如何从 AffineTransform 派生的形状对象中“获取”特定点

Question

作为一个自我项目，我正在尝试制作游戏“Asteroids”。

目前，我一直在试图弄清楚如何制作它，以便从我的船发射的激光从船的尖端出现。到目前为止，我已经尝试过使用Shape 对象的.getBounds2D().getX() 方法，但是因为getBounds2D() 在多边形周围绘制了一个矩形，激光最终出现在我的多边形@ 周围的假想“盒子”的角落。 987654325@.

Here's a gif of what I have so far.

有没有办法从 Shape 对象中“获取”特定点？在这种情况下，该特定点是船的尖端。

主类：

public class AsteroidGame implements ActionListener, KeyListener{

    public static AsteroidGame game;
    public Renderer renderer;

    public boolean keyDown = false;
    public int playerAngle = 0;

    public boolean left = false;
    public boolean right = false;
    public boolean go = false;
    public boolean back = false;
    public boolean still = true;
    public double angle = 0;
    public int turnRight = 5;
    public int turnLeft = -5;

    public Shape transformed;

    public ArrayList<Laser> lasers;
    public ArrayList<Shape> transformedLasers;

    public final int WIDTH = 1400;
    public final int HEIGHT = 800;

    public Ship ship;
    public Rectangle shipHead;
    public Shape shipHeadTrans;
    public Point headPoint;


    public AffineTransform transform = new AffineTransform();
    public AffineTransform lasTransform = new AffineTransform();
    public AffineTransform headTransform = new AffineTransform();

    public AsteroidGame(){
        JFrame jframe = new JFrame();
        Timer timer = new Timer(20, this);
        renderer = new Renderer();

        jframe.add(renderer);
        jframe.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        jframe.setSize(WIDTH, HEIGHT);
        jframe.setVisible(true);
        jframe.addKeyListener(this);
        jframe.setResizable(false);

        int xPoints[] = {800, 780, 800, 820};
        int yPoints[] = {400, 460, 440, 460}; 

        //(800, 400) is the initial location of the 'tip' of the ship'.
        headPoint = new Point(800, 400);

        lasers = new ArrayList<Laser>();
        transformedLasers = new ArrayList<Shape>();

        ship = new Ship(xPoints, yPoints, 4, 0);
        transformed = transform.createTransformedShape(ship);

        shipHead = new Rectangle(headPoint);
        shipHeadTrans = transform.createTransformedShape(shipHead);
        //shipHeadTrans.getBounds2D().

        timer.start();

    }

    public void repaint(Graphics g){

        g.setColor(Color.BLACK);
        g.fillRect(0, 0, WIDTH, HEIGHT);

        Graphics2D g2d = (Graphics2D)g;

        //drawing the ship
        g2d.setColor(Color.WHITE);
        g2d.draw(transformed);

        //drawing lasers
        g2d.setColor(Color.RED);
        for (int i = 0; i < transformedLasers.size(); i++){
            System.out.println(i);
            g2d.draw(transformedLasers.get(i));
        }



    }



    public void actionPerformed(ActionEvent arg0) {
        // TODO Auto-generated method stub

        /*The for if and else if statements are just to send the ship
         * to the other side of the canvas if it ever leaves the screen
         */
        if (transformed.getBounds2D().getMinX() > WIDTH){
            double tempAng = ship.getAng();
            double diff = 90-tempAng;

            transform.rotate(Math.toRadians(diff), ship.getCenterX(), ship.getCenterY());
            transform.translate(0,WIDTH);
            transform.rotate(Math.toRadians(-diff), ship.getCenterX(), ship.getCenterY());

