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On this page:
aabb3
aabb3?
aabb3-minimum
aabb3-maximum
aabb3-empty
aabb3-empty?
aabb3-union
aabb3-from-points
aabb3-transform
aabb3-center
aabb3-size
aabb3-contains?
ray3
plane3
plane3?
plane3-point
plane3-normal
ray3-plane-hit
ray3-aabb-hit
ray3-triangle-hit
ray3-at
ray3-intersect-plane
ray3-intersect-aabb
ray3-intersect-triangle
9.3
Racket
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85 3D: Bounds, rays, and planes🔗ℹ

3D reference map · First 3D picture

procedure

(aabb3 minimum maximum) → aabb3?

  minimum : (or/c #f vec3?)
  maximum : (or/c #f vec3?)
Constructs an inclusive axis-aligned box. Both corners must be vec3 values ordered coordinatewise, or both must be #f for the empty box.

procedure

(aabb3? value) → boolean?

  value : any/c
Recognizes a spatial AABB.

procedure

(aabb3-minimum bounds) → (or/c #f vec3?)

  bounds : aabb3?
Returns the lower corner or #f when empty.

procedure

(aabb3-maximum bounds) → (or/c #f vec3?)

  bounds : aabb3?
Returns the upper corner or #f when empty.

value

aabb3-empty : aabb3?

The empty AABB.

procedure

(aabb3-empty? bounds) → boolean?

  bounds : aabb3?
Reports whether bounds are empty.

procedure

(aabb3-union first second) → aabb3?

  first : aabb3?
  second : aabb3?
Returns their least enclosing AABB.

procedure

(aabb3-from-points points) → aabb3?

  points : (listof vec3?)
Returns enclosing bounds, or aabb3-empty for no points.

procedure

(aabb3-transform bounds map) → aabb3?

  bounds : aabb3?
  map : affine3?
Transforms all eight corners and encloses them.

procedure

(aabb3-center bounds) → vec3?

  bounds : aabb3?
Returns nonempty bounds’ centre; empty bounds raise an exception.

procedure

(aabb3-size bounds) → vec3?

  bounds : aabb3?
Returns nonempty bounds’ nonnegative size; empty bounds raise an exception.

procedure

(aabb3-contains? bounds point) → boolean?

  bounds : aabb3?
  point : vec3?
Tests inclusive containment.

struct

(struct ray3 (origin direction)
    #:transparent)
  origin : vec3?
  direction : vec3?
A ray (+ origin (* t direction)) for t at least zero. Its direction must be nonzero but is not normalized automatically.

procedure

(plane3 point normal) → plane3?

  point : vec3?
  normal : vec3?
Constructs a point-normal plane and normalizes its nonzero normal.

procedure

(plane3? value) → boolean?

  value : any/c
Recognizes a spatial plane.

procedure

(plane3-point plane) → vec3?

  plane : plane3?
Returns one point in the plane.

procedure

(plane3-normal plane) → vec3?

  plane : plane3?
Returns its normalized normal.

struct

(struct ray3-plane-hit (point distance)
    #:transparent)
  point : vec3?
  distance : nonnegative-real?
A forward ray-plane intersection.

struct

(struct ray3-aabb-hit (entry exit)
    #:transparent)
  entry : nonnegative-real?
  exit : nonnegative-real?
The inclusive ray-parameter interval inside an AABB.

struct

(struct ray3-triangle-hit (point distance barycentric normal)
    #:transparent)
  point : vec3?
  distance : nonnegative-real?
  barycentric : vec3?
  normal : vec3?
An exact, double-sided ray/triangle hit. barycentric holds the weights for the triangle’s first, second, and third vertices, and normal follows the triangle’s declared winding.

procedure

(ray3-at ray distance) → vec3?

  ray : ray3?
  distance : finite-real?
Returns the algebraic point at distance.

procedure

(ray3-intersect-plane ray plane) → (or/c #f ray3-plane-hit?)

  ray : ray3?
  plane : plane3?
Returns the nearest forward hit, or #f when parallel or behind the origin.

procedure

(ray3-intersect-aabb ray bounds) → (or/c #f ray3-aabb-hit?)

  ray : ray3?
  bounds : aabb3?
Returns forward entry/exit parameters, or #f for no hit.

procedure

(ray3-intersect-triangle ray    
  first    
  second    
  third) → (or/c #f ray3-triangle-hit?)
  ray : ray3?
  first : vec3?
  second : vec3?
  third : vec3?
Returns the nearest exact forward intersection with the finite triangle, or #f. Both windings are pickable; renderer back-face culling is a separate display decision.

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