def test_equals():
# test for equals
assert (equals(0.1, 0.1))
assert (equals(1.0, 1.0-1e-15))
assert (equals(1.0, 1.0-1e-5) is False)
assert (equals(-2.0, -2.0+1e-15))
assert (equals(-2.0, -2.0+1e-5) is False)
def test_phase_diff_complex():
# test for phase_diff_complex
assert (equals(phase_diff_complex(1.0+1.0j, 1.0+0.0j), 45.0))
assert (equals(phase_diff_complex(1.0+0.0j, 1.0+1.0j), 315.0))
assert (equals(phase_diff_complex(1.0+1.0j, -2.0+2.0j), 270.0))
assert (equals(phase_diff_complex(1.0+1.0j, 2.0-2.0j), 90.0))
assert (equals(phase_diff_complex(3.0+4.0j, 3.0+4.0j), 0.0))
def test_norm_complex():
# test for norm_complex
assert (equals(norm_complex(3.0+4.0j), 25.0))
assert (equals(norm_complex(3.0-4.0j), 25.0))
assert (equals(norm_complex(1.0+2.0j), 5.0))
assert (equals(norm_complex(-1.0+2.0j), 5.0))
assert (equals(norm_complex(-2.0-2.0j), 8.0))
def test_commonpoint_of_circles_complex():
# test for commonpoint_of_circles_complex
c1, c2 = commonpoint_of_circles_complex(0 + 1j, 5, 4 + 3j, math.sqrt(
5)) # x^2 + (y-1)^2 = 25, (x-4)^2 + (y-3)^2 = 5 の交点 (3,5), (5,1)
assert (equals(c1.real, 3))
assert (equals(c1.imag, 5))
assert (equals(c2.real, 5))
assert (equals(c2.imag, 1))
def test_commonpoint_of_line_circle_complex():
# test for commonpoint_of_line_circle_complex
c1, c2 = commonpoint_of_line_circle_complex(
0 + 1j, 1 + 2j, 0 + 0j, 1) # x^2+y^2=1 と y=x+1 の交点 (0,1), (-1,0)
assert (equals(c1.real, 0))
assert (equals(c1.imag, 1))
assert (equals(c2.real, -1))
assert (equals(c2.imag, 0))
def test_cross_point_of_segments_complex():
# test for crosspoint_of_segments_complex
assert (equals(
crosspoint_of_segments_complex(-1 - 1j, 1 + 3j, -1 + 1j, 1 - 1j).real,
-1 / 3)) # y = 2x + 1 と y = -x の交点 (-1/3, 1/3)
assert (equals(
crosspoint_of_segments_complex(-1 - 1j, 1 + 3j, -1 + 1j, 1 - 1j).imag,
1 / 3))
def test_dist_between_segments_complex():
# test for dist_between_segments_complex
assert (equals(
dist_between_segments_complex(0 + 0j, 2 + 2j, 0 + 2j, 2 + 0j),
0)) # 線分が交わる
assert (equals(
dist_between_segments_complex(0 + 0j, 10 + 0j, 5 + 5j, 5 + 6j), 5))
assert (equals(
dist_between_segments_complex(0 + 0j, 0 + 10j, 5 + 5j, 5 + 6j), 5))
def test_dist_between_point_line_complex():
# test for dist_between_point_line_complex
assert (equals(
dist_between_point_line_complex(0 + 0j, complex(1,
math.sqrt(3)), 2 + 0j),
math.sqrt(3))) # y = √3x と (2, 0) の距離 √3
assert (equals(dist_between_point_line_complex(0 + 0j, 0 + 1j, 2 + 0j),
2)) # y 軸と (2, 0) の距離 2
assert (equals(dist_between_point_line_complex(0 + 0j, 0 + 1j, 0 + 3j),
0)) # on line
def test_dist_between_point_segment_complex():
# test for dist_between_point_segment_complex
assert (equals(
dist_between_point_segment_complex(0 + 0j, 10 + 20j, 3 + 1j),
math.sqrt(5))) # 直線 y=2x と (3,1) の距離は √5 だが
assert (equals(dist_between_point_segment_complex(0 + 0j, -1 - 2j, 3 + 1j),
