CN113378434B - Cylindrical weft knitted fabric modeling method based on curved surface division - Google Patents
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- 239000004744 fabric Substances 0.000 title claims abstract description 46
- 238000000034 method Methods 0.000 title claims abstract description 37
- 238000009940 knitting Methods 0.000 claims abstract description 16
- 238000004364 calculation method Methods 0.000 claims description 9
- 238000009941 weaving Methods 0.000 claims description 5
- 238000010586 diagram Methods 0.000 claims description 4
- 238000004088 simulation Methods 0.000 abstract description 2
- 238000013461 design Methods 0.000 description 7
- 238000012986 modification Methods 0.000 description 4
- 230000004048 modification Effects 0.000 description 4
- 238000011166 aliquoting Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- PCTMTFRHKVHKIS-BMFZQQSSSA-N (1s,3r,4e,6e,8e,10e,12e,14e,16e,18s,19r,20r,21s,25r,27r,30r,31r,33s,35r,37s,38r)-3-[(2r,3s,4s,5s,6r)-4-amino-3,5-dihydroxy-6-methyloxan-2-yl]oxy-19,25,27,30,31,33,35,37-octahydroxy-18,20,21-trimethyl-23-oxo-22,39-dioxabicyclo[33.3.1]nonatriaconta-4,6,8,10 Chemical compound C1C=C2C[C@@H](OS(O)(=O)=O)CC[C@]2(C)[C@@H]2[C@@H]1[C@@H]1CC[C@H]([C@H](C)CCCC(C)C)[C@@]1(C)CC2.O[C@H]1[C@@H](N)[C@H](O)[C@@H](C)O[C@H]1O[C@H]1/C=C/C=C/C=C/C=C/C=C/C=C/C=C/[C@H](C)[C@@H](O)[C@@H](C)[C@H](C)OC(=O)C[C@H](O)C[C@H](O)CC[C@@H](O)[C@H](O)C[C@H](O)C[C@](O)(C[C@H](O)[C@H]2C(O)=O)O[C@H]2C1 PCTMTFRHKVHKIS-BMFZQQSSSA-N 0.000 description 2
- 238000010276 construction Methods 0.000 description 2
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- 230000009286 beneficial effect Effects 0.000 description 1
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- 238000004519 manufacturing process Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 239000002245 particle Substances 0.000 description 1
- 239000004753 textile Substances 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/12—Cloth
Abstract
The application discloses a cylindrical weft-knitted fabric modeling method based on curved surface division. The method comprises the steps of determining the number of divided parts according to the number of turns and the number of knitting needles of a tubular weft knitted fabric, and dividing a curved surface on a NURBS curved surface according to an equal chord length dividing method. Secondly, the combination of the grid weft-added plain stitch is a grid-stitch model. And meanwhile, according to the geometric structure of the weft plain stitch, selecting a model value point on the stitch, reversely solving the relation between the control points and the stitch width and height, according to the relation between four vertexes of a parameter domain grid and the control points and the stitch width and height, establishing control point parameters required by a grid-stitch model in a curved surface parameter domain, finally establishing the grid-stitch model through NURBS curved surfaces and curve formulas, and forming a three-dimensional model of the tubular weft knitted fabric according to the arrangement and distribution of the grid-stitch model. The application can be applied to tubular weft-knitted fabrics constructed by the NUBRS curved surfaces, and provides modeling basis for finite element and other simulation analysis of the knitted fabrics.
Description
Technical Field
The application relates to a modeling method, in particular to a cylindrical weft-knitted fabric modeling method based on curved surface division.
Background
With the improvement of aesthetic demands, the development of knitting technology, weft knitted fabrics show a trend of fashion and functionalization. In addition to the traditional knitted underwear, socks and the like, the requirements of functional weft knitted fabrics such as medical supplies, sports clothes and the like are also increasing, so that the design requirements of the complex and changeable weft knitted fabrics are met, the cost required by the design is reduced in order to simplify the design of textile products, and the establishment of a three-dimensional fabric model becomes a technology with development prospects.