        }

        else if (transformed.getBounds2D().getX() < 0){
            double tempAng = ship.getAng();
            double diff = 90-tempAng;
            transform.rotate(Math.toRadians(diff), ship.getCenterX(), ship.getCenterY());
            transform.translate(0,-WIDTH);
            transform.rotate(Math.toRadians(-diff), ship.getCenterX(), ship.getCenterY());
        }

        else if (transformed.getBounds2D().getY() > HEIGHT){
            double tempAng = ship.getAng();
            double diff = 180-tempAng;
            transform.rotate(Math.toRadians(diff), ship.getCenterX(), ship.getCenterY());
            transform.translate(0,HEIGHT);
            transform.rotate(Math.toRadians(-diff), ship.getCenterX(), ship.getCenterY());
        }

        else if (transformed.getBounds2D().getY() < 0){
            double tempAng = ship.getAng();
            double diff = 180-tempAng;
            transform.rotate(Math.toRadians(diff), ship.getCenterX(), ship.getCenterY());
            transform.translate(0,-HEIGHT);
            transform.rotate(Math.toRadians(-diff), ship.getCenterX(), ship.getCenterY());
        }


        if (right){
            ship.right();
            //rotating the ship
            transform.rotate(Math.toRadians(turnRight), ship.getCenterX(), ship.getCenterY());
            //rotating the 'tip' of the ship.
            headTransform.rotate(Math.toRadians(turnRight), ship.getCenterX(), ship.getCenterY());
        }

        else if (left){
            ship.left(); 
            //rotating the ship
            transform.rotate(Math.toRadians(turnLeft), ship.getCenterX(), ship.getCenterY());
            //rotating the 'tip' of the ship
            headTransform.rotate(Math.toRadians(turnLeft), ship.getCenterX(), ship.getCenterY());
        }
        if (go){
            ship.go();
        }
        else if (back){
            ship.reverse();
        }

        //moving and shaping each individual laser that had been shot
        for (int i = 0; i < transformedLasers.size(); i++){
            lasers.get(i).move();

            lasTransform = new AffineTransform();
            lasTransform.rotate(Math.toRadians(lasers.get(i).getAng()), transformed.getBounds2D().getX(), transformed.getBounds2D().getY());
            transformedLasers.set(i, lasTransform.createTransformedShape(lasers.get(i)));

        }

        //moving the ship
        ship.move();

        //moving the 'tip'
        shipHead.y -= ship.getSpeed();

        transformed = transform.createTransformedShape(ship);
        shipHeadTrans = headTransform.createTransformedShape(shipHead);


        renderer.repaint();

    }

    //defining a new laser
    public void fireLaser(){
        Laser tempLaser = new Laser((int)transformed.getBounds2D().getX(), (int)transformed.getBounds2D().getY(), 5, 10, ship.getAng());
        lasers.add(tempLaser);

        lasTransform = new AffineTransform();
        lasTransform.rotate(Math.toRadians(ship.getAng()), transformed.getBounds2D().getX(), transformed.getBounds2D().getY());
        transformedLasers.add(lasTransform.createTransformedShape(tempLaser));

    }

    public static void main(String[] args){
        game = new AsteroidGame();
    }

    @Override
    public void keyPressed(KeyEvent e) {
        // TODO Auto-generated method stub
        if (e.getKeyCode() == KeyEvent.VK_RIGHT){
            right = true;
            keyDown = true;
        }else if (e.getKeyCode() == KeyEvent.VK_LEFT){
            left = true;
            keyDown = true;
        }

        else if (e.getKeyCode() == KeyEvent.VK_UP){
            go = true;
        }
        else if (e.getKeyCode() == KeyEvent.VK_DOWN){
            back = true;
        }

        //fire laser
        if (e.getKeyCode() == KeyEvent.VK_SPACE){
            fireLaser();
        }

    }

    @Override
    public void keyReleased(KeyEvent e) {
        // TODO Auto-generated method stub
        if (e.getKeyCode() == KeyEvent.VK_RIGHT){
            right = false;
        }
        if (e.getKeyCode() == KeyEvent.VK_LEFT){
            left = false;
        }
        if (e.getKeyCode() == KeyEvent.VK_UP){
            go = false;
        }
        if (e.getKeyCode() == KeyEvent.VK_DOWN){
            back = false;
        }
        still = true;
        keyDown = false;
    }

