CN106960466B - Method for creating bra steel ring prototype based on least square method - Google Patents
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- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 110
- 239000010959 steel Substances 0.000 title claims abstract description 110
- 238000000034 method Methods 0.000 title claims abstract description 39
- 210000000481 breast Anatomy 0.000 claims abstract description 62
- 230000009466 transformation Effects 0.000 claims abstract description 16
- 239000011159 matrix material Substances 0.000 claims abstract description 11
- 238000006073 displacement reaction Methods 0.000 claims abstract description 7
- 230000001131 transforming effect Effects 0.000 claims abstract description 3
- 239000008267 milk Substances 0.000 claims description 22
- 210000004080 milk Anatomy 0.000 claims description 22
- 235000013336 milk Nutrition 0.000 claims description 22
- 238000013461 design Methods 0.000 claims description 12
- 238000010923 batch production Methods 0.000 abstract description 4
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- 238000010586 diagram Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 238000012937 correction Methods 0.000 description 2
- 238000000605 extraction Methods 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 206010008479 Chest Pain Diseases 0.000 description 1
- 206010040007 Sense of oppression Diseases 0.000 description 1
- 239000000470 constituent Substances 0.000 description 1
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- 230000008092 positive effect Effects 0.000 description 1
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract
The invention relates to a method for creating a bra steel ring prototype based on a least square method, which comprises the following steps: extracting a breast bottom contour line; generating a three-dimensional basic steel ring curve based on the breast bottom contour line, and deriving the three-dimensional basic steel ring curve in a point coordinate mode to obtain a three-dimensional space point coordinate; completing projection of the three-dimensional space point coordinates based on the principle of least square method, and obtaining coordinate points of the shape of the basic steel ring after projection; transforming the coordinate points of the projected basic steel ring shape according to a three-dimensional geometric transformation matrix, wherein the curve shape formed by the transformed points is a two-dimensional steel ring prototype stressed in the wearing state of the bra; and (3) positively and parallelly moving the highest point of the two-dimensional steel ring prototype, wherein the moving distance is the stress displacement of the recovered steel ring, so as to obtain a new highest point, and drawing the two-dimensional steel ring prototype in an unstressed natural state by using a smooth curve. The invention can generate the steel ring matched with the shape of the breast, and provides possibility for batch production and individual customization.
Description
Technical Field
The invention relates to the technical field of steel ring bra design, in particular to a method for creating a bra steel ring prototype based on a least square method.
Background
In the part that the steel ring brassiere constitutes, the steel ring is one of the most important factor of model design, and the steel ring has the close relation with functional properties such as brassiere travelling comfort, fit. The design of steel ring is based on breast base profile arc, because women's breast form is various, therefore the shape of steel ring needs the various change to come to laminate various breast base profile arc. If the improper shape design of steel ring can influence the anastomotic degree of cup and breast, cause the production vestige on the breast, more can not provide effectual support for the breast to influence the travelling comfort and the functionality of brassiere, can cause chest pain even. In order to solve this problem, the scholars have conducted related studies: (1) the average radius of the steel ring is an important factor influencing the design of the steel ring, the curve shape of the steel ring is proposed to be properly adjusted according to the difference of the breast shapes, but a method for creating a proper steel ring shape is not specifically proposed; (2) the relationship between the steel ring and the lower pushing arc of the bra, the research focuses only on the relationship between the steel ring and the bra sample plate, but does not relate to the research on the shapes of the steel ring and the breast; (3) the steel ring of new type is proposed, for example three-dimensional steel ring and three-dimensional soft steel ring, or replace the steel ring brassiere with no steel ring brassiere to solve the oppression problem that improper steel ring caused. But the soft steel ring and the film pressing cup cannot provide enough supporting function for the breasts. The above researches do not provide a specific method for solving the problem that the common steel ring is not suitable.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for creating a bra steel ring prototype based on a least square method, which can generate a steel ring matched with the shape of a breast and provides possibility for batch production and individual customization.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method for creating the bra steel ring prototype based on the least square method comprises the following steps:
(1) extracting a breast bottom contour line;
(2) generating a three-dimensional basic steel ring curve based on the breast bottom contour line, and deriving the three-dimensional basic steel ring curve in a point coordinate mode to obtain a three-dimensional space point coordinate;
(3) completing projection of the three-dimensional space point coordinates based on the principle of least square method, and obtaining coordinate points of the shape of the basic steel ring after projection;
(4) transforming the coordinate points of the projected basic steel ring shape according to a three-dimensional geometric transformation matrix, wherein the curve shape formed by the transformed points is a two-dimensional steel ring prototype stressed in the wearing state of the bra;
(5) and (3) positively and parallelly moving the highest point of the two-dimensional steel ring prototype, wherein the moving distance is the stress displacement of the recovered steel ring, so as to obtain a new highest point, and drawing the two-dimensional steel ring prototype in an unstressed natural state by using a smooth curve.
In the step (1), 12 points are selected as control points to draw the breast bottom contour line, wherein the 12 points are respectively as follows: medial border point, lateral border point, inferior border point, superior border point, 30 ° point of breast, 60 ° point of breast, 120 ° point of breast, 150 ° point of breast, 210 ° point of breast, 240 ° point of breast, 300 ° point of breast, and 330 ° point of breast.
The step (2) specifically comprises the following steps:
(21) taking the milk point as a reference point, and taking the milk passing point as a plane L parallel to the horizontal plane;
(22) adding the Y coordinate value of the milk point to the design value of the outer edge point of the steel ring to create a plane L parallel to the plane LOuter coverDetermining the coordinate value of the steel ring outer edge point;
(23) subtracting the design value of the inner edge point of the steel ring from the Y coordinate value of the milk point to create a plane L parallel to the plane LInner partDetermining the coordinate value of the inner edge point of the steel ring;
(24) plane LOuter coverPlane LInner partThe breast bottom contour line is divided into an upper part curve and a lower part curve, and the lower part curve is a three-dimensional basic steel ring curve;
(25) and (4) exporting the three-dimensional basic steel ring curve in a three-dimensional point coordinate mode to obtain n three-dimensional space point coordinates.
The step (3) is specifically as follows: and forming a projection plane by an inner edge point, an outer edge point and a lower edge point in the 12 control points, and projecting the three-dimensional space point coordinates based on the principle of a least square method to obtain the shape of the projected basic steel ring.
The step (4) is specifically as follows: selecting a lower edge point PLower partAnd point P1Constituting vector
As a rotating shaft, establishing a three-dimensional geometric transformation matrix according to the rotating shaft to transform coordinate points of the projected basic steel ring shape, wherein the curve shape formed by the transformed points is a two-dimensional steel ring prototype stressed in the wearing state of the bra; wherein, point P1Is a point on the projection plane, and point P1Y coordinate value and lower edge point PLower partThe Y coordinate values are the same.
The three-dimensional geometric transformation matrix is
Wherein, Tx、Ty、TzTo translate the lower edge point such that the lower edge point coincides with the origin O (0, 0, 0), the displacement occurring in the direction of the X, Y, Z axis; vector
The unit vector of (a) is u (b, c); θ is the angle of rotation about the Z axis.
Advantageous effects
Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects: the invention introduces the least square method to transform the three-dimensional space points to generate the two-dimensional fit bra steel ring prototype, thereby generating the steel ring matched with the shape of the breast and providing possibility for batch production and individual customization. The invention does not need real try-on verification, only needs virtual generation, and is very convenient to use. The invention can be well applied to the correction of the steel ring size and the production of the underwear sample plate, and provides an effective program for bra manufacturers to improve the quality and increase the efficiency.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of a three-dimensional basic brassiere steel ring;
wherein, 1 is an inner edge point, 2 is an outer edge point, 3 is a lower edge point, 4 is an upper edge point, 5 is a breast 30 degree point, 6 is a breast 60 degree point, 7 is a breast 120 degree point, 8 is a breast 150 degree point, 9 is a breast 210 degree point, 10 is a breast 240 degree point, 11 is a breast 300 degree point, and 12 is a breast 330 degree point;
FIG. 3 is a projected basic brassiere steel ring shape;
FIG. 4 shows a rotary shaft
A schematic diagram of (a);
FIG. 5 is a diagram of a two-dimensional bra steel ring prototype with the bra being in a worn state;
fig. 6 is a two-dimensional bra steel ring prototype diagram in an unstressed natural state.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The embodiment of the invention relates to a method for creating a bra steel ring prototype based on a least square method, which comprises the following steps of: the method comprises the specific application of extraction of a breast bottom contour line, generation of a three-dimensional basic steel ring curve, transformation of three-dimensional point coordinates, generation of projection points based on a least square method, and three-dimensional geometric transformation of point coordinates.
