.. role:: blue
   :class: blue

Reparametrized Curve MbReparamCurve3D
=====================================
.. _MbReparamCurve3D_Reparametrized_Curve_:

.. kernel version: 

The :blue:`MbReparamCurve3D` class is declared in the *cur_reparam_curve3d.h* file.

A reparametrized curve is defined by the base curve
:blue:`MbCurve3D` **basisCurve**, the start parameter *tmin*, the end
parameter *tmax*, and the derivative *dt* of the base curve parameter
with respect to the parameter of the reparametrized curve.

The reparametrized curve completely coincides with the base curve but
has a different parameter range.

In the :blue:`PointOn`\( double & *t*,
:ref:`MbCartPoint3D <MbCartPoint3D_Radius_Vector_of_Point_in_3D_Space_>` & **r**) method, the radius vector of the curve **r** is described by the vector function

.. math::

   \mathbf{r}(t) = \mathbf{basisCurve}(v(t)),

where

.. math::

   v(t) = b_{\min} \frac{trim2 - t}{trim2 - trim1} + b_{\max} \frac{t - trim1}{trim2 - trim1},

*bmin*, *bmax* are the boundary values of the domain
of the base curve parameter.

The curve parameter *t* takes values on the segment
*tmin* ≤ *t* ≤ *tmax*.

The reparametrized curve coincides with the base curve but has a different
parameter domain. A curve with a modified parameter length
is used to match the parameter ranges of two curves.
For example, if it is required that a line segment and an arc have the same
parameter ranges, then a reparametrized curve is constructed based on
one of these curves with the parameter range taken from
the other curve.

Another reparametrized curve must not be used as a base curve
for a reparametrized curve; the base curve of the latter must be used
instead.