Interpolations and Approximations

 

Approximations of Curves and Surfaces groups together a variety of functions used in 2D and 3D geometry for:

-   the interpolation of a set of 2D points using a 2D BSpline or Bezier curve

-   the approximation of a set of 2D points using a 2D BSpline or Bezier curve

-   the interpolation of a set of 3D points using a 3D BSpline or Bezier curve, or a BSpline surface

-   the approximation of a set of 3D points using a 3D BSpline or Bezier curve, or a BSpline surface.

 

You can program approximations in the following two ways:

-   Using high-level functions, designed to provide a simple method for obtaining approximations with minimal programming,

-   Using low-level functions, designed for users requiring more control over the approximations.

 

The low-level functions provide a second API with functions to:

-   Define compulsory tangents for an approximation. These tangents have origins and extremities.

-   Approximate a set of curves in parallel. This is to respect identical parameterization

-   Smooth approximations. This is to produce a faired curve.

 

The AppDef_MultiPointConstraints and AppDef_MultiLines classes allow you to organize the data.

The AppDef_Compute, AppDef_BSplineCompute and AppDef_TheVariational classes perform the approximation itself using Bezier curves, BSpline curves, and smooth BSpline curves, respectively.

You can also find functions to compute:

-   The minimal box which includes a set of points

-   The mean plane, line or point of a set of coplanar, collinear or coincident points.