Isoparametric Curves

One of the great things about advanced CAD packages like CATIA is that not only can you specify tangent or curvature continuity between surfaces and wireframe, but there are some commands that also allow you to adjust the tension (how long the tangency or curvature is maintained) thus enabling you to properly 'style' the component with small changes to the wireframe or surface boundaries.

A parametric surface patch can be considered as an infinite union of curves - tangent and normal vectors from any given point.  As a mathematical model in a program such as CATIA, these infinite number of curves are called Isoparametric curves and can be thought of as the natural 'grain' direction(s) of a surface - much like wood or metal.

When creating support wireframe geometry for a new surface bordering an existing surface, it is important to use this internal grain structure for continuity in order that the new wireframe and therefore supported surface geometry benefits from existing mathematical flow.

The Isoparametric Curve tool can be found on the right hand end of the wireframe toolbar, hidden behind the 3D spline tool.  You simply select the surface, a reference point (existing or not) and the tangent or normal direction.  Use the endpoint for connection and the curve for tangent direction.

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