GeoPoint
AnnularSectorZone::GetBoundaryParametric(fixed t) const
{
const Angle sweep = (GetEndRadial() - GetStartRadial()).AsBearing();
const fixed c0 = sweep.Radians() * inner_radius;
const fixed l = GetRadius() - inner_radius;
const fixed c1 = sweep.Radians() * GetRadius();
const fixed tt = t * (c0 + c1 + 2 * l);
Angle a;
fixed d;
if (tt < c0) {
d = inner_radius;
a = Angle::Radians((tt / c0) * sweep.Radians()) + GetStartRadial();
} else if (positive(l) && (tt < c0 + l)) {
d = (tt - c0) / l * (GetRadius() - inner_radius) + inner_radius;
a = GetEndRadial();
} else if (tt < c0 + l + c1) {
d = GetRadius();
a = GetEndRadial()
- Angle::Radians(((tt - c0 - l) / c1) * sweep.Radians());
} else if (positive(l)) {
d = (tt - c0 - l - c1) / l * (inner_radius - GetRadius()) + GetRadius();
a = GetStartRadial();
} else {
d = inner_radius;
a = GetStartRadial();
}
return GeoVector(d, a).EndPoint(GetReference());
}
//------------------------------------------------------------------------------
void
Canvas::DrawAnnulus(int x, int y,
unsigned inner_r, unsigned outer_r,
Angle start, Angle end)
{
QPainterPath p;
QRectF ri(x - inner_r, y - inner_r, 2 * inner_r, 2 * inner_r);
QRectF ro(x - outer_r, y - outer_r, 2 * outer_r, 2 * outer_r);
// Draw the inner radius of the annulus.
p.arcMoveTo(ri, start.Degrees());
p.arcTo(ri, start.Degrees(), end.Degrees() - start.Degrees());
if (start != end)
{ // Only draw the end caps when needed.
// The currentPosition() will be at the end of the inner circle. Draw
// one side of the annulus.
// \todo This doesn't work because Angle(360) != Angle(0)!
double xx = (outer_r - inner_r) * cos(end.Radians()) +
p.currentPosition().rx();
double yy = (outer_r - inner_r) * -sin(end.Radians()) +
p.currentPosition().ry();
p.lineTo(xx, yy);
}
else
p.arcMoveTo(ro, end.Degrees()); // Set up for the outer circle.
// The currentPosition() will be at the 'end' of the outer circle. Draw the
// outer to the start.
p.arcTo(ro, end.Degrees(), start.Degrees() - end.Degrees());
if (start != end)
{// And close it off to finish up.
p.closeSubpath();
}
this->pushObject(p, this->pen(), this->brush());
}
double
MoonPhaseFunc::operator()( double julianDay )
{
Angle phase = LunarPhase( julianDay );
Angle diff = m_phaseAngle - phase;
return diff.Radians();
}
AxisAngle<T>
RotationMatrix3<T>::GetAxisAngle( ) const
{
Angle angle = ArcCos( (Trace() - 1.) / 2. );
Vector3<T> axis;
if ( angle.Radians() <= 0. )
axis = Vector3<T>::UnitX; //arbitrary: there is no rotation.
else if ( angle.Radians() < M_PI )
{
axis.Set( m_matrix( 2, 1 ) - m_matrix( 1, 2 ),
m_matrix( 0, 2 ) - m_matrix( 2, 0 ),
m_matrix( 1, 0 ) - m_matrix( 0, 1 ) );
axis.Normalize( );
}
else
{
int i0 = 0;
int i1 = 1;
int i2 = 2;
T maxD = m_matrix( 0, 0 );
if ( m_matrix( 1, 1 ) > maxD )
{
i0 = 1;
i1 = 0;
maxD = m_matrix( 1, 1 );
}
if ( m_matrix( 2, 2 ) > maxD )
{
i0 = 2;
i1 = 0;
i2 = 1;
}
T axisComps[3];
axisComps[i0] = static_cast<T>( 0.5 ) * std::sqrt( m_matrix( i0, i0 )
- m_matrix( i1, i1 )
- m_matrix( i2, i2 )
+ static_cast<T>( 1. ) );
axisComps[i1] = m_matrix( i1, i0 )
/ (static_cast<T>( 2. ) * axisComps[i0]);
axisComps[i2] = m_matrix( i1, i0 )
/ (static_cast<T>( 2. ) * axisComps[i0]);
axis.Set( axisComps[0], axisComps[1], axisComps[2] );
}
return AxisAngle<T>( axis, angle );
}
GeoPoint
SectorZone::GetBoundaryParametric(fixed t) const
{
const Angle sweep = (EndRadial - StartRadial).AsBearing();
const fixed l = Radius;
const fixed c1 = sweep.Radians() * Radius;
const fixed tt = t * (c1 + 2 * l);
Angle a;
fixed d;
if (tt < l) {
d = (tt / l) * Radius;
a = StartRadial;
} else if (tt < l + c1) {
d = Radius;
a = StartRadial + Angle::Radians(((tt - l) / c1) * sweep.Radians());
} else {
d = Radius - (tt - l - c1) / l * Radius;
a = EndRadial;
}
return GeoVector(d, a).EndPoint(get_location());
}
GeoPoint
SectorZone::GetBoundaryParametric(fixed t) const
{
const Angle sweep = (end_radial - start_radial).AsBearing();
const fixed l = GetRadius();
const fixed c1 = sweep.Radians() * GetRadius();
const fixed tt = t * (c1 + 2 * l);
Angle a;
fixed d;
if (tt < l) {
d = (tt / l) * GetRadius();
a = start_radial;
} else if (tt < l + c1) {
d = GetRadius();
