A method for edge contour recognition of clothing pieces

Abstract

The invention relates to a method for identifying the edge contour of a garment piece, comprising the following steps: a garment piece placement and positioning step: placing a garment piece to be detected on a positioning jig, the positioning jig being a contour jig, the placement surface of the positioning jig corresponding to the surface contour of the garment piece to be detected, the placement surface of the positioning jig being provided with evenly distributed suction holes, after the garment piece to be detected is placed on the positioning jig, the suction holes inhale air, so that the garment piece to be detected is kept close to the placement surface of the positioning jig, and the positioned garment piece corresponds to the posture of a human body lying flat; a three-dimensional scanning step: performing a three-dimensional scanning on the edge of the garment piece to obtain a series of three-dimensional coordinate points on the edge of the garment piece; the invention can efficiently and accurately determine whether the edge contour of the garment piece meets the design requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent identification of clothing production, and in particular to a method for identifying edge contours of clothing pieces. Background Art

[0002] In order to fit the body shape of consumers more accurately, yoga clothes, fitness clothes and other clothes need to be made into pieces of clothes for different parts during the production process, and then the different pieces of clothes are sewn together to make yoga clothes and fitness clothes. Therefore, whether the finished yoga clothes and fitness clothes are close-fitting and whether they fit the body shape of consumers depends on the production accuracy of each piece of clothes.

[0003] Since clothing sheets are made of flexible and soft materials, they are prone to curling, wrinkling and stretching after being cut out. In addition, clothing sheets are spatial curved surfaces, and it is difficult to accurately determine manually whether the edge contours of the clothing sheets meet the design requirements. As a result, there are large errors in the sizes of the finished yoga clothes and fitness clothes, resulting in a high defective rate. Summary of the invention

[0004] The object of the present invention is to provide a method for identifying the edge contour of a garment piece, which can efficiently and accurately determine whether the edge contour of a garment piece meets the design requirements.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for identifying edge contours of clothing pieces, comprising the following steps:

[0007] The step of placing and positioning the garment piece is as follows: placing the garment piece to be tested on a positioning jig, the positioning jig is a contour jig, the placement surface of the positioning jig corresponds to the surface contour of the garment piece to be tested, the placement surface of the positioning jig is provided with evenly distributed suction holes, after the garment piece to be tested is placed on the positioning jig, the suction holes inhale air, so that the garment piece to be tested is kept close to the placement surface of the positioning jig, and the garment piece after positioning corresponds to the posture of a human body lying flat;

[0008] Three-dimensional scanning step: performing three-dimensional scanning on the edge of the clothing piece to obtain a series of three-dimensional coordinate points on the edge of the clothing piece;

[0009] Segmentation step: The sharp corners of the edge of the clothing piece are used as virtual segmentation points, so that the edge of the clothing piece is virtually segmented into several scanning segments

[0010] Three-dimensional scattered point projection step: determine the direction from the start point to the end point of each scanning segment one by one, and when it is determined that the direction from the start point to the end point of a scanning segment is along a certain direction axis, project a series of three-dimensional coordinate points belonging to the scanning segment to two vertical planes in the space with the direction axis as the intersection line, thereby obtaining a series of first-direction projection two-dimensional coordinate points of the scanning segment in the first vertical plane, and obtaining a series of second-direction projection two-dimensional coordinate points of the scanning segment in the second vertical plane;

[0011] Two-dimensional curve fitting step: using the least square method to fit a series of two-dimensional coordinate points of the scanning segment projected in the first direction in the first vertical plane into a first-direction projection fitting curve of the scanning segment, and fitting a series of two-dimensional coordinate points of the scanning segment projected in the second direction in the second vertical plane into a second-direction projection fitting curve of the scanning segment;

[0012] Three-dimensional design curve projection step: according to the principle of the segmentation step, the three-dimensional design curve of the garment body is segmented into a plurality of design segments, and according to the principle of the three-dimensional scattered point projection step, each design segment is sequentially projected onto two vertical planes in space, thereby obtaining a first direction projection line and a second direction projection line;

[0013] Control point setting steps:

