#include "vector.h"
#include <math.h>

void normalize(double *a)
{
    double c;
    c = 1.0/NORM(a);
    MUL(a,c);
}

void rotate(double *dest, double *v, double *n, double phi)
{
    /* Rotate the vector `v` through an angle `phi` about the axis `n`. */
    double temp[3], cos_theta;

    cos_theta = cos(phi);

    COPY(dest,v);
    MUL(dest,cos_theta);
    CROSS(temp,n,v);
    MUL(temp,sin(phi));
    ADD(dest,dest,temp);
    COPY(temp,n);
    MUL(temp,DOT(n,v)*(1-cos_theta));
    ADD(dest,dest,temp);
}