def test_angle_from_points(self):
for x in self.angle_checks:
angle = Triangle.angle_from_points(x[0], x[2], x[1])
self.assertAlmostEqual(
x[3], angle, places=10,
msg="Check failed for: {}; result is: {}".format(x, angle)
)
def central_angle(start_point, end_point, arc_point):
"""
Calculates the measure in radians of the arc between <start_point> and <end_point>
and containing <arc_point> in the circumscribed circle.
The result is equal to the central angle (S-O-E).
The inscribed angle S-A-E can be calculated as:
angle(S-A-E) = pi - angle(S-O-E) / 2
On degenerate input (e.g. identical start/end/arc points) will raise ValueError.
A
S _..-~~~+-._ E S _..-~~~--._ E
,-+ +-. ,-+ +-.
,' \ / `. ,' \ / `.
/ \ / \ / \ / \
/ \angle/ \ / \ / \
/ \.-./ \ / ,\ /. \
; \ / : ; / \ / \ :
| + | | ( + ) |
: O ; : \ O / ;
\ / \ `-----' /
\ / \ angle /
\ / \ /
`. ,' `. ,'
'-. _.-' '+. _.-'
`'------'' A `'------''
Notation:
S -> start_point
E -> end_point
A -> arc_point
angle -> result (expressed in radians)
"""
inscribed_angle = Triangle.angle_from_points(start_point, arc_point,
end_point)
return 2.0 * (math.pi - inscribed_angle)
def central_angle(start_point, end_point, arc_point):
"""
Calculates the measure in radians of the arc between <start_point> and <end_point>
and containing <arc_point> in the circumscribed circle.
The result is equal to the central angle (S-O-E).
The inscribed angle S-A-E can be calculated as:
angle(S-A-E) = pi - angle(S-O-E)/2
On degenerate input (e.g. identical start/end/arc points) will raise ValueError.
A
S _..-~~~+-._ E S _..-~~~--._ E
,-+ +-. ,-+ +-.
,' \ / `. ,' \ / `.
/ \ / \ / \ / \
/ \angle/ \ / \ / \
/ \.-./ \ / ,\ /. \
; \ / : ; / \ / \ :
| + | | ( + ) |
: O ; : \ O / ;
\ / \ `-----' /
\ / \ angle /
\ / \ /
`. ,' `. ,'
'-. _.-' '+. _.-'
`'------'' A `'------''
Notation:
S -> start_point
E -> end_point
A -> arc_point
angle -> result (expressed in radians)
"""
inscribed_angle = Triangle.angle_from_points(start_point, arc_point, end_point)
return 2.0 * (math.pi - inscribed_angle)
