/*
* Calc A0 matrix from lattice parameters and wavelength, and return it as r[][].
* Lattice spacings a,b,c and wavelength lambda are in same (arbitrary) units.
* Lattice angles alpha, beta, gamma are in units of degrees.
*/
int calc_A0(double a, double b, double c,
double alpha_arg, double beta_arg, double gamma_arg,
double lambda, double r[3][3], double r_i[3][3]) {
double A[3], B[3], C[3];
double AxB[3], BxC[3], CxA[3];
double tmp;
double alpha = alpha_arg * D2R;
double beta = beta_arg * D2R;
double gamma = gamma_arg * D2R;
if (orientDebug) printf("calc_A0: a=%f,b=%f,c=%f,alpha=%f,beta=%f,gamma=%f,lambda=%f\n",
a,b,c,alpha,beta,gamma,lambda);
A[0] = a;
A[1] = 0;
A[2] = 0;
if (orientDebug) printVector(A, "calc_A0:A");
B[0] = b * cos(gamma);
B[1] = b * sin(gamma);
B[2] = 0;
if (orientDebug) printVector(B, "calc_A0:B");
tmp = (cos(alpha) - cos(beta)*cos(gamma))/sin(gamma);
C[0] = c * cos(beta);
C[1] = c * tmp;
C[2] = c * sqrt(1 - cos(beta)*cos(beta) - tmp*tmp);
if (orientDebug) printVector(C, "calc_A0:C");
/* r = factor * |BxC, CxA, AxB| */
tmp = lambda/(2 * dotcross(A,B,C));
if (orientDebug) printf("calc_A0: lambda/(2*AXB.C) = %f\n", tmp);
cross(A, B, AxB);
cross(B, C, BxC);
cross(C, A, CxA);
if (orientDebug) {
printVector(AxB, "calc_A0:AxB");
printVector(BxC, "calc_A0:BxC");
printVector(CxA, "calc_A0:CxA");
}
r[0][0] = tmp * BxC[0];
r[0][1] = tmp * CxA[0];
r[0][2] = tmp * AxB[0];
r[1][0] = tmp * BxC[1];
r[1][1] = tmp * CxA[1];
r[1][2] = tmp * AxB[1];
r[2][0] = tmp * BxC[2];
r[2][1] = tmp * CxA[2];
r[2][2] = tmp * AxB[2];
if (invertArray(r, r_i)) {
int i, j;
/* error */
if (orientDebug) {
printf("calc_A0: can't invert A0 matrix\n");
printArray(r, "A0");
}
for (i=0; i<3; i++) {
for (j=0; j<3; j++) {
r[i][j] = r_i[i][j] = (i==j ? 1 : 0);
}
}
return(-1);
}
return(0);
}
num_t v3_t<num_t>::tetrahedron_volume(const v3_t<num_t>& a,
const v3_t<num_t>& b,
const v3_t<num_t>& c,
const v3_t<num_t>& d) {
return dotcross((a - d), (b - d), (c - d)) / num_t(6);
}
// Volume of a tetrahedron described by 4 points. Will be
// positive if the anticlockwise normal of a,b,c is oriented out
// of the tetrahedron.
//
// see: http://mathworld.wolfram.com/Tetrahedron.html
inline double tetrahedronVolume(const Vector &a,
const Vector &b,
const Vector &c,
const Vector &d) {
return dotcross((a - d), (b - d), (c - d)) / 6.0;
}
num_t v3_t<num_t>::orient(const v3_t<num_t>& a,
const v3_t<num_t>& b,
const v3_t<num_t>& c,
const v3_t<num_t>& d) {
return dotcross((a - d), (b - d), (c - d));
}
inline double orient3d(const Vector &a,
const Vector &b,
const Vector &c,
const Vector &d) {
return dotcross((a - d), (b - d), (c - d));
}