In the current stage, for three-dimensional modeling of knitted fabrics, most of researches mainly comprise two-dimensional plane designs, including pattern designs, plane tissues and simulation researches of knitting loops. The most important in the three-dimensional modeling of knitted fabrics is the modeling design of knitted loops, wherein the loop modeling design mainly comprises three methods of a Pierce model-based modeling method, a piecewise function modeling method and a spline curve modeling method, and a part of students can build a loop model through a spring-particle model by adding mechanical characteristics on the basis of the loop geometry. The fabric models obtained from these studies mostly do not exhibit the three-dimensional morphology of the fabric, and there is no three-dimensional model study on the target fabric with complex curved surfaces. In view of this, we propose a cylindrical weft knitted fabric modeling method based on curved surface division.
Disclosure of Invention
The application aims at the lack of the prior art of tubular weft knitting with complex curved surfaces
The object three-dimensional model research provides a modeling method for highlighting the three-dimensional effect of the knitting weft plain stitch three-dimensional model, wherein coil units are established on the basis of curved surface division through dividing the curved surface of the tubular weft knitting fabric, and the three-dimensional model of the tubular fabric is established through arrangement and distribution of the coil units.
The technical scheme adopted by the application is as follows: the method comprises the following steps:
step 1: on the basis of a curved surface parameter domain, equally dividing two parameter directions of a curved surface u and v respectively through equal chord lengths according to the required weaving turns and knitting needle numbers;
step 2: selecting a plurality of model value points according to the geometric structure characteristics of the weft plain stitch, establishing the relation between the model value points and the stitch width and height, and performing back calculation to obtain the relation between the control points and the stitch width and height;
step 3: in the curved surface parameter domain grid obtained by dividing, according to the relationship between the vertex and control point of the parameter domain grid and the width and height of the coil, establishing control point parameters of a grid-coil model, and obtaining the grid-coil model;
step 4: and obtaining a three-dimensional model of the tubular weft-knitted fabric by arranging the distributed grid-coil model.
As a preferred technical scheme of the application: the curved surfaces are all non-uniform reason B-splines.
As a preferred technical scheme of the application: the specific steps of equal chord length division are as follows:
when a certain parameter of the non-uniform reason B spline surface is fixed for a plurality of times, the surface becomes a constant parameter structure line taking the other parameter as a variable; the circumferential direction and the axial direction of the tubular weft-knitted fabric respectively correspond to the u direction and the v direction of the curved surface;
discretizing the parameter domain of the isoparametric structural line curve into w parts, taking the w parts into a curved surface formula to obtain the distance between two adjacent points, and accumulating all the distance values to obtain the length S of the curve ine ；
Assuming the number of needles is n, according to the total length S line Obtain an initial length l=s line According to the knitting needle number, the parameter step distance is preliminarily determined to be deltau=1/n, so that the parameter value u of each equal dividing point can be known i ；
By combining the parameter values u i Carrying out preliminary equal point P by using non-uniform rational B-spline surface i And obtain P i And P i-1 The linear distance s between the two points is halved in the parameter domain, and the distance u is calculated by i The value is adjusted until ζ= |l-s| reaches the required accuracy;
repeating the steps to obtain all the equal dividing points, and finishing dividing the directions of the single parameters;
the division of the other parameter direction is completed according to the method.
As a preferred technical scheme of the application: the method further comprises the steps of: and determining the relation between the control point and the coil width and height through non-uniform rational B-spline back calculation according to the relation between the 11 model value points and the coil width and height.
As a preferred technical scheme of the application: the method further comprises the steps of: establishing a grid-coil model control point parameter distribution diagram according to the obtained relation between the control points and the width and height of the coils and the coordinates of the parameter domain grid; and the control points are brought into a curved surface formula to obtain control points, and the control points form a grid-coil model under the curved surface formula.
As a preferred technical scheme of the application: the method further comprises the steps of: and 3, completing the three-dimensional model establishment of the tubular weft-knitted fabric through the arrangement and distribution of the grid-coil models.
