Projection
A 4×4 matrix for 3D projective transformations.
Description
A 4×4 matrix used for 3D projective transformations. It can represent transformations such as translation, rotation, scaling, shearing, and perspective division. It consists of four Vector4 columns.
For purely linear transformations (translation, rotation, and scale), it is recommended to use Transform3D, as it is more performant and requires less memory.
Used internally as Camera3D's projection matrix.
There are notable differences when using this API with C#. See the C# differences documentation for more information.
Properties
| Vector4 | w | Vector4(0, 0, 0, 1) |
|---|---|---|
| Vector4 | x | Vector4(1, 0, 0, 0) |
| Vector4 | y | Vector4(0, 1, 0, 0) |
| Vector4 | z | Vector4(0, 0, 1, 0) |
Constructors
| Projection | Projection\ (\ ) |
|---|---|
| Projection | Projection\ (\ from: Projection\ ) |
| Projection | Projection\ (\ from: Transform3D\ ) |
| Projection | Projection\ (\ x_axis: Vector4, y_axis: Vector4, z_axis: Vector4, w_axis: Vector4\ ) |
Methods
| Projection | create_depth_correction\ (\ flip_y: bool\ ) static |
|---|---|
| Projection | create_fit_aabb\ (\ aabb: AABB\ ) static |
| Projection | create_for_hmd\ (\ eye: int, aspect: float, intraocular_dist: float, display_width: float, display_to_lens: float, oversample: float, z_near: float, z_far: float\ ) static |
| Projection | create_frustum\ (\ left: float, right: float, bottom: float, top: float, z_near: float, z_far: float\ ) static |
| Projection | create_frustum_aspect\ (\ size: float, aspect: float, offset: Vector2, z_near: float, z_far: float, flip_fov: bool = false\ ) static |
| Projection | create_light_atlas_rect\ (\ rect: Rect2\ ) static |
| Projection | create_orthogonal\ (\ left: float, right: float, bottom: float, top: float, z_near: float, z_far: float\ ) static |
| Projection | create_orthogonal_aspect\ (\ size: float, aspect: float, z_near: float, z_far: float, flip_fov: bool = false\ ) static |
| Projection | create_perspective\ (\ fovy: float, aspect: float, z_near: float, z_far: float, flip_fov: bool = false\ ) static |
| Projection | create_perspective_hmd\ (\ fovy: float, aspect: float, z_near: float, z_far: float, flip_fov: bool, eye: int, intraocular_dist: float, convergence_dist: float\ ) static |
| float | determinant\ (\ ) const |
| Projection | flipped_y\ (\ ) const |
| float | get_aspect\ (\ ) const |
| Vector2 | get_far_plane_half_extents\ (\ ) const |
| float | get_fov\ (\ ) const |
| float | get_fovy\ (\ fovx: float, aspect: float\ ) static |
| float | get_lod_multiplier\ (\ ) const |
| int | get_pixels_per_meter\ (\ for_pixel_width: int\ ) const |
| Plane | get_projection_plane\ (\ plane: int\ ) const |
| Vector2 | get_viewport_half_extents\ (\ ) const |
| float | get_z_far\ (\ ) const |
| float | get_z_near\ (\ ) const |
| Projection | inverse\ (\ ) const |
| bool | is_orthogonal\ (\ ) const |
| Projection | jitter_offseted\ (\ offset: Vector2\ ) const |
| Projection | perspective_znear_adjusted\ (\ new_znear: float\ ) const |
Operators
| bool | operator !=\ (\ right: Projection\ ) |
|---|---|
| Projection | operator *\ (\ right: Projection\ ) |
| Vector4 | operator *\ (\ right: Vector4\ ) |
| bool | operator ==\ (\ right: Projection\ ) |
| Vector4 | operator []\ (\ index: int\ ) |
Enumerations
enum Planes: 🔗
Planes PLANE_NEAR = 0
The index value of the projection's near clipping plane.
Planes PLANE_FAR = 1
The index value of the projection's far clipping plane.
Planes PLANE_LEFT = 2
The index value of the projection's left clipping plane.
Planes PLANE_TOP = 3
The index value of the projection's top clipping plane.
