Java 中的 Bresenham 圆绘制算法实现

Question

我在 Java 中实现了 Bresenham Circle 绘图算法。但是输出没有正确绘制！我找不到问题出在哪里。

我的代码和输出图像如下。感谢任何帮助。

public void display(GLAutoDrawable drawable) {
    final GL2 gl = drawable.getGL().getGL2();
    gl.glBegin (GL2.GL_POINTS);
    double radius = 0.6;//sc.nextDouble();
    double x =0.0;
    double y = radius;
    gl.glVertex2d(0.0,0.0);
    gl.glVertex2d(x,y);
    gl.glVertex2d(-x,y);
    gl.glVertex2d(x,-y);
    gl.glVertex2d(-x,-y);
    gl.glVertex2d(y,x);
    gl.glVertex2d(-y,x);
    gl.glVertex2d(y,-x);
    gl.glVertex2d(-y,-x);
    double d = 5 - 4*radius;
    while(x<y){
        if(d<0){ //dE

            x+=.01;
            d+=(2*x + 3)*4;
        }else{

            x+=.01;
            y-=.01;
            d+=(2*x - 2*y +5)*4;
        }
        gl.glVertex2d(x,y);
        gl.glVertex2d(-x,y);
        gl.glVertex2d(x,-y);
        gl.glVertex2d(-x,-y);
        gl.glVertex2d(y,x);
        gl.glVertex2d(-y,x);
        gl.glVertex2d(y,-x);
        gl.glVertex2d(-y,-x);

    }
    gl.glEnd();
}

Answer 1

试试这个。我现在使用的计算机上没有 java，让我们看看它是否有效。确保使用整数，因为您要规范化的是块大小！

编辑： 添加了整数。

public void display(GLAutoDrawable drawable) {
    final GL2 gl = drawable.getGL().getGL2();
    gl.glBegin (GL2.GL_POINTS);
    double radius = 0.6;//sc.nextDouble();
    double x =0.0;
    double y = radius;
    gl.glVertex2d(0.0,0.0);
    gl.glVertex2d(x,y);
    gl.glVertex2d(-x,y);
    gl.glVertex2d(x,-y);
    gl.glVertex2d(-x,-y);
    gl.glVertex2d(y,x);
    gl.glVertex2d(-y,x);
    gl.glVertex2d(y,-x);
    gl.glVertex2d(-y,-x);
    double d = 3 - 2*radius;
    while(x<y){
        x++;
    if(d<0){ //dE

        d= d + 4x + 6;
    }else{

        y--;
        d= d+ 4(x - y) + 10;
    }
    gl.glVertex2d(x,y);
    gl.glVertex2d(-x,y);
    gl.glVertex2d(x,-y);
    gl.glVertex2d(-x,-y);
    gl.glVertex2d(y,x);
    gl.glVertex2d(-y,x);
    gl.glVertex2d(y,-x);
    gl.glVertex2d(-y,-x);

}
gl.glEnd();
}

Answer 2

请注意，原来的 Bresenham's circle algorithm 仅适用于整数。由于您的更新是 x_{n+1}=x_n+eps，您可以将 y 更新修改为

y_{n+1}^2 = y_n^2 - 2*eps*n-eps*eps

推导与维基页面给出的相同。

public void display(GLAutoDrawable drawable) {
    final GL2 gl = drawable.getGL().getGL2();
    gl.glBegin (GL2.GL_POINTS);
    double radius = 0.6;//sc.nextDouble();
    double x =0.0;
    double y = radius;
    gl.glVertex2d(0.0,0.0);
    gl.glVertex2d(x,y);
    gl.glVertex2d(-x,y);
    gl.glVertex2d(x,-y);
    gl.glVertex2d(-x,-y);
    gl.glVertex2d(y,x);
    gl.glVertex2d(-y,x);
    gl.glVertex2d(y,-x);
    gl.glVertex2d(-y,-x);

    double eps = .01;
    double eps2 = eps*eps;
    while(x<y){

        y = Math.sqrt(y*y-2*eps*x-eps2);
        x+= eps;
        gl.glVertex2d(x,y);
        gl.glVertex2d(-x,y);
        gl.glVertex2d(x,-y);
        gl.glVertex2d(-x,-y);
        gl.glVertex2d(y,x);
        gl.glVertex2d(-y,x);
        gl.glVertex2d(y,-x);
        gl.glVertex2d(-y,-x);

    }
    gl.glEnd();
}

结果：

还要小心aspect ratio。此算法适用于比率 1:1。但是，如果您的长宽比是 a:b，那么您的圆方程将变为 x^2/a^2+y^2/b^2=r^2。您可以相应地更改更新。

Answer 3

下面是使用 Bresenham 算法绘制自定义圆的示例。完整代码可以在我的仓库中找到：https://github.com/Maiakov/algorithms/tree/master/Task40

/**
 * Write a routine to draw a circle (x ** 2 + y ** 2 = r ** 2) without making use of any floating point
 * <p>
 * computations at all.
 */
public class DrawCircleAlgorithm {

    public static void drawCircle(int radius, int centerX, int centerY, Graphics g) {
        int y = radius;
        int x = 0;

        int delta = calculateStartDelta(radius);
        while (y >= x) {
            drawPixelAndReflect(centerX, centerY, x, y, g);

            if (delta < 0) {
                delta = calculateDeltaForHorizontalPixel(delta, x);
            } else {
                delta = calculateDeltaForDiagonalPixel(delta, x, y);
                y--;
            }
            x++;
        }
    }

    private static int calculateStartDelta(int radius) {
        return 3 - 2 * radius;
    }

    private static int calculateDeltaForHorizontalPixel(int oldDelta, int x) {
        return oldDelta + 4 * x + 6;
    }

    private static int calculateDeltaForDiagonalPixel(int oldDelta, int x, int y) {
        return oldDelta + 4 * (x - y) + 10;
    }

    private static void drawPixelAndReflect(int centerX, int centerY, int x, int y, Graphics g) {
        g.drawLine(centerX + x, centerY + y, centerX + x, centerY + y);
        g.drawLine(centerX + x, centerY - y, centerX + x, centerY - y);
        g.drawLine(centerX - x, centerY + y, centerX - x, centerY + y);
        g.drawLine(centerX - x, centerY - y, centerX - x, centerY - y);

        g.drawLine(centerX - y, centerY + x, centerX - y, centerY + x);
        g.drawLine(centerX - y, centerY - x, centerX - y, centerY - x);
        g.drawLine(centerX + y, centerY + x, centerX + y, centerY + x);
        g.drawLine(centerX + y, centerY - x, centerX + y, centerY - x);
    }
}

Java 中的 Bresenham 圆绘制算法实现

Bresenham circle drawing algorithm implementation in Java

java

algorithm

opengl

drawing

bresenham