    @Override
    public void keyTyped(KeyEvent e) {
        // TODO Auto-generated method stub

    }

船级（不过我认为这无关紧要）

package asteroidGame;

import java.awt.Polygon;
import java.util.Arrays;

public class Ship extends Polygon{

    /**
     * 
     */
    private double currSpeed = 0;

    private static final long serialVersionUID = 1L;
    public double angle;
    public int[] midX;
    public int[] midY;

    public Ship(int[] x, int[] y, int points, double angle){
        super(x, y, points);
        midX = x;
        midY = y;

        this.angle= angle;
    }


    public void right(){
        angle += 5;
    }
    public void left(){
        angle -= 5;
    }

    public void move(){
        for (int i = 0; i < super.ypoints.length; i++){
            super.ypoints[i] -= currSpeed;
            //System.out.println(super.ypoints[i]);
            //System.out.println(super.xpoints[i]);
        }
        //System.out.println(Arrays.toString(super.ypoints));



    }
    public double getSpeed(){
        return currSpeed;
    }


    public void reverse(){
        if (currSpeed  > -15) currSpeed -= 0.2;
    }

    public void go(){
        if (currSpeed < 25) currSpeed += 0.5;

    }

    public int getCenterX(){
        return super.xpoints[2];
    }
    public int getCenterY(){
        return super.ypoints[2];
    }

    public double getAng(){
        return angle;
    }
    public void test(){
        for (int x = 0; x < super.ypoints.length; x++){
            super.ypoints[x] += 1000;
        }
    }

    /*
    public void decrement(){
        if(currSpeed == 0){}

        else if (currSpeed > 0 && currSpeed < 15){
            currSpeed -= 0.05;

        }
        else if (currSpeed < 0 && currSpeed > -15){
            currSpeed += 0.05;

        }
        System.out.println("losing speed");
    }
    */
}

激光课程（我认为这也无关紧要，但你去吧。）

package asteroidGame;

import java.awt.Color;
import java.awt.Rectangle;
import java.awt.geom.Rectangle2D;

public class Laser extends Rectangle{

    private double angle;

    public Laser(int x, int y , int width, int height, double ang){
        super(x, y, width, height);
        angle = ang;
        Rectangle tst = new Rectangle(); 


    }

    public void move(){
        super.y -= 35;
    }

    public double getAng(){
        return angle;
    }

    public boolean intersects (Rectangle2D r){
        //if intersects
        if (super.intersects(r)){
            return true;
        }
        else{
            return false;
        }

    }


}

我在考虑是否可以将 Shape 对象 transformed 转回 Polygon 以理解这一点，但我不确定这将如何或是否可行。

Answer 1

您可以使用AffineTransform.transform(Point2D, Point2D) 转换多边形上的单个点。

如果不是尝试使用旋转变换来移动船，而是保留船所在位置的单个 (x,y) 位置，那么事情会简单得多。您将在move() 中移动船的位置，而不是尝试平移多边形。然后当你想画船时，例如做：

// Optionally copying the Graphics so the
// transform doesn't affect later painting.
Graphics2D temp = (Graphics2D) g2d.create();
temp.translate(ship.locX, ship.locY);
temp.rotate(ship.angle);
temp.draw(ship);

要根据速度移动一个点，你可以这样做来找到移动向量：

double velX = speed * Math.cos(angle);
double velY = speed * Math.sin(angle);
locX += timeElapsed * velX;
locY += timeElapsed * velY;

这本质上是从极坐标到笛卡尔坐标的转换。 x 和 y 速度是三角形的边，其斜边为speed，已知角度为angle：

             /|
            / |
           /  |
          /   |
   speed /    |
        /     |
       /      |velY
      / angle |
     /)_______|
         velX

