/* tri_basis.h  from Celia and Gray p 415, 416                            */
/* triangle T defined by:                                                 */
/* T[0] is x1, T[1] is y1, T[2] is x2, T[3] is y2, T[4] is x3, T[5] is y3 */

/* first order, about first point in T */
double phi(double T[], double x, double y);
double phix(double T[], double x, double y);
double phiy(double T[], double x, double y);

/* first order, same T, number is point in T */
double phi1(double T[], double x, double y);
double phi2(double T[], double x, double y);
double phi3(double T[], double x, double y);

/* second order, about first point in T */
double phi2p(double T[], double x, double y);
double phi2x(double T[], double x, double y);
double phi2y(double T[], double x, double y);
double phi2xx(double T[], double x, double y);
double phi2xy(double T[], double x, double y);
double phi2yy(double T[], double x, double y);

/* second order, about mid point between first and second point in T */
double phi2m(double T[], double x, double y);
double phi2mx(double T[], double x, double y);
double phi2my(double T[], double x, double y);
double phi2mxx(double T[], double x, double y);
double phi2mxy(double T[], double x, double y);
double phi2myy(double T[], double x, double y);

/* second order, same T, number is point in T */
double phi21(double T[], double x, double y);
double phi22(double T[], double x, double y);
double phi23(double T[], double x, double y);
double phi24(double T[], double x, double y);
double phi25(double T[], double x, double y);
double phi26(double T[], double x, double y);