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;
}
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[] 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 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);
}
public OrderedTriple(OrderedTriple t1, OrderedTriple t2) {
this(t2.minus(t1));
}
static double[] planeFrom3Points(OrderedTriple p1, OrderedTriple p2, OrderedTriple p3) {
return planeFromNormalAndPoint(p1.minus(p2).cross(p2.minus(p3)), p1);
}
/*
* 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);
}
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));
}
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);
}