Java 如何在2D中的两个点之间创建一条曲线，并获取每d距离生成该曲线的返回点？
我的数学不好 我有两个点，Java 如何在2D中的两个点之间创建一条曲线，并获取每d距离生成该曲线的返回点？,java,math,2d,java-2d,Java,Math,2d,Java 2d,我的数学不好 我有两个点，A（x1，y1）和B（x2，y2）在2D中 我需要创建一个从点a到B在R（半径）处弯曲的虚拟路径，然后返回一个描述该弯曲路径的点数组，这些点之间可能不是每D（距离）一个点 在Java中，我需要这样一种方法： private ArrayList<PointF> generateCurve(PointF pFrom,PointF pTo,float pRadius,float pMinDistance){ ArrayList<PointF>
A（x1，y1）B（x2，y2）aBprivate ArrayList<PointF> generateCurve(PointF pFrom,PointF pTo,float pRadius,float pMinDistance){
ArrayList<PointF> pOutPut = new ArrayList<PointF>();
// ...generate result to pOutPut
return pOutPut;
}
private ArrayList generateCurve（PointF pFrom、PointF pTo、float pRadius、float pMinDistance）{
ArrayList pOutPut=新的ArrayList（）；
//…生成要输出的结果
回灌；
}
private static double GetAngle(Point2D x, Point2D o, double R){
double cosa = (x.getX()-o.getX())/R;
double sina = (x.getY()-o.getY())/R;
double angle = Math.acos(cosa);
return Math.sin(angle)*sina >= 0 ? angle : 2*Math.PI - angle;
}
private static ArrayList<Point2D> generateCurve(Point2D pFrom,Point2D pTo,float pRadius,float pMinDistance){
ArrayList<Point2D> pOutPut = new ArrayList<Point2D>();
double dist = pFrom.distance(pTo);
double h = Math.sqrt(pRadius * pRadius - (dist * dist / 4.0));
double angleStep = pMinDistance/pRadius;
if(2*pRadius <= dist)
throw new Error("Radius is too small");
//find center
double x1 = pFrom.getX(), x2 = pFrom.getY();
double y1 = pTo.getX(), y2 = pTo.getY();
double m1 = (x1+y1)/2, m2 = (x2+y2)/2;
double u1 = - (y2-x2)/dist, u2 = (y1-x1)/dist;
double o1 = m1 + h * u1, o2 = m2 + h * u2;
Point2D o = new Point2D.Double(o1, o2);
double startAngle = GetAngle(pFrom, o, pRadius);
double endAngle = GetAngle(pTo, o, pRadius);
if(endAngle < startAngle)
endAngle += 2 * Math.PI;
for(double a = startAngle; a < endAngle; a+=angleStep){
pOutPut.add(new Point2D.Double(o1+pRadius*Math.cos(a), o2+pRadius*Math.sin(a)));
}
pOutPut.add(pTo);
return pOutPut;
}
私有静态双GetAngle（点2D x、点2D o、双R）{
双cosa=（x.getX（）-o.getX（））/R；
双新浪=（x.getY（）-o.getY（））/R；
双角度=数学acos（cosa）；
返回Math.sin（角度）*sina>=0？角度：2*Math.PI-角度；
}
专用静态ArrayList generateCurve（点2D pFrom、点2D pTo、浮点pRadius、浮点P状态）{
ArrayList pOutPut=新的ArrayList（）；
双距离=pFrom.距离（pTo）；
双h=数学sqrt（pRadius*pRadius-（dist*dist/4.0））；
双角度步进=pMinDistance/pRadius；
如果（2*pRadius我没有放弃，我已经为此工作了几个小时。结果如下：
我创建了一个方法，您可以指定是否需要点之间最长弧中的最短弧
下面是对它的一些调用，以及生成的输出：
generateCurve(pFrom, pTo, 100f, 7f, false, false);
正如你所看到的，它就像一个魔咒。下面是代码：
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, pTo, 100f, 7f, true, 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, 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, 0, 1000, 0);
g.drawLine(0, -1000, 0, 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, 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, PointF pTo, float pRadius, 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;
}
}
包装曲线；
导入java.awt.BasicStroke；
导入java.awt.Color；
导入java.awt.Graphics2D；
导入java.awt.RenderingHints；
导入java.awt.geom.Ellipse2D；
导入java.awt.geom.Line2D；
导入java.awt.geom.Rectangle2D；
导入java.awt.image.buffereImage；
导入java.io.File；
导入java.io.IOException；
导入java.util.ArrayList；
导入java.util.List；
导入javax.imageio.imageio；
/**
*
*@作者martijn
*/
公共班机
{
/**
*@param指定命令行参数
*/
公共静态void main（字符串[]args）引发IOException
{
点F pFrom=新点F（-10f，30.0f）；
点F pTo=新点F（-100f，0.0f）；
列表点=发电机曲线（pFrom、pTo、100f、7f、true、true）；
系统输出打印项次（点数）；
//计算曲线的边界
Float bounds=new Rectangle2D.Float（points.get（0）.x，points.get（0）.y，0,0）；
对于（int i=1；i0）{
Line2D.Float f=新的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.抽签（f）；
}
g、 填充（新的椭圆E2D.浮点（points.get（i）.x-0.8f，points.get（i）.y-0.8f，1.6f，1.6f））；
}
g、 setColor（Color.BLUE）；
g、 填充（新的椭圆E2D浮动（pFrom.x-1，pFrom.y-1，3，3））；
g、 填充（新的椭圆E2D浮子（pTo.x-1、pTo.y-1、3、3））；
g、 处置（）；
write（img，“PNG”，新文件（“result.PNG”）；
}
静态类PointF
{
公共浮动x，y；
公共点F（浮点x，浮点y）
{
这个.x=x；
这个。y=y；
}
@凌驾
公共字符串toString（）
{
返回“（“+x+”、“+y+”）”；
}
}
私有静态列表generateCurve（PointF pFrom、PointF pTo、float pRadius、float pMinDistance、布尔最短、布尔边）
{
List pOutPut=new ArrayList（）；
//计算两个给定点的中间。
点F mPoint=新点F（pFrom.x+pTo.x，pFrom.y+pTo.y）；
mPoint.x/=2.0f；
mPoint.y/=2.0f；
System.out.println（“介于From和To=“+mPoint”）之间；
//计算两点之间的距离
浮动xDiff=pTo.x-pFrom.x；
浮动yDiff=pTo.y-pFrom.y；
浮点距离=（float）Math.sqrt（xDiff*xDiff+yDiff*yDiff）；
System.out.println（“从到之间的距离=”+距离）；
如果（pRadius*2.0f<距离）{
抛出新的IllegalArgumentException（“半径太小！给定的点不会落在圆上。”）；
}
//计算预期曲线的中间。
浮动系数=（浮动）数学sqrt（（pRadius*pRadius）/（pTo.x-pFrom.x）*（pTo.x-pFrom.x）+（pTo.y-pFrom.y）*（pTo.y-pFrom.y））-0.25f；
PointF circleMiddlePoint=新的点F（0,0）；
如果（侧面）{
圆中点x=0.5f*（pFrom.x+pTo.x）+系数*（pTo.y-pFrom.y）；
圆中点y=0.5f*（pFrom.y+pTo.y）+系数*（pFrom.x-pTo.x）；
}否则{
圆中点x=0.5f*（pFrom.x+pTo.x）-系数*（pTo.y-pFrom.y）；
圆中点y=0.5f*（pFrom.y+pTo.y）-系数*（pFrom.x-pTo.x）；
}
System.out.println（“Middle=“+circleMiddlePoint”）；
//计算两个参考角
浮动角度1=（fl
generateCurve(pFrom, pTo, 100f, 7f, false, true);
generateCurve(pFrom, pTo, 100f, 7f, true, true);
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, pTo, 100f, 7f, true, 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, 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, 0, 1000, 0);
g.drawLine(0, -1000, 0, 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, 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, PointF pTo, float pRadius, 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;
}
}