CN117057090A - Knitted fabric high-precision modeling method based on TNB framework - Google Patents
Knitted fabric high-precision modeling method based on TNB framework Download PDFInfo
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Abstract
The invention relates to a knitted fabric high-precision modeling method based on a TNB frame, which comprises the following steps: calculating a strand center coordinate by a yarn center coordinate based on the TNB frame; calculating fiber coordinates from strand center coordinates based on the TNB frame; calculating yarn twisting parameters through a spiral parameter equation; expanding each fiber into a ribbon having a width; and connecting all coil-shaped value points of the fabric by using spline lines to obtain a three-dimensional model of the knitted fabric. The invention overcomes the defect of yarn detail caused by the traditional modeling mode and solves the problem that the knitted fabric lacks sense of reality in computer simulation.
Description
Technical Field
The invention belongs to the technical field of computer graphics, and particularly relates to a knitted fabric high-precision modeling method based on a TNB frame.
Background
The three-dimensional virtual simulation of the knitted garment is a leading edge hot spot problem in the information technology crossing fields of computer graphics, computer aided design, artificial intelligence, computer simulation and the like. Different from the simple warp and weft knitting process principle of the woven fabric, the knitting process uses loops as basic units to form knitted fabrics, various complicated pattern structures are formed through basic knitting actions such as looping, tucking, transferring and the like, and the simulation difficulty of the knitted fabric, clothing and production process is further increased. The coil is a basic unit for forming a three-dimensional model net surface of the knitted garment, the yarn is a foundation for forming the coil, and the yarn simulation effect and the coil modeling precision determine the rendering effect of the net surface unit, so that the overall visual fidelity of the three-dimensional simulation of the garment is affected.
Yarn modeling is currently the underlying technology of virtual simulation of knitted garments, and a common modeling approach is yarn simulation based on image processing technology. And scanning the yarns by using a yarn scanner, processing the pictures, and changing the color of the background into transparent to obtain the pictures of the yarns. According to the path of the coil, the coil is fitted by using a pipeline, the texture of the yarn is mapped onto a coil model, and the yarn twisting effect is simulated by yarn mapping. While most of these methods can produce a realistic fabric appearance from a remote location, the fiber details of the yarn cannot be reproduced.
The high-precision yarn simulation and the three-dimensional fabric modeling are based on a physical model, and the parameter diversity of the physical model and the complexity of the model are fundamental influencing factors for restricting the garment simulation effect. At present, compared with overseas in the aspect of three-dimensional virtual simulation technology of knitted clothing, the method has obvious difference, restricts intelligent interactive design quality and simulation proofing effect of the knitted clothing, influences production efficiency, and restricts brand and industry competitiveness of clothing manufacturing related enterprises in China.
Disclosure of Invention
The invention aims to solve the problems in the background art and provides a knitted fabric high-precision modeling method based on a TNB frame. Technical methods for fiber-level yarn model generation were developed by OpenGL, modeling yarn micro-geometry using a TNB framework. And (3) establishing a coil unit on the basis of the high-precision yarn model, and establishing a three-dimensional model of the fabric by connecting model value points of the fabric.
