Geometry Class Reference

#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.

• \(a\): Earth radius, the distance from the Earth's center to the radar
• \(b\): beam distance; the distance from the radar to the bin
• \(c\): distance from the Earth's center to the bin
• \(h = c - a\): altitude from ground to beam point
• \(g\): 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:

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

Always

\[ \sin(\gamma) = \sin(\eta+\pi/2) = \cos(\eta) \]

Because \( \alpha = \pi - \gamma - \beta \) in a triangle,

\[ \sin(\alpha) = \sin(\pi-\gamma-\beta) = \sin(\beta+\gamma) = \sin(\beta + \eta+\pi/2) = \cos(\beta + \eta) \]

Finally,

\[ h = a·( \frac{\cos(\eta)}{\cos(\beta + \eta)} - 1) \]

heightFromEtaGround()

double heightFromEtaGround ( double  eta, double  g  )

static

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

The altitude of a point at ground distance g and elevation eta.

Parameters

eta	Elevation in radians
g	Ground distance in metres

See also

#heightFromEtaBeta(double, double) which is preferred as being faster.

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The documentation for this class was generated from the following files:

• src/radar/Geometry.h
• src/radar/Geometry.cpp