public RectangleRn WrappingRectangle() {
Euler euler = new Euler();
euler.phi = phi;
euler.theta = theta;
euler.psi = psi;
euler.psi_a = Euler.AXIS_Z ;
euler.theta_a = Euler.AXIS_X;
euler.phi_a = Euler.AXIS_Z;
if (FP.zero(length)) {
Point3D beg3d = new Point3D();
Point3D end3d = new Point3D();
euler.transform(beg3d, new Point3D(0.0, 0.0));
euler.transform(end3d, new Point3D(length, 0.0));
RectangleRn r = beg3d.toRectangle();
end3d.addToRectangle(r);
return r;
} else {
double l, ls, lc;
Point3D[] v = new Point3D[4];
Point3D tv = new Point3D();
l = length / 2.0;
ls = Math.Sin(l);
lc = Math.Cos(l);
euler.phi += l;
v[0] = new Point3D(lc, lc<0 ? -1.0 : -ls, 0.0);
v[1] = new Point3D(1.0, lc<0 ? -1.0 : -ls, 0.0);
v[2] = new Point3D(lc, lc<0 ? +1.0 : +ls, 0.0);
v[3] = new Point3D(1.0, lc<0 ? +1.0 : +ls, 0.0) ;
Point3D min = new Point3D(1.0, 1.0, 1.0);
Point3D max = new Point3D(-1.0, -1.0, -1.0);
for (int i=0; i<4; i++) {
euler.transform(tv, v[i]);
if (tv.x < -1.0) {
min.x = -1.0;
} else if (tv.x > 1.0) {
max.x = 1.0;
} else {
if (tv.x < min.x) {
min.x = tv.x;
}
if (tv.x > max.x) {
max.x = tv.x;
}
}
if (tv.y < -1.0) {
min.y = -1.0;
} else if ( tv.y > 1.0 ) {
max.y = 1.0;
} else {
if (tv.y < min.y) {
min.y = tv.y;
}
if (tv.y > max.y) {
max.y = tv.y;
}
}
if (tv.z < -1.0) {
min.z = -1.0;
} else if (tv.z > 1.0) {
max.z = 1.0;
} else {
if (tv.z < min.z) {
min.z = tv.z;
}
if (tv.z > max.z) {
max.z = tv.z;
}
}
}
return new RectangleRn(new double[]{min.x, min.y, min.z, max.x, max.y, max.z});
}
}
public Line(Point beg, Point end) {
double l = beg.Distance(end);
if (FP.eq(l, Math.PI)) {
Debug.Assert(FP.eq(beg.ra, end.ra));
phi = -Math.PI/2;
theta = Math.PI/2;
psi = beg.ra < 0.0 ? Math.PI*2 + beg.ra : beg.ra;
length = Math.PI;
return;
}
if (beg.Equals(end)) {
phi = Math.PI/2;
theta = beg.dec;
psi = beg.ra - Math.PI/2;
length = 0.0;
} else {
Point3D beg3d = new Point3D(beg);
Point3D end3d = new Point3D(end);
Point3D tp = new Point3D();
Point spt = beg3d.cross(end3d).toSpherePoint();
Euler euler = new Euler();
euler.phi = - spt.ra - Math.PI/2;
euler.theta = spt.dec - Math.PI/2;
euler.psi = 0.0 ;
euler.psi_a = Euler.AXIS_Z;
euler.theta_a = Euler.AXIS_X;
euler.phi_a = Euler.AXIS_Z;
euler.transform(tp, beg3d);
spt = tp.toSpherePoint();
// invert
phi = spt.ra;
theta = -euler.theta;
psi = -euler.phi;
length = l;
}
}
public bool Contains(Point p) {
Euler euler = new Euler();
Point3D spt = new Point3D();
euler.phi = -psi;
euler.theta = -theta;
euler.psi = -phi;
euler.psi_a = Euler.AXIS_Z;
euler.theta_a = Euler.AXIS_X;
euler.phi_a = Euler.AXIS_Z;
euler.transform(spt, new Point3D(p));
Point sp = spt.toSpherePoint();
return FP.zero(sp.dec) && FP.ge(sp.ra, 0.0) && FP.le(sp.ra, length);
}
public RectangleRn WrappingRectangle() {
Point3D[] v = new Point3D[8];
Point3D tv = new Point3D();
Euler euler = new Euler();
double r0 = Math.Sin(rad0);
double r1 = Math.Sin(rad1);
double d = Math.Cos(rad1);
v[0] = new Point3D(d, -r0, -r1);
v[1] = new Point3D(d, +r0, -r1);
v[2] = new Point3D(d, -r0, r1);
v[3] = new Point3D(d, +r0, r1);
v[4] = new Point3D(1.0, -r0, -r1);
v[5] = new Point3D(1.0, +r0, -r1);
v[6] = new Point3D(1.0, -r0, r1);
v[7] = new Point3D(1.0, +r0, r1);
euler.psi_a = Euler.AXIS_Z ;
euler.theta_a = Euler.AXIS_Y;
euler.phi_a = Euler.AXIS_X;
euler.phi = phi;
euler.theta = theta;
euler.psi = psi;
Point3D min = new Point3D(1.0, 1.0, 1.0);
Point3D max = new Point3D(-1.0, -1.0, -1.0);
for (int i=0; i<8; i++) {
euler.transform(tv, v[i]);
if (tv.x < -1.0) {
min.x = -1.0;
} else if (tv.x > 1.0) {
max.x = 1.0;
} else {
if (tv.x < min.x) {
min.x = tv.x;
}
if (tv.x > max.x) {
max.x = tv.x;
}
}
if (tv.y < -1.0) {
min.y = -1.0;
} else if ( tv.y > 1.0 ) {
max.y = 1.0;
} else {
if (tv.y < min.y) {
min.y = tv.y;
}
if (tv.y > max.y) {
max.y = tv.y;
}
}
if (tv.z < -1.0) {
min.z = -1.0;
} else if (tv.z > 1.0) {
max.z = 1.0;
} else {
if (tv.z < min.z) {
min.z = tv.z;
}
if (tv.z > max.z) {
max.z = tv.z;
}
}
}
return new RectangleRn(new double[]{min.x, min.y, min.z, max.x, max.y, max.z});
}
internal Point3D cross(Point3D p) {
return new Point3D(y * p.z - z * p.y,
z * p.x - x * p.z,
x * p.y - y * p.x);
}
internal void transform(Point3D result, Point3D input)
{
int t = 0;
double a, sa, ca;
double x1, y1, z1;
double x2, y2, z2;
x1 = input.x;
y1 = input.y;
z1 = input.z;
for (int i=0; i<3; i++) {
switch (i) {
case 0:
a = phi;
t = phi_a;
break;
case 1:
a = theta;
t = theta_a;
break;
default:
a = psi;
t = psi_a;
break;
}
if (FP.zero(a)) {
continue;
}
sa = Math.Sin(a);
ca = Math.Cos(a);
switch (t) {
case AXIS_X :
x2 = x1;
y2 = ca*y1 - sa*z1;
z2 = sa*y1 + ca*z1;
break;
case AXIS_Y :
x2 = ca*x1 + sa*z1;
y2 = y1;
z2 = ca*z1 - sa*x1;
break;
default:
x2 = ca*x1 - sa*y1;
y2 = sa*x1 + ca*y1;
z2 = z1;
break;
}
x1 = x2;
y1 = y2;
z1 = z2;
}
result.x = x1;
result.y = y1;
result.z = z1;
}
