Abstract orthographic/perspective camera. More...

#include <camera.h>

Collaboration diagram for nngn::Camera:

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Public Types
enum	Flag : uint8_t { UPDATED = 1u << 1 , SCREEN_UPDATED = 1u << 2 , DASH = 1u << 3 , PERSPECTIVE = 1u << 4 , N_FLAGS = 1u << 5 , UPDATED = 1u << 1 , SCREEN_UPDATED = 1u << 2 , DASH = 1u << 3 , PERSPECTIVE = 1u << 4 , IGNORE_LIMITS = 1u << 4 }

enum	Flag : u8 { UPDATED = 1u << 1 , SCREEN_UPDATED = 1u << 2 , DASH = 1u << 3 , PERSPECTIVE = 1u << 4 , N_FLAGS = 1u << 5 , UPDATED = 1u << 1 , SCREEN_UPDATED = 1u << 2 , DASH = 1u << 3 , PERSPECTIVE = 1u << 4 , IGNORE_LIMITS = 1u << 4 }
	State flags and configuration. More...

Public Member Functions
bool	dash (void) const

bool	perspective (void) const

vec3	pos (void) const

vec3	eye (void) const

vec3	up (void) const

mat4	gen_proj (void) const

mat4	gen_screen_proj (void) const

mat4	gen_view (void) const

float	fov_z (void) const

vec3	to_clip (vec3 vp) const

vec4	to_view (vec3 vp) const

vec3	to_world (vec3 vp) const

void	set_perspective (bool b)

void	set_screen (const uvec2 &s)

void	set_pos (const vec3 &pos)

void	set_rot (const vec3 &rot)

void	set_zoom (float z)

void	set_fov_y (float f)

void	set_dash (bool b)

void	look_at (const vec3 &pos, const vec3 &eye, const vec3 &up)

bool	update (const Timing &t)

bool	dash (void) const

bool	perspective (void) const

void	set_dash (bool b)

void	set_perspective (bool b)

void	set_ignore_limits (bool b)

vec3	center (void) const
	p added to a unit vector in the view direction.

vec3	up (void) const
	The "up" vector for the view direction.

vec3	world_to_view (vec3 p) const
	Projects a point from world to view space.

vec3	view_to_clip (vec3 p) const
	Projects a point from view to clip space.

vec2	clip_to_screen (vec3 p)
	Projects a point from clip to screen space.

vec3	screen_to_clip (vec2 p)
	Projects a point from screen to clip space.

vec3	clip_to_view (vec3 p) const
	Projects a point from clip to view space.

vec3	view_to_world (vec3 p) const
	Projects a point from view to world space.

float	z_for_fov (void) const
	Derives Z coordinate from the camera's screen size and field of view.

float	scale_for_fov (void) const
	Derives orthographic scaling factor from camera parameters.

void	set_pos (vec3 p)

void	set_rot (vec3 r)

void	set_zoom (float z)

void	set_fov_y (float f)

void	set_fov_z (float z)

void	set_screen (uvec2 s)

void	set_limits (vec3 bl, vec3 tr)

void	look_at (vec3 center, vec3 pos, vec3 up)

bool	update (const Timing &t)

Static Public Member Functions
static constexpr float	fov (float distance, float length)

static constexpr float	fov (float z, float w)
	Calculates field of view based on screen size and distance.

Public Attributes
vec3	p = {}
	Position.

vec3	v = {}
	Velocity.

vec3	a = {}
	Acceleration.

vec3	r = {}

vec3	rv = {}

vec3	ra = {}

float	zoom = 1
	Scaling factor.

float	zoom_v = {}
	Scaling factor velocity.

float	zoom_a = {}
	Scaling factor acceleration.

uvec2	screen = {}
	Screen size.

float	fov_y = FOVY
	Field of view in perspective mode.

mat4	proj = mat4{1}
	Projection matrix (orthographic/perspective).

mat4	screen_proj = mat4{1}
	Projection matrix for screen coordinates.

mat4	view = mat4{1}
	View matrix.

float	max_v = std::numeric_limits<float>::infinity()
	Maximum value for v.

float	max_rv = std::numeric_limits<float>::infinity()

float	max_zv = std::numeric_limits<float>::infinity()

float	damp = {}
	Damping factor when not accelerating.

