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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:
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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原文地址:http://www.cnblogs.com/elvalad/p/4190736.html