# What is a regular curve?

**curve**is said to be

**regular**if its derivative never vanishes. ( In words, a

**regular curve**never slows to a stop or backtracks on itself.) Two differentiable

**curves**and. are said to be equivalent if there is a bijective map. such that the inverse map.

Regarding this, how do you define a curve?

**Curve** - **Definition** with Examples. What is **Curve**? A **curve** is a continuous and smooth flowing line without any sharp turns. One way to recognize a **curve** is that it bends and changes its direction at least once.

**smooth curve**is a

**curve**which is a

**smooth**function, where the word "

**curve**" is interpreted in the analytic geometry context. In particular, a

**smooth curve**is a continuous map from a one-dimensional space to an. -dimensional space which on its domain has continuous derivatives up to a desired order.

People also ask, can a curve be straight?

A **curve** is not a **straight** line, just as a **straight** line is not a **curve**. A **curved** line contains points that are not **linear** to two given points. The **curve** moves in other directions from the **straight** line created by joining collinear points.

**Unit speed curve** parameterization. If you change the time parameterization by inverting this function, solving for t as a function of s, then the total length of **curve** traversed by p(t(s)) up to time s is s. This is called either the **unit speed** parameterization or parameterization by arc length.