minor_arc class

minor_arc

The minor_arc class, a descendant of great_circle, defines an arc on a sphere. It requires two directions; one is the starting point, and the other is the end point.

Constructor

minor_arc(const direction_cosine& s, const direction_cosine& e)

Create a minor_arc from two directions.

s

the starting point of the arc.

e

the end point of the arc.

Functions

const double
separation_cosine(const great_circle& gc) const

Obtain cosθ, where θ is the separation angle between another great_circle instance. Inherited from great_circle.

gc

another great_circle instance.

const angle
separation(const great_circle& gc) const

Obtain θ, where θ is the separation angle between another great_circle instance. Inherited from great_circle.

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 this instance. Inherited from great_circle.

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 this instance. Inherited from great_circle.

p

a direction_cosine instance.

const direction_cosine
foot_of(const direction_cosine& p) const

Obtain the foot of the perpendicular from p to this instance. Inherited from great_circle.

p

a direction_cosine instance.

Caution

When p is identical to the pole, the foot cannot be specified. This function, however, does not throw an exception. Instead, it returns the foot from either (1,0,0) or (0,1,0).

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.

void
print(const size_t N=64) const

List the points on the circle in stdout. Inherited from great_circle.

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.

Attributes

pole

(direction_cosine) the pole of the arc. Inherited from great_circle.

s

(direction_cosine) the starting point of the arc.

e

(direction_cosine) the end point of the arc.