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Cycloid Curves
Among the famous planar curves is the cycloid. A cycloid is defined as the trace of a point on a disk when this disk rolls along a line. The disk is not allowed to slide.
The shape of the cycloid depends on two parameters, the radius r of the circle and the distance d of the point generating the cycloid to the center of rolling disk. The mathematical expression of a cycloid is
Cycloid[r, d](t) = (r t + d sin(t), r - d cos(t)).
We scale our experiment such that the radius of the circle is normalized to 1 and cannot be changed.
Controls:
| Slider "Cycloid Discr" | Number of vertices of discretely drawn cycloid. |
| Slider "Cycloid Length" | Length of definition interval for x. |
| Slider "Distance d" | Depending on the relation between distance d and radius r, the cycloid has different shapes. For d<r the cycloids waves up and down, and are embedded like a sine curve. For d=r the curve looks roughly like a collection of half-circles, and for d>r they have self-intersections. |
| Checkbox "Show Circle" | Switch evolving circle to be visible or invisible in display. |
| Checkbox "Show Cycloid" | Switch cycloid curve to be visible or invisible in display. |
| Checkbox "Show Surface" | Switch cycloid rotational surface to be visible or invisible in display. To see the surface in 3d, switch the display to 3d by F1->Inspector->Camera->Perspective. |
| Button "Animate" | Start and stop animation of evolving circle. |
| Button "Reset" | Set all sliders to their default values. |
By F4 or ctrl-a you can also get an Animation Panel .