The technical scheme of the invention is a knitted fabric high-precision modeling method based on a TNB frame, which specifically comprises the following steps:
step 1, taking the coordinates of a coil type value point in a model file of the knitted fabric as the center coordinates of a yarn spline, and calculating the center coordinates of the strand by using the TNB frame and the yarn center coordinates;
step 2, calculating the center coordinates of the fibers by using the TNB frame and the center coordinates of the strands;
step 3, calculating yarn twisting parameters through a spiral parameter equation;
step 4, expanding each fiber into a wide wire band;
step 5, connecting all coil-shaped value points of the fabric by using spline lines to obtain a three-dimensional model of the knitted fabric;
further, in step 1, by observing the yarn geometry microscopically, a yarn is generally composed of a plurality of strands, and the specific method for calculating the strand center coordinate point from the yarn center coordinate point based on the TNB framework is as follows:
firstly, starting a shader for generating a yarn geometric model, transmitting a central coordinate point of the yarn into the shader for processing, and setting a subdivision level in the U, V direction in a tessellation control shader;
next, in the tessellation evaluation shader, a coordinate point of the center of the strand is calculated using a TNB framing method, the TNB framing method principle and the calculation method are shown in the formulas (1) to (2),
the coordinate calculation formula is used for calculating the coordinate,
wherein,
in formula (1), where d/ds is the derivative of the arc length, κ is the curvature of the curve and τ is the flexibility of the curve. The change rule of the curvature flexibility rate of the space curve is described in the TNB frame formula. Where T (Tangent vector of curve) represents Tangent vector of advancing direction, N (Normal vector of curve) represents Normal vector of path bending direction, and B (Binormal vector of curve) represents auxiliary Normal vector of tendency to twist out of this plane. C in formula (2) yarn Is the spatial coordinates of the center of the yarn,for the j-th strand center space coordinate, +.>Is formed by the center c of the yarn yarn To the center of the jth strand->Space vector, R ply For strand radius>For the initial polar angle of the strand, n ply N is the number of strands yarn Is the unit normal vector of the yarn, B yarn Is the unit auxiliary normal vector of the yarn. The solution of the TNB coordinate frame is an existing algorithm, and is not described herein.
Finally, coordinate c yarn And (3) withAnd summing to obtain the center coordinates of the strands in the space.
Further, in step 2, by observing the geometry of the strands microscopically, one strand is typically composed of tens to hundreds of fibers with a diameter of micrometers, and the fiber coordinate point is calculated from the strand center coordinate point based on the TNB framework as follows:
firstly, in the enabled shader for generating the yarn geometric model, the distribution condition of the fibers in each strand is transmitted into the shader for processing in a one-dimensional texture mode, and the subdivision level in the direction of U, V is set in the tessellation control shader and is consistent with that in the step 1;
next, in the tessellation evaluation shader, coordinate points of the fibers are calculated using a TNB frame method, as shown in the formulas (3) and (4),
wherein,
wherein, c i In the form of the spatial coordinates of the fibers,for the j-th strand center space coordinate, Δc i Is centered by the j-th strandTo the ith fiber c i Space vector, R i For the distance θ of the ith fiber to the centerline of the strand i As the initial polar angle of the fiber,is the unit normal vector of the strand,>is the unit minor normal vector of the strand. e, e N And e B Is the scaling factor of ellipse, R min ，R max Representing the minimum radius and the maximum radius, respectively, of the fiber during migration, s is a parameter controlling the helical lead.
Finally, the coordinate c in the step 1 is calculated yarn And (3) withThe result of the summation is summed with deltac i And adding to obtain the spatial position of the ith fiber in the jth strand in the space.
Further, in step 3, the method for calculating the yarn twisting parameters by using the spiral parameter equation is as follows:
firstly, setting the number of yarn strands and the number of fibers in a single strand in a tessellation calculation shader, wherein the principle of a parameter equation of a cylindrical spiral line is shown in the following formula (5);
wherein x, y and z are European space coordinates, ω is the rotational angular velocity of the object about the axis, and v is the linear velocity of the object along the rotational axis.
Next, by modifying the ω parameter in the parameter equation, the yarn twist can be adjusted in combination with equation (2) in step 1.
Further, the method of expanding each fiber into a wide ribbon in step 4 is as follows:
firstly, after the input type value points are processed by the tessellation calculation shader, the coordinates of the subdivided fibers in a local space are transferred into the geometric shader through built-in variables, and meanwhile, the set fiber widths are transferred in together.
The dots are then expanded in a geometry shader into bands of width in the viewing space as shown in equations (6) through (7):
wherein,
in Pos i,0 Representing the point P i Points of expansion along the direction of the secondary normal, pos i,1 Representing the point P i The point along the opposite direction of the minor normal, r, represents the width of the expansion, which is half the width of the fiber. Here, T, B, and N are three orthogonal vectors constituting the observation space, respectively, a tangential axis, a sub normal axis, and a normal axis.
