102 3D: Surface constructors and queries

9.3

Racket

102 3D: Surface constructors and queries🔗ℹ

3D reference map · First 3D picture

value
adaptive-parametric-surface3d : procedure?

Constructs a deterministic adaptive parametric surface using the documented dyadic refinement policy.

value
trimmed-parametric-surface3d : procedure?

Constructs a parametric surface restricted by declared trim fields.

value
implicit-surface3d : procedure?

Constructs a sampled implicit surface from a scalar field and an iso value.

value
gen:surface3d : any/c

The generic interface implemented by every surface value. Custom producers implement its kind, local mesh, diagnostics, provenance, domain, evaluator, and local-frame methods.

value
surface3d-kind : procedure?

Returns a surface producer kind symbol.

value
surface3d-local-mesh : procedure?

Returns a surface-mesh3d with identity transform and opacity one.

value
surface3d-mesh : procedure?

Lowers a surface to its immutable indexed local mesh representation; it is retained as the concise established spelling for surface3d-local-mesh.

value
surface3d->mesh3d : procedure?

Returns a standalone mesh3d which preserves the surface’s authored transform and opacity.

value
surface3d-domain : procedure?

Returns the retained surface-domain3d, or #f for a producer without UV domain.

value
surface3d-evaluate : procedure?

Evaluates a retained parametric surface at one valid UV coordinate.

value
surface3d-frame-at : procedure?

Returns a surface-frame3d containing the point, two tangents, and normal at one valid UV coordinate.

value
surface3d-diagnostics : procedure?

Returns a serializable surface-diagnostics3d snapshot.

value
surface3d-provenance : procedure?

Returns immutable producer provenance aligned with the local surface mesh.

struct
(struct surface-domain3d (u-range v-range contains? cache-key)
    #:transparent)
  u-range : list?
  v-range : list?
  contains? : (or/c #f procedure?)
  cache-key : any/c

Stores a parametric bounding box, optional retained-domain predicate, and stable domain identity. The predicate is deliberately not part of diagnostics.

struct
(struct surface-diagnostics3d (kind fields)
    #:transparent)
  kind : symbol?
  fields : any/c

Stores serializable producer diagnostics.

struct
(struct surface-frame3d (point tangent-u tangent-v normal)
    #:transparent)
  point : vec3?
  tangent-u : vec3?
  tangent-v : vec3?
  normal : vec3?

A local parametric differential frame.

struct
(struct surface-mesh3d ( mesh
vertex-provenance
triangle-provenance
topology-key
diagnostics)
    #:transparent)
  mesh : mesh3d?
  vertex-provenance : vector?
  triangle-provenance : vector?
  topology-key : any/c
  diagnostics : any/c

The immutable indexed lowering returned by surface3d-local-mesh. Its provenance vectors are aligned with the mesh’s vertices and render triangles; the topology key and diagnostics retain producer-specific inspection information.

value
surface3d-domain-contains? : procedure?

Reports whether a parameter point is inside a surface’s retained domain.

value
surface3d-position-at? : procedure?

Returns a retained surface point when the parameter lies inside that domain.

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52	Find a task or a name
53	Modules to require
54	Scenes and sampling
55	Scene states
56	Animation requests
57	Native model details
58	Visuals
59	Geometry
60	Number Lines and Coordinate Decorations
61	Point Markers, Scatter Plots, and Filled Areas
62	Probability and Statistical Diagrams
63	Calculus lessons
64	Colors
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66	Slide command-line tools
67	Source Programs and Authored Timelines
68	Interactive Preview and Inspection
69	Preview controls and diagnostics
70	Projects and Final Rendering
71	Project execution and cache details
72	Pict Renderer Protocol
73	3D reference map
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
92	3D: Colour space and final output
93	3D: Relations and geometric annotations
94	3D: Projected labels
95	3D: Textured billboards
96	3D: Spatial curves and vector diagrams
97	3D: Spatial anchors and label layout
98	3D: Anchors and projected labels
99	3D: Parametric surfaces and calculus
100	3D: Adaptive, trimmed, and implicit surfaces
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