我绝对喜欢数学(或者你们大多数人都会说’数学’！)但是我还没有达到我知道这个问题答案的水平.我有一个主圆,可以在显示屏上的任何x和y处有一个中心点.其他圆圈将随意在显示器周围移动,但在任何给定的渲染方法调用中,我不仅要渲染与主圆相交的圆,而且只渲染在主圆内可见的圆的线段.类比将是对现实生活对象的阴影,我只想绘制那个被“照亮”的对象的一部分.
我想最好用Java做这个,但如果你有一个原始的公式,将不胜感激.我想知道如何绘制形状并用Java填充它,我确定曲线上的折线必须有一些变化吗？
非常感谢
最佳答案
设A和B为2 intersection points(当没有或1个截取点时,你可以忽略它).
然后计算A和B之间circular line segment的长度.
有了这些信息,您应该能够使用Graphics' drawArc(...)方法绘制弧线(如果我没有弄错……).
编辑
好吧,你甚至不需要圆形线段的长度.我有线交叉代码,所以我围绕它构建了一个小GUI,你可以如何绘制/查看这些相交圆的ARC(代码中有一些注释)：
import javax.swing.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.geom.Arc2D;
/**
* @author: Bart Kiers
*/
public class GUI extends JFrame {
private GUI() {
super("Circle Intersection Demo");
initGUI();
}
private void initGUI() {
super.setSize(600,640);
super.setDefaultCloSEOperation(EXIT_ON_CLOSE);
super.setLayout(new BorderLayout(5,5));
final Grid grid = new Grid();
grid.addMouseMotionListener(new MouseMotionAdapter() {
@Override
public void mouseDragged(MouseEvent e) {
Point p = new Point(e.getX(),e.getY()).toCartesianPoint(grid.getWidth(),grid.getHeight());
grid.showDraggedCircle(p);
}
});
grid.addMouseListener(new MouseAdapter() {
@Override
public void mouseReleased(MouseEvent e) {
Point p = new Point(e.getX(),grid.getHeight());
grid.released(p);
}
@Override
public void mousePressed(MouseEvent e) {
Point p = new Point(e.getX(),grid.getHeight());
grid.pressed(p);
}
});
super.add(grid,BorderLayout.CENTER);
super.setVisible(true);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(new Runnable() {
@Override
public void run() {
new GUI();
}
});
}
private static class Grid extends JPanel {
private Circle c1 = null;
private Circle c2 = null;
private Point screenClick = null;
private Point currentPosition = null;
public void released(Point p) {
if (c1 == null || c2 != null) {
c1 = new Circle(screenClick,screenClick.distance(p));
c2 = null;
} else {
c2 = new Circle(screenClick,screenClick.distance(p));
}
screenClick = null;
repaint();
}
public void pressed(Point p) {
if(c1 != null && c2 != null) {
c1 = null;
c2 = null;
}
screenClick = p;
repaint();
}
@Override
public void paintComponent(Graphics g) {
Graphics2D g2d = (Graphics2D) g;
g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING,RenderingHints.VALUE_ANTIALIAS_ON);
g2d.setColor(Color.WHITE);
g2d.fillRect(0,super.getWidth(),super.getHeight());
final int W = super.getWidth();
final int H = super.getHeight();
g2d.setColor(Color.LIGHT_GRAY);
g2d.drawLine(0,H / 2,W,H / 2); // x-axis
g2d.drawLine(W / 2,W / 2,H); // y-axis
if (c1 != null) {
g2d.setColor(Color.RED);
c1.drawOn(g2d,H);
}
if (c2 != null) {
g2d.setColor(Color.ORANGE);
c2.drawOn(g2d,H);
}
if (screenClick != null && currentPosition != null) {
g2d.setColor(Color.DARK_GRAY);
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER,0.5f));
Circle temp = new Circle(screenClick,screenClick.distance(currentPosition));
temp.drawOn(g2d,H);
currentPosition = null;
}
if (c1 != null && c2 != null) {
g2d.setColor(Color.BLUE);
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER,0.4f));
Point[] ips = c1.intersections(c2);
for (Point ip : ips) {
ip.drawOn(g,H);
}
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER,0.2f));
if (ips.length == 2) {
g2d.setStroke(new BasicStroke(10.0f));
c1.highlightArc(g2d,ips[0],ips[1],H);
}
}
g2d.dispose();
}
public void showDraggedCircle(Point p) {
currentPosition = p;
repaint();
