hi::v1::geo::matrix< D > Class Template Reference

#include <hikogui/geometry/matrix.hpp>

Public Member Functions
constexpr	matrix (matrix const &) noexcept=default
constexpr	matrix (matrix &&) noexcept=default
constexpr matrix &	operator= (matrix const &) noexcept=default
constexpr matrix &	operator= (matrix &&) noexcept=default
constexpr	matrix () noexcept
	Constructs an identity matrix.
constexpr	matrix (f32x4 col0, f32x4 col1, f32x4 col2, f32x4 col3=f32x4{0.0f, 0.0f, 0.0f, 1.0f}) noexcept
	Construct a matrix from four columns.
constexpr	matrix (vector3 col0, vector3 col1, vector3 col2, vector3 col3=vector3{}) noexcept
	Construct a matrix from four vectors.
constexpr	matrix (float c0r0, float c1r0, float c2r0, float c0r1, float c1r1, float c2r1, float c0r2, float c1r2, float c2r2) noexcept
	Construct a 3x3 matrix from scalar values.
constexpr	matrix (float c0r0, float c1r0, float c2r0, float c3r0, float c0r1, float c1r1, float c2r1, float c3r1, float c0r2, float c1r2, float c2r2, float c3r2, float c0r3, float c1r3, float c2r3, float c3r3) noexcept
	Construct a 4x4 matrix from scalar values.
template<int E> requires (E < D)
constexpr	matrix (matrix< E > const &other) noexcept
	Copy-construct a matrix from a smaller matrix.
template<int E> requires (E < D)
constexpr matrix &	operator= (matrix< E > const &rhs) noexcept
	Copy-assign a matrix from a smaller matrix.
constexpr	operator std::array< f32x4, 4 > () const noexcept
	Convert a point to its f32x4-nummeric_array.
constexpr bool	holds_invariant () const noexcept
constexpr f32x4	operator* (f32x4 const &rhs) const noexcept
	Transform a f32x4 numeric array by the matrix.
constexpr float	operator* (float const &rhs) const noexcept
	Transform a float by the scaling factor of the matrix.
constexpr corner_radii	operator* (corner_radii const &rhs) const noexcept
	Transform a float by the scaling factor of the matrix.
template<int E>
constexpr auto	operator* (vector< float, E > const &rhs) const noexcept
	Transform a vector by the matrix.
template<int E>
constexpr auto	operator* (extent< float, E > const &rhs) const noexcept
	Transform a extent by the matrix.
template<int E>
constexpr auto	operator* (point< float, E > const &rhs) const noexcept
	Transform a point by the matrix.
constexpr rectangle	operator* (aarectangle const &rhs) const noexcept
	Transform an axis-aligned rectangle by the matrix.
constexpr rectangle	operator* (rectangle const &rhs) const noexcept
	Transform a rectangle by the matrix.
constexpr quad	operator* (quad const &rhs) const noexcept
	Transform a quad by the matrix.
constexpr circle	operator* (circle const &rhs) const noexcept
	Transform a circle by the matrix.
constexpr line_segment	operator* (line_segment const &rhs) const noexcept
	Transform a line-segment by the matrix.
constexpr auto	operator* (color const &rhs) const noexcept
	Transform a color by a color matrix.
constexpr auto	operator* (matrix const &rhs) const noexcept
	Matrix/Matrix multiplication.
template<int E>
constexpr bool	operator== (matrix< E > const &rhs) const noexcept
	Compare two matrices potentially of different dimensions.
constexpr matrix	operator~ () const
	Invert matrix.

Static Public Member Functions
static constexpr matrix	uniform (aarectangle src_rectangle, aarectangle dst_rectangle, alignment alignment) noexcept
	Create a transformation matrix to translate and uniformly-scale a src_rectangle to a dst_rectangle.

Friends
template<int I>
constexpr f32x4 const &	get (matrix const &rhs) noexcept
	Get a column.
template<int I>
constexpr f32x4 &	get (matrix &rhs) noexcept
	Get a column.
constexpr matrix	transpose (matrix const &rhs) noexcept
	Matrix transpose.
template<char DstX, char DstY, char DstZ, char DstW = 'w'> requires (D == 3)
constexpr matrix	reflect (matrix const &rhs) noexcept
	Reflect axis of a matrix.

Detailed Description

template<int D>
class hi::v1::geo::matrix< D >

A 2D or 3D homogenius matrix for transforming homogenious vectors and points.

This matrix is in column major order. It is implemented as 4 columns made from a f32x4 numeric-array.

Constructor & Destructor Documentation

matrix() [1/6]

template<int D>

constexpr hi::v1::geo::matrix< D >::matrix ( )

inlineconstexprnoexcept

Constructs an identity matrix.

matrix() [2/6]

template<int D>

constexpr hi::v1::geo::matrix< D >::matrix ( f32x4 col0, f32x4 col1, f32x4 col2, f32x4 col3 = f32x4{0.0f, 0.0f, 0.0f, 1.0f} )

inlineconstexprnoexcept

Construct a matrix from four columns.

Parameters

col0	The 1st f32x4 column. @param col1 The 2ndf32x4 column.
col2	The 3rd f32x4 column. @param col3 The 4thf32x4 column.

matrix() [3/6]

template<int D>

constexpr hi::v1::geo::matrix< D >::matrix ( vector3 col0, vector3 col1, vector3 col2, vector3 col3 = vector3{} )

inlineconstexprnoexcept

Construct a matrix from four vectors.

Parameters

col0	The 1st f32x4 column. @param col1 The 2ndf32x4 column.
col2	The 3rd f32x4 column. @param col3 The 4thf32x4 column.

matrix() [4/6]

template<int D>

constexpr hi::v1::geo::matrix< D >::matrix ( float c0r0, float c1r0, float c2r0, float c0r1, float c1r1, float c2r1, float c0r2, float c1r2, float c2r2 )

inlineconstexprnoexcept

Construct a 3x3 matrix from scalar values.

The function parameters are in row-major order for pretty formatting in source code. The matrix itself remains in column-major order.

Parameters

c0r0	Value for column 0, row 0
c1r0	Value for column 1, row 0
c2r0	Value for column 2, row 0
c0r1	Value for column 0, row 1
c1r1	Value for column 1, row 1
c2r1	Value for column 2, row 1
c0r2	Value for column 0, row 2
c1r2	Value for column 1, row 2
c2r2	Value for column 2, row 2

matrix() [5/6]

template<int D>

constexpr hi::v1::geo::matrix< D >::matrix ( float c0r0, float c1r0, float c2r0, float c3r0, float c0r1, float c1r1, float c2r1, float c3r1, float c0r2, float c1r2, float c2r2, float c3r2, float c0r3, float c1r3, float c2r3, float c3r3 )

inlineconstexprnoexcept

Construct a 4x4 matrix from scalar values.

The function parameters are in row-major order for pretty formatting in source code. The matrix itself remains in column-major order.

Parameters

c0r0	Value for column 0, row 0
c1r0	Value for column 1, row 0
c2r0	Value for column 2, row 0
c3r0	Value for column 3, row 0
c0r1	Value for column 0, row 1
c1r1	Value for column 1, row 1
c2r1	Value for column 2, row 1
c3r1	Value for column 3, row 1
c0r2	Value for column 0, row 2
c1r2	Value for column 1, row 2
c2r2	Value for column 2, row 2
c3r2	Value for column 3, row 2
c0r3	Value for column 0, row 3
c1r3	Value for column 1, row 3
c2r3	Value for column 2, row 3
c3r3	Value for column 3, row 3

matrix() [6/6]

template<int D>

template<int E>
requires (E < D)

constexpr hi::v1::geo::matrix< D >::matrix ( matrix< E > const & other )

inlineconstexprnoexcept

Copy-construct a matrix from a smaller matrix.

Member Function Documentation

operator std::array< f32x4, 4 >()

template<int D>

constexpr hi::v1::geo::matrix< D >::operator std::array< f32x4, 4 > ( ) const

inlineexplicitconstexprnoexcept

Convert a point to its f32x4-nummeric_array.

operator*() [1/13]

template<int D>

constexpr rectangle hi::v1::geo::matrix< D >::operator* ( aarectangle const & rhs ) const

inlineconstexprnoexcept

Transform an axis-aligned rectangle by the matrix.

After transformation it can not be guaranteed that an axis-aligned rectangle remained aligned to axis, therefor a normal rectangle is returned

Note

It is undefined behavior to perspective transform a rectangle

Parameters

rhs	The axis-aligned rectangle to be transformed.

Returns

The transformed rectangle

operator*() [2/13]

template<int D>

constexpr circle hi::v1::geo::matrix< D >::operator* ( circle const & rhs ) const

inlineconstexprnoexcept

Transform a circle by the matrix.

Parameters

rhs	The circle to be transformed.

Returns

The transformed circle

operator*() [3/13]

template<int D>

constexpr auto hi::v1::geo::matrix< D >::operator* ( color const & rhs ) const

inlineconstexprnoexcept

Transform a color by a color matrix.

The alpha value is not included in the transformation and copied from the input.

Note

It is undefined behavior if the matrix contains a translation.

Parameters

rhs	The color to be transformed.

Returns

The transformed color.

operator*() [4/13]

template<int D>

constexpr corner_radii hi::v1::geo::matrix< D >::operator* ( corner_radii const & rhs ) const

inlineconstexprnoexcept

Transform a float by the scaling factor of the matrix.

The floating point number is transformed into a vector laying on the x-axis, then transformed, then extracting the hypot from it.

operator*() [5/13]

template<int D>

template<int E>

constexpr auto hi::v1::geo::matrix< D >::operator* ( extent< float, E > const & rhs ) const

inlineconstexprnoexcept

Transform a extent by the matrix.

Extents will not be translated.

Parameters

rhs	The extent to be transformed.

Returns

The transformed extent.

operator*() [6/13]

template<int D>

constexpr f32x4 hi::v1::geo::matrix< D >::operator* ( f32x4 const & rhs ) const

inlineconstexprnoexcept

Transform a f32x4 numeric array by the matrix.

Parameters

rhs	The f32x4 numeric array to transform.

Returns

The transformed numeric array.

operator*() [7/13]

template<int D>

constexpr float hi::v1::geo::matrix< D >::operator* ( float const & rhs ) const

inlineconstexprnoexcept

Transform a float by the scaling factor of the matrix.

The floating point number is transformed into a vector laying on the x-axis, then transformed, then extracting the hypot from it.

operator*() [8/13]

template<int D>

constexpr line_segment hi::v1::geo::matrix< D >::operator* ( line_segment const & rhs ) const

inlineconstexprnoexcept

Transform a line-segment by the matrix.

Parameters

rhs	The line-segment to be transformed.

Returns

The transformed line-segment

operator*() [9/13]

template<int D>

constexpr auto hi::v1::geo::matrix< D >::operator* ( matrix< D > const & rhs ) const

inlineconstexprnoexcept

Matrix/Matrix multiplication.

operator*() [10/13]

template<int D>

template<int E>

constexpr auto hi::v1::geo::matrix< D >::operator* ( point< float, E > const & rhs ) const

inlineconstexprnoexcept

Transform a point by the matrix.

Parameters

rhs	The point to be transformed.

Returns

The transformed point.

operator*() [11/13]

template<int D>

constexpr quad hi::v1::geo::matrix< D >::operator* ( quad const & rhs ) const

inlineconstexprnoexcept

Transform a quad by the matrix.

Parameters

rhs	The quad to be transformed.

