1999
DOI: 10.1177/004051759906900108
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A Three-Dimensional Analysis of Specular Reflection from Single-Jersey Knitted Fabrics

Abstract: This paper presents a mathematical model for calculating specular reflection of sin gle-jersey knitted fabrics using a three-dimensional analysis. A computer simulation program based on the model is developed to generate goniophotometric curves using Cartesian coordinates and Euler angles derived from the geometry of a knitted loop. Two correction factors are introduced by taking into consideration the sensor and sam ple geometry. The theoretical work is verified with a black monofilament yam with nine differe… Show more

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Cited by 10 publications
(5 citation statements)
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“…The existing mathematical models are classified into light fluxes models [4,5,6], fibers pileup models [7,8], fibers pileup-pores models [9,10] and ray trace models [11,12]. Among which, the two fluxes Kubelka-Munk model [4] has been most widely used, especially in the field of color technology.…”
Section: Classifying the Existing Modelsmentioning
confidence: 99%
“…The existing mathematical models are classified into light fluxes models [4,5,6], fibers pileup models [7,8], fibers pileup-pores models [9,10] and ray trace models [11,12]. Among which, the two fluxes Kubelka-Munk model [4] has been most widely used, especially in the field of color technology.…”
Section: Classifying the Existing Modelsmentioning
confidence: 99%
“…We will use the theory developed in our previous paper [ 11 ] for predicting the goniophotometric curves for knitted fabrics made from monofilament yarns to simulate the curves in order to investigate the effects of fabric parameters. The relative intensity is calculated as the amount of light reflected per unit area of fabrics, which has been projected by the incident light of unity intensity at a point p~:…”
Section: Theoretical Monofilament Yarnmentioning
confidence: 99%
“…The fiber cross section can be derived in the similar manner, and described as , where c and d are the major and minor axes of the fiber cross section, respectively; ym and zm are the coordinates of the center of the fiber; and a is the gradient angle of a normal line on the center point of the fiber, expressed as The angle a.,,, which is a derivative of the fiber cross section with respect to y, is where and From Equation 5, we use a mathematical treatment similar to that for monofilament yarn [ 11 ] to calculate the reflected angle and relative intensity of light. ' Calculation Parameters .…”
Section: Vious Paper Wasmentioning
confidence: 99%
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“…[1][2][3] These works focused on the dye/ light interaction, taking into account independent variables, such as the coefficient of dye absorption, refractive indexes of the fibers, the effect of color on the geometry of the fabric and yarn and the distribution of the dye within the fiber. 4,5 Theoretical models have been developed and expanded to apply to yarn and fabric, 6,7 taking into consideration the factors of dye concentration, the ratio of refractive indexes, 8,9 fiber fineness, [10][11][12] the structure of the textile substrate [13][14][15][16] and dye distribution. 17,18 However, the textile/light interaction needs to be further studied for enhancing the UV protection of the textile.…”
mentioning
confidence: 99%