[0014] For a scan segment with only one maximum point and a corresponding design segment: the two ends of the first-direction projection fitting curve of the scan segment and the two ends of the second-direction projection fitting curve are taken as actual control points, and the two ends of the first-direction projection line and the two ends of the second-direction projection line of the corresponding design segment are taken as design control points;

[0015] For the scanning segment and the corresponding design segment with two extreme value points: the first direction projection fitting curve and the second direction projection fitting curve of the scanning segment are respectively differentiated to obtain the two extreme value points of the first direction projection fitting curve and the second direction projection fitting curve of the scanning segment as two actual control points; the first direction projection line and the second direction projection line of the design segment are respectively differentiated to obtain the two extreme value points of the first direction projection line and the second direction projection line as two design control points;

[0016] Determination steps: in the first direction and the second direction, respectively, the scanning segments of the garment body are judged in turn, and the fitting curve projected in a certain direction of a certain scanning segment and the projection line of the corresponding design segment in this direction are translated and superimposed, that is, an actual control point of the fitting curve projected in the direction of the scanning segment coincides with a design control point of the projection line of the design segment in this direction, and then, the size of the area enclosed by the fitting curve projected in the direction of the scanning segment and the projection line of the design segment in the direction away from the actual control point is calculated by integration. If the enclosed area is less than the set value, it is determined that the contour of the scanning segment preliminarily meets the requirements; if the enclosed area is greater than the set value, it is necessary to further determine the contour of the scanning segment.

[0017] Specifically, in the determination step, if the enclosed area is smaller than a set value, the distance between another actual control point of the scan segment that projects the fitting curve in that direction and another design control point of the design segment that projects the line in that direction is obtained; if the distance is smaller than the set value, it is determined that the contour of the scan segment meets the requirements; if the distance is greater than the set value, it is determined that the contour of the scan segment does not meet the requirements.

[0018] Specifically, in the determination step, if the enclosed area is smaller than a set value, the scan segment is rotated around the actual control point by projecting the fitting curve in the direction so that the distance between another actual control point of the scan segment projecting the fitting curve in the direction and another design control point of the design segment projection line in the direction is minimized, and the areas enclosed by the scan segment projecting the fitting curve in the direction and the design segment projection line in the direction on the outside of the two actual control points are calculated by integration. If the sum of the two areas is smaller than the set value, it is determined that the contour of the scan segment meets the requirements; if the sum of the two areas is greater than the set value, it is determined whether the contour of the scan segment meets the requirements.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] The positioning jig is a profiling jig, which corresponds to the posture of a human body lying flat. After the garment to be tested is placed on the placement surface of the positioning jig, the air suction holes suck air to adsorb the garment, thereby accurately positioning the garment.

[0021] The clothing piece is a spatial surface, and its edge is a spatial annular three-dimensional curve. The spatial three-dimensional curve needs to be converted into a two-dimensional curve in order to be judged efficiently and quickly. Therefore, the spatial annular three-dimensional curve is first divided into several segments of spatial three-dimensional curves, and then a series of three-dimensional scanning points on each segment of the spatial three-dimensional curve are projected onto two vertical planes (such as the xoz plane and the xoy plane) in turn, so as to obtain the two-dimensional projection points of the segment of the spatial three-dimensional curve on the two vertical planes, and then the two-dimensional projection points on the two vertical planes are fitted respectively to obtain the fitting curve of the segment of the spatial three-dimensional curve on the two vertical planes.

[0022] Then, the design three-dimensional curve of the segment of the three-dimensional space curve is projected onto the two vertical planes to obtain projection lines on the two vertical planes. Then, the fitting curve and the projection line are compared on the two vertical planes.

[0023] When comparing, first set the actual control point and the design control point by taking derivation, and then translate the fitting curve until its single actual control point coincides with the single design control point of the projection line, so that the fitting curve and the projection line can be "translated and overlapped". In the "translation and overlap" state, calculate the difference area between the fitting curve and the projection line by integration, and calculate the distance between another actual control point of the fitting curve and another design control point of the projection line in the "translation and overlap" state to determine the degree of similarity of the two contours without relative swinging.

