component clarke3 "Clarke (3 phase to cartesian) transform";
description """The Clarke transform can be used to translate a vector
quantity from a three phase system (three components 120 degrees
apart) to a two phase Cartesian system (plus a homopolar component
if the three phases don't sum to zero).\n.P\n\\fBclarke3\\fR implements
the general case of the transform, using all three phases.  If the
three phases are known to sum to zero, see \\fBclarke2\\fR for a
simpler version.""";
see_also """\\fBclarke2\\fR for the 'a+b+c=0' case, \\fBclarkeinv\\fR for
the inverse transform.""";
pin in float a;
pin in float b;
pin in float c "three phase input vector";
pin out float x;
pin out float y "cartesian components of output";
pin out float h "homopolar component of output";
function _;
license "GPL";
;;

/* for the details, google "clarke transform", or see section 3 of
   http://focus.ti.com/lit/an/bpra048/bpra048.pdf and/or appendix B of
   http://www.esat.kuleuven.be/electa/publications/fulltexts/pub_1610.pdf
*/

#define K1 (0.666666666666667)  /* 2/3       */
#define K2 (0.333333333333333)  /* 1/3       */
#define K3 (0.577350269189626)  /* 1/sqrt(3) */
#define K4 (0.471404520791032)  /* sqrt(2)/3 */

FUNCTION(_) {
    x = K1*a - K2*(b+c);
    y = K3*(b-c);
    h = K4*(a+b+c);
}


#if 0
#define K1 (2.0/3.0)
#define K2 (1.0/3.0)
#define K3 1.154700538  /* 2/sqrt(3) */

FUNCTION(_) {
    x = K1 * a - K2 * (b - c);
    y = K3 * (b - c);
    h = K1 * (a + b + c);
}
#endif