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我正在尝试模拟一个球体，并在给定光的原点向量的情况下对其进行真实的着色，并且球体以原点为中心。此外，光的矢量是选定点处较大的不可见球体上的法线矢量。球体看起来不对劲。

https://imgur.com/a/IDIwQQF

问题是，很难修复这种程序的错误。特别是考虑到我知道我希望它在我脑海中的样子，但是当我查看程序中的数字时，它们几乎没有任何意义。

由于我不知道问题出在哪里，所以我不得不将所有内容都粘贴在这里。

public class SphereDrawing extends JPanel {
    private static final long serialVersionUID = 1L;
    private static final int ADJ = 320;
    private static final double LIGHT_SPHERE_RADIUS = 5;
    private static final double LIGHT_X = 3;
    private static final double LIGHT_Y = 4;
    private static final double LIGHT_Z = 0;
    private static final double DRAWN_SPHERE_RADIUS = 1;
    private static final int POINT_COUNT = 1000000;
    private static Coord[] points;
    private static final double SCALE = 200;

    public SphereDrawing() {
        setPreferredSize(new Dimension(640, 640));
        setBackground(Color.white);

        points = new Coord[POINT_COUNT];
        initializePoints();

        for (int i = 0; i < points.length; i++) {
            points[i].scale();
        }

        new Timer(17, (ActionEvent e) -> {
            repaint();
        }).start();
    }

    public void initializePoints() { //finding the points on the surface of the sphere (hopefully somewhat equidistant)
        double random = Math.random() * (double)POINT_COUNT;
        double offset = 2/(double)POINT_COUNT;
        double increment = Math.PI * (3 - Math.sqrt(5));

        for (int i = 0; i < POINT_COUNT; i++) {
            double y = ((i * offset) - 1) + (offset / 2); 
            double r = Math.sqrt(1 - Math.pow(y, 2));

            double phi = ((i + random) % (double)POINT_COUNT) * increment;

            double x = Math.cos(phi) * r;
            double z = Math.sin(phi) * r;

            points[i] = new Coord(x, y, z);
        }       
    }


    public void drawSphere(Graphics2D g) {
        g.translate(ADJ, ADJ); //shifting from origin for drawing purposes

        Arrays.sort(points); //sorting points by their z coordinates

        double iHat = -2 * LIGHT_X;
        double jHat = -2 * LIGHT_Y; //Light vector
        double kHat = -2 * LIGHT_Z;

        double angL1 = 0;
        if (Math.abs(iHat) != 0.0)
            angL1 = Math.atan(jHat / iHat); //converting light vector to spherical coordinates
        else
            angL1 = Math.PI/2;
        double angL2 = Math.atan(Math.sqrt(Math.pow(iHat, 2) + Math.pow(jHat, 2))/ kHat);

        double maxArcLength = LIGHT_SPHERE_RADIUS * Math.PI; // maximum arc length

        for (int i = 0; i < points.length; i++) {
            if(points[i].checkValid()) {
                double siHat = -2 * points[i].x; 
                double sjHat = -2 * points[i].y; //finding normal vector for the given point on the sphere
                double skHat = -2 * points[i].z;

                double angSF1 = -1 * Math.abs(Math.atan(sjHat / siHat)); // converting vector to spherical coordinates
                double angSF2 = Math.atan(Math.sqrt(Math.pow(siHat, 2) + Math.pow(sjHat, 2))/ skHat); 

                double actArcLength = LIGHT_SPHERE_RADIUS * Math.acos(Math.cos(angL1) * Math.cos(angSF1) + Math.sin(angL1) * Math.sin(angSF1) * Math.cos(angL2 - angSF2)); //calculating arc length at this point

                double comp = actArcLength / maxArcLength; // comparing the maximum arc length to the calculated arc length for this vector

                int col = (int)(comp * 255);
                col = Math.abs(col);
                g.setColor(new Color(col, col, col));

                double ovalDim = (4 * Math.PI * Math.pow(DRAWN_SPHERE_RADIUS, 2))/POINT_COUNT; //using surface area to determine how large size of each point should be drawn
                if (ovalDim < 1) // if it too small, make less small
                    ovalDim = 2;
                g.fillOval((int)points[i].x, (int)points[i].y, (int)ovalDim, (int)ovalDim); //draw this oval
            }
        }
    }

    @Override
    public void paintComponent(Graphics gg) {
        super.paintComponent(gg);
        Graphics2D g = (Graphics2D) gg;
        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                RenderingHints.VALUE_ANTIALIAS_ON);

        drawSphere(g);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            JFrame f = new JFrame();
            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            f.setTitle("Sphere");
            f.setResizable(false);
            f.add(new SphereDrawing(), BorderLayout.CENTER);
            f.pack();
            f.setLocationRelativeTo(null);
            f.setVisible(true);
        });
    }

    @SuppressWarnings("rawtypes")
    private class Coord implements Comparable {
        public double x;
        public double y;
        public double z;

        public Coord(double x2, double y2, double z2) {
            x = x2;
            y = y2;
            z = z2;
        }

        public void scale() {
            x *= SCALE;
            y *= SCALE; //drawing purposes
            z *= SCALE;
        }

        public String toString() {
            return x + " " + y + " " + z;
        }

        public int compareTo(Object c) {
            double diff = this.z - ((Coord)c).z;
            if (diff < 0)
                return -1;
            else if (diff > 0) //for sorting the array of points
                return 1;
            else
                return 0;
        }

        public boolean checkValid() {
            return (z > 0); //checks if need to draw this point
        }
    }
}

我希望至少能画出一个逼真的球体，即使不完全准确，我也不能告诉你我的到底是什么问题

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