Flags< Flag >	flags = {}

vec3	rot = {}
	Rotational Euler angles (ZYX).

vec3	rot_v = {}
	Rotational velocity.

vec3	rot_a = {}
	Rotational acceleration.

vec3	bl_limit = {-INFINITY, -INFINITY, -INFINITY}
	Bottom left point of the limit for p.

vec3	tr_limit = {+INFINITY, +INFINITY, +INFINITY}
	Top right point of the limit for p.

float	max_rot_v = INFINITY
	Maximum value for rot_v.

float	max_zoom_v = INFINITY
	Maximum value for zoom_v.

float	fov_z = {}
	Enable auto-adjustment of the field-of-view angle.

mat4	inv_proj = mat4{1}
	Inverse matrix of proj.

mat4	inv_view = mat4{1}
	Inverse matrix of view.

Static Public Attributes
static constexpr float	NEAR = 0.01f
	Perspective projection near plane.

static constexpr float	FAR = 2048.0f
	Perspective projection far plane.

static constexpr float	FOVY = Math::radians(60.0f)
	Perspective projection field of view along the Y axis (default).

static const float	TAN_FOVY

static const float	TAN_HALF_FOVY

Detailed Description

Abstract orthographic/perspective camera.

Two complementary projection modes are supported: orthographic and perspective. Some facilities are provided to make them as close to each other as possible.

Orthographic projection

In orthographic mode, objects ocupy the XY plane. The projection matrix is set up so that objects are displayed in their natural size, scaled by the zoom parameter. Their Z position is expected to be set such that they can be rendered in any order, using a depth buffer to sort overlaps.

The z value of the position is also used as a scaling factor. This preserves the size of objects on the XY plane when transitioning from ortographic to perspective mode, as long as the camera remains parallel to the Z axis. The scaling factor is the ratio of z_for_fov to the z position.

Perspective projection

In perspective mode, objects maintain their position in the XY plane but have a third dimension in the Z direction. A standing sprite thus has the same XY position but is rotated 90° at its base around the X axis. Although counter-intuitive, having the "up" vector parallel to the Z axis (as opposed to the Y axis, as is commonly done) allows sprites to occupy the same XY position in both projection modes.

This mode tries to be as close to the orthographic mode as possible, by adjusting the camera's projection matrix and Z position so that the position and relative scale of objects is maintained as long as the camera view vector is parallel to the Z axis. With the regular camera orientation facing the direction of the -Z axis, toggling between the two projection modes leaves objects in the XY plane (such as the map) unchanged.

Field of view

Calculations of dimensions, field-of-view, etc. are based on a 14"/35.5cm, 16:9 laptop monitor at a distance of 60cm from the camera/eye:

 x/y
-----  x = 31cm
\z| /  y = 17.4cm
 \|/   z = 60cm
 fov   fov = 2 * atan(31/60) ~= 60° = π/3

The initial size of the window is taken to be the full screen size and assigned a vertical field-of-view angle of 60° (π/3). This angle can be automatically adjusted when the window is resized (see set_fov_z): this ensures the image is not distorted — i.e. objects retain their size and proportion — in perspective mode.

Member Enumeration Documentation

◆ Flag [1/2]

enum nngn::Camera::Flag : uint8_t

Enumerator
UPDATED	Parameters of the camera have changed. This indicates the matrices need to be recalculated (via update).
SCREEN_UPDATED	The screen size has changed. Not used internally, but can be used by external code mid-frame to determine whether values dependent on the screen size need to be updated.
DASH	Increases the speed of displacement/rotation/etc.
PERSPECTIVE	Chooses between orthographic/perspective mode.
N_FLAGS
UPDATED	Parameters of the camera have changed. This indicates the matrices need to be recalculated (via update).
SCREEN_UPDATED	The screen size has changed. Not used internally, but can be used by external code mid-frame to determine whether values dependent on the screen size need to be updated.
DASH	Increases the speed of displacement/rotation/etc.
PERSPECTIVE	Chooses between orthographic/perspective mode.
IGNORE_LIMITS	The camera limits do not restrict movement when set.

◆ Flag [2/2]

enum nngn::Camera::Flag : u8

State flags and configuration.