Planes PLANE_RIGHT = 4
The index value of the projection's right clipping plane.
Planes PLANE_BOTTOM = 5
The index value of the projection bottom clipping plane.
Constants
IDENTITY = Projection(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1) 🔗
A Projection with no transformation defined. When applied to other data structures, no transformation is performed.
ZERO = Projection(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) 🔗
A Projection with all values initialized to 0. When applied to other data structures, they will be zeroed.
Property Descriptions
Vector4 w = Vector4(0, 0, 0, 1) 🔗
The projection matrix's W vector (column 3). Equivalent to array index 3.
Vector4 x = Vector4(1, 0, 0, 0) 🔗
The projection matrix's X vector (column 0). Equivalent to array index 0.
Vector4 y = Vector4(0, 1, 0, 0) 🔗
The projection matrix's Y vector (column 1). Equivalent to array index 1.
Vector4 z = Vector4(0, 0, 1, 0) 🔗
The projection matrix's Z vector (column 2). Equivalent to array index 2.
Constructor Descriptions
Projection Projection\ (\ ) 🔗
Constructs a default-initialized Projection identical to IDENTITY.
\ Note: In C#, this constructs a Projection identical to ZERO.
Projection Projection\ (\ from: Projection\ )
Constructs a Projection as a copy of the given Projection.
Projection Projection\ (\ from: Transform3D\ )
Constructs a Projection as a copy of the given Transform3D.
Projection Projection\ (\ x_axis: Vector4, y_axis: Vector4, z_axis: Vector4, w_axis: Vector4\ )
Constructs a Projection from four Vector4 values (matrix columns).
Method Descriptions
Projection create_depth_correction\ (\ flip_y: bool\ ) static 🔗
Creates a new Projection that projects positions from a depth range of -1 to 1 to one that ranges from 0 to 1, and flips the projected positions vertically, according to flip_y.
Projection create_fit_aabb\ (\ aabb: AABB\ ) static 🔗
Creates a new Projection that scales a given projection to fit around a given AABB in projection space.
Projection create_for_hmd\ (\ eye: int, aspect: float, intraocular_dist: float, display_width: float, display_to_lens: float, oversample: float, z_near: float, z_far: float\ ) static 🔗
Creates a new Projection for projecting positions onto a head-mounted display with the given X:Y aspect ratio, distance between eyes, display width, distance to lens, oversampling factor, and depth clipping planes.
\ eye creates the projection for the left eye when set to 1, or the right eye when set to 2.
Projection create_frustum\ (\ left: float, right: float, bottom: float, top: float, z_near: float, z_far: float\ ) static 🔗
Creates a new Projection that projects positions in a frustum with the given clipping planes.
Projection create_frustum_aspect\ (\ size: float, aspect: float, offset: Vector2, z_near: float, z_far: float, flip_fov: bool = false\ ) static 🔗
Creates a new Projection that projects positions in a frustum with the given size, X:Y aspect ratio, offset, and clipping planes.
\ flip_fov determines whether the projection's field of view is flipped over its diagonal.
Projection create_light_atlas_rect\ (\ rect: Rect2\ ) static 🔗
Creates a new Projection that projects positions into the given Rect2.
Projection create_orthogonal\ (\ left: float, right: float, bottom: float, top: float, z_near: float, z_far: float\ ) static 🔗
Creates a new Projection that projects positions using an orthogonal projection with the given clipping planes.
Projection create_orthogonal_aspect\ (\ size: float, aspect: float, z_near: float, z_far: float, flip_fov: bool = false\ ) static 🔗
Creates a new Projection that projects positions using an orthogonal projection with the given size, X:Y aspect ratio, and clipping planes.
\ flip_fov determines whether the projection's field of view is flipped over its diagonal.
Projection create_perspective\ (\ fovy: float, aspect: float, z_near: float, z_far: float, flip_fov: bool = false\ ) static 🔗
Creates a new Projection that projects positions using a perspective projection with the given Y-axis field of view (in degrees), X:Y aspect ratio, and clipping planes.
\ flip_fov determines whether the projection's field of view is flipped over its diagonal.
