public static OrderedTriple round(OrderedTriple ot, int mantissaLength) {
ot = new OrderedTriple(ot);
ot.x = Misc.round(ot.x, mantissaLength);
ot.y = Misc.round(ot.y, mantissaLength);
ot.z = Misc.round(ot.z, mantissaLength);
return ot;
}
public OrderedTriple arbitraryPerpendicular() {
OrderedTriple perp = new OrderedTriple(1, 1, 1);
if (x != 0) perp.x = (y + z) / -x;
else if (y != 0) perp.y = (x + z) / -y;
else if (z != 0) perp.z = (x + y) / -z;
else return null;
return perp;
}
public static OrderedTriple[] sectSphereLine(
OrderedTriple c, double r, OrderedTriple a, OrderedTriple b) {
// Find the intersection(s) of the sphere with radius length r and center at
// point c and the line containing points a and b
OrderedTriple v = b.minus(a);
OrderedTriple d = a.minus(c);
try {
double[] k = solveQuadratic(v.lengthSquared(), 2 * d.dot(v), d.lengthSquared() - r * r);
OrderedTriple[] answer = {v.times(k[0]).plus(a), v.times(k[1]).plus(a)};
return answer;
} catch (Exception e) {
return null;
}
}
public static OrderedTriple sectPlaneLine(
OrderedTriple P1, OrderedTriple P2, OrderedTriple P3, OrderedTriple L1, OrderedTriple L2) {
// Find the 3D coordinates of the intersection of the plane containing
// points P1, P2, P3 and the line containing L1, L2
OrderedTriple n = P2.minus(P1).cross(P3.minus(P2));
OrderedTriple l = L2.minus(L1);
double A = n.dot(l);
if (A == 0) return null;
double B = n.dot(P1);
double C = n.dot(L1);
double K = (B - C) / A;
return l.times(K).plus(L1);
}
public static OrderedTriple sectLines(
OrderedTriple p1, OrderedTriple p2, OrderedTriple p3, OrderedTriple p4) {
// line from p1 through p2 and line from p3 through p4
OrderedTriple A = p2.minus(p1);
OrderedTriple B = p4.minus(p3);
OrderedTriple C = p3.minus(p1);
OrderedDouble KT1 = OrderedDouble.solveEquations(A.x, -B.x, C.x, A.y, -B.y, C.y);
OrderedDouble KT2 = OrderedDouble.solveEquations(A.y, -B.y, C.y, A.z, -B.z, C.z);
OrderedDouble KT3 = OrderedDouble.solveEquations(A.z, -B.z, C.z, A.x, -B.x, C.x);
double K = 0;
if (KT1 == null && KT2 == null && KT3 == null) {
return LineLineIntersect(p1, p2, p3, p4);
// return null;
} else if (KT1 != null) {
K = KT1.x;
} else if (KT2 != null) {
K = KT2.x;
} else if (KT3 != null) {
K = KT3.x;
}
return A.times(K).plus(p1);
}
static double[] planeFrom3Points(OrderedTriple p1, OrderedTriple p2, OrderedTriple p3) {
return planeFromNormalAndPoint(p1.minus(p2).cross(p2.minus(p3)), p1);
}
static double[] planeFromNormalAndPoint(OrderedTriple n, OrderedTriple p) {
double[] answer = {n.x, n.y, n.z, n.dot(p)};
return answer;
}
/*
* static OrderedTriple sectPlaneLine( OrderedTriple P1, OrderedTriple P2,
* OrderedTriple P3, OrderedTriple L1, OrderedTriple L2 ){ OrderedTriple n =
* P2.minus( P1 ).cross( P3.minus( P2 ) ); OrderedTriple l = L2.minus( L1 );
* double A = n.dot( l ); if( A == 0 ) return null; double B = n.dot( P1 );
* double C = n.dot( L1 ); double K = ( B - C )/A; return l.times( K ).plus(
* L1 ); }
*/
public static double pointPlaneDistance(
OrderedTriple p, OrderedTriple P1, OrderedTriple P2, OrderedTriple P3) {
OrderedTriple n = P2.minus(P1).cross(P3.minus(P2));