Enumerator
UPDATED	Parameters of the camera have changed. This indicates the matrices need to be recalculated (via update).
SCREEN_UPDATED	The screen size has changed. Not used internally, but can be used by external code mid-frame to determine whether values dependent on the screen size need to be updated.
DASH	Increases the speed of displacement/rotation/etc.
PERSPECTIVE	Chooses between orthographic/perspective mode.
N_FLAGS
UPDATED	Parameters of the camera have changed. This indicates the matrices need to be recalculated (via update).
SCREEN_UPDATED	The screen size has changed. Not used internally, but can be used by external code mid-frame to determine whether values dependent on the screen size need to be updated.
DASH	Increases the speed of displacement/rotation/etc.
PERSPECTIVE	Chooses between orthographic/perspective mode.
IGNORE_LIMITS	The camera limits do not restrict movement when set.

Member Function Documentation

◆ center()

vec3 nngn::Camera::center ( void ) const

p added to a unit vector in the view direction.

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◆ clip_to_screen()

vec2 nngn::Camera::clip_to_screen ( vec3 p )

inline

Projects a point from clip to screen space.

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◆ clip_to_view()

vec3 nngn::Camera::clip_to_view ( vec3 p ) const

inline

Projects a point from clip to view space.

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◆ dash() [1/2]

bool nngn::Camera::dash ( void ) const

inline

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◆ dash() [2/2]

bool nngn::Camera::dash ( void ) const

◆ eye()

vec3 nngn::Camera::eye ( void ) const

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◆ fov() [1/2]

constexpr float nngn::Camera::fov	(	float	distance,
		float	length
	)

inlinestaticconstexpr

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◆ fov() [2/2]

static constexpr float nngn::Camera::fov	(	float	z,
		float	w
	)

staticconstexpr

Calculates field of view based on screen size and distance.

  w
-----  a = fov / 2, op = w / 2, adj = z
\z| /  tan(a) = op / adj
 \|/   tan(fov/2) = w / 2 / z
 fov

Parameters

z	Distance from the camera to the projection plane.
w	Width of the projection plane.

Returns: Angle such that the intersection of the field of view with a line/plane at distance z has width w.

◆ fov_z()

float nngn::Camera::fov_z ( void ) const

◆ gen_proj()

mat4 nngn::Camera::gen_proj ( void ) const

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◆ gen_screen_proj()

mat4 nngn::Camera::gen_screen_proj ( void ) const

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◆ gen_view()

mat4 nngn::Camera::gen_view ( void ) const

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◆ look_at() [1/2]

void nngn::Camera::look_at	(	const vec3 &	pos,
		const vec3 &	eye,
		const vec3 &	up
	)

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◆ look_at() [2/2]

void nngn::Camera::look_at	(	vec3	center,
		vec3	pos,
		vec3	up
	)

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◆ perspective() [1/2]

bool nngn::Camera::perspective ( void ) const

inline

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◆ perspective() [2/2]

bool nngn::Camera::perspective ( void ) const

◆ pos()

vec3 nngn::Camera::pos ( void ) const

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◆ scale_for_fov()

float nngn::Camera::scale_for_fov ( void ) const

inline

Derives orthographic scaling factor from camera parameters.

When an orthographic projection is used (i.e. when the camera's Z position does not alter the apparent size of objects), this factor can be used to preserve the size of objects directly on the XY plane as if a perspective projection were used (with the same constraints as z_for_fov).

   y'
---------  y = screen.y
\ z'|   /  z = z_for_fov(), z' = p.z
y\-----/   y' / z' = y / z
  \z| /    s = y / y'
   \|/     s = z / z'
   fov

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◆ screen_to_clip()

vec3 nngn::Camera::screen_to_clip ( vec2 p )

inline

Projects a point from screen to clip space.

