trajectory class

trajectory

Constructors

trajectory(const trail& t)

Construct a trajectory instance from a single trail instance.

t

the trail instance.

trajectory(const std::initializer_list list)

Construct a trajectory instance from a list of trail instances.

list

the list of trail instances.

trajectory(const std::vector list)

Construct a trajectory instance from a list of trail instances.

list

the vector array containing trail instances.

Functions

const trail&
arc() const

Obtain a reference to the current trail arc.

const footprint&
s() const

Obtain a reference to the starting point of the current trail arc.

const footprint&
e() const

Obtain a reference to the end point of the current trail arc.

const std::vector&
list() const

Obtain a reference to the vector array of the trail instances.

void
append(const trail& t)

Append a single trail instance.

t

the trail instance.

void
append(const std::initializer_list list)

Append trail instances in the list.

list

the list of trail instances.

void
append(const std::vector list)

Append trail instances in the vector array.

list

the vector array of trail instances.

const double
separation_cosine(const great_circle& gc) const

Obtain cosθ, where θ is the separation angle between a great_circle instance and the trail arc of this instance. This function takes into account the uncertainty of the trail arc.

gc

another great_circle instance.

const angle
separation(const great_circle& gc) const

Obtain θ, where θ is the separation angle between a great_circle instance and the trail arc of this instance. This function takes into account the uncertainty of the trail arc.

gc

another great_circle instance.

const double
separation_cosine(const direction_cosine& p) const

Obtain cosθ, where θ is the separation angle between the point p and the foot of the perpendicular from p to the trail arc of this instance. This function takes into account the uncertainty of the trail arc.

p

a direction_cosine instance.

const angle
separation(const direction_cosine& p) const

Obtain θ, where θ is the separation angle between the point p and the foot of the perpendicular from p to the trail arc of this instance. This function takes into account the uncertainty of the trail arc.

p

a direction_cosine instance.

const double
distance_cosine(const direction_cosine& p) const

Calculate cosθ, where θ is the separation angle between the nearest point on the arc and the point p. Note that the difference from separation_cosine(), which returns the separation angle to the great circle.

p

a direction_cosine instance.

const angle
distance(const direction_cosine& p) const

Calculate θ, where θ is the separation angle between the nearest point on the arc and the point p. Note that the difference from separation_cosine(), which returns the separation angle to the great circle.

p

a direction_cosine instance.

const direction_cosine
extrapolate(const double f) const

Calculate the extrapolated direction along the arc. This function returns the starting and end points for f=0.0 and f=1.0, respectively. Thus, the function interpolates the arc in case that f is between 0.0 and 1.0.

f

an extrapolation factor.

const footprint
propagate(const sec_t& dT, const double R = 100.0) const

Extrapolate the trail arc by the time span of dT. The uncertainty is calculated based on the uncertainties of the arc. This function partly takes into account the acceleration and deceleration of the trails.

dT

a propagation time span since the end point.

R

an optional regularization parameter to take into account acceleration.

const footprint
propagate(const timestamp_t& T, const double R = 100.0) const

Extrapolate the trail arc to the time point T. The uncertainty is calculated based on the uncertainties of the arc. This function partly takes into account the acceleration and deceleration of the trails.

T

a time point of the extrapolated point.

R

an optional regularization parameter to take into account acceleration.

const bool
intersect_with(const direction_cosine& p) const

Return true if the point p is located within the uncertainty region of the trail arc.

p

a direction_cosine instance.

const bool
intersect_with(const minor_arc& arc) const

Return true if a segment arc crosses the uncertainty region of the trail arc.

arc

a minor_arc instance.

const bool
intersect_with(const trail& arc) const

Return true if a trail arc crosses the uncertainty region of the trail arc.

arc

a trail instance.

const bool
intersect_with(const trajectory& trj) const

Return true if a trail arc crosses the uncertainty region of the trail arc.

trj

a trajectory instance.

const bool
colinear_with(const great_circle& gc, const angle& tol = degree(5.0)) const

Return true when the separation angle between the poles is smaller than tol.

gc

a great_circle instance.

tol

a tolerance of the separation angle.

const bool
colinear_with(const minor_arc& arc, const angle& tol = degree(5.0)) const

Return true when the separation angle between the poles is smaller than tol.

arc

a minor_arc instance.

tol

a tolerance of the separation angle.

const bool
colinear_with(const trail& arc, const angle& tol = degree(5.0)) const

Return true when the separation angle between the poles is smaller than tol. The uncertainties are taken into account.

arc

a trail instance.

tol

a tolerance of the separation angle.

const bool
colinear_with(const trajectory& trj, const angle& tol = degree(5.0)) const

Return true when the separation angle between the poles is smaller than tol. The uncertainties are taken into account.

arc

a trajectory instance.

tol

a tolerance of the separation angle.

const bool
match(const trail& arc, const angle& dtol = degree(5.0), const angle& rtol = arcmin(5.0), const double margin = 1.0) const

Return true when another trail instance is consistent with the current one. First, the distance between the poles of both instances should be smaller than rtol. Then, the current trail arc is extrapolated to the time of the given trail. The extrapolated starting and end points are compared with those of the given arc. The separation angles between the end points should be smaller than dtol, respectively.

arc

another trail instance.

dtol

a tolerance angle in the distance between the arcs.

rtol

a tolerance angle in the separation between the poles.

const bool
match(const trajectory& trj, const angle& dtol = degree(5.0), const angle& rtol = arcmin(5.0), const double margin = 1.0) const

Return true when another trajectory instance is consistent with the current one. First, the distance between the poles of both instances should be smaller than rtol. Then, the current trail arc is extrapolated to the time of the given trail. The extrapolated starting and end points are compared with those of the given arc. The separation angles between the end points should be smaller than dtol, respectively.

trj

another trajectory instance.

dtol

a tolerance angle in the distance between the arcs.

rtol

a tolerance angle in the separation between the poles.

const angle
error_at(const direction_cosine& q, const bool skip=true) const

Calculate the uncertainty at the foot of the perpendicular from q to the great circle.

q

a direction_cosine instance, a reference point.

skip

set true if q is certainly on the great circle of this instance.

void
print(const size_t N=64) const

List the points on the circle in stdout.

N

the number of vertices to be listed.

void
print_arc(const size_t N=64) const

List the points on the arc in stdout.

N

the number of vertices to be listed.

void
print_error(const size_t N=64) const

List the uncertainty region in stdout. This function outputs N pairs of footprint instances which define the boundary of the uncertainty region. The output format is optimized for the splot grid of gnuplot.

N

the number of partitions to be listed.