[0024] If the difference area in the "translation overlap" state is greater than the set value, the projection fitting curve is rotated around the actual control point (the one that coincides with the design control point) to minimize the distance between another actual control point of the projection fitting curve and another design control point of the projection line, that is, "rotation overlap" is performed, and the difference area between the two in the "rotation overlap" state is calculated to determine the degree of approximation between the two after a certain relative swing.

[0025] The edge contour recognition method of the clothing piece of the present invention decomposes a single-segment spatial three-dimensional curve into two two-dimensional curves for judgment, so that it can more accurately and efficiently judge whether the edge contour of a single-segment clothing piece meets the design requirements. In the judgment process, corresponding to whether a certain segment of the edge contour has a relative swing due to the deformation of the clothing, the two modes of "translation superposition" and "rotation superposition" are compared respectively, which fully considers the deformation form of the clothing piece in the actual use scene, so that it can efficiently and accurately judge whether the edge contour of the clothing piece meets the design requirements and reduce the defective rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0027] Figure 1 3D exploded view of yoga clothes and fitness clothes;

[0028] Figure 2 It is a three-dimensional exploded view of two clothing pieces;

[0029] Figure 3 It is a side exploded view of the garment piece and the positioning jig;

[0030] Figure 4 A three-dimensional view of a single garment piece;

[0031] Figure 5 It is a schematic diagram of the projection of a single-segment scan segment of a single clothing piece onto two vertical planes;

[0032] Figure 6 Schematic diagram of differentiating the fitting curve and the projection line on two perpendicular planes to obtain the tangent point;

[0033] Figure 7 It is a schematic diagram of translating and superimposing the fitting curve and the projection line;

[0034] Figure 8 Schematic diagram of rotating and superimposing the fitting curve and the projection line.

[0035] In the figure:

[0036] 1. Clothing body;

[0037] 2. Positioning fixture; 21. Suction hole. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0039] A method for identifying edge contours of clothing pieces, comprising the following steps:

[0040] The step of placing and positioning the garment piece: placing the garment piece 1 to be tested on the positioning jig 2, which is a contour jig corresponding to the posture of a human body lying flat (such as Figure 3The top side of the positioning jig 2 corresponds to the surface contour of the garment piece 1 to be tested. The positioning jig 2 is provided with uniformly distributed suction holes 21. After the garment piece 1 to be tested is placed on the positioning jig 2, the suction holes 21 suck air so that the garment piece 1 to be tested is kept close to the placement surface of the positioning jig 2. The garment piece 1 after positioning corresponds to the posture of a human body lying flat (as shown in FIG. Figure 3 shown).

[0041] Three-dimensional scanning step: performing three-dimensional scanning on the edge of the garment body 1 to obtain a series of three-dimensional coordinate points on the edge of the garment body 1;

[0042] Segmentation step: The sharp corners of the edge of the clothing piece 1 are used as virtual segmentation points, so that the edge of the clothing piece 1 is virtually segmented into several Scan segment ,like Figure 4 The middle segment is M segment, N segment, P segment and S segment.

[0043] Three-dimensional scattered point projection steps: Determine each Scan segment The direction from the starting point to the end point, when determining a certain scanning Segmentation After the direction from the starting point to the end point is along a certain direction axis, a series of three-dimensional coordinate points belonging to the scanning segment are projected onto two vertical planes in the space with the direction axis as the intersection line, thereby obtaining a series of first-direction projected two-dimensional coordinate points of the scanning segment in the first vertical plane, and obtaining a series of second-direction projected two-dimensional coordinate points of the scanning segment in the second vertical plane.

[0044] For example Figure 5 , after determining that the direction from the starting point to the end point of segment M is along the x-axis, a series of three-dimensional coordinate points belonging to segment M are projected onto the xoz plane and xoy plane with the x-axis as the intersection line, thereby obtaining a series of two-dimensional coordinate points of segment M projected on the xoz plane, such as mxz2, mxz6, etc., and obtaining a series of two-dimensional coordinate points of segment M projected on the xoy plane, such as mxy2, mxy6, etc.

[0045] Two-dimensional curve fitting step: use the least squares method to fit a series of first-direction projection two-dimensional coordinate points of the scanning segment in the first vertical plane into a first-direction projection fitting curve of the scanning segment, and fit a series of second-direction projection two-dimensional coordinate points of the scanning segment in the second vertical plane into a second-direction projection fitting curve of the scanning segment.

[0046] For example Figure 5 , Figure 6, fit a series of two-dimensional coordinate points such as mxz2 and mxz6 into the projection fitting curve Mxz of segment M on the xoz plane. Similarly, fit a series of two-dimensional coordinate points such as mxy2 and mxy6 into the projection fitting curve Mxy of segment M on the xoy plane.

[0047] Three-dimensional design curve projection step: According to the principle of the segmentation step, the three-dimensional design curve of the garment body 1 is segmented into several Design segmentation According to the principle of the three-dimensional scattered point projection step, each Design segmentation The three-dimensional design curve of the garment body 1 is known and existing data, which is composed of a series of three-dimensional data points and serves as a comparison standard for judging whether the garment body 1 actually produced is qualified or not.

[0048] For example Figure 6 , the first direction projection line Dxz is a certain Design segmentation The projection on the xoz plane, the second direction projection line Dxy is a certain Design segmentation Projection on the xoy plane.

[0049] Control point setting steps:

[0050] For a scan segment with only one maximum point (such as Figure 4 N segments, P segments) and the corresponding design segments: the two ends of the first direction projection fitting curve of the scanning segment and the two ends of the second direction projection fitting curve are taken as the actual control points, and the two ends of the first direction projection line and the two ends of the second direction projection line of the corresponding design segment are taken as the design control points.

[0051] For the scanning segment and the corresponding design segment with two extremum points: the first direction projection fitting curve and the second direction projection fitting curve of the scanning segment are respectively derived to obtain the two extremum points of the first direction projection fitting curve and the second direction projection fitting curve of the scanning segment as two actual control points. The first direction projection line and the second direction projection line of the design segment are respectively derived to obtain the two extremum points of the first direction projection line and the second direction projection line as two design control points.

[0052] For example Figure 6 , take the derivative of the fitting curve Mxz, and get two actual control points mxz1 and mxz2. Take the derivative of the fitting curve Mxy, and get two actual control points mxy1 and mxy2. Take the derivative of the projection line Dxz, and get two design control points dxz1 and dxz2. Take the derivative of the projection line Dxy, and get two design control points dxy1 and dxy2.

[0053] Determination steps: in the first direction and the second direction, respectively, the scanning segments of the garment body are judged in turn, and the fitting curve projected in a certain direction of a certain scanning segment and the projection line of the corresponding design segment in this direction are translated and superimposed, that is, an actual control point of the fitting curve projected in the direction of the scanning segment coincides with a design control point of the projection line of the design segment in this direction, and then, the size of the area enclosed by the fitting curve projected in the direction of the scanning segment and the projection line of the design segment in the direction away from the actual control point is calculated by integration. If the enclosed area is less than the set value, it is determined that the contour of the scanning segment preliminarily meets the requirements; if the enclosed area is greater than the set value, it is necessary to further determine the contour of the scanning segment.

[0054] For example, compared Figure 6 , Figure 7 , translate and overlap the fitting curve Mxz and the projection line Dxz, so that the actual control point mxz1 of the fitting curve Mxz coincides with the design control point dxz1 of the projection line Dxz, and then, by integration, find the size of the area S1 enclosed by the fitting curve Mxz and the projection line Dxz on the side away from the actual control point mxz1 (see Figure 7 ):

[0055] If the area S1 is less than the set value, it is determined that the contour of the scan segment meets the requirements preliminarily: it is necessary to further obtain the distance between another actual control point mxz2 of the fitting curve Mxz and another designed control point dxz2 of the projection line Dxz (see Figure 7 ), if the distance is less than the set value, it is determined that the profile of the scan segment meets the requirements; if the distance is greater than the set value, it is determined that the profile of the scan segment does not meet the requirements;

