Space Curve

The space curve is a vector function where the end of the vector follows a curve.

Where:

is the vector pointing from the origin to the value at time .
is the vector pointing from the origin to the value at time .
is the vector pointing from the origin to the value at time .

See Multivariable Calculus Notes - Chapter 13 - Sections 1-2 for examples and more information.

Related Topics

The space curve function is considered a vector function.
One can find the arc length of space curve, or the distance along a space curve between two points, by using multivariable calculus.
The unit tangent vector to a space curve is unit vector that is tangent to the space curve, generally written as a function.
curvature
One can find if/when two objects will collide using the space curves of the objects and their velocity and tangent vectors.

Interactive Graph

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