math.sqrt(10))) # このような線分になると (0, 0) との距離が最短となる
assert (equals(
dist_between_point_segment_complex(5 + 10j, 10 + 20j, 3 + 1j),
math.sqrt(85))) # このような線分になると (5, 10) との距離が最短となる
assert (equals(dist_between_point_segment_complex(0 + 0j, 0 + 10j, 0 + 5j),
0)) # on segment
def test_rotate_complex():
# test for rotate_complex
assert (equals(math.degrees(cmath.phase(rotate_complex(1.0+1.0j, 45))), 90))
assert (equals(math.degrees(cmath.phase(rotate_complex(1.0+1.0j, -45))), 0))
assert (equals(rotate_complex(3.0+4.0j, 180).real, -3.0))
assert (equals(rotate_complex(3.0+4.0j, 180).real, -3.0))
assert (equals(rotate_complex(1.0+0.0j, 90).real, 0.0))
assert (equals(rotate_complex(1.0+0.0j, 90).imag, 1.0))
assert (equals(rotate_complex(3.0+5.0j, 360).real, 3.0))
assert (equals(rotate_complex(3.0+5.0j, 360).imag, 5.0))
assert (rotate_complex(3.0+5.0j, 0) == 3.0+5.0j)
assert (rotate_complex(3.0+5.0j, 0) == 3.0+5.0j)
assert (equals(abs(rotate_complex(cmath.rect(1.3, math.radians(35)), 52)), 1.3))
assert (equals(math.degrees(cmath.phase(rotate_complex(cmath.rect(1.3, math.radians(35)), 52))), 87))
def test_ccw():
# test for ccw
assert (equals(ccw(0 + 0j, 1 + 1j, -1 + 1j), 2.0))
assert (equals(ccw(0 + 0j, -1 + 1j, 1 + 1j), -2.0))
assert (equals(ccw(1 + 1j, 2 + 2j, 3 + 3j), 0))
def test_reflection_complex():
# test for reflection_complex
assert (equals(reflection_complex(2.0+5.5j, 1.0+3.5j, -2.0+4.0j).real, 16/5)) # (-2, 4) からの 4x-2y+3=0 に対する反射
assert (equals(reflection_complex(2.0+5.5j, 1.0+3.5j, -2.0+4.0j).imag, 7/5))
assert (equals(reflection_complex(1.0+1.0j, 3.0+3.0j, 2.0+2.0j).real, 2.0)) # そもそも直線上
assert (equals(reflection_complex(1.0+1.0j, 3.0+3.0j, 2.0+2.0j).imag, 2.0))
def test_projection_complex():
# test for projection_complex
assert (equals(projection_complex(2.0-1.0j, 5.0-3.0j, 4.0+5.0j).real, 8/13)) # (4,5) から 2x+3y-1=0 への射影
assert (equals(projection_complex(2.0-1.0j, 5.0-3.0j, 4.0+5.0j).imag, -1/13))
assert (equals(projection_complex(1.0+1.0j, 3.0+3.0j, 2.0+2.0j).real, 2.0)) # そもそも直線上
assert (equals(projection_complex(1.0+1.0j, 3.0+3.0j, 2.0+2.0j).imag, 2.0))
def test_area_of_parallelogram_complex():
# test for area_of_parallelogram_complex
assert (equals(area_of_parallelogram_complex(3.0+4.0j, 5.0+6.0j), 2.0))
assert (equals(area_of_parallelogram_complex(1.0+3.0j, 5.0+7.0j), 8.0))
assert (equals(area_of_parallelogram_complex(-1.0-2.0j, -2.0-4.0j), 0)) # 直線
assert (equals(area_of_parallelogram_complex(2.0+3.0j, -3.0+2.0j), 13.0)) # 長方形
def test_dot_product_complex():
# test for dot_product_complex
assert (equals(dot_product_complex(2.0+3.0j, 4.0+5.0j), 23.0))
assert (equals(dot_product_complex(0+0j, 100+100j), 0))
assert (equals(dot_product_complex(1.0+1.0j, 2.0+2.0j), 4.0)) # 平行
assert (equals(dot_product_complex(1000+0j, 0+100j), 0)) # 直交