Geometry

Files
file	aarectangle.hpp
file	alignment.hpp
	types and utilities for alignment.
file	corner_radii.hpp
	Defined the corner_radii type.
file	extent2.hpp
	Defined the geo::extent, extent2 and extent3 types.
file	extent3.hpp
	Defined the geo::extent, extent2 and extent3 types.
file	line_end_cap.hpp
	Defined line_end_cap.
file	line_join_style.hpp
	Defines line_join_style.
file	line_segment.hpp
	Defines line_segment.
file	lookat.hpp
	Defines lookat.

Data Structures
class	hi::v1::aarectangle
	Class which represents an axis-aligned rectangle. More...
class	hi::v1::alignment
	Horizontal/Vertical alignment combination. More...
class	hi::v1::corner_radii
	The 4 radii of the corners of a quad or rectangle. More...
class	hi::v1::extent2
	A high-level geometric extent. More...
class	hi::v1::extent3
	A high-level geometric extent. More...
class	hi::v1::line_segment
	Line segment. More...
class	hi::v1::lookat
	Perspective transform. More...
class	hi::v1::margins
	The left, bottom, right and top margins. More...
class	hi::v1::perspective
	Perspective transform. More...
struct	hi::v1::box_constraints
	2D constraints. More...

Enumerations
enum class	hi::v1::vertical_alignment : uint8_t { hi::v1::vertical_alignment::none = 0 , hi::v1::vertical_alignment::top = 1 , hi::v1::vertical_alignment::middle = 2 , hi::v1::vertical_alignment::bottom = 3 }
	Vertical alignment. More...
enum class	hi::v1::horizontal_alignment : uint8_t {   hi::v1::horizontal_alignment::none = 0 , hi::v1::horizontal_alignment::flush = 1 , hi::v1::horizontal_alignment::left = 2 , hi::v1::horizontal_alignment::center = 3 ,   hi::v1::horizontal_alignment::justified = 4 , hi::v1::horizontal_alignment::right = 5 }
	Horizontal alignment. More...
enum class	hi::v1::axis : unsigned char {   none = 0 , x = 1 , y = 2 , z = 4 ,   both = x | y , all = x | y | z , horizontal = x , vertical = y }
	An enumeration of the 3 axis for 3D geometry. More...
enum class	hi::v1::line_end_cap { hi::v1::line_end_cap::flat , hi::v1::line_end_cap::round }
	The way two lines should be joined. More...
enum class	hi::v1::line_join_style { hi::v1::line_join_style::none , hi::v1::line_join_style::bevel , hi::v1::line_join_style::miter , hi::v1::line_join_style::round }
	The way two lines should be joined. More...

Functions
constexpr std::optional< float >	hi::v1::make_guideline (vertical_alignment alignment, float bottom, float top, float guideline_width)
	Create a guideline between two points.
constexpr std::optional< float >	hi::v1::make_guideline (horizontal_alignment alignment, float left, float right, float guideline_width=0.0f)
	Create a guideline between two points.
constexpr axis	hi::v1::operator& (axis const &lhs, axis const &rhs) noexcept
	AND the axis.
constexpr axis	hi::v1::operator| (axis const &lhs, axis const &rhs) noexcept
	OR the axis.
constexpr bool	hi::v1::to_bool (axis const &rhs) noexcept
	Check if any of the axis are set.
	hi_export_module (hikogui.geometry :margins)
	geometry/margins.hpp
std::pair< std::size_t, std::size_t >	v1::parse_spreadsheet_address (std::string_view address, std::size_t start_column_nr=0, std::size_t start_row_nr=0)
	Parse a spreadsheet address.
std::tuple< std::size_t, std::size_t, std::size_t, std::size_t >	v1::parse_spreadsheet_range (std::string_view address, std::size_t start_column_nr=0, std::size_t start_row_nr=0)
	Parse a spreadsheet range.

Detailed Description

Low level geometry types

numeric_array<T,N>

The simd is an array of numbers, with many mathematical operations on the array of numbers. The simd is designed to be useable in constexpr and easily to vectorize by the optimizer.

f32x4

The f32x4 is an simd<float,4>.

Many of the operations on a f32x4 are hand optimized using the intel intrinsics on SSE registers.

High level geometry type

geo::vector<D>

A vector is a direction and distance.

When transforming a vector, only scale, rotation and shear have effect.

Both vector2 and vector3 are implemented as a f32x4 homogeneous 4D coordinate with w = 0.0.

geo::point<D>

A point is a location in space.