As a preferred technical scheme of the application: the curved surface formula is as follows:
where i=0, 1,., n, j=0, 1,., m, k=3; d, d i,j Represents the control point omega i,j Is the weight of the corresponding control point, N i,k (u) and N j,l (v) The rational basis functions of B-splines in the u-direction and v-direction, respectively.
The application has the beneficial effects that:
(1) According to the method, the grid-coil model is built through the control points of the grid-coil model according to the number of knitting needles and the number of weaving turns, the building of the whole tubular weft-knitted fabric model is realized, the fabric model based on the grid-coil model is built according to the actual fabric curved surface, and a method is provided for quick building of the fabric model.
(2) The application can realize programming and can realize the establishment of a model.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed for the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application.
FIG. 1 is a curved view of a tubular weft knit fabric of the present application;
FIG. 2 is a schematic illustration of equal chord division according to the present application;
FIG. 3 is a view showing the effects of the curved surface division of the present application
FIG. 4 is a diagram of a grid-coil model in the parametric domain of the present application;
FIG. 5 is a profile of the present application;
fig. 6 is a schematic diagram of a tubular weft knitted fabric according to the present application.
Detailed Description
It should be noted that, under the condition of no conflict, the embodiments of the present application and features in the embodiments may be combined with each other, and the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Example 1:
the preferred embodiment of the application provides a cylindrical weft-knitted fabric modeling method based on curved surface division, which comprises the following steps: (1) And dividing the axial chord length and the circumferential chord length of the cylindrical curved surface according to the weaving turns and the knitting needles of the cylindrical weft-knitted fabric. (2) According to the weft plain stitch structure, 11 shaped value points are selected, the relation between the shaped value points and the stitch width and height is established, and the relation between the control points and the stitch width and height is obtained through back calculation of the control points. (3) And establishing control point parameters of the grid-coil model according to the parameter domain grid after the curved surface is divided and the relation between the control points and the coil width and height. (4) And establishing control point coordinates of the grid-coil model through the mapping relation between the curved surface and the curved surface parameter domain and establishing the grid-coil model. (5) And (3) establishing a three-dimensional model of the tubular weft-knitted fabric by arranging the distributed grid-coil model.
In one embodiment of the present application, the curved surface division specifically includes the following steps:
(1) The u and v directions of the curved surface parameter domain correspond to the circumferential direction and the axial direction of the tubular weft-knitted fabric respectively, and according to the nature of the curved surface, the curved surface is regarded as one parameter of the curved surfaceWhen the number is fixed, the curved surface is the isoparametric structure line taking the other parameter as a variable. And carrying out equal chord length division on the equivalent parameter structural lines so as to realize curved surface division. The initial length L first needs to be determined. Discretizing the parameter domain of the curve into w parts, wherein the parameter range is [0,1 ]]The distance between two adjacent points is obtained by bringing the curved surface formula, and the approximate length S of the curve can be obtained by adding all the distance values line 。
Considering that the circumferential direction of the fabric is circular, the number of knitting needles is the number of parts needed to be divided by the isoparametric structural line, and the initial length l=s is given that the number of knitting needles is n line And/n. At the same time, in order to make a subsequent modification and adjustment to the initial length, the length of the curve divided into n-1 part and n+1 part is calculated and recorded as the range L of the initial length L MIN ,L MAX ]。
(2) And determining the interval of parameter domain division, and calculating the length l between the model value points corresponding to the two parameter points. The u-direction parameter domain is divided into n parts, and the divided interval is set to deltau=1/n. Let the first type value point be P 0 Its parameter u0 is zero and its type value point P' 1 Corresponding parameter u' 1 The initial value is (0+Δu). Calculating to obtain P0 and P 'through a curved surface formula' 1 A linear distance s therebetween.
