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60 Number Lines and Coordinate Decorations
61 Point Markers, Scatter Plots, and Filled Areas
62 Probability and Statistical Diagrams
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74 3D:   Objects, groups, and paths
75 3D:   Cameras and projection
76 3D:   Views inside a Scene
77 3D:   Animating 3D objects
78 3D:   Animating the 3D camera
79 3D:   Cuts, caps, and section measurements
80 3D:   Supplementary surface, section, and annotation bindings
81 3D:   Cuts, sections, and numerical volume
82 3D:   Vectors
83 3D:   Linear maps and rotations
84 3D:   Affine transforms
85 3D:   Bounds, rays, and planes
86 3D:   Spatial maps and homotopies
87 3D:   Materials and lights
88 3D:   Lighting inspection
89 3D:   Shadow descriptors and stable bounds
90 3D:   Finite-light animation
91 3D:   Software finite-light evaluation
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95 3D:   Textured billboards
96 3D:   Spatial curves and vector diagrams
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99 3D:   Parametric surfaces and calculus
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101 3D:   Constructive solids
102 3D:   Surface constructors and queries
103 3D:   Meshes
104 3D:   Triangle topology
105 3D:   Polygonal faces
106 3D:   Deterministic convex hulls
107 3D:   Polyhedral duals
108 3D:   Schlegel diagrams and polyhedral nets
109 3D:   Conservative mesh correspondence
110 3D:   Topology-safe mesh matching
111 3D:   Checking and repairing mesh orientation
112 3D:   Clipping, sections, and transparency
113 3D:   Prepared spatial ODE trajectories and vector fields
114 3D:   Seeds and streamline sets
115 3D:   Poincare sections and return maps
116 3D:   Equilibria and local linearization
117 3D:   Flow maps and volume change
118 3D:   Drawing and inspecting trajectories
119 3D:   Reading prepared trajectories
120 3D:   Drawing vector fields and particles
121 3D:   Trajectory display
122 3D:   Spatial inspection and exact picking
123 3D:   Retained renderer backends
124 3D:   Compiled geometry and instances
125 3D:   Frame requests and results
126 3D:   Software rendering and statistics
127 3D:   Optional Racket/  Open  GL backend
128 Experimental Derived Visuals
129 Source Package Hygiene
On this page:
vec3
origin3
x-axis3
y-axis3
z-axis3
vec3+
vec3-
vec3*
vec3-scale
vec3-dot
vec3-cross
vec3-length
vec3-distance
vec3-normalize
vec3-lerp
vec3-finite?
9.3
Racket
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82 3D: Vectors🔗ℹ

3D reference map · First 3D picture

struct

(struct vec3 (x y z)
    #:transparent)
  x : finite-real?
  y : finite-real?
  z : finite-real?
An immutable spatial point or displacement. Positive z points out of the screen toward a conventional viewer.

value

origin3 : vec3? = (vec3 0 0 0)

The spatial origin.

value

x-axis3 : vec3? = (vec3 1 0 0)

The positive x unit vector.

value

y-axis3 : vec3? = (vec3 0 1 0)

The positive y unit vector.

value

z-axis3 : vec3? = (vec3 0 0 1)

The positive z unit vector.

procedure

(vec3+ first second) → vec3?

  first : vec3?
  second : vec3?
Adds components.

procedure

(vec3- first second) → vec3?

  first : vec3?
  second : vec3?
Subtracts components.

procedure

(vec3* first second) → vec3?

  first : vec3?
  second : vec3?
Multiplies components.

procedure

(vec3-scale scalar value) → vec3?

  scalar : finite-real?
  value : vec3?
Scales every component.

procedure

(vec3-dot first second) → finite-real?

  first : vec3?
  second : vec3?
Returns the Euclidean dot product.

procedure

(vec3-cross first second) → vec3?

  first : vec3?
  second : vec3?
Returns first × second in the right-handed coordinate system.

procedure

(vec3-length value) → nonnegative-real?

  value : vec3?
Returns Euclidean length.

procedure

(vec3-distance first second) → nonnegative-real?

  first : vec3?
  second : vec3?
Returns Euclidean distance.

procedure

(vec3-normalize value) → vec3?

  value : vec3?
Returns an inexact unit vector. The zero vector raises an exception.

procedure

(vec3-lerp first second progress) → vec3?

  first : vec3?
  second : vec3?
  progress : finite-real?
Linearly interpolates components; progress outside 0 through 1 performs extrapolation.

procedure

(vec3-finite? value) → boolean?

  value : any/c
Reports whether value is a finite vec3.

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