Supports, Windows, and Aggregate Merging

Mergefile records

The merge modules read one primary support per mergefile record. Use - to use a default option while supplying a later field.

For merge1d:

primary [secondary] [west/east] [window] [r1/r2]

For merge2d:

primary [secondary] [polygon] [xwindow/ywindow] [rx1/rx2/ry1/ry2]

For merge3d:

primary [secondary] [polygon] [zlo/zhi] [xwindow/ywindow/zwindow] \
    [rx1/rx2/ry1/ry2/rz1/rz2]

An omitted interval or polygon uses the full primary domain. Each record is valid only inside that primary support. A paired secondary supplies the transition partner, but does not become a tile outside the primary domain unless listed in the mergefile.

Windows

The default is a cosine window with a taper ratio of 0.2 at every supported boundary. A taper ratio is a dimensionless fraction that controls the width of the transition measured inward from that boundary. The selected window controls the shape of the transition: the primary merging-weight factor changes between the window’s boundary value and 1, and a paired secondary receives the complementary weight. Larger ratios produce broader transitions and leave a smaller full-primary interior. A ratio of 0 disables the taper on that side. The boxcar window ignores taper ratios and has unit weight throughout the support.

Beginning and ending mean low and high coordinate, respectively. Thus, the x ratios apply at west/east, the y ratios at south/north,`` and the z ratios at zlo/zhi. One ratio applies everywhere, dimension-count ratios apply symmetrically by dimension, and twice the dimension count sets beginning and ending tapers independently. Each ratio must be in [0, 0.5), i.e., can approach 0.5 but cannot equal 0.5.

For an interval or rectangular support, a ratio r uses approximately r times the support extent for that boundary’s transition. For polygon supports, BLEND evaluates the x and y tapers along local polygon cross-sections and adapts the transition width where a cross-section is too narrow for the nominal support-wide taper. In three dimensions, the z taper uses the complete extruded/extended zlo/zhi interval. Multidimensional taper factors are multiplied to obtain the primary merging weight, i.e., outer product of the window taper functions in each dimension.

Polygon supports must be xy-monotone after mapping to the output grid. The merge and SSH modules provide strict-envelope and best piecewise-envelope conversion modes. Their write modifier stores the converted polygon beside the original for inspection. See BLEND for more information.

Aggregate merging

Without aggregate mode, GQ follows mergefile availability order. Aggregate mode addresses edge effects where positive primary supports overlap. It normalizes and combines only the weights of overlapping primaries that share the same secondary pair.

Primaries with non-overlapping supports do not need a common secondary. Unpaired records remain ordered fallback tiles and do not enter aggregate weight normalization. A file that serves as a secondary on one record may still appear separately as a primary or fallback tile elsewhere.

SSH localization

SSH supports use the same BLEND window machinery, but multiply the window by the heterogeneity field rather than blending primary and secondary data. The stationary field is normalized before tapering and is not normalized again afterward.