(3) Comparing the magnitudes of s and L, wherein L is equal to the initial length L within the error range, i.e. L-s is less than or equal to epsilon, and the error epsilon is L multiplied by 10 -3 Then the parameter value u' 1 Equal parameter point u being P1 1 U is namely 1 ＝u' 1 . When s is greater than L, the equally dividing parameter point u is described 1 Is in (u) 0 ,u' 1 ) Between them; when s is smaller than L, it is necessary to continue increasing Deltau until s is larger than L and the number of intervals Deltau cannot exceed the divided number n of parts, at which time the parameter u' 1 The size of (2) is u' 1 I Δu, i=2, …, n. When the required aliquoting parameter is at (u) 0 ,u' 1 ) When the number is in the range, the method can be continuously approximated by a dichotomy until a parameter value u is found 1 The distance s between the model value point P1 corresponding to the parameter value and the model value point P0 corresponding to the last equal-divided parameter point is equal to the initial length L in the error range, the parameter value u 1 Is P1The parameter points are aliquoted.
(4) Repeating the steps 2 and 3, and finding the value of the equal-division parameter corresponding to the P2 under the condition of determining the type value point P1. And sequentially cycling until the last parameter point Pm.
(5) If the length s of the last segment last The curve division is completed when the phase difference value with the initial length L reaches the required precision, otherwise, the initial length L needs to be modified again new And dividing. The initial length range [ L ] set in the foregoing MIN ,L MAX ]The modification of the initial length is carried out in the method mainly by a dichotomy.
In one embodiment of the present application, the step of mesh-coil modeling includes:
(1) Placing the knitting weft plain stitch under a microscope, observing the stitch structure of the yarn, selecting 11 model value points and establishing a model value point q i The relation between the control point d and the coil width W and the coil height H is obtained through back calculation of the control point i Relation with coil width W, height H.
q i ＝(k qW W，k qH H)
Wherein k is qW W、k qH H is the proportionality coefficient between each type value point and the coil width and height.
d i ＝(k dW W，k dH H)
Wherein k is dW 、k dH For controlling the proportional coefficient between the point and the width and height of the coil
(2) Any grid in the parameter domain obtained by curved surface division, and four vertexes ABCD coordinates are (u) i ，v j )，(u i ，v j+1 )，(u i+1 ，v j+1 )，(u i+1 ，v j ) The control point parameters of the grid-coil model built in the grid are as follows:
d (i，j) x＝(k dW ×(u i+1 -u i )+u i ，k dH ×(v j+1 -v j )×1.25+v j )。
where x=1,..11. Wherein k is dW 、k dH And controlThe proportion coefficient of the manufacturing points is consistent. Considering that the first two and the last two coefficients of the control point scaling coefficients are identical, 11 coefficients are selected for the construction of the grid-coil model.
(3) After the control points of the grid-coil model are obtained, the grid-coil model is established through a curve formula.
In one embodiment of the application, the model formed by the coils and the grids of 11 control points is called a grid-coil model.
In one embodiment of the present application, the surface and the curve formula are non-uniform rational B-spline surfaces and curves, respectively.
The selected cylindrical weft knitted fabric curved surface is shown in fig. 1, and the curved surface is a three-time non-uniform rational B-spline curved surface, and is shown in the following formula:
where i=0, 1,., n, j=0, 1,., m, k=3; d, d i,j Represents the control point omega i,j Is the weight of the corresponding control point, N i,k (u) and N j,l (v) The rational basis functions of B-splines in the u-direction and v-direction, respectively.
The curved surface division comprises the following specific steps:
(1) And respectively corresponding the parameters u and v directions of the curved surface to the circumferential direction and the axial direction of the tubular weft-knitted fabric, and determining the dividing number of the two parameter directions of the curved surface according to the number of weaving turns and the number of knitting needles of the weft-knitted fabric.
(2) When one parameter is determined, the curved surface becomes an isoparametric structure curve formula taking the other parameter as a variable, as shown in the following formula.
