Polygon deflated

geometric-functions polygon deflated

syntax

  • polygon_dXd(polygon_data_item, deflatesize)
  • polygon_dXhv(polygon_data_item, deflatesize)

description

The polygon_iXX functions result in deflated versions of an original polygon_data_item.

There are different ways of deflating polygons related to how angles are treated.

Multiple functions are implemented, the figure shows 4 of these functions. See the differences in how the angles are rounded off.

The degree of roundness is obtained by increasing the value 4 to 16.

The suffix ‘d’ or ‘hv’ is used for the kernel; diagonal (diamond shaped) or horizontal-vertical (square shaped).

For these deflations the Minkowski sum method is used.

The deflatesize parameter indicates with how many units in the coordinate system used the original polygon is deflated.

applies to

  • attribute polygon_data_item and with an ipoint or spoint value-type.
  • parameter deflatesize with float64 value type.

conditions

  1. The composition type type of the polygon_data_item needs to be polygon.
  2. The order of the points in the polygon_data_item needs to be clockwise for exterior bounds and counter clockwise for holes in polygons (right-hand-rule).
  3. The current implementation of these functions request coordinate values to be less than 67.108.864. Convert detailed coordinates (e.g. in mm) to cm/dm if your coordinate values exceed this number.

These functions result in problems for (integer) coordinates larger than 2^25 (after translation where the first point is moved to (0, 0)). If your integer coordinates for instance represent mm, 2^25[mm] = about 33[km]. The reason is that for calculating intersections, products of coordinates are calculated and casted to float64 with a 53 bits mantissa (in the development/test environment of boost::polygon these were float80 values with a 64 bits mantissa). We advise to keep the size of your integer coordinates for polygons limited and for instance do not use a mm precision for country borders (meter or kilometer might be sufficient).

since version

7.042

examples 

attribute<ipoint> building_deflated_4D75 (polygon, source/bld) := polygon_d4D(bld/border, 75);
// deflates building borders with 75 units in the coordinate system
// angles are rounded off with 4 points per angle
// deflates using a diagonal kernel (diamond shaped).

attribute<ipoint> building_deflated_i_8D75 (polygon, source/bld) := polygon_d8D(bld/border, 75);
// deflates building borders with 75 units in the coordinate system
// angles are rounded off with 8 points per angle.
// deflates using a diagonal kernel (diamond shaped).

attribute<ipoint> building_deflated_i_16D75 (polygon, source/bld) := polygon_d16D(bld/border, 75);
// deflates building borders with 75 units in the coordinate system
// angles are rounded off with 16 points per angle.
// deflates using a diagonal kernel (diamond shaped).

attribute<ipoint> building_deflated_4HV75(polygon, source/bld) := polygon_d4HV(bld/border, 75d);
// deflates building borders with 75 units in the coordinate system
// angles are rounded off with 4 points per angle
// deflates using a horizonal-vertical kernel (square shaped).

see also