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.