Finally, the ribbon generated by the geometry shader is rasterized, so far, high precision yarn modeling has been completed.
Further, in step 5, all the coil-shaped value points of the fabric are connected by using spline lines, and the method for obtaining the three-dimensional model of the knitted fabric is as follows:
first, in the tessellation computation shader, the center of the yarn is given by a Catmull-Rom spline (Catmull-Rom spline) defined by four control points, and the parametric equations of the spline curve are shown in equations (8) to (9):
p(t)＝at 3 +bt 2 +ct+d, (8)
wherein,
wherein P is 0 ,P 2 ,P 3 ,P 4 Each of the 4 control points of the incoming shader. a, b, c, d are constants defining spline curves through which the catamur-lomb spline passes P 2 ,P 3 Two points.
Then, the tangent line of the current knitting loop curve is calculated, and the mode of calculating the tangent vector is shown as a formula (10):
T yarn ＝b+2c×t+3d×t 2 (10)
wherein T is yarn Is the direction of motion of the spline under the TNB frame. Thus, three-dimensional modeling of the fabric is completed.
Aiming at the limitations of the current high-precision yarn simulation and fabric three-dimensional modeling, the invention provides a knitted fabric high-precision modeling method based on a TNB frame according to the microscopic geometry of the yarn and the flexible continuity of a coil structure. Yarn models with different twists and high-fidelity details can be rapidly simulated, and flexible continuity of the knitted fabric is realized through spline curves. The invention overcomes the defect of yarn detail caused by the traditional modeling mode and solves the problem that the knitted fabric lacks sense of reality in computer simulation.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic view showing the positioning of fiber coordinate points in a cross section of a yarn under a TNB framework according to an embodiment of the invention.
FIG. 3 is a schematic representation of a yarn of different twist according to an embodiment of the present invention, wherein (a) (b) (c) is a yarn of 3 different twist.
Fig. 4 is a schematic representation of a yarn with fibers spread into a wide ribbon in accordance with an embodiment of the present invention.
Fig. 5 is a schematic diagram of a simulation of a high-fidelity knitted fabric according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention can be implemented by a person skilled in the art by adopting a computer software technology.
With reference to fig. 1, the embodiment of the invention provides a high-precision modeling method for a knitted fabric based on a TNB frame, which specifically comprises the following steps:
step 1, calculating the center coordinates of the strands by using a TNB frame and the center coordinates of the yarns;
step 2, calculating the center coordinates of the fibers by using the TNB frame and the center coordinates of the strands;
step 3, calculating yarn twisting parameters through a spiral parameter equation;
step 4, expanding each fiber into a wide wire band;
step 5, connecting all coil-shaped value points of the fabric by using spline lines to obtain a three-dimensional model of the knitted fabric;
the processing procedure of each step is specifically described below by way of examples: examples the method according to the invention was tested on the basis of a model file of the knitted fabric.
In step 1, the example uses 49745 stitch value point coordinates in the knitted fabric model file as the center coordinates of the yarn spline, and calculates the yarn strand center coordinates by the TNB framing method. The specific method for calculating the center coordinate point of the strand from the center coordinate point of the yarn based on the TNB frame is as follows:
firstly, starting a shader for generating a yarn geometric model, transmitting a central coordinate point of the yarn into the shader for processing, and setting a subdivision level in the U, V direction in a tessellation control shader;
next, in the tessellation evaluation shader, a coordinate point of the center of the strand is calculated using a TNB framing method, the TNB framing method principle and the calculation method are shown in the formulas (1) to (2),
the coordinate calculation formula is used for calculating the coordinate,
wherein,
in formula (1), where d/ds is the derivative of the arc length, κ is the curvature of the curve and τ is the flexibility of the curve. The change rule of the curvature flexibility rate of the space curve is described in the TNB frame formula. Where T (Tangent vector of curve) represents Tangent vector of advancing direction, N (Normal vector of curve) represents Normal vector of path bending direction, and B (Binormal vector of curve) represents auxiliary Normal vector of tendency to twist out of this plane. C in formula (2) yarn Is the spatial coordinates of the center of the yarn,for the j-th strand center space coordinate, +.>Is formed by the center c of the yarn yarn To the center of the jth strand->Space vector, R ply For strand radius>For the initial polar angle of the strand, n ply N is the number of strands yarn Is the unit normal vector of the yarn, B yarn Unit auxiliary method for yarnVector. In the embodiment, the subdivision level in the U, V direction is set to 64, 63, respectively. n is n ply The value is 3. Finally, coordinate c yarn And->And summing to obtain the center coordinates of the strands in the space.
