/**
 * Bezier curve drawing 
 *
 * Michael Sherman
 * msherman@dsbox.com
 */

#define STEP    0.1
#define EPSILON 0.0001

extern void DrawLine(int x1, int y1, int x2, int y2);

typedef struct pnt {
        int x;
        int y;
	int z;
} Point;
              
/**
 * Do matrix multiplication to get the point on the curve by the parameter
 * u by multiplying the [ u^3 u^2 u 1 ] vector my the Bezier basis matrix,
 * then multiply by the matrix of control points given by [p0 p1 p2 p3]^T.
 */
Point Q(float u, Point p0, Point p1, Point p2, Point p3) {
        Point temp;
        float S1, S2, S3, S4;
 
        S1 = -(u*u*u) + 3*(u*u) - 3*(u) + 1;
        S2 = 3*(u*u*u) - 6*(u*u) + 3*(u);
        S3 = -3*(u*u*u) + 3*(u*u);
        S4 = (u*u*u);
 
        temp.x = S1*p0.x + S2*p1.x + S3*p2.x + S4*p3.x;
        temp.y = S1*p0.y + S2*p1.y + S3*p2.y + S4*p3.y;

	/** 
	 * Do the same thing with temp.z if you need 3 dimenions:
	 * temp.z = S1*p0.z + S2*p1.z + S3*p2.z + S4*p3.z;
	 */
 
        return temp;
}                    


/**
 * Draw the curve
 */   
void DrawCurve() {
	float u;
	Point p0, p1, p2, p3;
	Point new_p, old_p;

	/**
	 * p0 = control point 1
	 * p1 = control point 2
	 * p2 = control point 3
	 * p3 = control point 4
	 */
	
        u=0.0;
        new_p = p0;
        while (u <= 1.0 + EPSILON) {
                old_p = new_p;
                new_p = Q(u, p0, p1, p2, p3);
                DrawLine(old_p.x, old_p.y, new_p.x, new_p.y);
                u += STEP;
        }                   
}

/*
 * Wow, that was easy!
 * End of spline.c
 */