[0056] If the area S1 is larger than the set value (see Figure 7 ), then it is necessary to further determine the contour of the scan segment: combined with Figure 7 , Figure 8 , rotate the fitting curve Mxz around the actual control point mxz1, so that another actual control point mxz2 of the fitting curve Mxz moves to the minimum distance from another design control point dxz2 of the projection line Dxz (such as Figure 8 As shown), at this time, the two areas S2 and S3 enclosed by the fitting curve Mxz and the projection line Dxz on the outside of the two actual control points mxz2 are obtained by integration. If the sum of the two areas S2 and S3 is less than the set value, it is determined that the contour of the scan segment meets the requirements; if the sum of the two areas S2 and S3 is greater than the set value, it is determined that the contour of the scan segment does not meet the requirements.

[0057] After completing the comparison of the fitting curves and projection lines of each scanning segment on the xoz plane, the fitting curves and projection lines of each scanning segment on the xoy plane are compared.

[0058] The principle of the edge contour recognition method of the clothing piece of the present invention is as follows:

[0059] The positioning fixture 2 is a contouring fixture, and the positioning fixture 2 corresponds to the posture of a human body lying flat (such as Figure 3 After the garment piece 1 to be inspected is placed on the placement surface of the positioning fixture 2, the air suction holes 21 suck air to adsorb the garment piece 1, thereby accurately positioning the garment piece 1.

[0060] The garment body 1 is a spatial curved surface, and its edge is a spatial annular three-dimensional curve. The spatial three-dimensional curve needs to be converted into a two-dimensional curve in order to be judged efficiently and quickly. Therefore, the spatial annular three-dimensional curve is first divided into several segments of spatial three-dimensional curves, and then a series of three-dimensional scanning points on each segment of the spatial three-dimensional curve are projected onto two vertical planes (such as the xoz plane and the xoy plane) in turn, so as to obtain the two-dimensional projection points of the segment of the spatial three-dimensional curve on the two vertical planes, and then the two-dimensional projection points on the two vertical planes are fitted respectively to obtain the fitting curve of the segment of the spatial three-dimensional curve on the two vertical planes.

[0061] Then, the design three-dimensional curve of the segment of the three-dimensional space curve is projected onto the two vertical planes to obtain projection lines on the two vertical planes. Then, the fitting curve and the projection line are compared on the two vertical planes.

[0062] When comparing, first set the actual control point and the design control point by taking derivation, and then translate the fitting curve until its single actual control point coincides with the single design control point of the projection line, so that the fitting curve and the projection line can be "translated and overlapped". In the "translation and overlap" state, calculate the difference area between the fitting curve and the projection line by integration, and calculate the distance between another actual control point of the fitting curve and another design control point of the projection line in the "translation and overlap" state to determine the degree of similarity of the two contours without relative swinging.

[0063] If the difference area in the "translation overlap" state is greater than the set value, the projection fitting curve is rotated around the actual control point (the one that coincides with the design control point) to minimize the distance between another actual control point of the projection fitting curve and another design control point of the projection line, that is, "rotation overlap" is performed, and the difference area between the two in the "rotation overlap" state is calculated to determine the degree of approximation between the two after a certain relative swing.

[0064] The edge contour recognition method of the clothing piece of the present invention decomposes a single-segment spatial three-dimensional curve into two two-dimensional curves for judgment, so that it can more accurately and efficiently judge whether the edge contour of a single-segment clothing piece meets the design requirements. In the judgment process, corresponding to whether a certain segment of the edge contour has a relative swing due to the deformation of the clothing, the two modes of "translation superposition" and "rotation superposition" are compared respectively, which fully considers the deformation form of the clothing piece in the actual use scene, so that it can efficiently and accurately judge whether the edge contour of the clothing piece meets the design requirements and reduce the defective rate.

