public static OrderedTriple findThirdVector(
OrderedTriple v1, OrderedTriple v2, double a1, double a2, OrderedTriple testv)
throws Exception {
// v1 and v2 must be equal lengths N. returns the vector a1 rad from v1, a2
// rad from v2 and N length. if there are two such vectors
// it returns the one with positive component of testv
// System.out.println( "angle between v1 & v2: " + v1.degBetween( v2 ) );
double epsilon = 0.0001;
if (isApprox(a1, 0, epsilon)) return new OrderedTriple(v1);
if (isApprox(a1, Math.PI, epsilon)) return v1.negative();
if (isApprox(a2, 0, epsilon)) return new OrderedTriple(v2);
if (isApprox(a2, Math.PI, epsilon)) return v2.negative();
OrderedTriple v3 = null;
double a = v1.x;
double b = v1.y;
double c = v1.z;
double d = v2.x;
double e = v2.y;
double f = v2.z;
double g, h, i;
double roots[] = null;
double N = v1.length();
double A = N * N * Math.cos(a1);
double B = N * N * Math.cos(a2);
double x12 = a * e - b * d;
double x23 = b * f - c * e;
double x31 = c * d - a * f;
double P, Q, R, S;
P = Q = R = S = 0;
if (!isApprox(x12, 0, epsilon)) {
// System.out.println( "route 1" );
P = x23 / x12;
Q = (e * A - b * B) / x12;
R = x31 / x12;
S = (a * B - d * A) / x12;
roots = solveQuadratic(1 + P * P + R * R, 2 * P * Q + 2 * R * S, Q * Q + S * S - N * N);
i = roots[0];
v3 = new OrderedTriple(P * i + Q, R * i + S, i);
if (testv != null && v3.dot(testv) < 0) {
i = roots[1];
v3.become(P * i + Q, R * i + S, i);
}
} else if (!isApprox(x23, 0, epsilon)) {
// System.out.println( "route 2" );
P = x31 / x23;
Q = (f * A - c * B) / x23;
R = x12 / x23;
S = (b * B - e * A) / x23;
roots = solveQuadratic(1 + P * P + R * R, 2 * P * Q + 2 * R * S, Q * Q + S * S - N * N);
g = roots[0];
v3 = new OrderedTriple(g, P * g + Q, R * g + S);
if (testv != null && v3.dot(testv) < 0) {
g = roots[1];
v3.become(g, P * g + Q, R * g + S);
}
} else if (!isApprox(x31, 0, epsilon)) {
// System.out.println( "route 3" );
P = x23 / x31;
Q = (c * B - f * A) / x31;
R = x12 / x31;
S = (d * A - a * B) / x31;
roots = solveQuadratic(1 + P * P + R * R, 2 * P * Q + 2 * R * S, Q * Q + S * S - N * N);
h = roots[0];
v3 = new OrderedTriple(P * h + Q, h, R * h + S);
if (testv != null && v3.dot(testv) < 0) {
h = roots[1];
v3.become(P * h + Q, h, R * h + S);
}
} else {
throw new Exception("EXCEPTION: no route found in findThirdVector");
}
// if( ! isApprox( v3.radBetween( v1 ), a1, 0.1 ) ) System.out.println(
// "error v1" );
// if( ! isApprox( v3.radBetween( v2 ), a2, 0.1 ) ) System.out.println(
// "error v2" );
return v3;
}
