How do I implement a Bézier curve in C++?

Question

I'd like to implement a Bézier curve. How should I go about creating a quadratic curve?

void printQuadCurve(float delta, Vector2f p0, Vector2f p1, Vector2f p2);

Clearly we'd need to use linear interpolation, but does this exist in the standard math library? If not, where can I find it?

I'm using Linux.

Answer 1

Recently I ran across the same question and wanted to implemented it on my own. This image from Wikipedia helped me:

The following code shows how to compute a quadratic bezier.

int interpolate( int from , int to , float percent )
{
    int difference = to - from;
    return from + ( difference * percent );
}    

for( float i = 0 ; i < 1 ; i += 0.01 )
{
    // The Green Line
    xa = interpolate( x1 , x2 , i );
    ya = interpolate( y1 , y2 , i );
    xb = interpolate( x2 , x3 , i );
    yb = interpolate( y2 , y3 , i );

    // The Black Dot
    x = interpolate( xa , xb , i );
    y = interpolate( ya , yb , i );
    
    drawPixel( x , y , COLOR_RED );
}

With (x1|y1), (x2|y2) and (x3|y3) being P0, P1 and P2 in the image. Just for showing the basic idea...

For the ones who ask for the cubic bezier, it just works analogue (also from Wikipedia):

This answer provides Code for it.