(1) Extraction of breast bottom contour
And taking the right breast as a research target, and selecting 12 points as control points in an editing module of Ployworks reverse engineering software to draw a breast bottom contour line. The 12 control points are (as shown in fig. 2): medial border point, lateral border point, inferior border point, superior border point, 30 ° point of breast, 60 ° point of breast, 120 ° point of breast, 150 ° point of breast, 210 ° point of breast, 240 ° point of breast, 300 ° point of breast, and 330 ° point of breast. And drawing a breast bottom contour line by connecting all points by using an ambiguous line.
(2) Generation of three-dimensional basic steel ring curve and transformation of three-dimensional point coordinates
1) Taking the milk point as a reference point, the milk passing point is taken as a plane L parallel to the XOZ plane of the three-dimensional coordinate system (the XOZ plane is defined as the three-dimensional coordinate system at the upper left corner of the figure 2).
2) Adding Y to Y (milk point) coordinate value of milk pointOuter covercm (the parameter value is determined according to the design of the bra outer edge style) (Y (outer) ═ Y (milk point) + YOuter cover) Creating a plane L parallel to the XOZ planeOuter coverAnd determining the Y (outer) coordinate value of the steel ring outer edge point.
3) Similarly, Y is subtracted from the Y (milk point) coordinate value of the milk pointInner partcm (the parameter value is designed according to the inner edge style of the bra) (Y (inner) ═ Y (milk point) -YInner part) Creating a plane L parallel to the XOZ planeInner partAnd determining the Y (inner) coordinate value of the inner edge point of the steel ring.
4) At this time, the plane LOuter coverPlane LInner partAnd the inner edge and the outer edge of the breast bottom contour arc line share four intersection points, and one point is selected from the inner edge and the outer edge and is respectively named as a point A and a point B.
5) Taking the point A and the point B as a demarcation point, the breast bottom contour line is divided into an upper curve and a lower curve, and the lower curve AB is a three-dimensional basic bra steel ring curve (as shown in figure 2).
6) And (4) exporting the three-dimensional basic bra steel ring curve in a three-dimensional point coordinate mode to obtain n three-dimensional space point coordinates.
(3) Projection point generation based on least square method
1) Let the known coordinates of the three-dimensional spatial points be
The projection point is
From the outer edge point P of the 12 control pointsOuter coverInner edge point PInner partAnd a lower edge point PLower partThe projection surface is aTx is b, i.e.
The problem of finding the proxels translates to:
to find
Namely, it is
2) Introducing a Lagrange multiplier method to obtain a Lagrange function:
L(x,λ)＝||x-z||2+λ(aTx-b), and lambda is a parameter.
The first partial derivative of L (x, λ) with respect to x is taken to be equal to zero and is associated with an additional condition, i.e.
The solution to the above equation set is:
N projected points P (x)1,x2,x3) And (3) introducing the cast basic bra steel ring into Polyworks reverse engineering software to obtain the shape of the projected basic bra steel ring (as shown in figure 3).
(4) Three-dimensional geometric transformation of point coordinates
1) Translation projection point
Selecting a lower edge point PLower partAnd P1(P1A projection surface a in the step (3)Tx is a point on b, and the coordinate value of Y and PLower partSame point) constituent vector
As the axis of rotation (as shown in fig. 4). The lower edge of the translation coincides with the origin O (0, 0, 0), and T is generated in the direction of the X, Y, Z axisx、Ty、TzIs expressed as T (T)x,Ty,Tz). The new coordinates of the projection point after translation are:
the transformation matrix is:
2) rotating about the X-axis to rotate the shaft
Falls in the XOZ plane
Due to P1Is a point on the projection plane, and the Y coordinate value and PLower partThe points are the same, so
Parallel to the XOZ plane. When the lower edge point translates, coinciding with the origin O (0, 0, 0), point P1Also falls within the XOZ plane, so
In the XOZ plane.
3) Rotating about the Y axis to rotate the shaft
Coincident with the Z axis
Let u (a, b, c) be the axis
The unit vector of (2). By translation, P1Has fallen into the XOZ plane, but at point P1The distance from the X axis remains constant.
Rotation β about the Y axis coincides with the Z axis, and the unit vector after rotation is u "(a,0, c).
4) Rotation of theta about Z axis
Theta is an included angle in the anticlockwise direction between the plane where the point rotates around the Y axis and the XOZ plane. The transformation matrix is:
thus, the matrix of the three-dimensional geometric transformation is represented as:
the transformation of the projected basic steel ring, namely the two-dimensional bra steel ring prototype of the bra wearing stress state, is realized in Matlab (as shown in figure 5). And (3) moving the highest point of the steel ring by v cm (the v parameter value is the stress displacement of the recovered steel ring) in a forward parallel mode along the Z axis to obtain a new highest point, and drawing a two-dimensional steel ring prototype (a right curve) in an unstressed natural state by using a smooth curve (as shown in fig. 6).
The present invention will be described below with reference to a 75C human body model as a specific example.
1) And (3) introducing a three-dimensional model of a human body into the Polyworks, and drawing a contour line of the breast bottom according to 12 control points (shown in figure 2).
2) Adding Y of milk(milk drop)The coordinate values plus 2cm (determined by the design of the bra's outer edge) create a plane L parallel to the XOZ planeOuter coverDetermining Y of outer edge point of steel ring(outer)Coordinate value (Y)(outer)＝Y(milk drop)+ 2); similarly, the Y of milk is added(milk drop)Subtracting 1cm from the coordinate values (determined by the design of the bra's inner skirt), creating a plane L parallel to the XOZ planeInner partDetermining the Y coordinate value (Y) of the inner edge point of the steel ring(inner)＝Y(milk drop)-1). A three-dimensional base steel ring curve (as shown in fig. 2) is extracted. The coordinates are derived in the form of point coordinates, and 261 three-dimensional space point coordinates are obtained.
3) The coordinates of the outer edge point, the inner edge point and the lower edge point are (-145.21,1176.51,15.18), (-25.15,1176.51,77.52) and (-75.03,1104.68,53.81), respectively, so the equation of the projection plane is as follows:
4477.529443x-262.654271y-8623.901827z+1090150.111634＝0
and finishing the projection of the three-dimensional points based on the principle of least square method. And (4) introducing the projection points into the polyfworks software to obtain the shape of the projected basic bra steel ring (as shown in figure 3).
4) Selecting a lower edge point PLower part(-75.03,1104.68,53.81) and P1(0,1104.68,92.77) constituting a vector
As the axis of rotation (as shown in fig. 4). Finally, obtaining a matrix of three-dimensional geometric transformation:
the transformed points present a curve shape in the plane of the coordinate system XOZ, that is, a two-dimensional steel ring prototype of the bra under stress in the wearing state (as shown in fig. 5).
5) The highest point of the steel ring is moved 1.5cm forward along the Z axis (namely, the stress displacement of the steel ring is recovered), a new highest point is obtained, and a smooth curve is used for drawing a two-dimensional bra steel ring prototype (a right curve) in an unstressed natural state (as shown in figure 6).
It is not easy to find that the invention introduces the least square method to transform the three-dimensional space points to generate the two-dimensional fit bra steel ring prototype, thereby generating the steel ring matched with the shape of the breast, and providing possibility for batch production and individual customization. The invention does not need real try-on verification, only needs virtual generation, and is very convenient to use. The invention can be well applied to the correction of the steel ring size and the production of the underwear sample plate, and provides an effective program for bra manufacturers to improve the quality and increase the efficiency.
