic curve is pre-processed and extracted, model and feature line feature point are integrally deformed to obtain Band wears model with high simulation, obtains key parameter, automatic to calculate data reasonability, automatically selects most fitting shoes in systems Last carving, foot last carving position local directed complete set, and adjustment obtains target shoe tree, dimensioning, detection model rule on script standard shoe last model Plasticity, obtains the calculating analysis report of Model Matching, and category of model integration is loaded into master pattern library;4. by shoe tree cardboard or card Plate is aligned each cardboard or snap-gauge position, obtains shoe tree side profile, and respectively degree of enclosing profile and sole profile, contour curve is loaded into Parametric modeling system, inputs shoe tree size and regional population, system calculate data reasonability automatically, is calculated automatically corresponding Professional parameter, in the automatic Parametric modeling procedure algorithm of internal system generate shoe tree nurbs surface model, label ruler Very little, detection model is normative, obtains the calculating analysis report of Model Matching, and category of model integration is loaded into master pattern library;5. by Shoes image reconstruction mode in kind obtains shoes point cloud model, and pretreatment measures and inputs corresponding position cladding thickness, in origin cloud mould Cladding thickness is uniformly removed on the basis of type, and the point cloud model of removal cladding thickness is pre-processed and extracts feature point feature Line obtains key parameter, automatic to calculate data reasonability, generates shoes in the automatic Parametric modeling procedure algorithm of internal system Last carving nurbs surface model, dimensioning, detection model is normative, obtains the calculating analysis report of Model Matching, category of model is whole It closes and is loaded into the methods of master pattern library.
In order to enrich shoe tree database data while not increase input step and processing inside, not to same moulding shoe tree With size model construction, using the scale value for calculating target shoe last model and existing size shoe last model, multidimensional scaling, which calculates, to be repaired Change and numbers storage.The grade of this step put operation is realized by three-dimension varying matrix, keep with stilt degree it is constant in the case where Model overall dimensions degree of enclosing is allowed to reach scaling standard.Three-dimension varying matrix includes: spin matrix, the geometric transformation square of equal proportion Battle array, translation matrix, whole projection matrix etc..Building for different shoes money shoe last models, using in existing shoes money customized shoe-last On the basis of, with different shoes money shoe trees by corresponding relationship, customized shoe-last, corresponding adjustment local size structure and scaling are docked, Style can be adjusted according to standard pattern model splicing.
Dimensioning content includes length of last sole degree, back height, preceding to lift up height, half sole touchdown point followed by touchdown point, foot Back height, mouth width degree of uniting, open height of uniting, mouth length of uniting, toe degree of enclosing, sole degree of enclosing, foot waist dimension, instep degree of enclosing, ankle enclose Degree etc..
Foot last carving Analysis of Human Comfort and inspection generate cross-section comparison's number at each position according to the foot last carving model matched According in conjunction with shoe tree comfort level rule, the mean square deviation of otherness, makes analysis between calculating last carving critical size and foot critical size With inspection.
Using Parametric designing, the pass between size and size is established with the method for mathematical relationship or logical relation System can shorten the time of modification model.Unified model type is sorted out respectively and is managed.Detection model is normative simultaneously, obtains The calculating analysis report of Model Matching facilitates modification and correction, improves shoe tree database data confidence level.
The method that the embodiment of the present invention drives shoe tree parametric reconstruction by using characteristic point passes through controlling feature line and control The parameters relationship of point is made to complete the parametric modeling of shoe tree, the control parameter by modifying shoe tree can complete new shoes model Building.And to people's foot, the extracting method of shoes and shoe tree characteristic parameter is studied, using the characteristic parameter Controlling model simplified Generation, and complete the rational inspection of model parameter, the inspection etc. of reconstruction model matching.Tune is stored in a manner of parametrization It is generated with shoe last model data, while with driving parameter model, model modification is facilitated to update and analysis management.
It should be noted that above-described embodiment is only used to illustrate structure and its working effect of the invention, and it is not used as It limits the scope of the invention.One of ordinary skilled in the art is right without prejudice to thinking of the present invention and structure The adjustment or optimization that above-described embodiment carries out, should regard as the claims in the present invention and be covered.

Claims (6)

1. a kind of human foot model positioning transformations method, which is characterized in that including executing following steps:
The sole contour line of foot's triangle grid model is extracted, with foot type sole contour line characteristic trend existing in database, is known Waist position inside and outside other sole;
The foot's broadside lines for extracting foot's triangle grid model, is become with foot type broadside lines feature existing in database Gesture identifies heel position of center line curve and instep position of center line curve;Triangle grid model is moved integrally into adjustment side Position, model coordinate systems are matched with rectangular coordinate system in space, obtain the coordinate value of individual features point;
Half sole width is obtained by rectangular space coordinate value followed by width, foot length, instep height, the first toe height and ankle are high Degree evidence;Thus in standard shoe tree number library, by manually selecting with height, shoes money type, gender and regional option, then by automatic It identifies the characteristic point characteristic curve data on foot's triangle grid model of reconstruct, according to standard foot last carving difference, selectes and reconstruct The highest shoe tree group of user's foot Model Matching degree, the standard shoe tree that system Auto-matching is most adapted to;
After selection obtains matched standard shoe tree, the alignment of space measurement Data Position, including adjustment foot need to be carried out to foot last carving model It type heel and shoe tree followed by is aligned, adjustment foot type is integrally evenly distributed in last carving body the right and left, adjustment sole touchdown point and last carving bottom The point contact that lands, but the step for during do not change corresponding relationship of the foot type model integrally between each position, with entirety Unified rotation translation is transformed to benchmark;
According to the obtained standard shoe tree of matching, and the back height value of selection, secondary alignment line to previous step setting and auxiliary Rotational circle position is helped, carries out profile line segment rotation and translation by certain pivot rule, and the minimum and maximum of rotation angle is set Limit value;
By the region rotated introversion line segment carry out translation make different zones line segment between original tie point as close as possible to not same district Crosspoint between the inner curve of domain is that point of cut-off trims curve, the curve being retained in region, then by between each curved section with Second order parameter continuity is smoothly connected, and equally the curved surface in different zones is trimmed and is smoothly connected.