A point can be transformed in the same way as a vector and also be translated.

Both point2 and point3 are implemented as a f32x4 homogeneous 4D coordinate with w = 1.0.

geo::extent<D>

An extent is a width, height and depth.

An extent can be transformed like a vector.

Both extent2 and extent3 are implemented as a f32x4 homogeneous 4D coordinate with w = 0.0.

corner_shapes

Corner shapes are 4 floating point numbers, one for the corner in the left-bottom, right-bottom, left-top and right-top corner. Each number has the following meaning:

• 0.0 Sharp corner,
• >0.0 Radius of a rounded corner,
• <0.0 Radius of a cut corner.

color

A 4D red, green, blue and alpha value. A color can be transformed like a vector3. In this case, the alpha value is ignored and copied into the result.

rectangle

A rectangle is a closed plane in three dimensions.

A rectangle can be transformed like a point3.

It should be implemented as a point3 in the left-bottom corner and two vector3s to the upper and right corners. However, it is currently implemented as 4 points, one for each corner.

aarectangle

The aarectangle class is a 2D axis-aligned rectangle.

When transforming an axis aligned rectangle in 3D or with rotation, the result will be a normal rectangle. A rectangle can be converted back to an aarectangle, as a bounding rectangle around the transformed rectangle.

An aarectangle is implemented as a f32x4 where:

• x: left-bottom point x
• y: left-bottom point y
• z: right-top point x
• w: right-top point y

Transformation types

geo::translate<D>

geo::scale<D>

geo::rotate<D>

geo::matrix<D>

The mat class is a 4x4 homogeneous transformation matrix in column-major order. Internally, this a vec for each column.

Vector * matrix multiplications are performed as if the vector is a column.

geo::transform

Coordinates

All origins (0, 0, 0) are at the bottom-left-far corner. With the x-axis pointing right, y-axis pointing up, z-axis pointing toward the camera. This is the same coordinate system as OpenGL; a right-handed coordinate system.

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

This is true for:

• Window
• Images
• Paths
• Font-glyphs

Window and Widget-surface coordinates

The coordinates in a window and widgets are in pixels.

With the center of the left bottom pixel having the coordinates (0.5, 0.5).

The alignment of borders to pixels is the responsibility of the widget that draws itself. The widget has access to the draw_context::draw_box_including_border() function to position the border's edge to the edge of the given rectangle, if the rectangle is rounded to integer coordinates; the rectangle, border and pixel will share the same edge.

Window depth

Z-coordinate for a window is between 0.0 (far) to 100.0 (near).

For better precision we use a reverse-z method, to combine 1/z together with float with linear precision.

• The window-widget is set to depth 0.0.
• Each nested widget, which needs to draw itself, is 1.0 nearer.
• Widgets which extends across other widgets, such as a combo-box-widget will be 25.0 nearer.

Image coordinates

The coordinates in an image are in pixels. With the center of the left bottom pixel having the coordinates (0.5, 0.5).

Path coordinates

The coordinates in a path are free from scale and origin, when rendering a path to an image, the path should be first be transformed to image coordinates.

Glyph/Font coordinates

Glyph coordinates are in the number of Em units. X-axis pointing right, Y-axis pointing up. The origin (0,0) is on the crossing of the base line and left side bearing. Vertices of front faces are specified in counter clockwise order.

Corners

Corners are enumerated as follows:

• 0: far bottom left
• 1: far bottom right
• 2: far top left
• 3: far top right
• 4: near bottom left
• 5: near bottom right
• 6: near top left
• 7: near top right

When corners are packed in a 4D vector:

• x: bottom-left
• y: bottom-right
• z: top-left
• w: top-right

Edges

When edges are packed in a 4D vector:

• x: bottom-edge
• y: left-edge
• z: top-edge
• w: right-edge

Triangles

A front facing triangle has the vertex ordered in counter-clockwise direction.

Quads

Quads are defined as two front facing triangles.

The vertex index order is: 0, 1, 2, 2, 1, 3.

As illustrated below:

2 <--- 3
| \    ^
|  \ B |
| A \  |
v    \ |
0 ---> 1

Enumeration Type Documentation

axis

enum class hi::v1::axis : unsigned char

strong

An enumeration of the 3 axis for 3D geometry.

It can be used as flags/mask for a set of axis.

horizontal_alignment

enum class hi::v1::horizontal_alignment : uint8_t

strong

Horizontal alignment.

