[alogo] Hypotrochoid

In the most general case hypotrochoids are curves generated by rolling a circle of radius b inside a circle of radius a > b. The curve is generated by a point rigidly attached to the inside of the rolling disc. The system below illustrates [Hypotrochoids] resulting when the radii ratio is an integer N = a/b. Given the radii a and b. The shape of the hypotrochoid depends on the distance h of the attached point from the center of the b-circle (h <b). For h=b we get the hypocycloids with N cusps (see Hypocycloid.html ). Thus, varying h in the interval [0,b] we get a deformation of the hypocycloid, via troichoids, to the circle with radius a-b.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]
[2_0] [2_1] [2_2] [2_3]

To change the shape of the hypotrochoid change N or/and the location of the moving point (red) inside the rolling disc. See the file Roulette.html for a generalization of the hypotrochoids.

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