Claims (6)
1. The method for creating the bra steel ring prototype based on the least square method is characterized by comprising the following steps of:
(1) extracting a breast bottom contour line;
(2) generating a three-dimensional basic steel ring curve based on the breast bottom contour line, and deriving the three-dimensional basic steel ring curve in a point coordinate mode to obtain a three-dimensional space point coordinate;
(3) completing projection of the three-dimensional space point coordinates based on the principle of least square method, and obtaining coordinate points of the shape of the basic steel ring after projection;
(4) transforming the coordinate points of the projected basic steel ring shape according to a three-dimensional geometric transformation matrix, wherein the curve shape formed by the transformed points is a two-dimensional steel ring prototype stressed in the wearing state of the bra;
(5) and (3) positively and parallelly moving the highest point of the two-dimensional steel ring prototype, wherein the moving distance is the stress displacement of the recovered steel ring, so as to obtain a new highest point, and drawing the two-dimensional steel ring prototype in an unstressed natural state by using a smooth curve.
2. The method for creating a bra steel ring prototype based on the least square method as claimed in claim 1, wherein 12 points are selected in the step (1) as control points to draw a bra bottom contour line, wherein the 12 points are respectively: medial border point, lateral border point, inferior border point, superior border point, 30 ° point of breast, 60 ° point of breast, 120 ° point of breast, 150 ° point of breast, 210 ° point of breast, 240 ° point of breast, 300 ° point of breast, and 330 ° point of breast.
3. The method for creating a bra steel ring prototype based on the least square method as claimed in claim 1, wherein the step (2) specifically comprises the following steps:
(21) taking the milk point as a reference point, and taking the milk passing point as a plane L parallel to the horizontal plane;
(22) adding the Y coordinate value of the milk point to the design value of the outer edge point of the steel ring to create a plane L parallel to the plane LOuter coverDetermining the coordinate value of the steel ring outer edge point;
(23) subtracting the design value of the inner edge point of the steel ring from the Y coordinate value of the milk point to create a plane L parallel to the plane LInner partDetermining the coordinate value of the inner edge point of the steel ring;
(24) plane LOuter coverPlane LInner partThe breast bottom contour line is divided into an upper part curve and a lower part curve, and the lower part curve is a three-dimensional basic steel ring curve;
(25) and (4) exporting the three-dimensional basic steel ring curve in a three-dimensional point coordinate mode to obtain n three-dimensional space point coordinates.
4. The method for creating a bra steel ring prototype based on the least square method as claimed in claim 1, wherein the step (3) is specifically as follows: and forming a projection plane by an inner edge point, an outer edge point and a lower edge point in the 12 control points, and projecting the three-dimensional space point coordinates based on the principle of a least square method to obtain the shape of the projected basic steel ring.
5. The method for creating a bra steel ring prototype based on the least square method as claimed in claim 4, wherein the step (4) is specifically as follows: selecting a lower edge point PLower partAnd point P1Constituting vector
As a rotating shaft, establishing a three-dimensional geometric transformation matrix according to the rotating shaft to transform coordinate points of the projected basic steel ring shape, wherein the curve shape formed by the transformed points is a two-dimensional steel ring prototype stressed in the wearing state of the bra; wherein, point P1Is a point on the projection plane, and point P1Y coordinate value and lower edge point PLower partThe Y coordinate values are the same.
6. The method for creating a bra steel ring prototype based on least squares of claim 5, wherein the three-dimensional geometric transformation matrix is
Wherein, Tx、Ty、TzA displacement in the direction of the X, Y, Z axis when the lower edge point is shifted so as to coincide with the origin O (0, 0, 0); vector
The unit vector of (a) is u (b, c); θ is the angle of rotation about the Z axis.
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| CN106235431A (en) * | 2016-08-31 | 2016-12-21 | 惠州学院 | A kind of women three-dimensional surveys the steel ring shape of body bra |
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