84 3D: Affine transforms

9.3

Racket

84 3D: Affine transforms🔗ℹ

3D reference map · First 3D picture

procedure
(affine3 linear translation) → affine3?
linear : linear3?
translation : vec3?

Constructs a full affine map. It can represent shear, reflection, and singular linear maps exactly.

procedure
(affine3? value) → boolean?
value : any/c

Recognizes a full affine map.

procedure
(affine3-linear map) → linear3?
map : affine3?

Returns the linear component.

procedure
(affine3-translation map) → vec3?
map : affine3?

Returns the translation component.

value
identity-affine3 : affine3?

The identity affine map.

procedure
(affine3-compose outer inner) → affine3?
outer : affine3?
inner : affine3?

Composes maps as outer ∘ inner.

procedure
(affine3-invert map) → affine3?
map : affine3?

Returns the inverse; singular maps raise an exception.

procedure
(affine3-apply-point map point) → vec3?
map : affine3?
point : vec3?

Applies both linear component and translation.

procedure
(affine3-apply-vector map value) → vec3?
map : affine3?
value : vec3?

Applies only the linear component.

procedure
(affine3-normal-transform map) → linear3?
map : affine3?

Returns the inverse-transpose normal map.

procedure
(affine3-lerp from to progress) → affine3?
  from : affine3?
  to : affine3?
  progress : (and/c finite-real? (>=/c 0) (<=/c 1))

Interpolates corresponding matrix entries and translation, with exact endpoints.

struct
(struct transform3 (translation rotation scale)
    #:transparent)
  translation : vec3?
  rotation : rotation3?
  scale : vec3?

An author-oriented transform with nonzero scale components. It applies local scale, then rotation, then translation. Negative scale is allowed, but an interpolation that would cross a zero scale is rejected.

procedure
(make-transform3 [ #:translation translation
#:rotation rotation
#:scale scale]) → transform3?
  translation : vec3? = origin3
  rotation : rotation3? = identity-rotation3
  scale : vec3? = (vec3 1 1 1)

Constructs a validated decomposed transform.

value
identity-transform3 : transform3?

The decomposed identity transform.

procedure
(transform3->affine3 transform) → affine3?
transform : transform3?

Converts a decomposed transform to an exact affine map.

procedure
(transform3-compose outer inner) → affine3?
outer : transform3?
inner : transform3?

Composes transforms as an affine3, retaining shear that arbitrary nonuniform-scale composition can induce.

procedure
(transform3-apply-point transform point) → vec3?
transform : transform3?
point : vec3?

Applies scale, rotation, then translation.

procedure
(transform3-lerp from to progress) → transform3?
  from : transform3?
  to : transform3?
  progress : (and/c finite-real? (>=/c 0) (<=/c 1))

Interpolates translation, scale, and shortest-arc rotation with exact endpoints.

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