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On this page:
polyhedral-plane3d
polyhedral-source-face-id3d
polyhedral-face-declaration3d
polyhedral-face3d
polyhedral-complex3d
polyhedral-complex3d?
polyhedral-complex3d-source-mesh
polyhedral-complex3d-analysis-mesh
polyhedral-complex3d-source-transform
polyhedral-complex3d-mesh
polyhedral-complex3d-topology
polyhedral-complex3d-faces
polyhedral-complex3d-edge-to-faces
polyhedral-complex3d-vertex-to-faces
polyhedral-complex3d-diagnostics
9.3
Racket
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105 3D: Polygonal faces🔗ℹ

3D reference map · First 3D picture

struct

(struct polyhedral-plane3d (normal offset)
    #:transparent)
  normal : vec3?
  offset : finite-real?
A transformed unit-normal plane with equation normal . point = offset.

struct

(struct polyhedral-source-face-id3d (triangle-index)
    #:transparent)
  triangle-index : exact-nonnegative-integer?
The transparent generated identity of an automatically grouped face. It names the least source triangle rather than hiding provenance in a hash string.

struct

(struct polyhedral-face-declaration3d (id triangle-indices)
    #:transparent)
  id : symbol?
  triangle-indices : (or/c vector? list?)
An explicit polygonal face declaration. All declarations together must partition the mesh’s source triangles exactly once.

struct

(struct polyhedral-face3d (id
    triangle-indices
    boundary-vertex-indices
    normal
    plane
    centroid
    area
    provenance)
    #:transparent)
  id : any/c
  triangle-indices : vector?
  boundary-vertex-indices : (or/c #f vector?)
  normal : (or/c #f vec3?)
  plane : (or/c #f polyhedral-plane3d?)
  centroid : (or/c #f vec3?)
  area : nonnegative-real?
  provenance : hash?
One mathematical polygonal face over one or more render triangles. A simple boundary is a cyclic immutable vertex-index vector. It is #f when the region has multiple loops, branches, or repeated boundary vertices; the enclosing complex retains the diagnostic rather than choosing a false polygon.

procedure

(polyhedral-complex3d mesh 
  [#:faces faces 
  #:coplanar-angle angle 
  #:plane-distance distance]) 
 → polyhedral-complex3d?
  mesh : mesh3d?
  faces : any/c = #f
  angle : nonnegative-real? = 1e-7
  distance : nonnegative-real? = 1e-7
Builds an immutable mathematical-face complex. With #:faces #f (the default) or 'coplanar, it merges only edge-connected, consistently oriented render triangles whose world-space planes agree within the stated angle (in radians) and distance tolerances. The source mesh is retained for provenance; all mathematical calculations use an immutable world-space analysis mesh with an identity transform.

Use 'triangles to retain every render triangle as a face. An explicit partition is a list/vector of polyhedral-face-declaration3d values or concise (face-id triangle-index ...) lists; explicit declarations always override automatic merging.

procedure

(polyhedral-complex3d? value) → boolean?

  value : any/c
Recognizes a polygonal-face complex.

procedure

(polyhedral-complex3d-source-mesh complex) → mesh3d?

  complex : polyhedral-complex3d?
Returns the unchanged authored mesh whose stable part identities are the source of the complex’s provenance.

procedure

(polyhedral-complex3d-analysis-mesh complex) → mesh3d?

  complex : polyhedral-complex3d?
Returns the immutable world-space mesh used for planes, topology, duals, Schlegel diagrams, and nets. Its local transform is identity-transform3. A reflected source transform is baked with reversed triangle winding so geometric normals remain consistent.

procedure

(polyhedral-complex3d-source-transform complex) → transform3?

  complex : polyhedral-complex3d?
Returns the authored local-to-world transform recorded before analysis-space baking.

procedure

(polyhedral-complex3d-mesh complex) → mesh3d?

  complex : polyhedral-complex3d?
Returns the analysis mesh. New code should use polyhedral-complex3d-source-mesh or polyhedral-complex3d-analysis-mesh to state which coordinate space it needs.

procedure

(polyhedral-complex3d-topology complex) → mesh-topology3d?

  complex : polyhedral-complex3d?
Returns the triangle topology used to build the complex.

procedure

(polyhedral-complex3d-faces complex) → vector?

  complex : polyhedral-complex3d?
Returns faces in deterministic least-source-triangle order.

procedure

(polyhedral-complex3d-edge-to-faces complex) → vector?

  complex : polyhedral-complex3d?
Returns one immutable polygonal-face-index vector per topological edge. A render diagonal inside a grouped square has one incident polygonal face.

procedure

(polyhedral-complex3d-vertex-to-faces complex) → vector?

  complex : polyhedral-complex3d?
Returns one immutable polygonal-face-index vector per source vertex.

procedure

(polyhedral-complex3d-diagnostics complex) → hash?

  complex : polyhedral-complex3d?
Returns the construction mode, tolerances, inherited triangle-topology diagnostics, and per-face boundary reports. 'invalid-face-indices identifies regions that are not simple polygons.

Limitations. Polygonal-face construction groups only existing triangles; it neither repairs nonmanifold/self-intersecting input nor creates a polygonal approximation. A region with holes is retained and diagnosed, but does not yet expose a usable multi-loop polygon. This constructor does not triangulate holes, construct duals, Schlegel diagrams or nets, or create face-transform animations.

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