Parameterized Vector Geometry
Vector geometry that is specific to vector-valued parametric functions.
Contents
Unit Tangent Vector
The tangent of a parametric curve r(t) is given by differentiating the curve.
Most often, it is helpful to calculate the normalized vector. To calculate the unit tangent vector, try:
Principal Unit Normal Vector
The principal normal vector is orthogonal to the tangent vector and points in the direction that a line is turning.
Most often, it is helpful to calculate the normalized vector. To calculate the principal unit normal vector, try:
Binormal Vector
The binormal vector is orthogonal to both the tangent vector and the principal normal vector. Naturally, this is calculated using the cross product.
By calculating this from unit vectors, the product will necessarily also be unit.
B(t) = T(t) × N(t)