A slight 2 dimensional extension of the cycloid. See also cyclohedron for an extension of the cycloid into three dimensions.

The curtate cycloid is defined to be a cycloid measured at a point outside the generating circle:
```                 ,.onOK@@@@@HQme.,
,.szF'`             `'Tux.,
,z'`                       `'c,
,x'`                           `'w,
.u'`                               `'n.
dy                                     qb
/7                                       VA
4y                                         \D
,I'                                          `U,
dp                                            qb
,j'                                            `t,
AV                                              VA
69                                              96--a--* (x,y)  <-- example point of measure,
VA                                              AV  distance "a" from the edge of the circle.
`t,                                            ,j'
qb                                            dp
`I,                                          ,U'
\D                                         4y
VA                                       /7
qb                                     dy
`'n.                               .u'`
`'w,                           ,x'`
`'c,                       ,z'`
`'Tux.,             ,.szF'`
`'TTOK@@@@@HQTT'`
```
Let (x,y) be a point of the curtate cycloid, where the generating circle has radius r, and the shortest distance from (x,y) to the edge of the circle is a at all angles t. Then,

x=r*(t-sin(t))-a*sin(t)

and

y=r*(1-cos(t))-a*cos(t)