在我的回答中有一个以这种方式进行移动的示例：https://stackoverflow.com/a/43692434/2891664。

---

对于您的 cmets：

你是说，不像我最初的移动功能，只是为了让ship 保持一个点，因此我只会翻译它吗？

或多或少，是的。你仍然有一个多边形来保持船的形状，但多边形上的点将相对于(0,0)。

假设有以下定义：

• 多边形上的每个(x,y) 点都是p<sub>i</sub>。 （换句话说，p<sub>0</sub>、p<sub>1</sub>、p<sub>2</sub> 和 p<sub>3</sub> 之一。）
• 翻译的(x,y)坐标是T

然后，翻译Graphics2D后，面板上的每个p<sub>i</sub>坐标变成p<sub>i</sub>+T。因此，如果您的多边形点是相对于(0,0) 定义的，那么平移到船的(locX,locY) 会将多边形移动到相对于(locX,locY) 的位置。

最简单的方法是将多边形的尖端定义为(0,0)，这样在平移后船的尖端就是船的位置：

// Your original points:
int xPoints[] = {800, 780, 800, 820};
int yPoints[] = {400, 460, 440, 460}; 
// Become these points relative to (0,0):
int xPoints[] = {0, -20, 0, 20};
int yPoints[] = {0, 60, 40, 60};

例如在同一个地方启动飞船，你可以将它的位置初始化为(800,400)。

---

我又在想这个问题，发现旋转有点复杂，因为你可能不想让船绕着尖端旋转。你可能想围绕它的中心旋转船。

所以，这里有一个 MCVE 演示如何完成所有这些操作。

package mcve.game;

import javax.swing.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.awt.Polygon;
import java.awt.RenderingHints;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Rectangle;
import java.awt.Insets;
import java.awt.Toolkit;
import java.awt.GraphicsConfiguration;
import java.util.Set;
import java.util.HashSet;
import java.util.List;
import java.util.ArrayList;

public class MovementExample implements ActionListener {
    public static void main(String[] args) {
        SwingUtilities.invokeLater(MovementExample::new);
    }

    final int fps    = 60;
    final int period = 1000 / fps;

    final JFrame    frame;
    final GamePanel panel;
    final Controls  controls;
    final Ship      ship;

    final List<Bullet> bullets = new ArrayList<>();

    MovementExample() {
        frame = new JFrame("Movement Example");

        Dimension size = getMaximumWindowSize(frame);
        size.width  /= 2;
        size.height /= 2;
        frame.setPreferredSize(size);

        panel = new GamePanel();
        frame.setContentPane(panel);

        frame.pack();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);

        controls = new Controls();

        ship = new Ship(panel.getWidth()  / 2,
                        panel.getHeight() / 2);

        new Timer(period, this).start();
    }

    @Override
    public void actionPerformed(ActionEvent e) {
        double secondsElapsed = 1.0 / fps;
        ship.update(secondsElapsed);

        bullets.forEach(b -> b.update(secondsElapsed));
        Rectangle bounds = panel.getBounds();
        bullets.removeIf(b -> !bounds.contains(b.locX, b.locY));

        panel.repaint();
    }

    class GamePanel extends JPanel {
        GamePanel() {
            setBackground(Color.WHITE);
        }

        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            Graphics2D g2 = (Graphics2D) g.create();
            g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                                RenderingHints.VALUE_ANTIALIAS_ON);

            if (ship != null) {
                ship.draw(g2);
            }
            bullets.forEach(b -> b.draw(g2));

            g2.dispose();
        }
    }

    abstract class AbstractGameObject {
        double maxSpeed;
        double rotationAngle;
        double locX;
        double locY;
        double velX;
        double velY;

        AbstractGameObject(double initialX, double initialY) {
            locX = initialX;
            locY = initialY;
        }

        abstract void update(double secondsElapsed);
        abstract void draw(Graphics2D g2);
    }

    class Ship extends AbstractGameObject {
        Polygon shape;
        double  rotationRate;

