Draw an ellipse using Shapely

There isn't any way to represent a polygon in Shapely without discretizing it.

At the base level Shapely deals with points. Everything from a LineString to a Polygon is just a list of points. A good example of this is what happens when you take a Point and buffer it out:

>>> import shapely
>>> from shapely.geometry.point import Point
>>> p = Point(0, 0)
>>> circle = p.buffer(1.0)
>>> list(circle.exterior.coords)
[(1.0, 0.0), (0.99518472667219693, -0.098017140329560506), (0.98078528040323054, -0.19509032201612808), (0.95694033573220894, -0.29028467725446211), (0.92387953251128696, -0.38268343236508939), (0.88192126434835527, -0.4713967368259972), (0.83146961230254557, -0.55557023301960173), (0.77301045336273744, -0.63439328416364493), (0.70710678118654813, -0.70710678118654691), (0.63439328416364626, -0.77301045336273633), (0.55557023301960307, -0.83146961230254468), (0.47139673682599859, -0.88192126434835449), (0.38268343236509084, -0.92387953251128629), (0.29028467725446361, -0.95694033573220849), (0.19509032201612964, -0.98078528040323021), (0.098017140329562089, -0.99518472667219671), (1.615542552166338e-15, -1.0), (-0.098017140329558883, -0.99518472667219704), (-0.19509032201612647, -0.98078528040323076), (-0.2902846772544605, -0.95694033573220938), (-0.38268343236508784, -0.92387953251128752), (-0.4713967368259957, -0.88192126434835605), (-0.55557023301960051, -0.83146961230254635), (-0.63439328416364393, -0.77301045336273821), (-0.70710678118654624, -0.70710678118654879), (-0.77301045336273588, -0.63439328416364682), (-0.83146961230254435, -0.55557023301960362), (-0.88192126434835427, -0.47139673682599903), (-0.92387953251128618, -0.38268343236509111), (-0.95694033573220849, -0.29028467725446366), (-0.98078528040323021, -0.19509032201612947), (-0.99518472667219682, -0.098017140329561714), (-1.0, -1.010639055082363e-15), (-0.99518472667219693, 0.098017140329559702), (-0.98078528040323065, 0.1950903220161275), (-0.95694033573220905, 0.29028467725446172), (-0.92387953251128696, 0.38268343236508923), (-0.88192126434835527, 0.47139673682599725), (-0.83146961230254546, 0.55557023301960196), (-0.7730104533627371, 0.63439328416364527), (-0.70710678118654768, 0.70710678118654746), (-0.63439328416364593, 0.77301045336273666), (-0.55557023301960295, 0.83146961230254479), (-0.4713967368259987, 0.88192126434835449), (-0.38268343236509117, 0.92387953251128618), (-0.29028467725446411, 0.95694033573220838), (-0.19509032201613041, 0.98078528040322999), (-0.098017140329563102, 0.9951847266721966), (-2.8482262121737323e-15, 1.0), (0.098017140329557426, 0.99518472667219715), (0.19509032201612481, 0.9807852804032311), (0.29028467725445867, 0.95694033573220993), (0.3826834323650859, 0.9238795325112884), (0.47139673682599365, 0.88192126434835716), (0.55557023301959818, 0.8314696123025479), (0.63439328416364149, 0.77301045336274021), (0.70710678118654358, 0.70710678118655146), (0.77301045336273322, 0.63439328416365004), (0.83146961230254179, 0.5555702330196074), (0.88192126434835194, 0.47139673682600342), (0.92387953251128407, 0.38268343236509617), (0.95694033573220671, 0.29028467725446927), (0.98078528040322899, 0.19509032201613569), (0.99518472667219615, 0.098017140329568472), (1.0, 8.2385270480656025e-15), (1.0, 0.0)]

As you can see, the circle is made up of 65 points that are spaced 0.0966 units from each other.

For those who are interested, here is an example to create an ellipse with axis length of 15 and 20.

import shapely.affinity
from shapely.geometry import Point

circle = Point(0, 0).buffer(1)  # type(circle)=polygon
ellipse = shapely.affinity.scale(circle, 15, 20)  # type(ellipse)=polygon