ellipse_geometry Class Reference

Ellipse geometry class. More...

#include <sc_ellipse_geometry.h>

Public Member Functions
	ellipse_geometry ()
	Constructor. More...
	ellipse_geometry (double A, double B, double C, double D, double E, double F)
	Constructor for Coefficients. More...
	ellipse_geometry (ellipse_coefficients coeffs)
	Constructor for Coefficients as a struct. More...
	ellipse_geometry (double x0, double y0, double a1, double a2, double phi)
	Constructor for Parameters. More...
	ellipse_geometry (ellipse_geometry_struct params)
	Constructor for Parameters. More...
ellipse_geometry_struct	get_ellipse_params ()
	Retrieve ellipse geometric parameters. More...
ellipse_coefficients	get_ellipse_coeff ()
	Retrieve ellipse equation coefficients. More...
ellipse_points	get_ellipse_pts (int n, double th0=0)
	Compute the (x,y) coordinates for n points around an ellipse. More...
ellipse_point_on_tangent	get_ellipse_point_on_tangent (double alpha)
	Compute point on ellipse where given tangent line touches. More...
ellipse_min_dist	get_ellipse_min_dist (double xp, double yp, int sense=-1)
	Compute the minimum distance from a point to a general 2D ellipse. More...
ellipse_geometry_struct	ellipsoid_to_ellipse (ml_matrix M, ml_matrix p)
	Compute parameters of ellipse, projection of ellipsoid onto XZ plane. More...

Static Public Member Functions
static ellipse_geometry_struct	get_ellipse_with_index (ellipse_geometry_struct_m ellipse_geom_m, int index)
	Get a specific ellipse_geometry_struct from ellipse_geometry_struct_m. More...
static void	set_ellipse_with_index (ellipse_geometry_struct_m &ellipse_geom_m, int index, double x0, double y0, double a1, double a2, double phi)
	set a set of ellipse_geometry parameters to a ellipse_geometry_struct_m More...

Detailed Description

Ellipse geometry class.

Constructor & Destructor Documentation

ellipse_geometry() [1/5]

ellipse_geometry::ellipse_geometry

(

)

Constructor.

Default constructor.

References ellipse_coefficients::A, ellipse_geometry_struct::a1, ellipse_geometry_struct::a2, ellipse_coefficients::B, ellipse_coefficients::C, ellipse_coefficients::D, ellipse_coefficients::E, ellipse_coefficients::F, ellipse_geometry_struct::phi, ellipse_geometry_struct::x0, and ellipse_geometry_struct::y0.

ellipse_geometry() [2/5]

ellipse_geometry::ellipse_geometry	(	double	A,
		double	B,
		double	C,
		double	D,
		double	E,
		double	F
	)

Constructor for Coefficients.

Creates an ellipse_geometry Object given the coefficients for the general equation of an ellipse A*x^2 + 2*B*x*y + C*y^2 + 2*D*x + 2*E*y + F = 0.

Parameters

A	Ellipse coefficient on x^2
B	Ellipse coefficient on xy
C	Ellipse coefficient on y^2
D	Ellipse coefficient on x
E	Ellipse coefficient on y
F	Ellipse constant term

References ellipse_coefficients::A, ellipse_coefficients::B, ellipse_coefficients::C, ellipse_coefficients::D, ellipse_coefficients::E, and ellipse_coefficients::F.

ellipse_geometry() [3/5]

ellipse_geometry::ellipse_geometry

(

ellipse_coefficients

coeffs

)

Constructor for Coefficients as a struct.

Creates an ellipse_geometry Object given the coefficients for the general equation of an ellipse A*x^2 + 2*B*x*y + C*y^2 + 2*D*x + 2*E*y + F = 0.

Parameters

coeffs

data structure of ellipse coefficients

ellipse_geometry() [4/5]

ellipse_geometry::ellipse_geometry	(	double	x0,
		double	y0,
		double	a1,
		double	a2,
		double	phi
	)

Constructor for Parameters.

Creates an ellipse_geometry Object given the geometric parameters of an ellipse A*x^2 + 2*B*x*y + C*y^2 + 2*D*x + 2*E*y + F = 0.

Parameters

x0	x-coordinate center of ellipse
y0	y-coordinate center of ellipse
a1	Semi-major axis
a2	Semi-minor axis
phi	Angle from x axis to semi-major axis

References ellipse_geometry_struct::a1, ellipse_geometry_struct::a2, ellipse_geometry_struct::phi, ellipse_geometry_struct::x0, and ellipse_geometry_struct::y0.

ellipse_geometry() [5/5]

ellipse_geometry::ellipse_geometry

(

ellipse_geometry_struct

params

)

Constructor for Parameters.

Creates an ellipse_geometry Object given the geometric parameters of an ellipse A*x^2 + 2*B*x*y + C*y^2 + 2*D*x + 2*E*y + F = 0.

Parameters

params

data structure of ellipse grometry parameters

Member Function Documentation

get_ellipse_params()

ellipse_geometry_struct ellipse_geometry::get_ellipse_params

(

)

Retrieve ellipse geometric parameters.

Returns

Data structure with x-coordinate center, y-coordinate center, Semi-major axis, Semi-minor axis, Angle from x axis to semi-major axis (0,pi)

get_ellipse_coeff()

ellipse_coefficients ellipse_geometry::get_ellipse_coeff

(

)

Retrieve ellipse equation coefficients.

