/** Calculates the tangent for a given point on a bezier curve
* @param p x- or y-values of four points describing the bezier
* @param u position on the curve between[0 .. 1]
* @return the x- or y-part of the tangent vector
*/
real
bezier_eval_tangent(const real p[4], real u)
{
real A,B,C,D;
bernstein_develop(p,&A,&B,&C,&D);
return 3*A*u*u+2*B*u+C;
}
/** Evaluates the Bernstein polynoms for a given position
* @param p x- or y-values of four points describing the bezier
* @param u position on the curve [0 .. 1]
* @returns the evaluate x- or y-part of the point
*/
real
bezier_eval(const real p[4], real u)
{
real A,B,C,D;
bernstein_develop(p,&A,&B,&C,&D);
return A*u*u*u+B*u*u+C*u+D;
}
int bicubicbezier_extrema(const double p[4],double u[2])
{
double A,B,C,D,delta;
bernstein_develop(p,&A,&B,&C,&D);
delta = 4*B*B - 12*A*C;
u[0] = u[1] = 0.0;
if (delta<0) return 0;
u[0] = (-2*B + sqrt(delta)) / (6*A);
if (delta==0) return 1;
u[1] = (-2*B - sqrt(delta)) / (6*A);
return 2;
}
/**
* Calculates the extrma of the given curve in x- or y-direction.
* @param p x- or y-values of four points describing the bezier
* @param u The position of the extrema [0 .. 1]
* @return The number of extrema found.
*/
static int
bicubicbezier_extrema(const real p[4],real u[2])
{
real A,B,C,D,delta;
bernstein_develop(p,&A,&B,&C,&D);
delta = 4*B*B - 12*A*C;
u[0] = u[1] = 0.0;
if (delta<0) return 0;
/* just a quadratic contribution? */
if (fabs(A) < 1e-6) {
u[0] = -C/(2*B);
return 1;
}
u[0] = (-2*B + sqrt(delta)) / (6*A);
if (delta==0) return 1;
u[1] = (-2*B - sqrt(delta)) / (6*A);
return 2;
}
double bezier_eval_tangent(const double p[4], double u)
{
double A,B,C,D;
bernstein_develop(p,&A,&B,&C,&D);
return 3*A*u*u+2*B*u+C;
}
double bezier_eval(const double p[4], double u)
{
double A,B,C,D;
bernstein_develop(p,&A,&B,&C,&D);
return A*u*u*u+B*u*u+C*u+D;
}