        Ship(double initialX, double initialY) {
            super(initialX, initialY);
            maxSpeed      = 128; // pixels/second
            rotationAngle = Math.PI * 3 / 2;
            rotationRate  = (2 * Math.PI) / 2; // radians/second

            int xPoints[] = {0, -20, 0, 20};
            int yPoints[] = {0, 60, 40, 60};
            shape = new Polygon(xPoints, yPoints, 4);
        }

        Point2D.Double getTip() {
            Point2D.Double center = getCenter();
            // The tip is at (0,0) and it's already centered
            // on the x-axis origin, so the distance from the
            // tip to the center is just center.y.
            double distance = center.y;
            // Then find the location of the tip, relative
            // to the center.
            double tipX = distance * Math.cos(rotationAngle);
            double tipY = distance * Math.sin(rotationAngle);
            // Now find the actual location of the center.
            center.x += locX;
            center.y += locY;
            // And return the actual location of the tip, relative
            // to the actual location of the center.
            return new Point2D.Double(tipX + center.x, tipY + center.y);
        }

        Point2D.Double getCenter() {
            // Returns the center point of the ship,
            // relative to (0,0).
            Point2D.Double center = new Point2D.Double();
            for (int i = 0; i < shape.npoints; ++i) {
                center.x += shape.xpoints[i];
                center.y += shape.ypoints[i];
            }
            center.x /= shape.npoints;
            center.y /= shape.npoints;
            return center;
        }

        @Override
        void update(double secondsElapsed) {
            // See my answer here: https://stackoverflow.com/a/43692434/2891664
            // for a discussion of why this logic is the way it is.
            double speed = 0;
            if (controls.isUpHeld()) {
                speed += maxSpeed;
            }
            if (controls.isDownHeld()) {
                speed -= maxSpeed;
            }
            velX  = speed * Math.cos(rotationAngle);
            velY  = speed * Math.sin(rotationAngle);
            locX += secondsElapsed * velX;
            locY += secondsElapsed * velY;

            double rotation = 0;
            if (controls.isLeftHeld()) {
                rotation -= rotationRate;
            }
            if (controls.isRightHeld()) {
                rotation += rotationRate;
            }
            rotationAngle += secondsElapsed * rotation;
            // Cap the angle so it can never e.g. get so
            // large that it loses precision.
            if (rotationAngle > 2 * Math.PI) {
                rotationAngle -= 2 * Math.PI;
            }

            if (controls.isFireHeld()) {
                Point2D.Double tipLoc = getTip();
                Bullet bullet = new Bullet(tipLoc.x, tipLoc.y, rotationAngle);
                bullets.add(bullet);
            }
        }

        @Override
        void draw(Graphics2D g2) {
            Graphics2D copy = (Graphics2D) g2.create();
            copy.setColor(Color.RED);

            // Translate to the ship's location.
            copy.translate(locX, locY);
            // Rotate the ship around its center.
            Point2D.Double center = getCenter();
            // The PI/2 offset is necessary because the
            // polygon points are defined with the ship
            // already vertical, i.e. at an angle of -PI/2.
            copy.rotate(rotationAngle + (Math.PI / 2), center.x, center.y);

            copy.fill(shape);
        }
    }

    class Bullet extends AbstractGameObject {
        Ellipse2D.Double shape = new Ellipse2D.Double();

        Bullet(double initialX, double initialY, double initialRotation) {
            super(initialX, initialY);
            maxSpeed      = 512;
            rotationAngle = initialRotation;
            velX          = maxSpeed * Math.cos(rotationAngle);
            velY          = maxSpeed * Math.sin(rotationAngle);

            double radius = 3;
            shape.setFrame(-radius, -radius, 2 * radius, 2 * radius);
        }

        @Override
        void update(double secondsElapsed) {
            locX += secondsElapsed * velX;
            locY += secondsElapsed * velY;
        }

