Polygons

BLEND polygon windows require valid simple polygons. A polygon file is a text file with two columns:

x y

Blank lines and comments are ignored in module input where supported.

xy-monotone requirement

The 2-D and 3-D window modules use row and column stepping vectors. Before assembly, BLEND maps each support polygon to its local support grid and snaps vertices to grid nodes. For assembly to be well-defined, that grid-snapped support must be xy-monotone under BLEND’s current boundary model. The definition required for the window2d and window3d modules is a strictly increasing condition as opposed to the usual nondecreasing condition in the standard definition of xy-monotonicity.

Use:

blend monotone polygon.txt

to check a polygon for xy-monotonicity.

Conversion methods

-Me

Full xy-monotone envelope, i.e., convex hull.

-Mb

Highest-IoU(Intersection Over Union) piecewise envelope, evaluated over a sampling grid.

-ME

Strict envelope for polygons that must satisfy BLEND’s current window boundary assembly.

-MB

Strict highest-IoU piecewise envelope for polygons that must satisfy BLEND’s current window boundary assembly.