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;
}
/*
* 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()));
}