#include <Geometry.h>

Public Member Functions
double	bFromGH (double g, double h)

double	normalizedBeamPower (double angle)

void	findClosestElevations (const float &elevationAngle, int &elevationIndexLower, float &elevationAngleLower, int &elevationIndexUpper, float &elevationAngleUpper)

Static Public Member Functions
static double	heightFromEtaBeam (double eta, double b)
	Altitude, given elevation [rad] and bin distance [m].

static double	heightFromEtaBeta (double eta, double beta)
	Altitude, given elevation [rad] and ground angle [rad].

static double	heightFromEtaGround (double eta, double g)
	Altitude, given elevation [rad] and ground distance [m].

static double	betaFromGround (double g)

static double	beamFromBetaH (double beta, double h)

static double	beamFromEtaH (double eta, double h)
	The on-beam distance at (elevation) and (altitude).

static double	beamFromEtaBeta (double eta, double beta)
	The on-beam distance at (elevation) and ground angle (beta).

static double	beamFromEtaGround (float eta, float g)
	The on-beam distance at (elevation) and ground distance (groundDist).

static double	groundFromEtaBeam (double eta, double beam)
	Given elevation in radians and on-beam distance, returns the distance from radar to the ground point under the bin.

static double	gammaFromEtaH (double eta, double height)
	Given elevation angle `eta` and altitude `h`, returns the ground angle.

static double	groundFromEtaH (double eta, double h)

static double	etaFromBetaH (double beta, double h)
	Given ground angle `beta` and altitude `h`, returns the elevation angle.

static double	etaFromGH (double g, double h)
	Given ground distance `g` and altitude `h`, returns elevation angle.

Public Attributes
float	beamWidth

std::vector< float >	elevationAngles
	Note: radians!

std::vector< unsigned int >	bins

Static Public Attributes
static double	EARTH_RADIUS_43 = 4.0/3.0 * drain::EARTH_RADIUS

Detailed Description

Distances in meters, angles in radians.

: Earth radius, the distance from the Earth's center to the radar
: beam distance; the distance from the radar to the bin
: distance from the Earth's center to the bin
: altitude from ground to beam point
: ground distance; surface distance from the radar to the ground point

eta $\eta$ : beam elevation

alpha $\alpha = \angle(b,c)$ : "sky angle",
beta $\beta = \angle(a,c)$ : "ground angle"
gamma $\gamma = \angle(a,b) = \eta + \pi/2$ : "radar angle"
r = radian
d = degree

Cosine rule:

$c^2 = a^2 + b^2 - 2ab·\cos(\gamma);$

Sine rule:

$\frac{\sin\alpha}{a} = \frac{\sin\beta}{b} = \frac{\sin\gamma}{c}$

Member Function Documentation

◆ beamFromBetaH()

double beamFromBetaH	(	double	beta,
		double	h
	)

static

The on-beam distance at ground angle beta and altitude h.

By cosine rule:

$b^2 = a^2 + c^2 - 2ac\cos\beta = a^2 + (a^2 + 2ah+ h^2) - 2a(a + h)\cos\beta = 2a(a+h) + h^2 - 2a(a + h)\cos\beta = 2a(a+h)(1-\cos\beta) + h^2$

◆ beamFromEtaBeta()

double beamFromEtaBeta	(	double	eta,
		double	beta
	)

static

The on-beam distance at (elevation) and ground angle (beta).

By sine rule: sin(beta)/b = sin(alpha)/a => b = sin(beta) * a/sin(alpha).

◆ beamFromEtaGround()

double beamFromEtaGround	(	float	eta,
		float	g
	)

static

The on-beam distance at (elevation) and ground distance (groundDist).

Let b = beam distance and a = EARTH_RADIUS_. By sine rule: sin(beta)/b = sin(alpha)/a => b = sin(beta) * a/sin(alpha).

Angle(RADAR,BIN)

Angle(BIN->RADAR,BIN->GROUND_POINT)

◆ beamFromEtaH()

double beamFromEtaH	(	double	eta,
		double	h
	)

static

The on-beam distance at (elevation) and (altitude).

By sine rule: sin(gamma)/c = sin(beta)/b => b = sin(beta)*c/sin(gamma).

◆ etaFromBetaH()

double etaFromBetaH	(	double	beta,
		double	h
	)

static

Given ground angle beta and altitude h, returns the elevation angle.

By sine rule:

$\sin(\beta)/b = \sin(\gamma)/c \Leftrightarrow \sin(\beta) * c/b = \sin(\gamma) /// = \sin(\pi-\gamma) = /// \sin(\pi-(\eta + \pi/2)) = \sin(\pi/2-\eta) = \cos(\eta) \sin(\pi/2+\eta) = \sin(\pi-(\pi/2+\eta)) = \sin(\pi/2-\eta) = \cos(\eta) \Rightarrow \eta = \arccos( \sin(\beta) * c/b ) // WRONG! ALWAYS POSITIVE!$

By cosine rule:

$c^2 = a^2 + b^2 - 2ab\cos\gamma \Leftrightarrow \cos\gamma = (a^2 + b^2 - c^2) / 2ab = = (a^2 + (a^2 + c^2 - 2ac\cos\beta) - c^2) / 2ab = (2a^2 - 2ac\cos\beta) / 2ab = (a-c\cos\beta) / b$

◆ gammaFromEtaH()

double gammaFromEtaH	(	double	eta,
		double	h
	)

static

Given elevation angle eta and altitude h, returns the ground angle.

By sine rule:

$\frac{\sin\alpha}{a} = \frac{\sin\gamma}{c} = \frac{\sin\gamma}{a+h} \Leftrightarrow \sin\alpha =\frac{a}{a+h}\sin\gamma \Rightarrow \gamma = \pi - \gamma - \alpha = \pi - (\eta+\pi/2) - \arcsin \left( \frac{a}{a+h}\sin(\eta+\pi/2) \right)$

◆ heightFromEtaBeam()

double heightFromEtaBeam	(	double	eta,
		double	b
	)

static

Altitude, given elevation [rad] and bin distance [m].

The altitude of a point at beam distance (b) and elevation (eta).

By cosine rule:

$c^2 = a^2 + b^2 - 2ab\cos(\gamma);$

◆ heightFromEtaBeta()

double heightFromEtaBeta	(	double	eta,
		double	beta
	)

static

Altitude, given elevation [rad] and ground angle [rad].

The altitude of a point above ground.

Parameters

eta	Elevation in radians
beta	Ground angle

By sine rule:

$\sin(\gamma)/c = \sin(\alpha)/a \Leftrightarrow c = a · \frac{\sin(\gamma)}{\sin(\alpha)} \Leftrightarrow h = c-a = a·( \frac{\sin(\gamma)}{\sin(\alpha)} - 1)$