[0065] The above are only preferred embodiments of the present invention, and are not intended to limit the present invention in any form. Although the present invention has been disclosed as above in the form of preferred embodiments, it is not intended to limit the present invention. Any technical personnel in the field can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for identifying edge contours of clothing pieces, characterized in that: The following steps are involved: The step of placing and positioning the garment piece is as follows: placing the garment piece to be tested on a positioning jig, the positioning jig is a contour jig, the placement surface of the positioning jig corresponds to the surface contour of the garment piece to be tested, the placement surface of the positioning jig is provided with evenly distributed suction holes, after the garment piece to be tested is placed on the positioning jig, the suction holes inhale air, so that the garment piece to be tested is kept close to the placement surface of the positioning jig, and the garment piece after positioning corresponds to the posture of a human body lying flat; Three-dimensional scanning step: performing three-dimensional scanning on the edge of the clothing piece to obtain a series of three-dimensional coordinate points on the edge of the clothing piece; Segmentation step: The sharp corners of the edge of the clothing piece are used as virtual segmentation points, so that the edge of the clothing piece is virtually segmented into several scanning segments Three-dimensional scattered point projection step: determine the direction from the start point to the end point of each scanning segment one by one, and when it is determined that the direction from the start point to the end point of a scanning segment is along a certain direction axis, project a series of three-dimensional coordinate points belonging to the scanning segment to two vertical planes in the space with the direction axis as the intersection line, thereby obtaining a series of first-direction projection two-dimensional coordinate points of the scanning segment in the first vertical plane, and obtaining a series of second-direction projection two-dimensional coordinate points of the scanning segment in the second vertical plane; Two-dimensional curve fitting step: using the least square method to fit a series of two-dimensional coordinate points of the scanning segment projected in the first direction in the first vertical plane into a first-direction projection fitting curve of the scanning segment, and fitting a series of two-dimensional coordinate points of the scanning segment projected in the second direction in the second vertical plane into a second-direction projection fitting curve of the scanning segment; Three-dimensional design curve projection step: according to the principle of the segmentation step, the three-dimensional design curve of the garment body is segmented into a plurality of design segments, and according to the principle of the three-dimensional scattered point projection step, each design segment is sequentially projected onto two vertical planes in space, thereby obtaining a first direction projection line and a second direction projection line; Control point setting steps: For a scan segment with only one maximum point and a corresponding design segment: the two ends of the first-direction projection fitting curve of the scan segment and the two ends of the second-direction projection fitting curve are taken as actual control points, and the two ends of the first-direction projection line and the two ends of the second-direction projection line of the corresponding design segment are taken as design control points; For the scanning segment and the corresponding design segment with two extreme value points: the first direction projection fitting curve and the second direction projection fitting curve of the scanning segment are respectively differentiated to obtain the two extreme value points of the first direction projection fitting curve and the second direction projection fitting curve of the scanning segment as two actual control points; the first direction projection line and the second direction projection line of the design segment are respectively differentiated to obtain the two extreme value points of the first direction projection line and the second direction projection line as two design control points; Determination step: in the first direction and the second direction, the scanning segments of the garment body are judged in turn, and the fitting curve projected in a certain direction of a scanning segment is translated and superimposed with the projection line of the corresponding design segment in that direction, that is, an actual control point of the fitting curve projected in that direction of the scanning segment coincides with a design control point of the projection line of the design segment in that direction, and then, the size of the area enclosed by the fitting curve projected in that direction of the scanning segment and the projection line of the design segment in that direction, which is far away from the actual control point, is obtained by integration. If the enclosed area is smaller than the set value, the distance between another actual control point of the scan segment projecting the fitting curve in the direction and another design control point of the design segment projecting line in the direction is obtained: if the distance is smaller than the set value, it is determined that the contour of the scan segment meets the requirements; if the distance is greater than the set value, it is determined that the contour of the scan segment does not meet the requirements; If the enclosed area is greater than the set value, the scan segment is projected in the direction of the fitting curve and rotated around the actual control point to minimize the distance between another actual control point of the scan segment that projects the fitting curve in the direction and another design control point of the design segment's projection line in the direction. The area enclosed by the scan segment's projection of the fitting curve in the direction and the design segment's projection line in the direction on the outside of the two actual control points is calculated by integration. If the sum of the two areas is less than the set value, it is determined that the contour of the scan segment meets the requirements; if the sum of the two areas is greater than the set value, it is determined that the contour of the scan segment does not meet the requirements.

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