A curve in space.
Unit Tangent Vector
where
Unit Normal Vector
Also known as “principal unit normal”
where
Unit Binormal Vector
Misc
- Unit normal vector and unit tangent vector are always perpendicular to each other.
- Unit normal vector is always normal to the curve. Unit tangent vector is always tangent to the curve, so their perpness is a natural consequence.
Curvature
The curvature of a Space Curve
where
is the Unit Tangent Vector and is Arc Length Osculating Circle
The circle whose curvature is the same as a Space Curve at a particular point, and whose radius
is reciprocal to the curvature at that point. That is to say:
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