我有这个极性功能:
r = A / log(B * tan(t / 2 * N)
其中A,B,N是任意参数,t是极坐标系中的角度θ。
A=8, B=0.5, N=4
如何将此函数绘制到笛卡尔坐标网格上,以便得到如上图所示的图像?
谢谢
答案 0 :(得分:2)
不完整的伪代码样本,但你应该明白这个想法:
for t in [0, 2pi):
r = /* whatever you got depending on t */
x = r * cos(t)
y = r * sin(t)
draw line to (x,y)
答案 1 :(得分:1)
好的,我明白了。一些示例Java代码:
import static java.lang.Math.*;
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.image.BufferedImage;
import javax.swing.ImageIcon;
import javax.swing.JFrame;
import javax.swing.JLabel;
public class TestPolarPlot {
public static void main(String[] args) {
final int width = 512;
final int height = 512;
BufferedImage img = new BufferedImage(width, height, BufferedImage.TYPE_4BYTE_ABGR);
Graphics g = img.getGraphics();
g.setColor(Color.black);
g.fillRect(0, 0, width, height);
g.setColor(Color.white);
final double A = 8;
final double B = 0.5;
final double N = 4;
final double scale = 128;
final double zoom = 50;
final double step = 1 / scale;
Point last = null;
final Point origin = new Point(width/2, height/2);
for (double t = 0; t <= 2*PI; t+= step) {
final double r = zoom * polarFunction(t, A, B, N);
final int x = (int)round(r * cos(t));
final int y = (int)round(r * sin(t));
Point next = new Point(x, y);
if (last != null) {
g.drawLine(origin.x + last.x, origin.y + last.y,
origin.x + next.x, origin.y + next.y);
}
last = next;
}
JFrame frame = new JFrame("testit");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.getContentPane().add(new JLabel(new ImageIcon(img)));
frame.pack();
frame.setLocationRelativeTo(null);
frame.setVisible(true);
}
public static double polarFunction(double t, double A, double B, double N) {
return A / log(B * tan(t / (2 * N)));
}
}
我没想到这会创建平滑的曲线,但效果非常好。