libcamera: Add Transform enum to represent 2D plane transforms.

We implement 2D transforms as an enum class with 8 elements,
consisting of the usual 2D plane transformations (flips, rotations
etc.).

The transform is made up of 3 bits, indicating whether the transform
includes: a transpose, a horizontal flip (mirror) and a vertical flip.

Signed-off-by: David Plowman <david.plowman@raspberrypi.com>
Reviewed-by: Laurent Pinchart <laurent.pinchart@ideasonboard.com>
Reviewed-by: Kieran Bingham <kieran.bingham@ideasonboard.com>
Signed-off-by: Kieran Bingham <kieran.bingham@ideasonboard.com>

4 files changed, 402 insertions, 0 deletions

diff --git a/include/libcamera/meson.build b/include/libcamera/meson.build
index 692931a5..3d5fc701 100644
--- a/include/libcamera/meson.build
+++ b/include/libcamera/meson.build
@@ -19,6 +19,7 @@ libcamera_public_headers = files([
     'span.h',
     'stream.h',
     'timer.h',
+    'transform.h',
 ])
 
 include_dir = join_paths(libcamera_include_dir, 'libcamera')
diff --git a/include/libcamera/transform.h b/include/libcamera/transform.h
new file mode 100644
index 00000000..71b43da7
--- /dev/null
+++ b/include/libcamera/transform.h
@@ -0,0 +1,78 @@
+/* SPDX-License-Identifier: LGPL-2.1-or-later */
+/*
+ * Copyright (C) 2020, Raspberry Pi (Trading) Limited
+ *
+ * transform.h - 2D plane transforms
+ */
+
+#ifndef __LIBCAMERA_TRANSFORM_H__
+#define __LIBCAMERA_TRANSFORM_H__
+
+#include <string>
+
+namespace libcamera {
+
+enum class Transform : int {
+	Identity = 0,
+	Rot0 = Identity,
+	HFlip = 1,
+	VFlip = 2,
+	HVFlip = HFlip | VFlip,
+	Rot180 = HVFlip,
+	Transpose = 4,
+	Rot270 = HFlip | Transpose,
+	Rot90 = VFlip | Transpose,
+	Rot180Transpose = HFlip | VFlip | Transpose
+};
+
+constexpr Transform operator&(Transform t0, Transform t1)
+{
+	return static_cast<Transform>(static_cast<int>(t0) & static_cast<int>(t1));
+}
+
+constexpr Transform operator|(Transform t0, Transform t1)
+{
+	return static_cast<Transform>(static_cast<int>(t0) | static_cast<int>(t1));
+}
+
+constexpr Transform operator^(Transform t0, Transform t1)
+{
+	return static_cast<Transform>(static_cast<int>(t0) ^ static_cast<int>(t1));
+}
+
+constexpr Transform &operator&=(Transform &t0, Transform t1)
+{
+	return t0 = t0 & t1;
+}
+
+constexpr Transform &operator|=(Transform &t0, Transform t1)
+{
+	return t0 = t0 | t1;
+}
+
+constexpr Transform &operator^=(Transform &t0, Transform t1)
+{
+	return t0 = t0 ^ t1;
+}
+
+Transform operator*(Transform t0, Transform t1);
+
+Transform operator-(Transform t);
+
+constexpr bool operator!(Transform t)
+{
+	return t == Transform::Identity;
+}
+
+constexpr Transform operator~(Transform t)
+{
+	return static_cast<Transform>(~static_cast<int>(t) & 7);
+}
+
+Transform transformFromRotation(int angle, bool *success = nullptr);
+
+const char *transformToString(Transform t);
+
+} /* namespace libcamera */
+
+#endif /* __LIBCAMERA_TRANSFORM_H__ */
diff --git a/src/libcamera/meson.build b/src/libcamera/meson.build
index 18ea3261..1351dbba 100644
--- a/src/libcamera/meson.build
+++ b/src/libcamera/meson.build
@@ -44,6 +44,7 @@ libcamera_sources = files([
     'sysfs.cpp',
     'thread.cpp',
     'timer.cpp',
+    'transform.cpp',
     'utils.cpp',
     'v4l2_controls.cpp',
     'v4l2_device.cpp',
diff --git a/src/libcamera/transform.cpp b/src/libcamera/transform.cpp
new file mode 100644
index 00000000..f3e37f31
--- /dev/null
+++ b/src/libcamera/transform.cpp
@@ -0,0 +1,322 @@
+/* SPDX-License-Identifier: LGPL-2.1-or-later */
+/*
+ * Copyright (C) 2020, Raspberry Pi (Trading) Limited
+ *
+ * transform.cpp - 2D plane transforms.
+ */
+
+#include <libcamera/transform.h>
+
+/**
+ * \file transform.h
+ * \brief Enum to represent and manipulate 2D plane transforms
+ */
+
+namespace libcamera {
+
+/**
+ * \enum Transform
+ * \brief Enum to represent a 2D plane transform
+ *
+ * The Transform can take 8 distinct values, representing the usual 2D plane
+ * transforms listed below. Each of these transforms can be constructed
+ * out of 3 basic operations, namely a horizontal flip (mirror), a vertical
+ * flip, and a transposition (about the main diagonal). The transforms are
+ * encoded such that a single bit indicates the presence of each of the 3
+ * basic operations:
+ *
+ * - bit 0 - presence of a horizontal flip
+ * - bit 1 - presence of a vertical flip
+ * - bit 2 - presence of a transposition.
+ *
+ * We regard these 3 basic operations as being applied in a specific order:
+ * first the two flip operations (actually they commute, so the order between
+ * them is unimportant) and finally any transpose operation.
+ *
+ * Functions are provided to manipulate directly the bits within the transform
+ * encoding, but there are also higher-level functions to invert and compose
+ * transforms. Transforms are composed according to the usual mathematical
+ * convention such that the right transform is applied first, and the left
+ * transform is applied second.
+ *
+ * Finally, we have a total of 8 distinct transformations, as follows (a
+ * couple of them have additional synonyms for convenience). We illustrate each
+ * with its nominal effect on a rectangle with vertices labelled A, B, C and D.
+ *
+ * **Identity**
+ *
+ * Identity transform.
+~~~
+              A-B                          A-B
+Input image   | |   goes to output image   | |
+              C-D                          C-D
+~~~
+ * Numeric value: 0 (no bits set).
+ *
+ * **Rot0**
+ *
+ * Synonym for `Identity` (zero degree rotation).
+ *
+ * **HFlip**
+ *
+ * Horizontal flip.
+~~~
+              A-B                          B-A
+Input image   | |   goes to output image   | |
+              C-D                          D-C
+~~~
+ * Numeric value: 1 (horizontal flip bit set only).
+ *
+ * **VFlip**
+ *
+ * Vertical flip.
+~~~
+              A-B                          C-D
+Input image   | |   goes to output image   | |
+              C-D                          A-B
+~~~
+ * Numeric value: 2 (vertical flip bit set only).
+ *
+ * **HVFlip**
+ *
+ * Horizontal and vertical flip (identical to a 180 degree rotation).
+~~~
+              A-B                          D-C
+Input image   | |   goes to output image   | |
+              C-D                          B-A
+~~~
+ * Numeric value: 3 (horizontal and vertical flip bits set).
+ *
+ * **Rot180**
+ *
+ * Synonym for `HVFlip` (180 degree rotation).
+ *
+ * **Transpose**
+ *
+ * Transpose (about the main diagonal).
+~~~
+              A-B                          A-C
+Input image   | |   goes to output image   | |
+              C-D                          B-D
+~~~
+ * Numeric value: 4 (transpose bit set only).
+ *
+ * **Rot270**
+ *
+ * Rotation by 270 degrees clockwise (90 degrees anticlockwise).
+~~~
+              A-B                          B-D
+Input image   | |   goes to output image   | |
+              C-D                          A-C
+~~~
+ * Numeric value: 5 (transpose and horizontal flip bits set).
+ *
+ * **Rot90**
+ *
+ * Rotation by 90 degrees clockwise (270 degrees anticlockwise).
+~~~
+              A-B                          C-A
+Input image   | |   goes to output image   | |
+              C-D                          D-B
+~~~
+ * Numeric value: 6 (transpose and vertical flip bits set).
+ *
+ * **Rot180Transpose**
+ *
+ * Rotation by 180 degrees followed by transpose (alternatively, transposition
+ * about the "opposite diagonal").
+~~~
+              A-B                          D-B
+Input image   | |   goes to output image   | |
+              C-D                          C-A
+~~~
+ * Numeric value: 7 (all bits set).
+ *
+ * \sa https://en.wikipedia.org/wiki/Examples_of_groups#dihedral_group_of_order_8
+ *
+ * The set of 2D plane transforms is also known as the symmetry group of a
+ * square, described in the link. Note that the group can be generated by
+ * only 2 elements (the horizontal flip and a 90 degree rotation, for
+ * example), however, the encoding used here makes the presence of the vertical
+ * flip explicit.
+ */
+
+/**
+ * \fn operator &(Transform t0, Transform t1)
+ * \brief Apply bitwise AND operator between the bits in the two transforms
+ * \param[in] t0 The first transform
+ * \param[in] t1 The second transform
+ */
+
+/**
+ * \fn operator |(Transform t0, Transform t1)
+ * \brief Apply bitwise OR operator between the bits in the two transforms
+ * \param[in] t0 The first transform
+ * \param[in] t1 The second transform
+ */
+
+/**
+ * \fn operator ^(Transform t0, Transform t1)
+ * \brief Apply bitwise XOR operator between the bits in the two transforms
+ * \param[in] t0 The first transform
+ * \param[in] t1 The second transform
+ */
+
+/**
+ * \fn operator &=(Transform &t0, Transform t1)
