Let $P(t)$ be a cubic Bezier curve. I want to create a second curve $P_r(t)$, in which each point is a fixed distance $r$ from a point in $P$.
In other words, add the vector of magnitude $r$ that is perpendicular to the tangent of each point in $P(t)$, and call the result $P_r(t)$. Something like:
$$P_r(t) = P(t) + r\frac{P'(t)^\perp}{|P'(t)|}$$
To describe the problem visually, consider the following image:
A cubic Bezier curve w/ outline
The curve I am describing can be seen as either edge of the shaded region (top or bottom, depending on whether $r$ is positive or negative).
My question is:
- Can this curve also be described as a cubic Bezier curve?
- If so, how can its control points be computed?