Deriving a Curve from an Existing Curve
A curve can be defined from a set of formulas alone or can be derived from formulas and an existing curve (the root curve). If a curve is derived, then these values can be referenced in the equations.
These values are derived from the Frenet frame of the root curve and are updated depending on the value of "t", the curve parameter. All these values begin with an underscore.
| Value | Description |
|---|---|
_rx |
x coordinate of root curve's position |
_ry |
y coordinate of root curve's position |
_rz |
z coordinate of root curve's position |
_tx |
x coordinate of root curve's tangent |
_ty |
y coordinate of root curve's tangent |
_tz |
z coordinate of root curve's tangent |
_mx |
x coordinate of root curve's normal |
_my |
y coordinate of root curve's normal |
_mz |
z coordinate of root curve's normal |
_bx |
x coordinate of root curve's binormal |
_by |
y coordinate of root curve's binormal |
_bz |
z coordinate of root curve's binormal |
_kappa |
curvature of root curve |
_tau |
torsion of root curve |
The following constants can be referenced in equations: