STRUCT

ImageMath

public struct ImageMath

Provides affine transformation utilities for image processing.

All affine matrices returned by this class operate in normalized coordinates, where image space is mapped to the [0, 1] range in both axes with origin at top-left.

Methods

reprojection(aspect:fovRadians:zNear:zFar:referenceView:targetView:backProjectionDistance:)

public static func reprojection(aspect: Float, fovRadians: Float, zNear: Float, zFar: Float,
                                referenceView: matrix_float4x4, targetView: matrix_float4x4, backProjectionDistance: Float = 0.9
) -> matrix_float3x3

Returns a 3×3 homography matrix as matrix_float3x3 that reprojects image coordinates from a reference camera view into a target camera view. The image coordinates are expected to be normalized [0..1].

• Parameters:
  • aspect: The aspect ratio of the image (width / height).
  • fovRadians: The vertical field of view in radians.
  • zNear: Near clipping plane distance.
  • zFar: Far clipping plane distance.
  • referenceView: The reference camera view.
  • targetView: The target camera view.
  • backProjectionDistance: Depth at which to reproject, normalized between clipping planes near (0) and far (1). Recommended: 0.9.
• Returns: A 3×3 homography matrix in column-major order.

Parameters

Name	Description
aspect	The aspect ratio of the image (width / height).
fovRadians	The vertical field of view in radians.
zNear	Near clipping plane distance.
zFar	Far clipping plane distance.
referenceView	The reference camera view.
targetView	The target camera view.
backProjectionDistance	Depth at which to reproject, normalized between clipping planes near (0) and far (1). Recommended: 0.9.

displayTransform(for:viewportSize:imageSize:)

public static func displayTransform(for orientation: UIInterfaceOrientation,
                                    viewportSize: CGSize,
                                    imageSize: CGSize) -> CGAffineTransform

Returns an affine transform that maps normalized image coordinates into a coordinate space suitable for rendering the camera image in the given viewport and orientation.

This method replicates ARKit’s displayTransform(for:viewportSize:) by computing a transform that accounts for the camera image’s aspect ratio, the device’s interface orientation, and the desired viewport size.

• Parameters:
  • orientation: The current interface orientation of the device’s UI.
  • viewportSize: The size of the viewport in which the image will be rendered.
  • imageSize: The dimensions of the camera image.
• Returns: A CGAffineTransform that converts normalized image coordinates (with origin at top-left, ranging from 0.0 to 1.0) into the coordinate space of the viewport, accounting for orientation and aspect ratio.

Parameters

Name	Description
orientation	The current interface orientation of the device’s UI.
viewportSize	The size of the viewport in which the image will be rendered.
imageSize	The dimensions of the camera image.

viewRotation(fromOrientation:toOrientation:)

public static func viewRotation(fromOrientation: UIInterfaceOrientation, toOrientation: UIInterfaceOrientation) -> CGAffineTransform

Returns an affine transform that rotates between two interface orientations around the center.

This method models UI rotation (opposite to physical device rotation). For example, rotating from .landscapeRight to .portrait results in a counter-clockwise transform.

• Parameters:
  • fromOrientation: The starting interface orientation.
  • toOrientation: The target interface orientation.
• Returns: A CGAffineTransform representing the rotation.

Parameters

Name	Description
fromOrientation	The starting interface orientation.
toOrientation	The target interface orientation.

deviceRotation(fromOrientation:toOrientation:)

public static func deviceRotation(fromOrientation: UIInterfaceOrientation, toOrientation: UIInterfaceOrientation) -> CGAffineTransform

Returns an affine transform that rotates between two interface orientations around the center.

This method models physical device rotation. For example, rotating from .landscapeRight to .portrait results in a clockwise transform.

• Parameters:
  • fromOrientation: The starting interface orientation.
  • toOrientation: The target interface orientation.
• Returns: A CGAffineTransform representing the rotation.

Parameters

Name	Description
fromOrientation	The starting interface orientation.
toOrientation	The target interface orientation.

affineCrop(source:target:)

public static func affineCrop(source: CGSize, target: CGSize) -> CGAffineTransform

Returns an affine transformation that crops the source size to match the aspect ratio of the target size.

• Parameters:
  • source: The size of the source container.
  • target: The size of the target container.
• Returns: An affine transformation matrix that crops the source to fit the target aspect ratio.

Parameters

Name	Description
source	The size of the source container.
target	The size of the target container.

affineFit(source:sourceOrientation:target:targetOrientation:)

public static func affineFit(source: CGSize, sourceOrientation: UIInterfaceOrientation,
                             target: CGSize, targetOrientation: UIInterfaceOrientation) -> CGAffineTransform

Returns an affine transformation that maps normalized coordinates in the source frame to normalized coordinates in the target frame.

• Note: In portrait, this function aligns the top and bottom edges to the target.

• Parameters:

  • source: The size of the source container.
  • sourceOrientation: The orientation of the source container.
  • target: The size of the target container.
  • targetOrientation: The orientation of the target container.

• Returns: An affine transformation matrix that fits the source into the target.

Parameters

Name	Description
source	The size of the source container.
sourceOrientation	The orientation of the source container.
target	The size of the target container.
targetOrientation	The orientation of the target container.

affineRotation(radians:)

public static func affineRotation(radians: Float) -> CGAffineTransform

Returns an (u, v) -> (u', v') transformation that represents a 2D affine rotation.

affineTranslation(tx:ty:)

public static func affineTranslation(tx: Float, ty: Float) -> CGAffineTransform

Returns an (u, v) -> (u', v') transformation that represents a 2D affine translation.

affineScaling(sx:sy:)

public static func affineScaling(sx: Float, sy: Float) -> CGAffineTransform

Returns an (u, v) -> (u', v') transformation that represents a 2D affine scaling.

affineInvertHorizontal()

public static func affineInvertHorizontal() -> CGAffineTransform

Returns an (u, v) -> (u', v') transformation that represents a horizontal mirroring, i.e. (u, v) -> (1 - u, v).

affineInvertVertical()

public static func affineInvertVertical() -> CGAffineTransform

Returns an (u, v) -> (u', v') transformation that represents a vertical mirroring, i.e. (u, v) -> (u, 1 - v).