Like Curves, Surfaces can be described both geometrically and numerically.

The numeric description of any NURBS Surface can be understood as the “Parameter Space” of the Surface. This space is two dimensional and not necessarily tied to the Euclidean space of the modeling environment but is always tied to the topology of the surface which is a consequence of the geometry that created that surface. The bounds of this space is called the “Surface Domain” which can be navigated numerically through the native domain or through a “Reparameterized” domain that forces both dimension’s bounds to be 0.0 and 1.0. The current value at which this navigation is possible is called the UV Coordinate.

This Surface Primer constructs surfaces and their unrolled counterparts allowing user interaction as well as generating live visual feedback.

Download the Grasshopper Definition (version 0.6.0019) from modeLab.

Lines, Polylines, and Curves can be described both geometrically and numerically.

The numeric description of any of these geometry types can be understood as the “Parameter Space” of the curve. This space is one dimensional and not necessarily tied to the Euclidean space of the modeling environment but is always tied to the topology of the curve. The bounds of this space is called the “Curve Domain” which can be navigated numerically through the native domain or through a “Reparameterized” domain that forces the bounds to be 0.0 and 1.0. The current value at which this navigation is possible is called the “t” value or “parameter.”

This Curve Primer constructs curves and their unrolled counterparts allowing user interaction as well as generating live visual feedback.

Download the Grasshopper Definition (version 0.6.0019) from modeLab.