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Koch曲线

2024-08-10 10:25:46   274人阅读

Koch曲线是一种分形，完整的Koch曲线像雪花，维基百科上记录Koch曲线最早出现在海里格·冯·科赫的论文《关于一条连续而无切线，可由初等几何构作的曲线》中，它的定义如下，给定线段AB，科赫曲线可以由以下步骤生成：

  • 将线段分成三等份（AC,CD,DB）
  • 以CD为底，向外（内外随意）画一个等边三角形DMC
  • 将线段CD移去
  • 分别对AC,CM,MD,DB重复1~3

完整的Koch雪花是由一个等边三角形分别按照以上步骤得到的分形曲线。

一些关于Koch曲线的介绍：

http://en.wikipedia.org/wiki/Koch_snowflake

http://www.matrix67.com/blog/archives/243

用Java实现Koch曲线的代码Koch.java

package com.elvalad;import java.awt.*;/** * Created by elvalad on 2014/12/28. */public class Koch {    private double x1;    private double y1;    private double x2;    private double y2;    private Color color = new Color(43, 77, 219);    /**     * Koch曲线构造函数     * @param x1 Koch曲线起始点横坐标     * @param y1 Koch曲线起始点纵坐标     * @param x2 Koch曲线终止点横坐标     * @param y2 Koch曲线终止点纵坐标     * @param color Koch曲线的颜色     */    public Koch(double x1, double y1, double x2, double y2, Color color) {        this.x1 = x1;        this.y1 = y1;        this.x2 = x2;        this.y2 = y2;        this.color = color;    }    /**     * @param g     */    public void draw(Graphics g) {        g.setColor(this.color);        this.drawShape(g, this.x1, this.y1, this.x2, this.y2);    }    /**     *     * @param g     * @param x1 Koch曲线起始点横坐标     * @param y1 Koch曲线起始点纵坐标     * @param x2 Koch曲线终止点横坐标     * @param y2 Koch曲线终止点纵坐标     */    private void drawShape(Graphics g, double x1, double y1, double x2, double y2) {        double c = 1.0;        double x3 = 0;        double y3 = 0;        double x4 = 0;        double y4 = 0;        double x5 = 0;        double y5 = 0;        double l = 0;        double alpha = 0;        g.setColor(this.color);        if (((x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y2)) < c) {            g.drawLine((int)x1, 500 - (int)y1, (int)x2, 500 - (int)y2);        } else {            x3 = x1 + (x2 - x1) / 3;            y3 = y1 + (y2 - y1) / 3;            x4 = x2 - (x2 - x1) / 3;            y4 = y2 - (y2 - y1) / 3;            l = Math.sqrt(((y2 - y1)*(y2 - y1) + (x2 - x1)*(x2 - x1))) / 3;            alpha = Math.atan((y4 - y3) / (x4 - x3));            if ((alpha >= 0) && (x4 - x3) < 0 ||                    (alpha <= 0) && (x4 - x3 < 0)) {                alpha = alpha + Math.PI;            }            x5 = x3 + Math.cos(alpha + Math.PI / 3)*l;            y5 = y3 + Math.sin(alpha + Math.PI / 3)*l;            drawShape(g, x1, y1, x3, y3);            drawShape(g, x3, y3, x5, y5);            drawShape(g, x5, y5, x4, y4);            drawShape(g, x4, y4, x2, y2);        }    }}

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Koch曲线


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