Returns

Data strucure with ellipse coefficients on x^2, xy, y^2, x, y, constant term

get_ellipse_pts()

ellipse_points ellipse_geometry::get_ellipse_pts	(	int	n,
		double	th0 = 0
	)

Compute the (x,y) coordinates for n points around an ellipse.

Parameters

n	Number of points around ellipse to compute
th0	Angle from semi-major axis for first point. Default 0.

Returns

Data structure with x-coordinate on ellipse at tangent line, y-coordinate on ellipse at tangent line, Radial distance from center to points around ellipse, dr/dtheta, dx/dtheta, dy/dtheta, Slope dy/dx for tangent line, Phase angle starting at th0

References ellipse_geometry_struct::a1, ellipse_geometry_struct::a2, ellipse_points::drdt, ellipse_points::dxdt, ellipse_points::dydt, ellipse_geometry_struct::phi, ellipse_points::r, ellipse_points::slope, ellipse_points::theta, ellipse_points::x, ellipse_geometry_struct::x0, ellipse_points::y, and ellipse_geometry_struct::y0.

get_ellipse_point_on_tangent()

ellipse_point_on_tangent ellipse_geometry::get_ellipse_point_on_tangent

(

double

alpha

)

Compute point on ellipse where given tangent line touches.

Given a tangent line direction, compute point on ellipse where the tangent line touches.

Also compute the slope and offset for the equation: y = m*x+b

Parameters

alpha

Angle that the tangent line makes with x-axis (rad)

Returns

Data stucture with x-coordinate on ellipse at tangent line, y-coordinate on ellipse at tangent line, b: Constant y-offset for tangent line (y=m*x+b), m: Slope dy/dx for tangent line (y=m*x+b)

References ellipse_coefficients::A, ellipse_coefficients::B, ellipse_point_on_tangent::b, ellipse_coefficients::C, ellipse_coefficients::D, ellipse_coefficients::E, ellipse_coefficients::F, ellipse_point_on_tangent::m, sc_warn(), ellipse_point_on_tangent::x, and ellipse_point_on_tangent::y.

get_ellipse_min_dist()

ellipse_min_dist ellipse_geometry::get_ellipse_min_dist	(	double	xp,
		double	yp,
		int	sense = -1
	)

Compute the minimum distance from a point to a general 2D ellipse.

Parameters

xp	x-coordinate of point
yp	y-coordinate of point
sense	Minimum distance (-1) or maximum distance (1). Default is -1.

Returns

Datastructure with Distance from point on ellipse (x,y) to point (xp,yp), x-coord. on ellipse where distance to point is minimum, y-coord. on ellipse where distance to point is minimum, Flag indicating whether the point (x0,y0) is in the ellipse or not.

References ellipse_geometry_struct::a1, ellipse_geometry_struct::a2, ellipse_min_dist::d, ellipse_min_dist::in_ellipse, ellipse_geometry_struct::phi, ellipse_min_dist::x, ellipse_geometry_struct::x0, ellipse_min_dist::y, and ellipse_geometry_struct::y0.

ellipsoid_to_ellipse()

ellipse_geometry_struct ellipse_geometry::ellipsoid_to_ellipse	(	ml_matrix	M,
		ml_matrix	p
	)

Compute parameters of ellipse, projection of ellipsoid onto XZ plane.

Parameters

M	(3,3) matrix of principal axes directions
p	(3,1) matrix of Semi-major axes, [a;b;c]

Returns

Data structure with Semi-major axis, Semi-minor axis, Angle from x axis to semi-major axis (0,pi) of ellipse projection

References ellipse_coefficients::A, ellipse_coefficients::B, ellipse_coefficients::C, ellipse_coefficients::D, ellipse_coefficients::E, and ellipse_coefficients::F.

get_ellipse_with_index()

ellipse_geometry_struct ellipse_geometry::get_ellipse_with_index ( ellipse_geometry_struct_m  ellipse_geom_m, int  index  )

static

Get a specific ellipse_geometry_struct from ellipse_geometry_struct_m.

Parameters

ellispe_geom_m	data structure of matricex representing ellipse geometry data
index	index number of the specific ellipse_geometry_struct to retrieve

Returns

Data structure with x-coordinate center, y-coordinate center, Semi-major axis, Semi-minor axis, Angle from x axis to semi-major axis (0,pi) for a specific ellipse

References ellipse_geometry_struct::a1, ellipse_geometry_struct_m::a1, ellipse_geometry_struct::a2, ellipse_geometry_struct_m::a2, ellipse_geometry_struct::phi, ellipse_geometry_struct_m::phi, ellipse_geometry_struct::x0, ellipse_geometry_struct_m::x0, ellipse_geometry_struct::y0, and ellipse_geometry_struct_m::y0.

set_ellipse_with_index()

void ellipse_geometry::set_ellipse_with_index ( ellipse_geometry_struct_m &  ellipse_geom_m, int  index, double  x0, double  y0, double  a1, double  a2, double  phi  )

static

set a set of ellipse_geometry parameters to a ellipse_geometry_struct_m

Parameters

ellispe_geom_m	data structure of matricex representing ellipse geometry data
index	index number to add the parameters to
x0	x-coordinate center of ellipse
y0	y-coordinate center of ellipse
a1	Semi-major axis
a2	Semi-minor axis
phi	Angle from x axis to semi-major axis

References ellipse_geometry_struct_m::a1, ellipse_geometry_struct_m::a2, ellipse_geometry_struct_m::phi, ellipse_geometry_struct_m::x0, and ellipse_geometry_struct_m::y0.