Referring to fig. 2 for equal chord length division of the reference structure line, an initial length L needs to be determined first. Discretizing the parameter domain of the curve into w parts, wherein the parameter range is [0,1 ]]The distance between two adjacent points is obtained by bringing the curved surface formula, and the approximate length S of the curve can be obtained by adding all the distance values line . Let the number of needles be n, the initial length be l=s line And/n. At the same time, in order to make a subsequent modification and adjustment to the initial length, the lengths of the curves divided into n-1 parts and n+1 parts are respectively calculated and recorded as the range of the initial length L [ LMIN, LMAX]。
And determining the interval of parameter domain division, and calculating the length s between the model value points corresponding to the two parameter points. The u-direction parameter domain is divided into n parts, and the divided interval is set to deltau=1/n. Let the first model point be P0, its parameter u0 be zero, and the model point P' 1 Corresponding parameter u' 1 The initial value is (0+Δu). Calculating to obtain P0 and P 'through a curved surface formula' 1 A linear distance s therebetween.
Comparing the magnitudes of s and L, wherein s is equal to the initial length L within the error range, i.e. L-s is less than or equal to epsilon, and the error epsilon is L multiplied by 10 -3 Then the parameter value u' 1 Equal parameter point u being P1 1 U is namely 1 ＝u' 1 . When s is greater than L, the equally dividing parameter point u is described 1 Is in (u) 0 ,u' 1 ) Between them; when s is smaller than L, it is necessary to continue increasing Deltau until s is larger than L and the number of intervals Deltau cannot exceed the divided number n of parts, at which time the parameter u' 1 The size of (2) is u' 1 I Δu, i=2, …, n. When the required aliquoting parameter is at (u) 0 ,u' 1 ) When the number is in the range, the method can be continuously approximated by a dichotomy until a parameter value u is found 1 The distance s between the model value point P1 corresponding to the parameter value and the model value point P0 corresponding to the last equal-divided parameter point is equal to the initial length L in the error range, the parameter value u 1 Is P 1 Is equal to the bisection parameter point of (a).
Repeating the steps 2 and 3, and at the determined type value point P 1 In the case of (1), find P 2 Corresponding value of the aliquoting parameter. Sequentially cycling until the last parameter point P m 。
If the length s of the last segment last The curve division is completed when the phase difference value with the initial length L reaches the required precision, otherwise, the initial length L needs to be modified again new And dividing. The initial length range [ L ] set in the foregoing MIN ,L MAX ]The modification of the initial length is carried out in the method mainly by a dichotomy.
After u-direction division is completed, v-direction is divided similarly, and the effect after division is shown in fig. 3.
The three-dimensional model building method based on curved surface division comprises the following steps:
(1) And selecting a model value point on a coil picture according to a weft plain stitch obtained by shooting under a super-depth-of-field microscope, wherein the distribution of the model value point is shown in fig. 5. Simultaneously establishing the relation between the coil type value point and the coil width and height
q i ＝(k qW W,k qH H)
Wherein k is qW W、k qH H is the proportionality coefficient between each type value point and the coil width and height, as shown in table 1:
TABLE 1 value point scaling factor
The non-uniform rational B-spline curve is shown as follows:
wherein w is selected in consideration of engineering practicability j ＝1，k＝3,N j,k (u) is a B-spline rational basis function.
Performing control point back calculation according to a three-time non-uniform rational B-spline curve, wherein the node vector is determined by using an accumulated chord length parameterization method, and the solved parameter nodes are as follows:
the boundary condition designed by the back calculation control point is a practical condition:
the control point obtained by back calculation and the relation between the control point and the coil width and height:
d i ＝(k dW W,k dH H)
wherein k is dW 、k dH Specific values for the ratio between the control point and the coil width and height are shown in Table 2
TABLE 2 control Point scaling factors
Referring to fig. 4, in the parametric domain obtained by surface division, any one mesh is selected, and four vertices ABCD have coordinates (u i ，v j )，(u i ，v j+1 )，(u i+1 ，v j+1 )，(u i+1 ，v j ) The control point parameters of the grid-coil model built in the grid are as follows:
d (i，j) x＝(k dW ×(u i+1 -u i )+u i ，k dH ×(v j+1 -v j )×1.25+v j )。
where x=1,..11. Wherein k is dW 、k dH And the control point proportionality coefficient is consistent. Considering that the first two and the last two coefficients of the control point scaling coefficients are identical, 11 coefficients are selected for the construction of the grid-coil model.
A cylindrical weft knitted fabric model is determined from the arrangement distribution of the mesh-coil model, see fig. 6.
