Leonhard Euler constructed curves of constant width from involutes of curves with an odd number of cusp singularities, having only one tangent line in each direction (that is, projective hedgehogs). An intuitive way to describe the involute construction is to roll a line segment around such a curve, keeping it tangent to the curve without sliding along it, until it returns to its starting point of tangency. The line segment must be long enough to reach the cusp points of the curve, so that it can roll past each cusp to the next part of the curve, and its starting position should be carefully chosen so that at the end of the rolling process it is in the same position it started from. When that happens, the curve traced out by the endpoints of the line segment is an involute that encloses the given curve without crossing it, with constant width equal to the length of the line segment. If the starting curve is smooth (except at the cusps), the resulting curve of constant width will also be smooth. An example of a starting curve with the correct properties for this construction is the deltoid curve, and the involutes of the deltoid that enclose it form smooth curves of constant width, not containing any circular arcs.