◆ set_dash() [1/2]

void nngn::Camera::set_dash ( bool b )

inline

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◆ set_dash() [2/2]

void nngn::Camera::set_dash ( bool b )

◆ set_fov_y() [1/2]

void nngn::Camera::set_fov_y ( float f )

inline

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◆ set_fov_y() [2/2]

void nngn::Camera::set_fov_y ( float f )

◆ set_fov_z()

void nngn::Camera::set_fov_z ( float z )

inline

◆ set_ignore_limits()

void nngn::Camera::set_ignore_limits ( bool b )

inline

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◆ set_limits()

void nngn::Camera::set_limits	(	vec3	bl,
		vec3	tr
	)

inline

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◆ set_perspective() [1/2]

void nngn::Camera::set_perspective ( bool b )

inline

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◆ set_perspective() [2/2]

void nngn::Camera::set_perspective ( bool b )

◆ set_pos() [1/2]

void nngn::Camera::set_pos ( const vec3 & pos )

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◆ set_pos() [2/2]

void nngn::Camera::set_pos ( vec3 p )

inline

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◆ set_rot() [1/2]

void nngn::Camera::set_rot ( const vec3 & rot )

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◆ set_rot() [2/2]

void nngn::Camera::set_rot ( vec3 r )

inline

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◆ set_screen() [1/2]

void nngn::Camera::set_screen ( const uvec2 & s )

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◆ set_screen() [2/2]

void nngn::Camera::set_screen ( uvec2 s )

inline

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◆ set_zoom() [1/2]

void nngn::Camera::set_zoom ( float z )

inline

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◆ set_zoom() [2/2]

void nngn::Camera::set_zoom ( float z )

◆ to_clip()

vec3 nngn::Camera::to_clip ( vec3 vp ) const

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◆ to_view()

vec4 nngn::Camera::to_view ( vec3 vp ) const

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◆ to_world()

vec3 nngn::Camera::to_world ( vec3 vp ) const

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◆ up() [1/2]

vec3 nngn::Camera::up ( void ) const

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◆ up() [2/2]

vec3 nngn::Camera::up ( void ) const

The "up" vector for the view direction.

◆ update() [1/2]

bool nngn::Camera::update ( const Timing & t )

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◆ update() [2/2]

bool nngn::Camera::update ( const Timing & t )

◆ view_to_clip()

vec3 nngn::Camera::view_to_clip ( vec3 p ) const

inline

Projects a point from view to clip space.

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◆ view_to_world()

vec3 nngn::Camera::view_to_world ( vec3 p ) const

inline

Projects a point from view to world space.

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◆ world_to_view()

vec3 nngn::Camera::world_to_view ( vec3 p ) const

inline

Projects a point from world to view space.

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◆ z_for_fov()

float nngn::Camera::z_for_fov ( void ) const

inline

Derives Z coordinate from the camera's screen size and field of view.

When changing the camera's projection matrix from perspective to orthographic, using this Z coordinate will preserve the size of objects directly on the XY plane (provided the camera's view vector is perpendicular to it, i.e. parallel to the Z axis).

  y
-----   a = fov / 2, op = y / 2, adj = z
\z| /   tan(a) = op / adj
 \|/    tan(fov / 2) = y / 2 / z
 fov    z = y / 2 / tan(fov / 2)

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Member Data Documentation

◆ a

vec3 nngn::Camera::a = {}

Acceleration.

◆ bl_limit

vec3 nngn::Camera::bl_limit = {-INFINITY, -INFINITY, -INFINITY}

Bottom left point of the limit for p.

◆ damp

float nngn::Camera::damp = {}

Damping factor when not accelerating.

◆ FAR

static constexpr float nngn::Camera::FAR = 2048.0f

staticconstexpr

Perspective projection far plane.

◆ flags

Flags< Flag > nngn::Camera::flags = {}

◆ fov_y

float nngn::Camera::fov_y = FOVY

Field of view in perspective mode.

◆ fov_z

float nngn::Camera::fov_z ( void ) = {}

Enable auto-adjustment of the field-of-view angle.

In perspective mode, this makes the image retain its size when the window is resized. The value should be z_for_fov. A value of zero disables auto-adjustment.

◆ FOVY

static constexpr float nngn::Camera::FOVY = Math::radians(60.0f)

staticconstexpr

Perspective projection field of view along the Y axis (default).

◆ inv_proj

mat4 nngn::Camera::inv_proj = mat4{1}

Inverse matrix of proj.

◆ inv_view

mat4 nngn::Camera::inv_view = mat4{1}

Inverse matrix of view.

◆ max_rot_v

float nngn::Camera::max_rot_v = INFINITY

Maximum value for rot_v.

