75 3D: Cameras and projection

9.3

Racket

75 3D: Cameras and projection🔗ℹ

A camera’s local x axis is screen-right, local y is screen-up, and local negative z is forward. A default camera is at (vec3 0 0 8) and looks at origin3. The camera is reusable: viewport aspect is supplied when projecting or rendering, rather than stored in the camera.

struct
(struct perspective-projection3d (vertical-field-of-view)
#:transparent)
vertical-field-of-view : finite-real?

A perspective projection measured in radians.

struct
(struct orthographic-projection3d (vertical-size)
#:transparent)
vertical-size : positive-real?

An orthographic projection with the stated visible vertical size.

procedure
(perspective-camera3d [ #:position position
#:look-at target
#:up up
#:rotation rotation
#:near near
#:far far
#:vertical-field-of-view field-of-view])
→ camera3d?
  position : vec3? = (vec3 0 0 8)
  target : vec3? = origin3
  up : vec3? = y-axis3
  rotation : (or/c #f rotation3?) = #f
  near : positive-real? = 1/10
  far : positive-real? = 100
  field-of-view : finite-real? = (/ pi 4)

Creates a perspective camera. An explicit rotation wins over the look-at fields.

procedure
(orthographic-camera3d [ #:position position
#:look-at target
#:up up
#:rotation rotation
#:near near
#:far far
#:vertical-size size]) → camera3d?
  position : vec3? = (vec3 0 0 8)
  target : vec3? = origin3
  up : vec3? = y-axis3
  rotation : (or/c #f rotation3?) = #f
  near : positive-real? = 1/10
  far : positive-real? = 100
  size : positive-real? = 6

Creates a parallel orthographic camera.

procedure
(camera3d? value) → boolean?
value : any/c

Recognizes an immutable camera.

procedure
(camera3d-position camera) → vec3?
camera : camera3d?

Returns its world position.

procedure
(camera3d-rotation camera) → rotation3?
camera : camera3d?

Returns camera-local axes in world coordinates.

procedure
(camera3d-near camera) → positive-real?
camera : camera3d?

Returns nearest visible forward depth.

procedure
(camera3d-far camera) → positive-real?
camera : camera3d?

Returns farthest visible forward depth.

procedure
(camera3d-projection camera)
→ (or/c perspective-projection3d? orthographic-projection3d?)
camera : camera3d?

Returns its lens.

procedure
(camera3d-forward camera) → vec3?
camera : camera3d?

Returns world-space local negative z.

procedure
(camera3d-right camera) → vec3?
camera : camera3d?

Returns world-space local positive x.

procedure
(camera3d-up camera) → vec3?
camera : camera3d?

Returns world-space local positive y.

procedure
(camera3d-look-at camera target [#:up up]) → camera3d?
  camera : camera3d?
  target : vec3?
  up : vec3? = y-axis3

Returns an immutable reorientation toward target.

procedure
(camera3d-world->view camera point) → vec3?
camera : camera3d?
point : vec3?

Converts a world point to camera coordinates; visible forward points have negative z.

procedure
(camera3d-view-depth camera point) → finite-real?
camera : camera3d?
point : vec3?

Returns positive depth along the camera’s forward axis.

procedure
(camera3d-project camera
point
[ #:aspect aspect]) → (or/c #f vec2?)
  camera : camera3d?
  point : vec3?
  aspect : positive-real? = 1

Projects to normalized viewport coordinates. It returns #f behind the camera or outside the inclusive near/far interval.

procedure
(camera3d-pixel-ray camera
pixel-x
pixel-y
#:width width
#:height height) → ray3?
  camera : camera3d?
  pixel-x : finite-real?
  pixel-y : finite-real?
  width : exact-positive-integer?
  height : exact-positive-integer?

Returns a world ray through a top-left-origin pixel coordinate.

procedure
(camera3d-frustum camera [#:aspect aspect]) → vector?
camera : camera3d?
aspect : positive-real? = 1

Returns immutable inward-facing near, far, left, right, bottom, and top planes.

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