        @Override
        void draw(Graphics2D g2) {
            Graphics2D copy = (Graphics2D) g2.create();
            copy.setColor(Color.BLACK);
            copy.translate(locX, locY);
            copy.fill(shape);
        }
    }

    // See https://docs.oracle.com/javase/tutorial/uiswing/misc/keybinding.html
    class Controls {
        final Set<Integer> keysHeld = new HashSet<>();

        Controls() {
            bind(KeyEvent.VK_A, "left");
            bind(KeyEvent.VK_D, "right");
            bind(KeyEvent.VK_W, "up");
            bind(KeyEvent.VK_S, "down");
            bind(KeyEvent.VK_SPACE, "fire");
        }

        boolean isLeftHeld()  { return keysHeld.contains(KeyEvent.VK_A); }
        boolean isRightHeld() { return keysHeld.contains(KeyEvent.VK_D); }
        boolean isUpHeld()    { return keysHeld.contains(KeyEvent.VK_W); }
        boolean isDownHeld()  { return keysHeld.contains(KeyEvent.VK_S); }
        boolean isFireHeld()  { return keysHeld.contains(KeyEvent.VK_SPACE); }

        void bind(int keyCode, String name) {
            bind(keyCode, name, true);
            bind(keyCode, name, false);
        }

        void bind(int keyCode, String name, boolean isOnRelease) {
            KeyStroke stroke = KeyStroke.getKeyStroke(keyCode, 0, isOnRelease);
            name += isOnRelease ? ".released" : ".pressed";
            panel.getInputMap(JComponent.WHEN_IN_FOCUSED_WINDOW)
                 .put(stroke, name);
            panel.getActionMap()
                 .put(name, new AbstractAction() {
                     @Override
                     public void actionPerformed(ActionEvent e) {
                         if (isOnRelease) {
                             keysHeld.remove(keyCode);
                         } else {
                             keysHeld.add(keyCode);
                         }
                     }
                 });
        }
    }

    // This returns the usable size of the display which
    // the JFrame resides in, as described here:
    // http://docs.oracle.com/javase/8/docs/api/java/awt/GraphicsEnvironment.html#getMaximumWindowBounds--
    static Dimension getMaximumWindowSize(JFrame frame) {
        GraphicsConfiguration config = frame.getGraphicsConfiguration();
        Dimension size   = config.getBounds().getSize();
        Insets    insets = Toolkit.getDefaultToolkit().getScreenInsets(config);
        size.width  -= insets.left + insets.right;
        size.height -= insets.top  + insets.bottom;
        return size;
    }
}

还有其他方法可以计算船尖，但我在 MCVE 中是这样计算的：

1. 获取船的中心点，相对于(0,0)。
2. 获取从中心点到尖端的距离。提示位于(0,0)，所以这只是中心的 y 坐标。
3. 然后计算尖端相对于中心的(x,y) 位置。这与上图的速度和速度非常相似，但斜边是船中心和船头之间的距离。
4. 将中心转换为相对于船的位置。
5. 将尖端的位置（相对于中心）转换为相对于船的位置。

也可以使用AffineTransform 完成，类似于您在问题中的代码中所做的，但您需要在每次更新时设置它。像这样的：

AffineTransform transform = new AffineTransform();

@Override
void update(double secondsElapsed) {
    ...
    // Clear the previous translation and rotation.
    transform.setToIdentity();
    // Set to current.
    transform.translate(locX, locY);
    Point2D.Double center = getCenter();
    transform.rotate(rotationAngle + (Math.PI / 2), center.x, center.y);

    if (controls.isFireHeld()) {
        Point2D.Double tip = new Point2D.Double(0, 0);
        transform.transform(tip, tip);
        Bullet bullet = new Bullet(tip.x, tip.y, rotationAngle);
        bullets.add(bullet);
    }
}

您仍然可以使用变换来进行这种计算，但您不会因为依赖变换进行移动而感到奇怪。 （在问题的代码中，例如，船仅沿 y 轴移动。明显的侧向移动是由于一系列旋转串联造成的。）