◆ max_rv

float nngn::Camera::max_rv = std::numeric_limits<float>::infinity()

◆ max_v

float nngn::Camera::max_v = std::numeric_limits<float>::infinity()

Maximum value for v.

◆ max_zoom_v

float nngn::Camera::max_zoom_v = INFINITY

Maximum value for zoom_v.

◆ max_zv

float nngn::Camera::max_zv = std::numeric_limits<float>::infinity()

◆ NEAR

static constexpr float nngn::Camera::NEAR = 0.01f

staticconstexpr

Perspective projection near plane.

◆ p

vec3 nngn::Camera::p = {}

Position.

◆ proj

mat4 nngn::Camera::proj = mat4{1}

Projection matrix (orthographic/perspective).

◆ r

vec3 nngn::Camera::r = {}

◆ ra

vec3 nngn::Camera::ra = {}

◆ rot

vec3 nngn::Camera::rot = {}

Rotational Euler angles (ZYX).

◆ rot_a

vec3 nngn::Camera::rot_a = {}

Rotational acceleration.

◆ rot_v

vec3 nngn::Camera::rot_v = {}

Rotational velocity.

◆ rv

vec3 nngn::Camera::rv = {}

◆ screen

uvec2 nngn::Camera::screen = {}

Screen size.

◆ screen_proj

mat4 nngn::Camera::screen_proj = mat4{1}

Projection matrix for screen coordinates.

◆ TAN_FOVY

const float nngn::Camera::TAN_FOVY

static

◆ TAN_HALF_FOVY

const float nngn::Camera::TAN_HALF_FOVY

static

◆ tr_limit

vec3 nngn::Camera::tr_limit = {+INFINITY, +INFINITY, +INFINITY}

Top right point of the limit for p.

◆ v

vec3 nngn::Camera::v = {}

Velocity.

◆ view

mat4 nngn::Camera::view = mat4{1}

View matrix.

◆ zoom

float nngn::Camera::zoom = 1

Scaling factor.

◆ zoom_a

float nngn::Camera::zoom_a = {}

Scaling factor acceleration.

◆ zoom_v

float nngn::Camera::zoom_v = {}

Scaling factor velocity.

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

master/src/math/camera.h
src/math/camera.h
master/src/math/camera.cpp
src/math/camera.cpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Orthographic projection

Perspective projection

Field of view

Member Enumeration Documentation

◆ Flag [1/2]

◆ Flag [2/2]

Member Function Documentation

◆ center()

◆ clip_to_screen()

◆ clip_to_view()

◆ dash() [1/2]

◆ dash() [2/2]

◆ eye()

◆ fov() [1/2]

◆ fov() [2/2]

◆ fov_z()

◆ gen_proj()

◆ gen_screen_proj()

◆ gen_view()

◆ look_at() [1/2]

◆ look_at() [2/2]

◆ perspective() [1/2]

◆ perspective() [2/2]

◆ pos()

◆ scale_for_fov()

◆ screen_to_clip()

◆ set_dash() [1/2]

◆ set_dash() [2/2]

◆ set_fov_y() [1/2]

◆ set_fov_y() [2/2]

◆ set_fov_z()

◆ set_ignore_limits()

◆ set_limits()

◆ set_perspective() [1/2]

◆ set_perspective() [2/2]

◆ set_pos() [1/2]

◆ set_pos() [2/2]

◆ set_rot() [1/2]

◆ set_rot() [2/2]

◆ set_screen() [1/2]

◆ set_screen() [2/2]

◆ set_zoom() [1/2]

◆ set_zoom() [2/2]

◆ to_clip()

◆ to_view()

◆ to_world()

◆ up() [1/2]

◆ up() [2/2]

◆ update() [1/2]

◆ update() [2/2]

◆ view_to_clip()

◆ view_to_world()

◆ world_to_view()

◆ z_for_fov()

Member Data Documentation

◆ a

◆ bl_limit

◆ damp

◆ FAR

◆ flags

◆ fov_y

◆ fov_z

◆ FOVY

◆ inv_proj

◆ inv_view

◆ max_rot_v

◆ max_rv

◆ max_v

◆ max_zoom_v

◆ max_zv

◆ NEAR

◆ p

◆ proj

◆ r