polar_trans_regionpolar_trans_regionPolarTransRegionpolar_trans_regionPolarTransRegionPolarTransRegion (Operator)

Name

polar_trans_regionpolar_trans_regionPolarTransRegionpolar_trans_regionPolarTransRegionPolarTransRegion — Transform a region within an annular arc to polar coordinates.

Signature

polar_trans_region(Region : PolarTransRegion : Row, Column, AngleStart, AngleEnd, RadiusStart, RadiusEnd, Width, Height, Interpolation : )

Description

polar_trans_regionpolar_trans_regionPolarTransRegionpolar_trans_regionPolarTransRegionPolarTransRegion transforms a RegionRegionRegionRegionRegionregion within the annular arc specified by the center point (RowRowRowRowRowrow, ColumnColumnColumnColumnColumncolumn), the radii RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart and RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd and the angles AngleStartAngleStartAngleStartAngleStartAngleStartangleStart and AngleEndAngleEndAngleEndAngleEndAngleEndangleEnd to its polar coordinate version in a virtual image of the dimensions WidthWidthWidthWidthWidthwidth x HeightHeightHeightHeightHeightheight.

The polar transformation is a change of the coordinate system. Instead of a row and a column coordinate, each point's position is expressed by its radius r (i.e. the distance to the center point RowRowRowRowRowrow, ColumnColumnColumnColumnColumncolumn) and the angle phi between the column axis (through the center point) and the line from the center point towards the point. Note that this transformation is not affine.

The coordinate (0,0) in the output region always corresponds to the point in the input region that is specified by RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart and AngleStartAngleStartAngleStartAngleStartAngleStartangleStart. Analogously, the coordinate (HeightHeightHeightHeightHeightheight-1, WidthWidthWidthWidthWidthwidth-1) corresponds to the point in the input region that is specified by RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd and AngleEndAngleEndAngleEndAngleEndAngleEndangleEnd. In the usual mode (AngleStartAngleStartAngleStartAngleStartAngleStartangleStart < AngleEndAngleEndAngleEndAngleEndAngleEndangleEnd and RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart < RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd), the polar transformation is performed in the mathematically positive orientation (counterclockwise). Furthermore, points with smaller radii lie in the upper part of the output region. By suitably exchanging the values of these parameters (e.g., AngleStartAngleStartAngleStartAngleStartAngleStartangleStart > AngleEndAngleEndAngleEndAngleEndAngleEndangleEnd or RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart > RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd), any desired orientation of the output region can be achieved.

The angles can be chosen from all real numbers. Center point and radii can be real as well. However, if they are both integers and the difference of RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd and RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart equals HeightHeightHeightHeightHeightheight-1, calculation will be sped up through an optimized routine.

The radii and angles are inclusive, which means that the first row of the virtual target image contains the circle with radius RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart and the last row contains the circle with radius RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd. For complete circles, where the difference between AngleStartAngleStartAngleStartAngleStartAngleStartangleStart and AngleEndAngleEndAngleEndAngleEndAngleEndangleEnd equals (360 degrees), this also means that the first column of the target image will be the same as the last.

To avoid this, do not make this difference , but degrees instead.

The parameter InterpolationInterpolationInterpolationInterpolationInterpolationinterpolation is used to select the interpolation method 'bilinear'"bilinear""bilinear""bilinear""bilinear""bilinear" or 'nearest_neighbor'"nearest_neighbor""nearest_neighbor""nearest_neighbor""nearest_neighbor""nearest_neighbor". Setting InterpolationInterpolationInterpolationInterpolationInterpolationinterpolation to 'bilinear'"bilinear""bilinear""bilinear""bilinear""bilinear" leads to smoother region boundaries, especially if regions are enlarged. However, the runtime increases significantly.

If more than one region is passed in RegionRegionRegionRegionRegionregion, their polar transformations are computed individually and stored as a tuple in PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion. Please note that the indices of an input region and its transformation only correspond if the system variable 'store_empty_regions'"store_empty_regions""store_empty_regions""store_empty_regions""store_empty_regions""store_empty_regions" is set to 'true'"true""true""true""true""true" (see set_systemset_systemSetSystemset_systemSetSystemSetSystem). Otherwise empty output regions are discarded and the length of the input tuple RegionRegionRegionRegionRegionregion is most likely not equal to the length of the output tuple PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion.

