c++ - OpenGLでテーパードアーク(厚みが減少する曲線)を描く方法は?

Question

任意の弧を描く次のコードがあります。

void CenteredArc::drawPolygonArc(float radius, float thickness, float startAngle, float arcAngle) {
    float num_segments = 360.0;

    float radiusOuter = radius + thickness / 2;
    float radiusInner = radius - thickness / 2;
    float theta = arcAngle / num_segments; 
    float tangetial_factor = tanf(theta);//calculate the tangential factor 

    float radial_factor = cosf(theta);//calculate the radial factor 

    float xxOuter = radiusOuter * cosf(startAngle);
    float yyOuter = radiusOuter * sinf(startAngle);
    float xxInner = radiusInner * cosf(startAngle);
    float yyInner = radiusInner * sinf(startAngle);  

    float prevXXOuter = -1;
    float prevYYOuter = -1;
    float prevXXInner = -1;
    float prevYYInner = -1;

    glPolygonMode(GL_FRONT, GL_FILL);
    for(int ii = 0; ii < num_segments; ii++) 
    { 
        if (prevXXOuter != -1) {
            glBegin(GL_POLYGON);
                glVertex2f(prevXXOuter, prevYYOuter);
                glVertex2f(xxOuter,     yyOuter);
                glVertex2f(xxInner,     yyInner);
                glVertex2f(prevXXInner, prevYYInner);
            glEnd();
        }

        //calculate the tangential vector 
        //remember, the radial vector is (x, y) 
        //to get the tangential vector we flip those coordinates and negate one of them 

        float txOuter = -yyOuter; 
        float tyOuter =  xxOuter; 
        float txInner = -yyInner; 
        float tyInner =  xxInner; 

        //add the tangential vector 

        prevXXOuter = xxOuter;
        prevYYOuter = yyOuter;
        prevXXInner = xxInner;
        prevYYInner = yyInner;

        xxOuter += txOuter * tangetial_factor; 
        yyOuter += tyOuter * tangetial_factor; 
        xxInner += txInner * tangetial_factor; 
        yyInner += tyInner * tangetial_factor; 

        //correct using the radial factor 
        xxOuter *= radial_factor; 
        yyOuter *= radial_factor; 
        xxInner *= radial_factor; 
        yyInner *= radial_factor; 
    }
}

ただし、アークが一方の端で指定された厚さから始まり、もう一方の端で厚さがゼロになるまで徐々に減少するようにしたいと思います。助言がありますか？

編集:次GL_LINE_STRIPのように線やギャップが重ならないようにしようとしているので、使用していません: