Polygon inflated

geometric-functions polygon inflated

syntax

  • polygon_iXd(polygon_data_item, inflatesize)
  • polygon_iXhv(polygon_data_item, inflatesize)

description

These functions result in inflated versions of an original polygon_data_item.

There are different ways of inflating 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.

X represents a user defined degree of roundness, which can be 4, 8 or 16.

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

For these inflations the Minkowski sum method is used.

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

applies to

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

conditions

  1. The composition 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_inflated_4D75 (polygon, source/bld) := polygon_i4D(bld/border, 75);
// inflates building borders with 75 units in the coordinate system 
// angles are rounded off with 4 points per angle
// inflates using a diagonal kernel (diamond shaped).

attribute<ipoint> building_inflated_i_8D75 (polygon, source/bld) := polygon_i8D(bld/border, 75);
// inflates building borders with 75 units in the coordinate system
// angles are rounded off with 8 points per angle.
// inflates using a diagonal kernel (diamond shaped).

attribute<ipoint> building_inflated_i_16D75 (polygon, source/bld) := polygon_i16D(bld/border, 75);
// inflates building borders with 75 units in the coordinate system
// angles are rounded off with 16 points per angle.
// inflates using a diagonal kernel (diamond shaped).

attribute&lt;ipoint&gt; building_inflated_4HV75 (polygon, source/bld) := polygon_i4HV(bld/border, 75d);
// inflates building borders with 75 units in the coordinate system
// angles are rounded off with 4 points per angle
// inflates using a horizonal-vertical kernel (square shaped).

see also