﻿ 服装CAD制版系统中曲线绘制自动化方法研究 Research on Automatic Method of Curves Drawing in Garment CAD Pattern System

Computer Science and Application
Vol. 09  No. 01 ( 2019 ), Article ID: 28400 , 10 pages
10.12677/CSA.2019.91002

Research on Automatic Method of Curves Drawing in Garment CAD Pattern System

Yifan Gu, Youqun Shi

Computer Science Technology College, Donghua University, Shanghai

Received: Dec. 17th, 2018; accepted: Jan. 2nd, 2019; published: Jan. 10th, 2019

ABSTRACT

In the garment CAD pattern system, the garment structure curve was manually drawn by the pattern maker and adjusted by his experience and design principles. Each curve took several operations to generate. Bézier curves and NURBS curves based curve drawing methods need to calculate control points. These control points were not on the curve and were computationally complex. In order to make curve drawing not depend on the manual operations of the pattern maker, by studying the drawing process of garment structure curve, an automatic method of curve drawing based on control points of Bézier curves was proposed. The method only relies on several fixed points of the curve and can calculate the control points of the curve automatically; the fixed points are obtained through the design principle of the garment structure curve. Thus, garment structure curve drawing automation is realized; the method can be used for garment CAD pattern system based on parameters design to improve the efficiency of garment patterning.

Keywords:Bézier Curves, Control Points, Garment CAD, Garment Patterning

1. 引言

2. 相关工作

3. 服装结构曲线拟合

3.1. 服装结构曲线特征

Figure 1. Back plate of the shirt

Figure 2. Back plate of the shirt layout with pattern process

Figure 3. Collar arc layout with pattern process

3.2. 服装版型结构常用曲线

3.2.1. 贝塞尔曲线 [5]

(a) C型曲线 (b) S型曲线

Figure 4. Shape of Bézier curve

3.2.2. NURBS曲线 [5]

4. 贝塞尔曲线的控制点计算方法

$B\left(t\right)={\left(1-t\right)}^{3}{B}_{0}+3t{\left(1-t\right)}^{2}{B}_{1}+3{t}^{2}\left(1-t\right){B}_{2}+{t}^{3}{B}_{3},0\le t\le 1$ (1)

4.1. 基于梯度下降法的控制点计算方法

${x}_{0}^{n+1}={x}_{0}^{n}-\alpha \nabla f\left({x}_{0}^{n}\right),n\ge 0$ (2)

${X}_{B}\left(t\right)={\left(1-t\right)}^{3}{x}_{B0}+3t{\left(1-t\right)}^{2}{x}_{B1}+3{t}^{2}\left(1-t\right){x}_{B2}+{t}^{3}{x}_{B3},0\le t\le 1$ (3)

$\nabla {X}_{B}\left({x}_{B1}\right)=\frac{\partial {X}_{B}\left(t\right)}{\partial {x}_{B1}}=\sum _{i=0}^{100}\left({x}_{i}-{x}_{bi}\right)3t{\left(1-t\right)}^{2}$ (4)

 (5)

4.2. 基于解方程组法的控制点计算方法

1) 传统方法

$\left\{\begin{array}{l}{Q}_{0}={B}_{0}\\ \cdots \\ {Q}_{i}={C}_{n}^{0}{\left(1-{t}_{i}\right)}^{n}{B}_{0}+{C}_{n}^{1}\left({t}_{i}\right){\left(1-{t}_{i}\right)}^{n-1}{B}_{1}+\cdots +{C}_{n}^{n-1}{\left({t}_{i}\right)}^{n-1}\left(1-{t}_{i}\right){B}_{n-1}+{C}_{n}^{n}{\left({t}_{i}\right)}^{n}{B}_{n}\\ \cdots \\ {Q}_{n}={B}_{n}\end{array}$ (6)

2) 改进的解方程组法

$\left\{\begin{array}{l}{Q}_{0}{}^{\prime }={B}_{0}\\ \cdots \\ {Q}_{i}{}^{\prime }={C}_{n}^{0}{\left(1-\frac{i}{n}\right)}^{n}{B}_{0}+{C}_{n}^{1}\left(\frac{i}{n}\right){\left(1-\frac{i}{n}\right)}^{n-1}{B}_{1}+\cdots +{C}_{n}^{n-1}{\left(\frac{i}{n}\right)}^{n-1}\left(1-\frac{i}{n}\right){B}_{n-1}+{C}_{n}^{n}{\left(\frac{i}{n}\right)}^{n}{B}_{n}\\ \cdots \\ {Q}_{n}{}^{\prime }={B}_{n}\end{array}$ (7)

 (8)

5. 曲线绘制实验

Figure 5. Linear fitted curves

5.1. 贝塞尔曲线的控制点计算和绘制

Table 1. Calculation results of Bézier curve control point

(a) 曲线编号1 (b) 曲线编号2 (c) 曲线编号3 (d) 曲线编号4

Figure 6. Linear fitted curves

Figure 7. Linear fitted curves

5.2. 曲线的误差分析

Table 2. Error analysis table

5.3. 曲线绘制自动化的应用

Table 3. Parameters of shirt back plate

Figure 8. Linear fitted curves

6. 结论

Research on Automatic Method of Curves Drawing in Garment CAD Pattern System[J]. 计算机科学与应用, 2019, 09(01): 9-18. https://doi.org/10.12677/CSA.2019.91002

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