a = start_radial + Angle::Radians(((tt - l) / c1) * sweep.Radians());
} else {
d = GetRadius() - (tt - l - c1) / l * GetRadius();
a = end_radial;
}
return GeoVector(d, a).EndPoint(GetReference());
}
//------------------------------------------------------------------------------
inline Angle
Canvas::normalize(const Angle& a) const
{
double r = fmod(a.Radians(), 2.0 * M_PI);
Angle ra = Angle::Radians(r);
#ifndef NDEBUG
double ad = a.Degrees();
double rd = ra.Degrees();
std::cerr << __LINE__ << ": " << ad << ", " << rd << std::endl;
#endif
return (ra);
}
void
UpdateInfoBoxCircleDiameter(InfoBoxData &data)
{
if (!CommonInterface::Basic().airspeed_available.IsValid()) {
data.SetInvalid();
return;
}
const Angle turn_rate =
CommonInterface::Calculated().turn_rate_heading_smoothed.Absolute();
// deal with div zero and small turn rates
if (turn_rate < Angle::Degrees(1)) {
data.SetInvalid();
return;
}
const fixed circle_diameter = CommonInterface::Basic().true_airspeed
/ turn_rate.Radians()
* fixed(2); // convert turn rate to radians/s and double it to get estimated circle diameter
if (circle_diameter > fixed (2000)){ // arbitrary estimated that any diameter bigger than 2km will not be interesting
data.SetInvalid();
return;
}
TCHAR buffer[32];
Unit unit = FormatSmallUserDistance(buffer, circle_diameter, false, 0);
data.SetValue (buffer);
data.SetValueUnit(unit);
const fixed circle_duration =
Angle::FullCircle().Native() / turn_rate.Native();
StaticString<16> duration_buffer;
duration_buffer.Format(_T("%u s"), int(circle_duration));
_tcscpy (buffer, duration_buffer);
data.SetComment (buffer);
}
gcc_const
static int16_t Import(Angle x) {
return (int16_t)(x.Radians() * 4096);
}
SunEphemeris::Result
SunEphemeris::CalcSunTimes(const GeoPoint &location,
const BrokenDateTime &date_time,
const fixed time_zone)
{
Result result;
assert(date_time.Plausible());
fixed days_to_j2000 = FNday(date_time);
Angle l = GetMeanSunLongitude(days_to_j2000);
// Use GetEclipticLongitude to find the ecliptic longitude of the Sun
Angle lambda = GetEclipticLongitude(days_to_j2000, l);
// Obliquity of the ecliptic
Angle obliquity = Angle::Degrees(fixed(23.439) - fixed(.0000004) * days_to_j2000);
// Find the RA and DEC of the Sun
Angle alpha = Angle::FromXY(lambda.cos(), obliquity.cos() * lambda.sin());
Angle delta = Angle::asin(obliquity.sin() * lambda.sin());
// Find the Equation of Time in minutes
// Correction suggested by David Smith
fixed ll = (l - alpha).Radians();
if (l.Radians() < fixed_pi)
ll += fixed_two_pi;
fixed equation = fixed(1440) * (fixed(1) - ll / fixed_two_pi);
Angle hour_angle = GetHourAngle(location.latitude, delta);
Angle hour_angle_twilight = GetHourAngleTwilight(location.latitude, delta);
result.azimuth = CalculateAzimuth(location, date_time, time_zone, delta);
// length of twilight in hours
fixed twilight_hours = (hour_angle_twilight - hour_angle).Hours();
// Conversion of angle to hours and minutes
result.day_length = Double(hour_angle.Hours());
if (result.day_length < fixed(0.0001))
// arctic winter
result.day_length = fixed(0);
result.time_of_sunrise = fixed(12) - hour_angle.Hours() + time_zone
- location.longitude.Degrees() / 15 + equation / 60;
if (result.time_of_sunrise > fixed(24))
result.time_of_sunrise -= fixed(24);
result.time_of_sunset = result.time_of_sunrise + result.day_length;
result.time_of_noon = result.time_of_sunrise + hour_angle.Hours();
// morning twilight begin
result.morning_twilight = result.time_of_sunrise - twilight_hours;
// evening twilight end
result.evening_twilight = result.time_of_sunset + twilight_hours;
return result;
}
/**
* Convert a an angle on Earth's surface to a pixel distance.
*/
gcc_pure
fixed AngleToPixels(Angle angle) const {
return fast_mult(angle.Radians(), draw_scale, 12);
}
/**
* Convert a an angle on Earth's surface to a pixel distance.
*/
gcc_pure
double AngleToPixels(Angle angle) const {
return angle.Radians() * draw_scale;
}
/**
* Convert an angle to the according distance on earth's surface [m],
* assuming the earth is a sphere.
*/
constexpr
static inline fixed
AngleToEarthDistance(Angle angle)
{
return angle.Radians() * REARTH;
}