class segment

A class for the parametric representation of a line segment in 2-D.

Public Fields

bool periodic

set this to true if segment closes upon itself

double tmin

min of time-like parameter

double tmax

max of time-like parameter

double xg

x position of centre of gravity

double yg

y position of centre of gravity

double length

typical length scale of segment

Public Methods

segment()

Constructor.

segment(const Vec &t_in, const Vec &x_in, const Vec &y_in, bool periodic_in=false)

Constructor.

bool operator==(const segment &sb)

Identity (check is based on memory address, thus the test returns false if the two objects have the same (t, x, y) support but are not the same instance).

void load(const Vec &t_in, const Vec &x_in, const Vec &y_in, bool periodic_in=true)

Build object.

void plot(bool hold=true, bool display=true, bool freshstart=true)

Simple 2-D plot.

double x(const double &ti)

Get x at ti.

Vec x(const Vec &ti)

Get x at ti.

double y(const double &ti)

Get y at ti.

Vec y(const Vec &ti)

Get y at ti.

double xDot(const double &ti)

Get dx/dt at ti.

Vec xDot(const Vec &ti)

Get dx/dt at ti.

double yDot(const double &ti)

Get dy/dt at ti.

Vec yDot(const Vec &ti)

Get dy/dt at ti.

double arcLengthIntegral(double (f)(double* ))

Get integral dl*f(t) over segment.

double arcLengthIntegral(double (f)(double* ), const double &ti)

Get integral dl*f(t) up to ti.

Vec arcLengthIntegral(double (f)(double* ), const Vec &ti)

Get integral dl*f(t) up to ti.

double arcLength(void)

Get the arc length.

double arcLength(const double &ti)

Get the arc length up to ti.

Vec arcLength(const Vec &ti)

Get the arc length up to ti.

double arcLengthDot(const double &ti)

Get dl/dt at ti.

Vec arcLengthDot(const Vec &ti)

Get dl/dt at ti.

Documentation

A class for the parametric representation of a line segment in 2-D. Segment uses a cubic spline representation of x(t) and y(t) where t is the parametric variable and plays the role of a time-like variable. Segment has methods to compute the derivative of x and y versus t at any point. Likewise, there are methods to compute the arc length and other integrals.

bool periodic

set this to true if segment closes upon itself

double tmin

min of time-like parameter

double tmax

max of time-like parameter

double xg

x position of centre of gravity

double yg

y position of centre of gravity

double length

typical length scale of segment

segment()

Constructor.

See Also:

load

segment(const Vec &t_in, const Vec &x_in, const Vec &y_in, bool periodic_in=false)

Constructor. Similar to calling segment() followed by load method.

Parameters:

t_in - time-like sampling (must be in increasing order)
x_in - x positions
y_in - y positions
periodic_in - set this to true if segment closes upon itself

See Also:

load

bool operator==(const segment &sb)

Identity (check is based on memory address, thus the test returns false if the two objects have the same (t, x, y) support but are not the same instance).

Parameters:

other - segment

void load(const Vec &t_in, const Vec &x_in, const Vec &y_in, bool periodic_in=true)

Build object. Use this method if nor argument c'tor was used.

Parameters:

t_in - time-like slices (must be in increasing order)
x_in - x positions
y_in - y positions
periodic_in - set this to true if segment closes upon itself

See Also:

segment()

void plot(bool hold=true, bool display=true, bool freshstart=true)

Simple 2-D plot.

Parameters:

- hold set this to true if several segment plots are to overlap
- display set this to true to have window popping up
- freshstart set this to true to erase any previously stored plot object

double x(const double &ti)

Get x at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

x position

Vec x(const Vec &ti)

Get x at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

x position

double y(const double &ti)

Get y at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

y position

Vec y(const Vec &ti)

Get y at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

y position

double xDot(const double &ti)

Get dx/dt at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

xt = dx/dt

Vec xDot(const Vec &ti)

Get dx/dt at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

xt = dx/dt

double yDot(const double &ti)

Get dy/dt at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

yt = dy/dt

Vec yDot(const Vec &ti)

Get dy/dt at ti. Uses a cubic spline interpolation to get the coordinate.

Parameters:

ti - 'time'

Returns:

yt = dy/dt

double arcLengthIntegral(double (f)(double* ))

Get integral dl*f(t) over segment. Here, dl is the infinitesimal arc length element.

Parameters:

f - integrand

Returns:

integral = integral dl*f(t)

double arcLengthIntegral(double (f)(double* ), const double &ti)

Get integral dl*f(t) up to ti. Here, dl is the infinitesimal arc length element.

Parameters:

f - integrand
ti - right end point

Returns:

integral = integral dl*f(t) to ti

Vec arcLengthIntegral(double (f)(double* ), const Vec &ti)

Get integral dl*f(t) up to ti. Here, dl is the infinitesimal arc length element.

Parameters:

f - integrand
ti - right end point

Returns:

integral = integral dl*f(t) to ti

double arcLength(void)

Get the arc length. Equivalent to integral dl. Here, dl is the infinitesimal arc element.

Returns:

integral = integral dl over segment

double arcLength(const double &ti)

Get the arc length up to ti. Equivalent to integral dl over[tmin, ti].

Parameters:

ti - right end point

Returns:

integral = integral dl over segment

Vec arcLength(const Vec &ti)

Get the arc length up to ti. Equivalent to integral dl over[tmin, ti].

Parameters:

ti - right end point

Returns:

integral = integral dl over segment

double arcLengthDot(const double &ti)

Get dl/dt at ti. Here, dl is the infinitesimal arc length element.

Parameters:

ti - 'time'

Returns:

lt the derivative dl/dt l is the arc length

Vec arcLengthDot(const Vec &ti)

Get dl/dt at ti.

Parameters:

ti - 'time'

Returns:

lt the derivative dl/dt l is the arc length

This class has no child classes.

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