Parametric Patches
A form of 3D representation which is commonly used in CAD.
Often referred to as a curvilinear quadrilaterals.
We define a patch (surface) with multiple [see page 3, control structures] that can be used to alter the surface of the patch. Think of it as a continuous curve with a known mathematical equation. We define \(n\) points for which the value of the curve is known and then use a [see page 4, blending] function to interpret how the surface of the patch varies across the different control structures between those points..
In 2 dimensions the \(n=2\), in 3D \(n=4\).
We can [see page 7, display] patches as polygons through:
- Incremental Evaluation - sample \(Q(u,v)\) at certain steps to create a polygon network.
- Recursive Subdivision - Continually divide each patch into smaller patches within the limits of our resolution.
Note: texture mapping a parametric patch is [see page 35, easy] because the surface of the patch already has \((u,v)\) parameters like texture-color mapping.