All Questions

Let $S$ be a patch of a smooth 2-manifold in $\mathbb{R}^3$, and pick two distinct points $a,\ b \in S$. Let $c$ be the set of points on $S$ equidistant to $a$ and $b$, where distance is defined by ...

A Dubins car follows a Dubins path in $\mathbb{R}^2$, with constant wheel speed and limited turning radius. It is known that the shortest Dubins path in the absence of obstacles follows circular arcs ...

I'm trying to draw on the computer a curve that keeps always the same distance(given as parameter) from a given curve. I know the formula for the given curve. I tried moving perpendicular to the first ...

Let $C_1=(v_1,v_2,\ldots,v_{i-1},v_i)$ and $C_2=(v_1,v_2,\ldots,v_{i-1},v'_i)$ be two cycles that are drawn in $R^3$ in the shape of an unknot (not knotted) with straight line segments as their edges (...

The reach $\tau_M$ of a manifold $M$ is the largest number such that any point at distance less than $\tau_M$ from $M$ has a unique nearest point on $M$. This concept seems quite related to the local ...

I'm interested in the following question: Given two sets $S = \{x_1, ..., x_N\}$ and $T = \{y_1, ..., y_N\}$ each consisting of $N$ distinct points in $\mathbb{R}^n$, how can we construct a ...