Projection create_perspective_hmd\ (\ fovy: float, aspect: float, z_near: float, z_far: float, flip_fov: bool, eye: int, intraocular_dist: float, convergence_dist: float\ ) static 🔗
Creates a new Projection that projects positions using a perspective projection with the given Y-axis field of view (in degrees), X:Y aspect ratio, and clipping distances. The projection is adjusted for a head-mounted display with the given distance between eyes and distance to a point that can be focused on.
\ eye creates the projection for the left eye when set to 1, or the right eye when set to 2.
\ flip_fov determines whether the projection's field of view is flipped over its diagonal.
float determinant\ (\ ) const 🔗
Returns a scalar value that is the signed factor by which areas are scaled by this matrix. If the sign is negative, the matrix flips the orientation of the area.
The determinant can be used to calculate the invertibility of a matrix or solve linear systems of equations involving the matrix, among other applications.
Projection flipped_y\ (\ ) const 🔗
Returns a copy of this Projection with the signs of the values of the Y column flipped.
float get_aspect\ (\ ) const 🔗
Returns the X:Y aspect ratio of this Projection's viewport.
Vector2 get_far_plane_half_extents\ (\ ) const 🔗
Returns the dimensions of the far clipping plane of the projection, divided by two.
Returns the horizontal field of view of the projection (in degrees).
float get_fovy\ (\ fovx: float, aspect: float\ ) static 🔗
Returns the vertical field of view of the projection (in degrees) associated with the given horizontal field of view (in degrees) and aspect ratio.
\ Note: Unlike most methods of Projection, aspect is expected to be 1 divided by the X:Y aspect ratio.
float get_lod_multiplier\ (\ ) const 🔗
Returns the factor by which the visible level of detail is scaled by this Projection.
int get_pixels_per_meter\ (\ for_pixel_width: int\ ) const 🔗
Returns for_pixel_width divided by the viewport's width measured in meters on the near plane, after this Projection is applied.
Plane get_projection_plane\ (\ plane: int\ ) const 🔗
Returns the clipping plane of this Projection whose index is given by plane.
\ plane should be equal to one of PLANE_NEAR, PLANE_FAR, PLANE_LEFT, PLANE_TOP, PLANE_RIGHT, or PLANE_BOTTOM.
Vector2 get_viewport_half_extents\ (\ ) const 🔗
Returns the dimensions of the viewport plane that this Projection projects positions onto, divided by two.
Returns the distance for this Projection beyond which positions are clipped.
float get_z_near\ (\ ) const 🔗
Returns the distance for this Projection before which positions are clipped.
Projection inverse\ (\ ) const 🔗
Returns a Projection that performs the inverse of this Projection's projective transformation.
bool is_orthogonal\ (\ ) const 🔗
Returns true if this Projection performs an orthogonal projection.
Projection jitter_offseted\ (\ offset: Vector2\ ) const 🔗
Returns a Projection with the X and Y values from the given Vector2 added to the first and second values of the final column respectively.
Projection perspective_znear_adjusted\ (\ new_znear: float\ ) const 🔗
Returns a Projection with the near clipping distance adjusted to be new_znear.
\ Note: The original Projection must be a perspective projection.
Operator Descriptions
bool operator !=\ (\ right: Projection\ ) 🔗
Returns true if the projections are not equal.
\ Note: Due to floating-point precision errors, this may return true, even if the projections are virtually equal. An is_equal_approx method may be added in a future version of Redot.
Projection **operator ***\ (\ right: Projection\ ) 🔗
Returns a Projection that applies the combined transformations of this Projection and right.
Vector4 **operator ***\ (\ right: Vector4\ ) 🔗
Projects (multiplies) the given Vector4 by this Projection matrix.
bool operator ==\ (\ right: Projection\ ) 🔗
Returns true if the projections are equal.
\ Note: Due to floating-point precision errors, this may return false, even if the projections are virtually equal. An is_equal_approx method may be added in a future version of Redot.
Vector4 operator []\ (\ index: int\ ) 🔗
Returns the column of the Projection with the given index.
Indices are in the following order: x, y, z, w.