### PQ Hybrid

Discretization of complex surfaces into continuous planar quadrilaterals is not a terribly complex process; however, it is very sensitive to small adjustments in the initial conditions, so optimizing the panelization is. The simplest solution is to iterate many, many times over the entire mesh searching for an equilibrium. This definition is not concerned with optimization but takes advantage of parametric visualization to allow the user to adjust the initial conditions and observe the difference these small changes make. In this way, some of the irregularity of the unoptimized discretization is preserved and provides resistance to the smooth surface input in a way that can be manipulated but not entirely controlled.

The VB.NET script works from an origin point outward across a surface in quadrants, so the seams which pass through the origin will all be on the surface with increasing divergence toward the corners. This means that positioning the origin on an edge ensures that the discretized edge is consistent with the surface’s edge. Should the quadrilateral panelization diverge too much from base surface, the threshold slider sets a limit (in absolute distance from the surface) at which a quadrilateral will be split into two triangles to force realignment. Setting the threshold to 0.0 obviously produces an entirely triangular panelization.

(ghx download)