Returns

The transformed quad

operator*() [12/13]

template<int D>

constexpr rectangle hi::v1::geo::matrix< D >::operator* ( rectangle const & rhs ) const

inlineconstexprnoexcept

Transform a rectangle by the matrix.

Note

It is undefined behavior to perspective transform a rectangle

Parameters

rhs	The rectangle to be transformed.

Returns

The transformed rectangle

operator*() [13/13]

template<int D>

template<int E>

constexpr auto hi::v1::geo::matrix< D >::operator* ( vector< float, E > const & rhs ) const

inlineconstexprnoexcept

Transform a vector by the matrix.

Vectors will not be translated.

Parameters

rhs	The vector to be transformed.

Returns

The transformed vector.

operator=()

template<int D>

template<int E>
requires (E < D)

constexpr matrix & hi::v1::geo::matrix< D >::operator= ( matrix< E > const & rhs )

inlineconstexprnoexcept

Copy-assign a matrix from a smaller matrix.

operator==()

template<int D>

template<int E>

constexpr bool hi::v1::geo::matrix< D >::operator== ( matrix< E > const & rhs ) const

inlineconstexprnoexcept

Compare two matrices potentially of different dimensions.

Parameters

rhs	The right-hand-side matrix.

Return values

true	When the two matrices compare equal.

operator~()

template<int D>

constexpr matrix hi::v1::geo::matrix< D >::operator~ ( ) const

inlineconstexpr

Invert matrix.

uniform()

template<int D>

constexpr matrix< D > v1::geo::matrix::uniform ( aarectangle src_rectangle, aarectangle dst_rectangle, alignment alignment )

staticconstexprnoexcept

Create a transformation matrix to translate and uniformly-scale a src_rectangle to a dst_rectangle.

The implementation is located in scale.hpp since the definition requires both scale and translate.

Parameters

src_rectangle	The rectangle to be transformed.
dst_rectangle	The rectangle after transformation.
alignment	How the src_rectangle should be aligned inside the dst_rectangle after scaling and moving.

Returns

A transformation matrix to move and scale the src_rectangle to the dst_rectangle.

Friends And Related Symbol Documentation

get [1/2]

template<int D>

template<int I>

constexpr f32x4 & get ( matrix< D > & rhs )

friend

Get a column.

Template Parameters

I	The index of the column.

Returns

A reference to the selected column as a f32x4.

get [2/2]

template<int D>

template<int I>

constexpr f32x4 const & get ( matrix< D > const & rhs )

friend

Get a column.

Template Parameters

I	The index of the column.

Returns

A const reference to the selected column as a f32x4.

reflect

template<int D>

template<char DstX, char DstY, char DstZ, char DstW = 'w'>
requires (D == 3)

constexpr matrix reflect ( matrix< D > const & rhs )

friend

Reflect axis of a matrix.

The default axis of HikoGUI's geometry system are:

       +y
       |   -z (away from camera)
       |  /
       | /
       |/
-x ----+---- +x
      /|
     / |
    /  |
  +z   |
       -y

In Vulkan the Y axis is downward; so to translate a matrix from HikoGUI to Vulkan you can use:

auto vulkan_M = reflect<'x', 'Y', 'z'>(hikogui_M);

The original axis are defined as the lower-case characters 'x', 'y', 'z' and 'w'; or for the negated axis as the upper-case characters 'X', 'Y', 'Z' and 'W'.

Template Parameters

DstX	Which of the original axis to use for the new matrix's x-axis.
DstY	Which of the original axis to use for the new matrix's y-axis.
DstZ	Which of the original axis to use for the new matrix's z-axis.
DstW	Which of the original axis to use for the new matrix's w-axis.

Parameters

The	matrix to reflect

Returns

The reflected matrix.

transpose

template<int D>

constexpr matrix transpose ( matrix< D > const & rhs )

friend

Matrix transpose.

---

The documentation for this class was generated from the following files:

• hikogui/src/hikogui/geometry/matrix.hpp
• hikogui/src/hikogui/geometry/scale.hpp