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Description

Objects 1.

And the method of the sphere can be extended to several objects,
overlapping or even intersecting if necessary!

IMHO this is the most spectacular one. What you see:
Intersections of diagonal vertical planes with a torus,
a drop-like and a red bloodcell-like object,
rotated over various angles (-12°, 0°, +12°).

Red bloodcell:
bottom side: ellipsoid z = -a sqrt(1 - x^2 / b - y^2 / c)
top side: z = a (1 - r^2 / b) (1 - 1 / (1 + r^2 / c))
(inspired by the ovals of Cassini)

Drop:
bottom: hemisphere z = d - sqrt(a - r^2)
top: z = d + a sqrt(b / (r + c) - 1)

Torus:
z = c ± sqrt(a - (sqrt(x^2 + y^2) - b)^2)

Note: a, b, c and d are simply used to denote constants here.
They don't have the same value for the different functions.

Description

Objects 1.

And the method of the sphere can be extended to several objects,
overlapping or even intersecting if necessary!

IMHO this is the most spectacular one. What you see:
Intersections of diagonal vertical planes with a torus,
a drop-like and a red bloodcell-like object,
rotated over various angles (-12°, 0°, +12°).

Red bloodcell:
bottom side: ellipsoid z = -a sqrt(1 - x^2 / b - y^2 / c)
top side: z = a (1 - r^2 / b) (1 - 1 / (1 + r^2 / c))
(inspired by the ovals of Cassini)

Drop:
bottom: hemisphere z = d - sqrt(a - r^2)
top: z = d + a sqrt(b / (r + c) - 1)

Torus:
z = c ± sqrt(a - (sqrt(x^2 + y^2) - b)^2)

Note: a, b, c and d are simply used to denote constants here.
They don't have the same value for the different functions.