Enumerator
none	No alignment.
flush	Align the text naturally based on the writing direction of each paragraph. This will act as flush_left if the paragraph is in left-to-right direction, and as flush_right if the paragraph is in right-to-left direction.
left	Align the text to the left side. The text will be flush-left independent of the writing direction.
center	Align the text in the center. Since the text is centered, the writing direction is unimportant.
justified	Stretch the text to be flush to both sides. Since the text is flush on both sides, the writing direction is unimportant.
right	Align the text to the right side. The text will be flush-left independent of the writing direction.

line_end_cap

enum class hi::v1::line_end_cap

strong

The way two lines should be joined.

Enumerator
flat	The end cap of the line is flat.
round	The end cap of the line is round.

line_join_style

enum class hi::v1::line_join_style

strong

The way two lines should be joined.

Enumerator
none	Both lines have flat caps and are not joined.
bevel	The outer vertices of both lines are connected and filled in to make a blunt corner.
miter	The outer edge of both lines are extended until they meet to form a sharp corner.
round	Both lines have round caps and with a shared mid-point making a round corner.

vertical_alignment

enum class hi::v1::vertical_alignment : uint8_t

strong

Vertical alignment.

Enumerator
none	No alignment.
top	Align to the top.
middle	Align to the vertical-middle.
bottom	Align to the bottom.

Function Documentation

hi_export_module()

hi_export_module

(

hikogui.geometry :margins

)

geometry/margins.hpp

make_guideline() [1/2]

constexpr std::optional< float > hi::v1::make_guideline ( horizontal_alignment alignment, float left, float right, float guideline_width = 0.0f )

constexpr

Create a guideline between two points.

The horizontal guideline is may used to create alignment for text or numerics. The guideline_width should probably be set to zero.

• aligned-left: The left of the guideline will be flush with the left-padding.
• aligned-right: The right of the guideline will be flush with the right-padding.
• aligned-center: The center of the guideline will be in the center between left and right; clamped by the padding.
• aligned-none: nullopt.

Note

The padding is a soft-constraint and may be ignored if needed.

Parameters

alignment	The horizontal alignment where to put the guideline.
left	The x-coordinate of the left.
right	The x-coordinate of the right.
guideline_width	The thickness of the guideline

Returns

The x-coordinate of the left of the guideline.

Return values

std::nullopt

No alignment, or guideline does not fit in the space.

make_guideline() [2/2]

constexpr std::optional< float > hi::v1::make_guideline ( vertical_alignment alignment, float bottom, float top, float guideline_width )

constexpr

Create a guideline between two points.

The vertical guideline is mostly used to create a baseline; in this case the guideline_width is set to the cap-height of a font.

• aligned-top: The top of the guideline will be flush with the top-padding.
• aligned-bottom: The bottom of the guideline will be flush with the bottom-padding.
• aligned-middle: The middle of the guideline will be in the middle between bottom and top; clamped by the padding.
• aligned-none: nullopt.

Parameters

alignment	The vertical alignment how to place the guideline.
bottom	The y-coordinate of the bottom.
top	The y-coordinate of the top.
guideline_width	The thickness of the guideline

Returns

The y-coordinate of the bottom of the guideline.

Return values

nullopt

No alignment, or guideline does not fit in the space.

operator&()

constexpr axis hi::v1::operator& ( axis const & lhs, axis const & rhs )

constexprnoexcept

AND the axis.

operator|()

constexpr axis hi::v1::operator| ( axis const & lhs, axis const & rhs )

constexprnoexcept

OR the axis.

parse_spreadsheet_address()

std::pair< std::size_t, std::size_t > v1::parse_spreadsheet_address ( std::string_view address, std::size_t start_column_nr = 0, std::size_t start_row_nr = 0 )

inline

Parse a spreadsheet address.

Parameters

address	The address to parse.
start_column_nr	A relative column in the address is added to the start-column.
start_row_nr	A relative row in the address is added to the start-row.

Returns

The zero-based column and row index.

parse_spreadsheet_range()

std::tuple< std::size_t, std::size_t, std::size_t, std::size_t > v1::parse_spreadsheet_range ( std::string_view address, std::size_t start_column_nr = 0, std::size_t start_row_nr = 0 )

inline

Parse a spreadsheet range.

Parameters

address	A spreadsheet address in the form "A1" or "A1:B3"
start_column_nr	The start column for relative column addressing.
start_row_nr	The start row for relative row addressing.

Returns

first_column, first_row, last_column, last_row. last_column and last_row point one beyond the last.

to_bool()

constexpr bool hi::v1::to_bool ( axis const & rhs )

constexprnoexcept

Check if any of the axis are set.