+ * \brief Apply bitwise AND-assignment operator between the bits in the two
+ * transforms
+ * \param[in] t0 The first transform
+ * \param[in] t1 The second transform
+ */
+
+/**
+ * \fn operator |=(Transform &t0, Transform t1)
+ * \brief Apply bitwise OR-assignment operator between the bits in the two
+ * transforms
+ * \param[in] t0 The first transform
+ * \param[in] t1 The second transform
+ */
+
+/**
+ * \fn operator ^=(Transform &t0, Transform t1)
+ * \brief Apply bitwise XOR-assignment operator between the bits in the two
+ * transforms
+ * \param[in] t0 The first transform
+ * \param[in] t1 The second transform
+ */
+
+/**
+ * \brief Compose two transforms together
+ * \param[in] t1 The second transform
+ * \param[in] t0 The first transform
+ *
+ * Composing transforms follows the usual mathematical convention for
+ * composing functions. That is, when performing `t1 * t0`, \a t0 is applied
+ * first, and then \a t1.
+ * For example, `Transpose * HFlip` performs `HFlip` first and then the
+ * `Transpose` yielding `Rot270`, as shown below.
+~~~
+             A-B                 B-A                     B-D
+Input image  | |   -> HFLip ->   | |   -> Transpose ->   | |   = Rot270
+             C-D                 D-C                     A-C
+~~~
+ * Note that composition is generally non-commutative for Transforms,
+ * and not the same as XOR-ing the underlying bit representations.
+ */
+Transform operator*(Transform t1, Transform t0)
+{
+	/*
+	 * Reorder the operations so that we imagine doing t0's transpose
+	 * (if any) after t1's flips. The effect is to swap t1's hflips for
+	 * vflips and vice versa, after which we can just xor all the bits.
+	 */
+	Transform reordered = t1;
+	if (!!(t0 & Transform::Transpose)) {
+		reordered = t1 & Transform::Transpose;
+		if (!!(t1 & Transform::HFlip))
+			reordered |= Transform::VFlip;
+		if (!!(t1 & Transform::VFlip))
+			reordered |= Transform::HFlip;
+	}
+
+	return reordered ^ t0;
+}
+
+/**
+ * \brief Invert a transform
+ * \param[in] t The transform to be inverted
+ *
+ * That is, we return the transform such that `t * (-t)` and `(-t) * t` both
+ * yield the identity transform.
+ */
+Transform operator-(Transform t)
+{
+	/* All are self-inverses, except for Rot270 and Rot90. */
+	static const Transform inverses[] = {
+		Transform::Identity,
+		Transform::HFlip,
+		Transform::VFlip,
+		Transform::HVFlip,
+		Transform::Transpose,
+		Transform::Rot90,
+		Transform::Rot270,
+		Transform::Rot180Transpose
+	};
+
+	return inverses[static_cast<int>(t)];
+}
+
+/**
+ * \fn operator!(Transform t)
+ * \brief Return `true` if the transform is the `Identity`, otherwise `false`
+ * \param[in] t The transform to be tested
+ */
+
+/**
+ * \fn operator~(Transform t)
+ * \brief Return the transform with all the bits inverted individually
+ * \param[in] t The transform of which the bits will be inverted
+ *
+ * This inverts the bits that encode the transform in a bitwise manner. Note
+ * that this is not the proper inverse of transform \a t (for which use \a
+ * operator-).
+ */
+
+/**
+ * \brief Return the transform representing a rotation of the given angle
+ * clockwise
+ * \param[in] angle The angle of rotation in a clockwise sense. Negative values
+ * can be used to represent anticlockwise rotations
+ * \param[out] success Set to `true` if the angle is a multiple of 90 degrees,
+ * otherwise `false`
+ * \return The transform corresponding to the rotation if \a success was set to
+ * `true`, otherwise the `Identity` transform
+ */
+Transform transformFromRotation(int angle, bool *success)
+{
+	angle = angle % 360;
+	if (angle < 0)
+		angle += 360;
+
+	if (success != nullptr)
+		*success = true;
+
+	switch (angle) {
+	case 0:
+		return Transform::Identity;
+	case 90:
+		return Transform::Rot90;
+	case 180:
+		return Transform::Rot180;
+	case 270:
+		return Transform::Rot270;
+	}
+
+	if (success != nullptr)
+		*success = false;
+
+	return Transform::Identity;
+}
+
+/**
+ * \brief Return a character string describing the transform
+ * \param[in] t The transform to be described.
+ */
+const char *transformToString(Transform t)
+{
+	static const char *strings[] = {
+		"identity",
+		"hflip",
+		"vflip",
+		"hvflip",
+		"transpose",
+		"rot270",
+		"rot90",
+		"rot180transpose"
+	};
+
+	return strings[static_cast<int>(t)];
+}
+
+} /* namespace libcamera */