2. the method according to claim 1, wherein for the human foot model after realignment, along positive direction of the x-axis It is that line segment A1B length 25% and 68% point are set as point F1, F2, then choose the long point abscissa of 68% foot respectively and increase that interception foot is long respectively The two o'clock for adding 15mm and abscissa to reduce 20mm is set to point F3, F4, draws respectively in tri- data points of F1F3F4 of interception Auxiliary rotational circle system one the secondary alignment line perpendicular to x-axis and be parallel to xz plane, and in auxiliary line position respectively by foot Portion's triangle grid model, sole contour line and foot broadside lines are divided into four parts, by the step for the contour line that obtains with Foot's triangle grid model forms four groups by different parts, and the auxiliary line of same position and auxiliary circle are formed a group Group, the step for secondary alignment line it is parallel with z-axis and intersect with x-axis, assist the co-located auxiliary in the center of circle of rotational circle The intersection point of alignment line and x-axis.
3. the method according to claim 1, wherein first region 1 is revolved using point F3 as rotary middle point in auxiliary It is upper rotated counterclockwise by angle α (degree) to turn circle,α∈[2,8];
Then region 3 is rotated clockwise into angle beta (degree) on auxiliary rotational circle using point F4 as rotary middle point,
Then by region 4 using point F2 as rotary middle point auxiliary rotational circle on rotated counterclockwise by angle γ (degree),
4. a kind of human foot model positioning transformations system characterized by comprising
First extraction unit, for extracting the sole contour line of foot's triangle grid model, with foot type sole existing in database Contour line characteristic trend identifies waist position inside and outside sole;
Second proposes member, for extracting foot's broadside lines of foot's triangle grid model, with foot type existing in database Broadside lines characteristic trend identifies heel position of center line curve and instep position of center line curve;By triangle gridding mould Type moves integrally adjustment orientation, and model coordinate systems are matched with rectangular coordinate system in space, obtains the coordinate value of individual features point;
Matching unit, for obtaining half sole width followed by width, foot length, instep height, the first toe by rectangular space coordinate value Height and ankle altitude information;Thus in standard shoe tree number library, by manually selecting with height, shoes money type, gender and area Option, then by the characteristic point characteristic curve data on foot's triangle grid model of automatic identification reconstruct, according to standard foot last carving difference, The selected highest shoe tree group of user's foot Model Matching degree with reconstruct, the standard shoe tree that system Auto-matching is most adapted to;
Adjustment unit after obtaining matched standard shoe tree for selection, need to carry out space measurement Data Position pair to foot last carving model Standard, including adjustment foot type heel and shoe tree followed by be aligned, adjustment foot type is integrally evenly distributed in last carving body the right and left, adjustment sole Touchdown point and last carving bottom land point contact, but the step for during do not change correspondence of the foot type model integrally between each position Relationship is transformed to benchmark with whole unified rotation translation;
Rotary unit, the standard shoe tree for being obtained according to matching, and the back height value of selection, to the auxiliary of previous step setting Alignment line and auxiliary rotational circle position are helped, carry out profile line segment rotation and translation by certain pivot rule, and rotation angle is set Minimum and maximum limit value;
Processing unit, for by the region rotated introversion line segment carry out translation make different zones line segment between original tie point as far as possible It is close, curve is trimmed using the crosspoint between different zones inner curve as point of cut-off, the curve being retained in region, then will It is smoothly connected between each curved section with second order parameter continuity, the curved surface in different zones is equally subjected to trimming and is smoothly connected It connects.
5. system according to claim 4, which is characterized in that for the human foot model after realignment, along positive direction of the x-axis It is that line segment A1B length 25% and 68% point are set as point F1, F2, then choose the long point abscissa of 68% foot respectively and increase that interception foot is long respectively The two o'clock for adding 15mm and abscissa to reduce 20mm is set to point F3, F4, draws respectively in tri- data points of F1F3F4 of interception Auxiliary rotational circle system one the secondary alignment line perpendicular to x-axis and be parallel to xz plane, and in auxiliary line position respectively by foot Portion's triangle grid model, sole contour line and foot broadside lines are divided into four parts, by the step for the contour line that obtains with Foot's triangle grid model forms four groups by different parts, and the auxiliary line of same position and auxiliary circle are formed a group Group, the step for secondary alignment line it is parallel with z-axis and intersect with x-axis, assist the co-located auxiliary in the center of circle of rotational circle The intersection point of alignment line and x-axis.
6. system according to claim 4, which is characterized in that first region 1 is revolved using point F3 as rotary middle point in auxiliary It is upper rotated counterclockwise by angle α (degree) to turn circle,α∈[2,8];
Then region 3 is rotated clockwise into angle beta (degree) on auxiliary rotational circle using point F4 as rotary middle point,
Then by region 4 using point F2 as rotary middle point auxiliary rotational circle on rotated counterclockwise by angle γ (degree),
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