# smallest_rectangle2 (Operator)

## Name

`smallest_rectangle2` — Smallest surrounding rectangle with any orientation.

## Signature

`smallest_rectangle2(Regions : : : Row, Column, Phi, Length1, Length2)`

## Description

The operator `smallest_rectangle2` determines the smallest surrounding rectangle of a region, i.e., the rectangle with the smallest area of all rectangles containing the region. For this rectangle the center, the inclination and the two radii are calculated. The calculation of the rectangle is based on the center coordinates of the region pixels.

In the documentation of this chapter (Regions / Features), you can find an image illustrating regions which vary in the length and phi of their smallest surrounding rectangle.

The smallest surrounding rectangle of a region. Note that the calculation is based on the center coordinates of the region pixels.

The operator is applied when, for example, the location of a scenery of several regions (e.g., printed text on a rectangular paper or in rectangular print (justified lines)) must be found. The parameters of `smallest_rectangle2` are chosen in such a way that they can be used directly as input for the operators `disp_rectangle2` and `gen_rectangle2`.

If more than one region is passed in `Regions` the results are stored in tuples, the index of a value in the tuple corresponding to the index of a region in the input. In case of empty region all parameters have the value 0.0 if no other behavior was set (see `set_system`).

## Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on tuple level.

## Parameters

`Regions` (input_object)  region(-array) `→` object

Regions to be examined.

`Row` (output_control)  rectangle2.center.y(-array) `→` (real)

Line index of the center.

`Column` (output_control)  rectangle2.center.x(-array) `→` (real)

Column index of the center.

`Phi` (output_control)  rectangle2.angle.rad(-array) `→` (real)

Orientation of the surrounding rectangle (arc measure)

Assertion: `- pi / 2 < Phi && Phi <= pi / 2`

`Length1` (output_control)  rectangle2.hwidth(-array) `→` (real)

First radius (half length) of the surrounding rectangle.

Assertion: `Length1 >= 0.0`

`Length2` (output_control)  rectangle2.hheight(-array) `→` (real)

Second radius (half width) of the surrounding rectangle.

Assertion: `Length2 >= 0.0 && Length2 <= Length1`

## Example (HDevelop)

```read_image(Image,'fabrik')
regiongrowing(Image,Regions,5,5,6,100)
smallest_rectangle2(Regions,Row,Column,Phi,Length1,Length2)
gen_rectangle2(Rectangle,Row,Column,Phi,Length1,Length2)
dev_set_draw ('margin')
dev_display(Rectangle)
```

## Complexity

If F is the area of the region and N is the number of supporting points of the convex hull, the runtime complexity is O(sqrt(F) + N^2).

## Result

The operator `smallest_rectangle2` returns the value 2 (H_MSG_TRUE) if the input is not empty. The behavior in case of empty input (no input regions available) is set via the operator `set_system('no_object_result',<Result>)`. The behavior in case of empty region (the region is the empty set) is set via `set_system('empty_region_result',<Result>)`. If necessary an exception is raised.

## Possible Predecessors

`threshold`, `regiongrowing`, `connection`, `runlength_features`

## Possible Successors

`disp_rectangle2`, `gen_rectangle2`

## Alternatives

`elliptic_axis`, `smallest_rectangle1`

`smallest_circle`, `set_shape`