In step 2, fiber coordinates are calculated using the TNB frame method by microscopically observing the geometry of the strands, one strand typically consisting of tens to hundreds of micron diameter fibers. The concrete method for calculating the fiber coordinate point from the strand center coordinate point based on the TNB frame comprises the following steps:
first, in the activated shader that generates the yarn geometric model, the distribution of the fibers in each strand is processed by being transferred into the shader in the form of a one-dimensional texture, and the subdivision level in the direction of the set U, V in the tessellation control shader is kept consistent with that in step 1, and in the embodiment, the subdivision level in the direction of U, V is set to 64, 63, respectively.
Next, in the tessellation evaluation shader, coordinate points of the fibers are calculated using a TNB frame method, as shown in the formulas (3) and (4),
wherein,
wherein, c i In the form of the spatial coordinates of the fibers,for the j-th strand center space coordinate, Δc i Is centered by the j-th strandTo the ith fiber c i Space vector, R i For the distance θ of the ith fiber to the centerline of the strand i As the initial polar angle of the fiber,is the unit normal vector of the strand,>is the unit minor normal vector of the strand. e, e N And e B Is the scaling factor of ellipse, R min ，R max Representing the minimum radius and the maximum radius, respectively, of the fiber during migration, s is a parameter controlling the helical lead. In the embodiment, let θ i ＝2π/21，e N And e B Are respectively set to 1.0,2.0 and R min ，R max Set to 0.0,1.0, s to 0.5, respectively.
Finally, the coordinate c in the step 1 is calculated yarn And (3) withThe result of the summation is summed with deltac i And adding to obtain the spatial position of the ith fiber in the jth strand in the space. In real-time example, a schematic diagram of the positioning of fiber coordinate points in the cross section of the yarn under the TNB frame is shown in fig. 2.
In step 3, different twist yarns are simulated through a spiral parameter equation. The method for calculating the yarn twisting parameters is as follows:
firstly, setting the number of yarn strands and the number of fibers in a single strand in a tessellation calculation shader, wherein in the embodiment, the number of strands is 3, the number of fibers in the single strand is 21, and the principle of a parameter equation of a cylindrical spiral is shown in the following formula (5);
wherein x, y and z are European space coordinates, ω is the rotational angular velocity of the object about the axis, and v is the linear velocity of the object along the rotational axis.
Next, by modifying the ω parameter in the parameter equation, the yarn twist can be adjusted in combination with equation (2) in step 1. In the example, the ω parameters were modeled as described above for 3 different twist yarns, respectively, as shown in fig. 3.
In step 4, each fiber is expanded into a wide ribbon, and the method for expanding the fiber into the wide ribbon is as follows:
firstly, after the input type value points are processed by the tessellation calculation shader, the coordinates of the subdivided fibers in a local space are transferred into the geometric shader through built-in variables, and meanwhile, the set fiber widths are transferred in together.
The dots are then expanded in a geometry shader into bands of width in the viewing space as shown in equations (6) through (7):
wherein,
in Pos i,0 Representing the point P i Points of expansion along the direction of the secondary normal, pos i,1 Representing the point P i The point along the opposite direction of the minor normal, r, represents the width of the expansion, which is half the width of the fiber. Here, T, B, and N are three orthogonal vectors constituting the observation space, respectively, a tangential axis, a sub normal axis, and a normal axis. In an embodiment, r is set to 0.001. The resulting yarn was simulated according to the procedure described above, as shown in fig. 4. Finally, the ribbon generated by the geometry shader is rasterized, so far, high precision yarn modeling has been completed.
