使用递归绘制树
我正在尝试使用递归绘制一棵树。 树需要看起来像这样：
我应该怎么做的简短总结：
length和宽度的width 以下是我如何解决问题。 我想画出树干，左枝和右枝。 我设法做到这一点，具有以下功能：
public void drawTree(double length, double min_length, double width, double alpha) {
//Draws the trunk of the tree
StdDraw.setPenRadius(width);
StdDraw.line(250, 150, 250, 150+length);
//Left branch
double hypotenuse = (3.0/4.0)*length;
double opposite = Math.sin(alpha) * hypotenuse;
double adjacent = Math.sqrt(Math.pow(hypotenuse, 2)-Math.pow(opposite, 2));
StdDraw.setPenRadius(width*3.0/4.0);
StdDraw.line(250,150+length,250-adjacent,150+length+opposite);
//Right branch
double hypotenuse2 = (2.0/3.0)*length;
double opposite2 = Math.sin(alpha) * hypotenuse2;
double adjacent2 = Math.sqrt(Math.pow(hypotenuse2, 2)-Math.pow(opposite2, 2));
StdDraw.setPenRadius(width*1.0/2.0);
StdDraw.line(250,150+length,250+adjacent2,150+length+opposite2);
}
这是输出，它正如我所希望的那样：
我认为其余的会很容易，但在过去的3个小时里我没有取得任何进展：/。 我在if语句中包含了停止条件。 但是我对递归部分没有想法。 我试过这个：
if (length > min_length) {
//Left branch
double hypotenuse = (3.0/4.0)*length;
double opposite = Math.sin(alpha) * hypotenuse;
double adjacent = Math.sqrt(Math.pow(hypotenuse, 2)-Math.pow(opposite, 2));
StdDraw.setPenRadius(width*3.0/4.0);
StdDraw.line(250,150+length,250-adjacent,150+length+opposite);
//Right branch
double hypotenuse2 = (2.0/3.0)*length;
double opposite2 = Math.sin(alpha) * hypotenuse2;
double adjacent2 = Math.sqrt(Math.pow(hypotenuse2, 2)-Math.pow(opposite2, 2));
StdDraw.setPenRadius(width*1.0/2.0);
StdDraw.line(250,150+length,250+adjacent2,150+length+opposite2);
//My first attempt
drawTree(hypotenuse*hypotenuse, min_length, width, alpha);
drawTree(hypotenuse2*hypotenuse2, min_length, width, alpha);
//My second attempt
drawTree(hypotenuse, min_length, width, alpha);
drawTree(hypotenuse2, min_length, width, alpha);
}
我理解简单的递归，比如因式分解，回文等等，但是我被困在这一个，我会很感激任何帮助。
正如在评论和当前答案中已经指出的那样，使drawTree方法不drawTree树的哪一部分当前被绘制是至关重要的。
这种方法不能使用绝对坐标。 你必须跟踪你现在的位置。 例如，可以通过将Point2D传递给描述当前树部分起点的递归方法来完成此操作。
您甚至不需要显式代码来绘制分支：请注意， 单个行已经是一棵树。 这些分支就是“小树”：它们又是单行的 ，但长度和宽度不同。
（和前一棵树相比有一定的角度，你没有提到这个，但根据屏幕截图，角度似乎是Math.PI / 5 ）
import java.awt.BasicStroke;
import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.GridLayout;
import java.awt.RenderingHints;
import java.awt.geom.Line2D;
import java.awt.geom.Point2D;
import java.util.function.DoubleConsumer;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JSlider;
import javax.swing.SwingUtilities;
import javax.swing.event.ChangeEvent;
import javax.swing.event.ChangeListener;
public class RecursiveTreeDrawing
{
public static void main(String[] args)
{
SwingUtilities.invokeLater(new Runnable()
{
@Override
public void run()
{
createAndShowGUI();
}
});
}
private static void createAndShowGUI()
{
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.getContentPane().setLayout(new BorderLayout());
RecursiveTreeDrawingPanel p = new RecursiveTreeDrawingPanel();
p.setPreferredSize(new Dimension(500,500));
f.getContentPane().add(p, BorderLayout.CENTER);
JPanel c = new JPanel(new GridLayout(0,1));
c.add(createControl("left length", 0, 0.9,
d -> p.setLeftLengthFactor(d)));
c.add(createControl("left width", 0, 0.9,
d -> p.setLeftWidthFactor(d)));
c.add(createControl("left angle", 0, Math.PI,
