# Rotate

Rotate image by specified angle

## Library

Geometric Transformations

`visiongeotforms`

## Description

Use the Rotate block to rotate an image by an angle specified in radians.

### Note

This block supports intensity and color images on its ports.

PortDescription

Image

M-by-N matrix of intensity values or an M-by-N-by-P color video signal where P is the number of color planes

Angle

Rotation angle

Output

Rotated matrix

The Rotate block uses the 3-pass shear rotation algorithm to compute its values, which is different than the algorithm used by the `imrotate` function in the Image Processing Toolbox™.

### Fixed-Point Data Types

The following diagram shows the data types used in the Rotate block for bilinear interpolation of fixed-point signals.

You can set the angle values, product output, accumulator, and output data types in the block mask.

The Rotate block requires additional data types. The Sine table value has the same word length as the angle data type and a fraction length that is equal to its word length minus one. The following diagram shows how these data types are used inside the block.

### Note

If overflow occurs, the rotated image might appear distorted.

## Parameters

Output size

Specify the size of the rotated matrix. If you select `Expanded to fit rotated input image`, the block outputs a matrix that contains all the rotated image values. If you select `Same as input image`, the block outputs a matrix that contains the middle part of the rotated image. As a result, the edges of the rotated image might be cropped. Use the Background fill value parameter to specify the pixel values outside the image.

Rotation angle source

Specify how to enter your rotation angle. If you select `Specify via dialog`, the Angle (radians) parameter appears in the dialog box.

If you select `Input port`, the Angle port appears on the block. The block uses the input to this port at each time step as your rotation angle. The input to the Angle port must be the same data type as the input to the I port.

Enter a real, scalar value for your rotation angle. This parameter is visible if, for the Rotation angle source parameter, you select `Specify via dialog`.

When the rotation angle is a multiple of pi/2, the block uses a more efficient algorithm. If the angle value you enter for the Angle (radians) parameter is within 0.00001 radians of a multiple of pi/2, the block rounds the angle value to the multiple of pi/2 before performing the rotation.

Maximum angle (enter pi radians to accommodate all positive and negative angles)

Enter the maximum angle by which to rotate the input image. Enter a scalar value, between `0` and $\pi$ radians. The block determines which angle, $0\le angle\le \mathrm{max}angle$, requires the largest output matrix and sets the dimensions of the output port accordingly.

This parameter is visible if you set the Output size parameter, to `Expanded to fit rotated input image`, and the Rotation angle source parameter to`Input port`.

Display rotated image in

Specify how the image is rotated. If you select `Center`, the image is rotated about its center point. If you select `Top-left corner`, the block rotates the image so that two corners of the rotated input image are always in contact with the top and left sides of the output image.

This parameter is visible if, for the Output size parameter, you select ```Expanded to fit rotated input image```, and, for the Rotation angle source parameter, you select ```Input port```.

Sine value computation method

Specify the value computation method. If you select `Trigonometric function`, the block computes sine and cosine values it needs to calculate the rotation of your image during the simulation. If you select ```Table lookup```, the block computes and stores the trigonometric values it needs to calculate the rotation of your image before the simulation starts. In this case, the block requires extra memory.

Background fill value

Specify a value for the pixels that are outside the image.

Interpolation method

Specify which interpolation method the block uses to rotate the image. If you select `Nearest neighbor`, the block uses the value of one nearby pixel for the new pixel value. If you select `Bilinear`, the new pixel value is the weighted average of the four nearest pixel values. If you select `Bicubic`, the new pixel value is the weighted average of the sixteen nearest pixel values.

The number of pixels the block considers affects the complexity of the computation. Therefore, the `Nearest-neighbor` interpolation is the most computationally efficient. However, because the accuracy of the method is proportional to the number of pixels considered, the `Bicubic` method is the most accurate. For more information, see Nearest Neighbor, Bilinear, and Bicubic Interpolation Methods in the Computer Vision Toolbox™ User's Guide.

Rounding mode

Select the rounding mode for fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Angle values

Choose how to specify the word length and the fraction length of the angle values.

• When you select ```Same word length as input```, the word length of the angle values match that of the input to the block. In this mode, the fraction length of the angle values is automatically set to the binary-point only scaling that provides you with the best precision possible given the value and word length of the angle values.

• When you select `Specify word length`, you can enter the word length of the angle values, in bits. The block automatically sets the fraction length to give you the best precision.

• When you select `Binary point scaling`, you can enter the word length and the fraction length of the angle values, in bits.

• When you select `Slope and bias scaling`, you can enter the word length, in bits, and the slope of the angle values. The bias of all signals in the Computer Vision Toolbox blocks is 0.

This parameter is only visible if, for the Rotation angle source parameter, you select `Specify via dialog`.

Product output

As depicted in the previous figure, the output of the multiplier is placed into the product output data type and scaling. Use this parameter to specify how to designate this product output word and fraction lengths.

• When you select `Same as first input`, these characteristics match those of the input to the block.

• When you select `Binary point scaling`, you can enter the word length and the fraction length of the product output, in bits.

• When you select `Slope and bias scaling`, you can enter the word length, in bits, and the slope of the product output. The bias of all signals in the Computer Vision Toolbox blocks is 0.

Accumulator

As depicted in the previous figure, inputs to the accumulator are cast to the accumulator data type. The output of the adder remains in the accumulator data type as each element of the input is added to it. Use this parameter to specify how to designate this accumulator word and fraction lengths.

• When you select `Same as product output`, these characteristics match those of the product output.

• When you select `Same as first input`, these characteristics match those of the first input to the block.

• When you select `Binary point scaling`, you can enter the word length and the fraction length of the accumulator, in bits.

• When you select `Slope and bias scaling`, you can enter the word length, in bits, and the slope of the accumulator. The bias of all signals in the Computer Vision Toolbox blocks is 0.

Output

Choose how to specify the word length and fraction length of the output of the block:

• When you select `Same as first input`, these characteristics match those of the first input to the block.

• When you select `Binary point scaling`, you can enter the word length and the fraction length of the output, in bits.

• When you select `Slope and bias scaling`, you can enter the word length, in bits, and the slope of the output. The bias of all signals in the Computer Vision Toolbox blocks is 0.

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see `fxptdlg`, a reference page on the Fixed-Point Tool in the Simulink® documentation.

## Supported Data Types

PortSupported Data Types

Image

• Double-precision floating point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned integer

Angle

Same as Image port

Output

Same as Image port

If the data type of the input signal is floating point, the output signal is the same data type as the input signal.

## References

[1] Wolberg, George. Digital Image Warping. Washington: IEEE Computer Society Press, 1990.

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