return sectPlaneLine(P1, P2, P3, p, p.plus(n)).distance(p);
}
public double radBetween(OrderedTriple t) {
return Math.acos((dot(t)) / (length() * t.length()));
}
void towardsEquals(OrderedTriple p, double distance) {
OrderedTriple v = p.minus(this);
plus(v.times(distance / v.length()));
}
OrderedTriple towards(OrderedTriple p, double distance) {
OrderedTriple v = p.minus(this);
return plus(v.times(distance / v.length()));
}
public OrderedTriple mid(OrderedTriple p, double percent) {
percent /= 100;
return plus(p.minus(this).times(percent));
}
private static OrderedTriple LineLineIntersect(
OrderedTriple p1, OrderedTriple p2, OrderedTriple p3, OrderedTriple p4) {
double EPS = 1e-12;
OrderedTriple p13 = new OrderedTriple(),
p43 = new OrderedTriple(),
p21 = new OrderedTriple(),
pa = new OrderedTriple(),
pb = new OrderedTriple();
double d1343, d4321, d1321, d4343, d2121;
double numer, denom, mua, mub;
p13.x = p1.x - p3.x;
p13.y = p1.y - p3.y;
p13.z = p1.z - p3.z;
p43.x = p4.x - p3.x;
p43.y = p4.y - p3.y;
p43.z = p4.z - p3.z;
if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS) return (null);
p21.x = p2.x - p1.x;
p21.y = p2.y - p1.y;
p21.z = p2.z - p1.z;
if (Math.abs(p21.x) < EPS && Math.abs(p21.y) < EPS && Math.abs(p21.z) < EPS) return (null);
d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;
denom = d2121 * d4343 - d4321 * d4321;
if (Math.abs(denom) < EPS) return (null);
numer = d1343 * d4321 - d1321 * d4343;
mua = numer / denom;
mub = (d1343 + d4321 * (mua)) / d4343;
pa.x = p1.x + mua * p21.x;
pa.y = p1.y + mua * p21.y;
pa.z = p1.z + mua * p21.z;
pb.x = p3.x + mub * p43.x;
pb.y = p3.y + mub * p43.y;
pb.z = p3.z + mub * p43.z;
return pa.mid(pb);
}
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;
}
public double cos(OrderedTriple v) {
// returns the cosine of the angle between them
return dot(v) / (length() * v.length());
}
static OrderedTriple[] sectPlanes(
OrderedTriple p11,
OrderedTriple p12,
OrderedTriple p13,
OrderedTriple p21,
OrderedTriple p22,
OrderedTriple p23) {
OrderedTriple n1 = p11.minus(p12).cross(p12.minus(p13));
OrderedTriple n2 = p21.minus(p22).cross(p22.minus(p23));
OrderedTriple n3 = n1.cross(n2);
double[] m1 = {n1.x, n1.y, n1.z};
double[] m2 = {n2.x, n2.y, n2.z};
double[] m3 = {n3.x, n3.y, n3.z};
double[][] m = {m1, m2, m3};
Matrix M = new Matrix(m);
double[] b1 = {n1.dot(p11)};
double[] b2 = {n2.dot(p21)};
double[] b3 = {0};
double[][] b = {b1, b2, b3};
Matrix B = new Matrix(b);
Matrix S = M.inverse().times(B);
// OrderedTriple s1 = new OrderedTriple( S.mat[0][0], S.mat[1][0],
// S.mat[2][0] );
OrderedTriple s1 = new OrderedTriple(S.mat[0][0], S.mat[1][0], S.mat[2][0]);
OrderedTriple s2 = s1.plus(n3);
OrderedTriple[] answer = {s1, s2};
return answer;
}
OrderedTriple bisectAngle(OrderedTriple v) {
// v = v.times( length()/v.length() );
v = v.unit().times(length());
return mid(v);
}
public OrderedTriple(OrderedTriple t1, OrderedTriple t2) {
this(t2.minus(t1));
}
public double distance(OrderedTriple p1, OrderedTriple p2) {
// distance to line through p1 and p2
OrderedTriple v1 = p2.minus(p1);
OrderedTriple v2 = minus(p1);
return v2.length() * v2.sin(v1);
}