我的数学不好.
我在2D中有2个点,A(x1,y1)和B(x2,y2).
我需要创建一个从R点(半径)弯曲的A点到B点的虚拟路径,然后返回一个描述这个弯曲路径的点数组,而不是每个D(距离)彼此之间的距离.
private ArrayList<PointF> generateCurve(PointF pFrom,PointF pTo,float pRadius,float pMinDistance){
ArrayList<PointF> pOutPut = new ArrayList<PointF>();
// ...generate result to pOutPut
return pOutPut;
}
这该怎么做 ？
解决方法
我没有放弃,而且我已经开始工作了几个小时.这是结果：
我创建了一个方法,您可以指定是否需要点之间最长的最长弧.
generateCurve(pFrom,pTo,100f,7f,false,false);
generateCurve(pFrom,true,true);
generateCurve(pFrom,true);
正如你所看到的,它就像一个魅力.这是代码：
package curve;
import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.geom.Ellipse2D;
import java.awt.geom.Line2D;
import java.awt.geom.Rectangle2D;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import javax.imageio.ImageIO;
/**
*
* @author martijn
*/
public class Main
{
/**
* @param args the command line arguments
*/
public static void main(String[] args) throws IOException
{
PointF pFrom = new PointF(-10f,30.0f);
PointF pTo = new PointF(-100f,0.0f);
List<PointF> points = generateCurve(pFrom,true);
System.out.println(points);
// Calculate the bounds of the curve
Rectangle2D.Float bounds = new Rectangle2D.Float(points.get(0).x,points.get(0).y,0);
for (int i = 1; i < points.size(); ++i) {
bounds.add(points.get(i).x,points.get(i).y);
}
bounds.add(pFrom.x,pFrom.y);
bounds.add(pTo.x,pTo.y);
BufferedImage img = new BufferedImage((int) (bounds.width - bounds.x + 50),(int) (bounds.height - bounds.y + 50),BufferedImage.TYPE_4BYTE_ABGR_PRE);
Graphics2D g = img.createGraphics();
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,RenderingHints.VALUE_ANTIALIAS_ON);
g.translate(25.0f - bounds.getX(),25.0f - bounds.getY());
g.setStroke(new BasicStroke(1.0f));
g.setColor(Color.DARK_GRAY);
g.drawLine(-1000,1000,0);
g.drawLine(0,-1000,1000);
g.setColor(Color.RED);
for (int i = 0; i < points.size(); ++i) {
if (i > 0) {
Line2D.Float f = new Line2D.Float(points.get(i - 1).x,points.get(i - 1).y,points.get(i).x,points.get(i).y);
System.out.println("Dist : " + f.getP1().distance(f.getP2()));
// g.draw(f);
}
g.fill(new Ellipse2D.Float(points.get(i).x - 0.8f,points.get(i).y - 0.8f,1.6f,1.6f));
}
g.setColor(Color.BLUE);
g.fill(new Ellipse2D.Float(pFrom.x - 1,pFrom.y - 1,3,3));
g.fill(new Ellipse2D.Float(pTo.x - 1,pTo.y - 1,3));
g.dispose();
ImageIO.write(img,"PNG",new File("result.png"));
}
static class PointF
{
public float x,y;
public PointF(float x,float y)
{
this.x = x;
this.y = y;
}
@Override
public String toString()
{
return "(" + x + "," + y + ")";
}
}
private static List<PointF> generateCurve(PointF pFrom,float pMinDistance,boolean shortest,boolean side)
{
List<PointF> pOutPut = new ArrayList<PointF>();
// Calculate the middle of the two given points.
PointF mPoint = new PointF(pFrom.x + pTo.x,pFrom.y + pTo.y);
mPoint.x /= 2.0f;
mPoint.y /= 2.0f;
System.out.println("Middle Between From and To = " + mPoint);
// Calculate the distance between the two points
float xDiff = pTo.x - pFrom.x;
float yDiff = pTo.y - pFrom.y;
float distance = (float) Math.sqrt(xDiff * xDiff + yDiff * yDiff);
System.out.println("Distance between From and To = " + distance);
if (pRadius * 2.0f < distance) {
throw new IllegalArgumentException("The radius is too small! The given points wont fall on the circle.");
}
// Calculate the middle of the expected curve.
float factor = (float) Math.sqrt((pRadius * pRadius) / ((pTo.x - pFrom.x) * (pTo.x - pFrom.x) + (pTo.y - pFrom.y) * (pTo.y - pFrom.y)) - 0.25f);
PointF circleMiddlePoint = new PointF(0,0);
if (side) {
circleMiddlePoint.x = 0.5f * (pFrom.x + pTo.x) + factor * (pTo.y - pFrom.y);
circleMiddlePoint.y = 0.5f * (pFrom.y + pTo.y) + factor * (pFrom.x - pTo.x);
} else {
circleMiddlePoint.x = 0.5f * (pFrom.x + pTo.x) - factor * (pTo.y - pFrom.y);
circleMiddlePoint.y = 0.5f * (pFrom.y + pTo.y) - factor * (pFrom.x - pTo.x);
}
System.out.println("Middle = " + circleMiddlePoint);
// Calculate the two reference angles
float angle1 = (float) Math.atan2(pFrom.y - circleMiddlePoint.y,pFrom.x - circleMiddlePoint.x);
float angle2 = (float) Math.atan2(pTo.y - circleMiddlePoint.y,pTo.x - circleMiddlePoint.x);
// Calculate the step.
float step = pMinDistance / pRadius;
System.out.println("Step = " + step);
// Swap them if needed
if (angle1 > angle2) {
float temp = angle1;
angle1 = angle2;
angle2 = temp;
}
boolean flipped = false;
if (!shortest) {
if (angle2 - angle1 < Math.PI) {
float temp = angle1;
angle1 = angle2;
angle2 = temp;
angle2 += Math.PI * 2.0f;
flipped = true;
}
}
for (float f = angle1; f < angle2; f += step) {
PointF p = new PointF((float) Math.cos(f) * pRadius + circleMiddlePoint.x,(float) Math.sin(f) * pRadius + circleMiddlePoint.y);
pOutPut.add(p);
}
if (flipped ^ side) {
pOutPut.add(pFrom);
} else {
pOutPut.add(pTo);
}
return pOutPut;
}
}
请享用！
PS：我创建了两个关于数学的问题来解决你的问题：
> Analytic Geometry: Point coordinates,same distance from two points.
> Trigonometry: Solve (1−cosα)2+sin2α=d2 for α