Attention

If WidthWidthWidthWidthWidthwidth or HeightHeightHeightHeightHeightheight are chosen greater than the dimensions of the current image, the system variable 'clip_region'"clip_region""clip_region""clip_region""clip_region""clip_region" should be set to 'false'"false""false""false""false""false" (see set_systemset_systemSetSystemset_systemSetSystemSetSystem). Otherwise, an output region that does not lie within the dimensions of the current image can produce an error message.

Parallelization

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on tuple level.
Automatically parallelized on internal data level.

Parameters

RegionRegionRegionRegionRegionregion (input_object) region(-array) → object

Input region.

PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion (output_object) region(-array) → object

Output region.

RowRowRowRowRowrow (input_control) number → (real / integer)

Row coordinate of the center of the arc.

Default value: 256

Suggested values: 0, 16, 32, 64, 128, 240, 256, 480, 512

Typical range of values: 0 ≤ Row Row Row Row Row row ≤ 32767

Restriction: Row >= -131068 && Row <= 131068

ColumnColumnColumnColumnColumncolumn (input_control) number → (real / integer)

Column coordinate of the center of the arc.

Default value: 256

Suggested values: 0, 16, 32, 64, 128, 256, 320, 512, 640

Typical range of values: 0 ≤ Column Column Column Column Column column ≤ 32767

Restriction: Column >= -131068 && Column <= 131068

AngleStartAngleStartAngleStartAngleStartAngleStartangleStart (input_control) number → (real)

Angle of the ray to be mapped to column coordinate 0 of PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion.

Default value: 0.0

Suggested values: 0.0, 0.78539816, 1.57079632, 3.141592654, 6.2831853, 12.566370616

Typical range of values: -6.2831853 ≤ AngleStart AngleStart AngleStart AngleStart AngleStart angleStart ≤ 6.2831853

AngleEndAngleEndAngleEndAngleEndAngleEndangleEnd (input_control) number → (real)

Angle of the ray to be mapped to column coordinate WidthWidthWidthWidthWidthwidth-1 of PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion.

Default value: 6.2831853

Suggested values: 0.0, 0.78539816, 1.57079632, 3.141592654, 6.2831853, 12.566370616

Typical range of values: -6.2831853 ≤ AngleEnd AngleEnd AngleEnd AngleEnd AngleEnd angleEnd ≤ 6.2831853

RadiusStartRadiusStartRadiusStartRadiusStartRadiusStartradiusStart (input_control) number → (real / integer)

Radius of the circle to be mapped to row coordinate 0 of PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion.

Default value: 0

Suggested values: 0, 16, 32, 64, 100, 128, 256, 512

Typical range of values: 0 ≤ RadiusStart RadiusStart RadiusStart RadiusStart RadiusStart radiusStart ≤ 32767

RadiusEndRadiusEndRadiusEndRadiusEndRadiusEndradiusEnd (input_control) number → (real / integer)

Radius of the circle to be mapped to row coordinate HeightHeightHeightHeightHeightheight-1 of PolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionPolarTransRegionpolarTransRegion.

Default value: 100

Suggested values: 0, 16, 32, 64, 100, 128, 256, 512

Typical range of values: 0 ≤ RadiusEnd RadiusEnd RadiusEnd RadiusEnd RadiusEnd radiusEnd ≤ 32767

WidthWidthWidthWidthWidthwidth (input_control) number → (integer)

Width of the virtual output image.

Default value: 512

Suggested values: 256, 320, 512, 640, 800, 1024

Typical range of values: 2 ≤ Width Width Width Width Width width ≤ 32767

HeightHeightHeightHeightHeightheight (input_control) number → (integer)

Height of the virtual output image.

Default value: 512

Suggested values: 240, 256, 480, 512, 600, 1024

Typical range of values: 2 ≤ Height Height Height Height Height height ≤ 32767

InterpolationInterpolationInterpolationInterpolationInterpolationinterpolation (input_control) string → (string)

Interpolation method for the transformation.

Default value: 'nearest_neighbor' "nearest_neighbor" "nearest_neighbor" "nearest_neighbor" "nearest_neighbor" "nearest_neighbor"

List of values: 'bilinear'"bilinear""bilinear""bilinear""bilinear""bilinear", 'nearest_neighbor'"nearest_neighbor""nearest_neighbor""nearest_neighbor""nearest_neighbor""nearest_neighbor"

Module

Foundation

Operators