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SPHERO-CYLINDRICAL CURVE
Other name: cyclo-cylindrical curve. |
The sphero-cylindrical curves are the intersections
between a sphere and a cylinder of revolution.
For a sphere centered on O with radius a,
a cylinder with radius b, and axis at distance c from O:
System of Cartesian equations: Biquadratic. Cartesian parametrization: |
Case :
The curve is not empty iff Opposite, the case a = b = c. |
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Case b < a;
b + c < a: the curve has two
components
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b + c = a: eight-like curve called hippopede. ![]() |
a – b < c ![]() |
It can be generalized by the intersection of the sphere and an elliptic cylinder, that is a spherical ellipse when the axes of the cylinder goes through the center of the sphere. | ![]() |
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© Robert FERRÉOL 2022