java - Bresenham画圆算法Java实现

Question

我已经用 Java 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。感谢您的帮助。

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

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

推导与维基页面上给出的推导相同。

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:

还要注意 aspect ratio .此算法适用于比率 1:1。但是，如果您的宽高比是 a:b，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。