使用 OpenGL 或 D3D 绘制椭圆的有效方法

Question

有一种快速的方法可以像这样画圆

void DrawCircle(float cx, float cy, float r, int num_segments) 
{ 
    float theta = 2 * 3.1415926 / float(num_segments); 
    float c = cosf(theta);//precalculate the sine and cosine
    float s = sinf(theta);
    float t;

    float x = r;//we start at angle = 0 
    float y = 0; 

    glBegin(GL_LINE_LOOP); 
    for(int ii = 0; ii < num_segments; ii++) 
    { 
        glVertex2f(x + cx, y + cy);//output vertex 

        //apply the rotation matrix
        t = x;
        x = c * x - s * y;
        y = s * t + c * y;
    } 
    glEnd(); 
}

我想知道是否有类似的方法来绘制椭圆，其中它的长/短轴向量和大小都是已知的。

Answer 1

如果我们以您的示例为例，我们可以使用内部半径 1 并分别应用水平/垂直半径以获得椭圆：

void DrawEllipse(float cx, float cy, float rx, float ry, int num_segments) 
{ 
    float theta = 2 * 3.1415926 / float(num_segments); 
    float c = cosf(theta);//precalculate the sine and cosine
    float s = sinf(theta);
    float t;

    float x = 1;//we start at angle = 0 
    float y = 0; 

    glBegin(GL_LINE_LOOP); 
    for(int ii = 0; ii < num_segments; ii++) 
    { 
        //apply radius and offset
        glVertex2f(x * rx + cx, y * ry + cy);//output vertex 

        //apply the rotation matrix
        t = x;
        x = c * x - s * y;
        y = s * t + c * y;
    } 
    glEnd(); 
}