Sat Oct 15 09:07:40 2022

ellipse_test():
  Python version: 3.6.9
  Test ellipse().

ellipse_area1_test():
  ellipse_area1() computes the area of an ellipse.

  R = 10
  Matrix A in ellipse definition x*A*x=r^2
[[5. 1.]
 [1. 2.]]
  Area = 104.72

ellipse_area2_test():
  ellipse_area2() computes the area of an ellipse.

  Ellipse: 5 * x^2 + 2 * xy + 2 * y^2 = 10
  Area = 104.72

ellipse_area3_test():
  ellipse_area3() computes the area of an ellipse.

  Ellipse: (x/10)^2 + (y/3.33333)^2 = 1
  Area = 104.72

ellipse_aspect_ratio_test():
  ellipse_aspect_ratio() computes the aspect ratio of an ellipse.

      A      B      Ratio

    1.0    0.0    0.000000
    1.0    0.1    0.100000
    1.0    0.2    0.200000
    1.0    0.3    0.300000
    1.0    0.4    0.400000
    1.0    0.5    0.500000
    1.0    0.6    0.600000
    1.0    0.7    0.700000
    1.0    0.8    0.800000
    1.0    0.9    0.900000
    1.0    1.0    1.000000

ellipse_eccentricity_test():
  ellipse_eccentricity() computes the eccentricity of an ellipse.

      A      B      Ecc

    1.0    0.0    1.000000
    1.0    0.1    0.994987
    1.0    0.2    0.979796
    1.0    0.3    0.953939
    1.0    0.4    0.916515
    1.0    0.5    0.866025
    1.0    0.6    0.800000
    1.0    0.7    0.714143
    1.0    0.8    0.600000
    1.0    0.9    0.435890
    1.0    1.0    0.000000

ellipse_flattening_test():
  ellipse_flattening() computes the flattening of an ellipse.

      A      B      Flat

    1.0    0.0    1.000000
    1.0    0.1    0.900000
    1.0    0.2    0.800000
    1.0    0.3    0.700000
    1.0    0.4    0.600000
    1.0    0.5    0.500000
    1.0    0.6    0.400000
    1.0    0.7    0.300000
    1.0    0.8    0.200000
    1.0    0.9    0.100000
    1.0    1.0    0.000000

ellipse_perimeter_test():
  ellipse_perimeter() computes the perimeter of an ellipse.

      A      B      P

    1.0    0.0    4.000000
    1.0    0.1    4.063974
    1.0    0.2    4.202009
    1.0    0.3    4.385910
    1.0    0.4    4.602623
    1.0    0.5    4.844224
    1.0    0.6    5.105400
    1.0    0.7    5.382369
    1.0    0.8    5.672334
    1.0    0.9    5.973160
    1.0    1.0    6.283185

ellipse_point_near_test():
  ellipse_point_near() is given a point P, and
  finds the nearest point PN on an ellipse in 2D.

  The ellipse is (X/A)^2 + (Y/B)^2 = 1

  A = 3.000000
  B = 2.000000

           P                PN

   -1.200000    3.900000     -0.823689    1.923138
   -0.800000    3.600000     -0.583461    1.961810
   -0.400000    3.300000     -0.309401    1.989335
    0.000000    3.000000      0.000000    2.000000
    0.400000    2.700000      0.344958    1.986734
    0.800000    2.400000      0.723898    1.940902
    1.200000    2.100000      1.132592    1.851994
    1.600000    1.800000      1.562334    1.707384
    2.000000    1.500000      1.995923    1.493138
    2.400000    1.200000      2.400000    1.200000
    2.800000    0.900000      2.719790    0.843996
    3.200000    0.600000      2.908697    0.489662
    3.600000    0.300000      2.984218    0.204879
    4.000000    0.000000      3.000000    0.000000
    4.400000   -0.300000      2.992027   -0.145716
    4.800000   -0.600000      2.976051   -0.252210
    5.200000   -0.900000      2.958199   -0.332704

ellipsoid_area_test():
  ellipsoid_area_test() computes the surface area of the ellipsoid
    (x/a)^2+(y/b)^2+(z/c)^2=1

           A           B           C        Area

           1         0.8       0.625       8.152
           1           1         0.5       8.672
           1           1           1       12.57
           2           1        0.25        13.7
           2           3           4       111.5

ellipsoid_volume_test():
  ellipsoid_volume() computes the volume of the ellipsoid
    (X-V)' * A * (X-V) <= R * R.

  M = 3
  Matrix A:
[[9. 3. 3.]
 [3. 5. 3.]
 [3. 3. 3.]]
  Vector V:
[2. 3. 1.]

  Volume =       0.698132

ellipse_test():
  Normal end of execution.
Sat Oct 15 09:07:40 2022