}
}
private static class Circle {
public final Point center;
public final double radius;
public Circle(Point center,double radius) {
this.center = center;
this.radius = radius;
}
public void drawOn(Graphics g,int width,int height) {
// translate Cartesian(x,y) to Screen(x,y)
Point screenP = center.toScreenPoint(width,height);
int r = (int) Math.rint(radius);
g.drawOval((int) screenP.x - r,(int) screenP.y - r,r + r,r + r);
// draw the center
Point screenCenter = center.toScreenPoint(width,height);
r = 4;
g.drawOval((int) screenCenter.x - r,(int) screenCenter.y - r,r + r);
}
public void highlightArc(Graphics2D g2d,Point p1,Point p2,int height) {
double a = center.degrees(p1);
double b = center.degrees(p2);
// translate Cartesian(x,height);
int r = (int) Math.rint(radius);
// find the point to start drawing our arc
double start = Math.abs(a - b) < 180 ? Math.min(a,b) : Math.max(a,b);
// find the minimum angle to go from `start`-angle to the other angle
double extent = Math.abs(a - b) < 180 ? Math.abs(a - b) : 360 - Math.abs(a - b);
// draw the arc
g2d.draw(new Arc2D.Double((int) screenP.x - r,start,extent,Arc2D.OPEN));
}
public Point[] intersections(Circle that) {
// see: http://mathworld.wolfram.com/Circle-CircleIntersection.html
double d = this.center.distance(that.center);
double d1 = ((this.radius * this.radius) - (that.radius * that.radius) + (d * d)) / (2 * d);
double h = Math.sqrt((this.radius * this.radius) - (d1 * d1));
double x3 = this.center.x + (d1 * (that.center.x - this.center.x)) / d;
double y3 = this.center.y + (d1 * (that.center.y - this.center.y)) / d;
double x4_i = x3 + (h * (that.center.y - this.center.y)) / d;
double y4_i = y3 - (h * (that.center.x - this.center.x)) / d;
double x4_ii = x3 - (h * (that.center.y - this.center.y)) / d;
double y4_ii = y3 + (h * (that.center.x - this.center.x)) / d;
if (Double.isNaN(x4_i)) {
// no intersections
return new Point[0];
}
// create the intersection points
Point i1 = new Point(x4_i,y4_i);
Point i2 = new Point(x4_ii,y4_ii);
if (i1.distance(i2) < 0.0000000001) {
// i1 and i2 are (more or less) the same: a single intersection
return new Point[]{i1};
}
// two unique intersections
return new Point[]{i1,i2};
}
@Override
public String toString() {
return String.format("{center=%s,radius=%.2f}",center,radius);
}
}
private static class Point {
public final double x;
public final double y;
public Point(double x,double y) {
this.x = x;
this.y = y;
}
public double degrees(Point that) {
double deg = Math.toDegrees(Math.atan2(that.y - this.y,that.x - this.x));
return deg < 0.0 ? deg + 360 : deg;
}
public double distance(Point that) {
double dX = this.x - that.x;
double dY = this.y - that.y;
return Math.sqrt(dX * dX + dY * dY);
}
public void drawOn(Graphics g,y)
Point screenP = toScreenPoint(width,height);
int r = 7;
g.fillOval((int) screenP.x - r,r + r);
}
public Point toCartesianPoint(int width,int height) {
double xCart = x - (width / 2);
double yCart = -(y - (height / 2));
return new Point(xCart,yCart);
}
public Point toScreenPoint(int width,int height) {
double screenX = x + (width / 2);
double screenY = -(y - (height / 2));
return new Point(screenX,screenY);
}
@Override
public String toString() {
return String.format("(%.2f,%.2f)",x,y);
}
}
}
如果您启动上面的GUI,然后在文本框中键入100 0 130 -80 55 180并点击return,您将看到以下内容：…
更改了代码,以便通过按下并拖动鼠标来绘制圆圈.截图：