d -> p.setLeftAngleDelta(d)));
c.add(createControl("right length", 0, 0.9,
d -> p.setRightLengthFactor(d)));
c.add(createControl("right width", 0, 0.9,
d -> p.setRightWidthFactor(d)));
c.add(createControl("right angle", -Math.PI, 0,
d -> p.setRightAngleDelta(d)));
f.getContentPane().add(c, BorderLayout.SOUTH);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
}
private static JPanel createControl(
String name, double min, double max, DoubleConsumer doubleConsumer)
{
JPanel p = new JPanel(new GridLayout(1,0));
p.add(new JLabel(name));
JSlider slider = new JSlider(0, 100, 0);
slider.addChangeListener(new ChangeListener()
{
@Override
public void stateChanged(ChangeEvent e)
{
int value = slider.getValue();
double v = value / 100.0;
double d = min + v * (max - min);
doubleConsumer.accept(d);
}
});
p.add(slider);
return p;
}
}
class RecursiveTreeDrawingPanel extends JPanel
{
private double leftLengthFactor = 3.0 / 4.0;
private double leftWidthFactor = 3.0 / 4.0;
private double leftAngleDelta = Math.PI / 5.0;
private double rightLengthFactor = 2.0 / 3.0;
private double rightWidthFactor = 1.0 / 2.0;
private double rightAngleDelta = - Math.PI / 5.0;
@Override
protected void paintComponent(Graphics gr)
{
super.paintComponent(gr);
Graphics2D g = (Graphics2D)gr;
g.setColor(Color.BLACK);
g.fillRect(0,0,getWidth(),getHeight());
g.setRenderingHint(
RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
Point2D start = new Point2D.Double(
getWidth() * 0.5,
getHeight() * 0.7);
g.setColor(Color.GRAY);
drawTree(g, start, 100.0, 2.0, 10.0, 0);
}
private void drawTree(Graphics2D g,
Point2D start, double length, double minLength,
double width, double alpha)
{
if (length < minLength)
{
return;
}
g.setStroke(new BasicStroke((float)width,
BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
Point2D end = new Point2D.Double(
start.getX() + Math.sin(alpha + Math.PI) * length,
start.getY() + Math.cos(alpha + Math.PI) * length);
g.draw(new Line2D.Double(start, end));
drawTree(g, end, length * leftLengthFactor, minLength,
width * leftWidthFactor, alpha + leftAngleDelta);
drawTree(g, end, length * rightLengthFactor, minLength,
width * rightWidthFactor, alpha + rightAngleDelta);
}
public void setLeftLengthFactor(double leftLengthFactor)
{
this.leftLengthFactor = leftLengthFactor;
repaint();
}
public void setLeftWidthFactor(double leftWidthFactor)
{
this.leftWidthFactor = leftWidthFactor;
repaint();
}
public void setLeftAngleDelta(double leftAngleDelta)
{
this.leftAngleDelta = leftAngleDelta;
repaint();
}
public void setRightLengthFactor(double rightLengthFactor)
{
this.rightLengthFactor = rightLengthFactor;
repaint();
}
public void setRightWidthFactor(double rightWidthFactor)
{
this.rightWidthFactor = rightWidthFactor;
repaint();
}
public void setRightAngleDelta(double rightAngleDelta)
{
this.rightAngleDelta = rightAngleDelta;
repaint();
}
}
你的drawTree（）太复杂了。 称它为drawTrunk，然后画出树的树干。 然后创建一个drawTree例程，如下所示：
drawTree(basePoint, length, width, angle)
if length > min_length
drawTrunk(length, width, angle)
newBasePoint = top of trunk
drawTree(newBasePoint, 3/4. * length, 3/4. * width, angle + 45)
drawTree(newBasePoint, 2/3. * length, 2/3. * width, angle - 45)