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This commit is contained in:
Timur A. Fatkhullin 2025-04-20 01:26:45 +03:00
parent 3205db3ee1
commit f2a7806f5f
1 changed files with 74 additions and 10 deletions
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84
cxx/mount_pz.h
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@ -61,30 +61,94 @@ private:
};
class MccElliipsePZ
/*
* a general planar ellipse equation:
* A*(x-xc)^2 + B*(x-xc)(y-yc) + C*(y-yc)^2 = 1
*
* A = cos(t)^2/a^2 + sin(t)^2/b^2
* B = sin(2*t)/a^2 - sin(2*t)/b^2
* C = cos(t)^2/b^2 + sin(t)^2/a^2
*
* t - angle between X-axis and big semi-axis (a)
*
*
* Ellipse on unit sphere (Az, Alt):
* x^2/a^2 + y^2/b^2 = 1,
* where a = tan(alpha), b = tan(beta),
* a and b - big and small spherical semi-axis
* also:
* let delta is a spherical distance between ellipse focuses, then
* d = tan(delta) and b^2 = (a^2 - d^2)/(1 + d^2)
*
* tangent coordinates:
* x = tan(Az)
* y = tan(Alt)*sqrt(1+tan(Az)^2)
*
*
* --------------------------------------------
*
* let P - point with (Az_P, Zd_P),
* (Az_C, Zd_C) - center of ellipse, a and b big and small semi-axis,
* vec_a and vec_b - unit vectors along a an b (it lie in tangent surface to point C!!!), then
*
* ((vec_P-vec_C)*vec_b)^2/a^2 + ((vec_P-vec_C)*vec_b)^2/b^2 <= 1.0
* {((vec_P-vec_C)*vec_b)^2/tan(a)^2 + ((vec_P-vec_C)*vec_b)^2/tan(b)^2 <= 1.0}
* * - dot-product
*
* vec_P = (sin(Zd_P)*cos(Az_P), sin(Zd_P)*sin(Az_P), cos(Zd_P))
* vec_C = (sin(Zd_C)*cos(Az_C), sin(Zd_C)*sin(Az_C), cos(Zd_C))
*
*/
class MccEllipsePZ
{
public:
MccElliipsePZ(const MccCoordinate& xc, const MccCoordinate& yc, const MccCoordinate& a, const MccCoordinate& b)
: _xc(xc), _yc(yc), _a(a), _b(b), _a2(a * a), _b2(b * b)
MccEllipsePZ(const MccCoordinate& xc,
const MccCoordinate& yc,
const MccCoordinate& a,
const MccCoordinate& b,
const MccCoordinate& theta = 0.0)
: _xc(xc), _yc(yc), _a(a), _b(b), _theta(theta), _tanXc(std::tan(xc)), _tanYc(std::tan(yc))
{
_tanYc *= std::sqrt(1.0 + _tanXc * _tanXc);
auto _tan2A = tan(a);
auto _tan2B = tan(b);
_tan2A *= _tan2A;
_tan2B *= _tan2B;
auto ct = cos(theta);
auto ct2 = ct * ct;
auto st = sin(theta);
auto st2 = st * st;
auto sin2t = sin(2.0 * theta);
cxx = ct2 / _tan2A + st2 / _tan2B;
cyy = st2 / _tan2A + ct2 / _tan2B;
cxy = sin2t / _tan2A - sin2t / _tan2B;
}
// circle
MccElliipsePZ(const MccCoordinate& xc, const MccCoordinate& yc, const MccCoordinate& a)
: mcc::MccElliipsePZ(xc, yc, a, a)
MccEllipsePZ(const MccCoordinate& xc, const MccCoordinate& yc, const MccCoordinate& a)
: mcc::MccEllipsePZ(xc, yc, a, a)
{
}
private:
double _xc, _yc, _a, _b, _a2, _b2;
double _xc, _yc, _a, _b, _theta;
double _tanXc, _tanYc, cxx, cxy, cyy;
bool inZoneImpl(const MccCoordinate& alt, const MccCoordinate& zd)
bool inZoneImpl(const MccCoordinate& x, const MccCoordinate& y)
{
auto x2 = alt - _xc;
auto y2 = zd - _yc;
auto tanX = tan(x);
auto tanY = tan(y) * sqrt(1.0 + tanX * tanX);
auto xr = tanX - _tanXc;
auto yr = tanY - _tanYc;
return (x2 * x2 / _a2 + y2 * y2 / _b2) <= 1.0;
return (cxx * xr * xr + cxy * xr * yr + cyy * yr * yr) <= 1.0;
}
};