It will be evident to those skilled in the art that the application is not limited to the details of the foregoing illustrative embodiments, and that the present application may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (5)
1. A method for modeling a tubular weft-knitted fabric based on curved surface division is characterized by comprising the following steps: the method comprises the following steps:
step 1: on the basis of a curved surface parameter domain, equally dividing two parameter directions of a curved surface u and v respectively through equal chord lengths according to the required weaving turns and knitting needle numbers;
step 2: selecting a plurality of model value points according to the geometric structure characteristics of the weft plain stitch, establishing the relation between the model value points and the stitch width and height, and performing back calculation to obtain the relation between the control points and the stitch width and height;
step 3: in the curved surface parameter domain grid obtained by dividing, according to the relationship between the vertex and control point of the parameter domain grid and the width and height of the coil, establishing control point parameters of a grid-coil model, and obtaining the grid-coil model;
step 4: obtaining a three-dimensional model of the tubular weft-knitted fabric by arranging and distributing the grid-coil model;
the curved surfaces are non-uniform reason B splines for a plurality of times;
the specific steps of equal chord length division are as follows:
when a certain parameter of the non-uniform reason B spline surface is fixed for a plurality of times, the surface becomes a constant parameter structure line taking the other parameter as a variable; the circumferential direction and the axial direction of the tubular weft-knitted fabric respectively correspond to the u direction and the v direction of the curved surface;
discretizing the parameter domain of the isoparametric structural line curve into w parts, taking the w parts into a curved surface formula to obtain the distance between two adjacent points, and accumulating all the distance values to obtain the length S of the curve line ；
Assuming the number of needles is n, according to the total length S line Obtain an initial length l=s line According to the knitting needle number, the parameter step distance is preliminarily determined to be deltau=1/n, so that the parameter value u of each equal dividing point can be known i ；
By combining the parameter values u i Carrying out preliminary equal point P by using non-uniform rational B-spline surface i And obtain P i And P i-1 The linear distance s between the two points is halved in the parameter domain, and the distance u is calculated by i The value is adjusted until ζ= |l-s| reaches the required accuracy;
repeating the steps to obtain all the equal dividing points, and finishing dividing the directions of the single parameters;
the division of the other parameter direction is completed according to the method.
2. The method for modeling a tubular weft-knitted fabric based on curved surface division according to claim 1, wherein: the method further comprises the steps of: and determining the relation between the control points and the coil width and height through non-uniform rational B-spline back calculation according to the relation between a plurality of model value points and the coil width and height.
3. The method for modeling a tubular weft-knitted fabric based on curved surface division according to any one of claims 1 to 2, wherein: the method further comprises the steps of: establishing a grid-coil model control point parameter distribution diagram according to the obtained relation between the control points and the width and height of the coils and the coordinates of the parameter domain grid; and the control points are brought into a curved surface formula to obtain control points, and the control points form a grid-coil model under the curved surface formula.
4. A method of modeling a tubular weft-knitted fabric based on surface division according to claim 3, characterized in that: the method further comprises the steps of: and 3, completing the three-dimensional model establishment of the tubular weft-knitted fabric through the arrangement and distribution of the grid-coil models.
5. The method for modeling a tubular weft-knitted fabric based on curved surface division according to claim 4, wherein: the curved surface formula is as follows:
where i=0, 1,., n, j=0, 1,., m, k=3; d, d i,j Represents the control point omega i,j Is the weight of the corresponding control point, N i,k (u) and N j,l (v) The rational basis functions of B-splines in the u-direction and v-direction, respectively.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107273568A (en) * | 2017-05-09 | 2017-10-20 | 浙江大学 | A kind of complex free curved surface Meshing Method based on surface fitting |
| CN112080842A (en) * | 2020-08-31 | 2020-12-15 | 浙江理工大学 | Knitted fabric knitting method and knitted fabric thereof |
| CN112906085A (en) * | 2021-03-05 | 2021-06-04 | 上海青甲智能科技有限公司 | Three-dimensional simulation modeling technology for weft knitting coils |
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