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## Geometric determinants (GD).

A array of points (primitive 3D Mesh) in FairCurveModeler is used as a carrier of derived objects (set of curves, the network of curves, surfaces), built on the rows and columns of the array of points.
To work with the derived objects is necessary to selected the carrier - net of points (primitive 3D Mesh).
Removing the carrier destroys derived objects.
On the primitive 3d Mesh is possible to construct NURBzS surface, b-spline surface and NURBS surfaces:
1) NURBzS surface - rational Bezier spline surface of degree (3.3) or (6.6). It is constructed only on networks with affinity-dependent flat rows and columns. It allows to represent geometrically exactly the quadratic surfaces (sphere, ellipsoid, torus).
Types of initial geometric determinants:
- Point net of incidence. Modeled surface exactly goes through over the vertices of network;
- Network with tangent lines. Lines of the network tangent to modeled surface;
- A uniform set of cubic NURBzS curves. Set of curves belongs to the surface;
- A uniform network of cubic NURBzS curves. Network of curves belongs to the surface;

2) B-spline surface of arbitrary even degrees m, n (m, n = 6/8/10). The particular case of NURBS surfaces with unit weights, and with uniform parameterization of u, v. Built on networks with spatial rows and columns.
Algorithms based on the construction of v-curve allows to receive high quality directing and forming curves. In particular, algorithms of construction allows to approximate with high accuracy, significantly exceeds the accuracy of existing methods in CAD systems, quadratic surfaces (sphere, ellipsoid, torus). Editing techniques allow you to control the quality and form of arbitrary isoparametric curve.
To construct a b-spline surfaces, you can use a large set of types of geometric determinants. Both classic and directly related to the NURBS model.

Types of initial geometric determinants:
- Point net of incidence. Modeled surface exactly goes through over the vertices of network;
- Network with tangent lines. Lines of the network tangent to modeled surface;
- Network with tangent lines and tangent columns. Lines and columns of the network tangent to modeled surface;
- A uniform set of b-spline curves. Set of curves belongs to the surface;

- S-frame of b-spline surface of arbitrary degrees m, n (m, n = 2,...,10). Direct determination of the b-spline surface by control frame.

3) NURBS surface of arbitrary degrees m, n of general form.
Is used two types of GD:
- Set of NURBS curves;
- Four NURBS curves, formed topological rectangle.
Methods of constructing and editing allow you to test and control the shape of the families of isoparms of surface.

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