And 5, connecting all coil-shaped value points of the fabric by using spline lines to obtain a three-dimensional model of the knitted fabric. In the embodiment, 4 coil-shaped value point coordinates are taken from a model file of the knitted fabric each time and are input into a colorant, and the basic method is as follows:
first, in the tessellation computation shader, the center of the yarn is given by a Catmull-Rom spline (Catmull-Rom spline) defined by four control points, and the parametric equations of the spline curve are shown in equations (8) to (9):
p(t)＝at 3 +bt 2 +ct+d, (8)
wherein,
wherein P is 0 ,P 2 ,P 3 ,P 4 Each of the 4 control points of the incoming shader. a, b, c, d are constants defining spline curves through which the catamur-lomb spline passes P 2 ,P 3 Two points.
Then, the tangent line of the current knitting loop curve is calculated, and the mode of calculating the tangent vector is shown as a formula (10):
T yarn ＝b+2c×t+3d×t 2 (10)
wherein T is yarn Is the direction of motion of the spline under the TNB frame. Thus, three-dimensional modeling of the fabric is completed. In an embodiment, a simulation diagram of a high-fidelity knitted fabric is shown in fig. 5.
The specific embodiments described herein are offered by way of example only to illustrate the spirit of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions thereof without departing from the spirit of the invention or exceeding the scope of the invention as defined in the accompanying claims.
Claims (9)
1. The high-precision modeling method for the knitted fabric based on the TNB framework is characterized by comprising the following steps of:
step 1, taking the coordinates of a coil type value point in a model file of the knitted fabric as the center coordinates of a yarn spline, and calculating the center coordinates of the strand by using the TNB frame and the yarn center coordinates;
step 2, calculating the center coordinates of the fibers by using the TNB frame and the center coordinates of the strands;
step 3, calculating yarn twisting parameters through a spiral parameter equation;
step 4, expanding each fiber into a wide wire band;
and 5, connecting all coil-shaped value points of the fabric by using spline lines to obtain a three-dimensional model of the knitted fabric.
2. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 1, wherein the method comprises the following steps: the specific implementation method of the step 1 is as follows:
firstly, starting a shader for generating a yarn geometric model, transmitting a central coordinate point of the yarn into the shader for processing, and setting a subdivision level in the U, V direction in a tessellation control shader;
next, in the tessellation evaluation shader, a coordinate point of the center of the strand is calculated using a TNB framing method, the TNB framing method principle and the calculation method are shown in the formulas (1) to (2),
the coordinate calculation formula is used for calculating the coordinate,
wherein,
in the formula (1), d/ds is the differential of arc length, kappa is the curvature of the curve, tau is the bending rate of the curve, and the law of change of the bending rate of the curvature of the space curve is described in TNB frame formula, wherein T represents the unit tangent vector of the advancing direction, N represents the unit normal vector of the bending direction of the path, and B represents the curveA minor normal vector of the plane twist-out trend; c in formula (2) yarn Is the spatial coordinates of the center of the yarn,for the j-th strand center space coordinate, +.>Is formed by the center c of the yarn yarn To the center of the jth strand->Space vector, R ply For strand radius>For the initial polar angle of the strand, n ply N is the number of strands yarn Is the unit normal vector of the yarn, B yarn Is the unit auxiliary normal vector of the yarn;
finally, coordinate c yarn And (3) withAnd summing to obtain the center coordinates of the strands in the space.
3. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 2, wherein the method comprises the following steps: the specific implementation method of the step 2 is as follows:
firstly, in the enabled shader for generating the yarn geometric model, the distribution condition of the fibers in each strand is transmitted into the shader for processing in a one-dimensional texture mode, and the subdivision level in the U, V direction is set in the tessellation control shader;
next, in the tessellation evaluation shader, coordinate points of the fibers are calculated using a TNB frame method, as shown in the formulas (3) and (4),
wherein,
wherein, c i In the form of the spatial coordinates of the fibers,for the j-th strand center space coordinate, Δc i Is from the center of the j-th strand->To the ith fiber c i Space vector, R i For the distance θ of the ith fiber to the centerline of the strand i As the initial polar angle of the fiber,is the unit normal vector of the strand,>is the unit minor normal vector of the strand. e, e N And e B Is the scaling factor of ellipse, R min ，R max Respectively representing the minimum radius and the maximum radius of the fiber during migration, s being a parameter controlling the helical lead;
finally, the coordinate c in the step 1 is calculated yarn And (3) withThe result of the summation is summed with deltac i And adding to obtain the spatial position of the ith fiber in the jth strand in the space.
4. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 2, wherein the method comprises the following steps: in the step 3, the method for calculating the yarn twisting parameters through a spiral parameter equation is as follows:
firstly, setting the number of yarn strands and the number of fibers in a single strand in a tessellation calculation shader, wherein the principle of a parameter equation of a cylindrical spiral line is shown in the following formula (5);
wherein x, y and z are European space coordinates, ω is the rotational angular velocity of the object about the axis, and v is the linear velocity of the object along the direction of the rotational axis;
next, by modifying the ω parameter in the parameter equation, the yarn twist can be adjusted in combination with equation (2) in step 1.
5. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 1, wherein the method comprises the following steps: the method of expanding each fiber into a wide ribbon in step 4 is as follows:
firstly, after the input type value points are processed by a tessellation calculation shader, transmitting coordinates of subdivided fibers in a local space to the geometric shader through built-in variables, and simultaneously transmitting the set fiber widths together;
the dots are then expanded in a geometry shader into bands of width in the viewing space as shown in equations (6) through (7):
wherein,
in Pos i,0 Representing the point P i Points of expansion along the direction of the secondary normal, pos i,1 Representing the point P i Points extending in opposite directions of the minor normal, r representingThe expansion width is half of the fiber width, wherein T, B and N are three orthogonal vectors forming an observation space respectively and are tangential axis, auxiliary normal axis and normal axis respectively;
finally, the ribbon generated by the geometry shader is rasterized, so far, high precision yarn modeling has been completed.
6. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 1, wherein the method comprises the following steps: in the step 5, all coil-shaped value points of the fabric are connected by spline lines, and the method for obtaining the three-dimensional model of the knitted fabric is as follows:
first, in the tessellation computation shader, the center of the yarn is given by a Catmull-Rom spline (Catmull-Rom spline) defined by four control points, and the parametric equations of the spline curve are shown in equations (8) to (9):
p(t)＝at 3 +bt 2 +ct+d, (8)
wherein,
wherein P is 0 ,P 2 ,P 3 ,P 4 The 4 control points, a, b, c, d, respectively, of the incoming shader are constants defining spline curves through which the Cartesian-Rohm spline passes 2 ,P 3 Two points;
then, the tangent line of the current knitting loop curve is calculated, and the mode of calculating the tangent vector is shown as a formula (10):
T yarn ＝b+2c×t+3d×t 2 (10)
wherein T is yarn And (3) the motion direction of the spline curve under the TNB frame is used for completing three-dimensional modeling of the fabric.
7. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 2, wherein the method comprises the following steps: the subdivision level in the U, V direction is set to64，63，n ply The value is 3.
8. A method for modeling a knitted fabric with high precision based on a TNB framework according to claim 3, characterised in that: θ i ＝2π/21，e N And e B Are respectively set to 1.0,2.0 and R min ，R max Set to 0.0,1.0, s to 0.5, respectively.
9. The high-precision modeling method for the knitted fabric based on the TNB framework as claimed in claim 4, wherein the method comprises the following steps: the number of strands was 3 and the number of fibers in a single strand was 21.
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