Reparametrized Curve MbReparamCurve3D

The MbReparamCurve3D class is declared in the cur_reparam_curve3d.h file.

A reparametrized curve is defined by the base curve 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 PointOn( double & t, MbCartPoint3D & r) method, the radius vector of the curve r is described by the vector function

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

where

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

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.