meshing-around

Validation

Validation module

Validation~Num function

|1.0?Input

Source code

Num          ← °0type

Validation~Char function

|1.0?Input

Source code

Char         ← °1type

Validation~Box function

|1.0?Input

Source code

Box          ← °2type

Validation~Vec₂ function

|1.0?Input

Source code

Vec₂         ← ⊃(Num|°[2]△)

Validation~Vec₃ function

|1.0?Input

Source code

Vec₃         ← ⊃(Num|°[3]△)

Validation~Quat function

|1.0?Input

Source code

Quat         ← ⊃(Num|°[4]△)

Validation~ColorImg function

|1.0?Input

Source code

ColorImg     ← ⊃(Num|⊃(°3⊣|°3⧻)△)

Validation~AlphaImg function

|1.0?Input

Source code

AlphaImg     ← ⊃(Num|⊃(°2⊣|°3⧻)△)

Validation~GreyscaleImg function

|1.0?Input

Source code

GreyscaleImg ← ⊃(Num|°2⧻△)

Transform

Transform module

Transform is used to represent the translation, rotation, and scale of an object.

Transform~ data boxed

PositionV~Vec₃

ScaleV~Vec₃

RotationV~Quat

Transform~Forward function

|1Output?Input

Get the 3D vector pointing in the object’s local forward direction.

Source code

Forward ← ˜QRot 0_1_0 Rotation

Transform~Right function

|1Output?Input

Get the 3D vector pointing in the object’s local right direction.

Source code

Right ← ˜QRot 1_0_0 Rotation

Transform~Up function

|1Output?Input

Get the 3D vector pointing in the object’s local up direction.

Source code

Up ← ˜QRot 0_0_1 Rotation

Transform~Rotate function

|2Output?Input1Input2

Source code

Rotate ← °⊸Rotation Qqp⊸⊙Rotation

Transform~V function

|1.0?Input

Source code

V ← °1≍"Transform"ID

Material

Material module

Materials are used to represent a particular set of shading values. Each field of a material contains a texture, which will be mapped to the surface of any triangle using it. To use a single value rather than a texture, ¤¤ the value.

Material~ data boxed

AlbedoV~ColorImg

RoughnessV~GreyscaleImg

ReflectivityV~GreyscaleImg

Material~V function

|1.0?Input

Source code

V ← °1≍"Material"ID

Mesh

Mesh module

A mesh represents a single object to render. It holds a set of triangles, their normal vectors, their UV coordinates, the materials to shade with, which triangles use which materials, a transform, and a set of textures to be moved around with the mesh.

Mesh~ data boxed

TrianglesV~Num°¤°(˜⊂3_3)△

NormalsV~Num°¤°(˜⊂3)△

UVsV~Num°¤°(˜⊂3_2)△

MaterialIndex⊃(V~Num|°1⧻△)

TransformTransform~V

Materials≡Material~V

TextureSet≡V~Box

Mesh~InitNormals function

|1Output?Input

Source code

InitNormals       ← ⍥(°⊸Normals≡TriNorm⊸Triangles)≍¤˙⊟₃∞ ⊸Normals

Mesh~CalculateNormals function

|1Output?Input

Source code

CalculateNormals  ← °⊸Normals≡TriNorm⊸Triangles

Mesh~InitUVs function

|1Output?Input

Source code

InitUVs           ← ⍥(°⊸UVs ˜↯0 ˜⊂3_2 ⧻⊸Triangles)≍↯1_3_2 ∞ ⊸UVs

Mesh~InitMaterialIndex function

|1Output?Input

Source code

InitMaterialIndex ← ⍥(°⊸MaterialIndex˜↯0 ¤⧻⊸Triangles)≍¤∞ ⊸MaterialIndex

Mesh~ApplyScale function

|1Output?Input

Source code

ApplyScale        ← °⊸Transform≈Scale↯3 1°⊸Triangles⧋×⊸⊃Transform≈Scale Triangles

Mesh~ApplyRot function

|1Output?Input

Source code

ApplyRot          ← °⊸Transform≈Rotation RQuat0˙⊟₃0°⊸⊃(Normals|Triangles) ∩⌞QRot⊸⊃(Transform≈Rotation|Normals|Triangles)

Mesh~ApplyPos function

|1Output?Input

Source code

ApplyPos          ← °⊸Transform≈Position⊚3°⊸Triangles⧋+⊸⊃Transform≈Position Triangles

Mesh~ApplyTransform function

|1Output?Input

Source code

ApplyTransform    ← ApplyPos ApplyRot ApplyScale

Mesh~Rotate function

|2Output?Input1Input2

Source code

Rotate            ← °⊸Mesh~Transform≈Rotation Qqp⊸⊙Mesh~Transform≈Rotation

Mesh~Call function

|1Output?Input

Source code

Call ← InitUVs InitMaterialIndex InitNormals New

Mesh~V function

|1.0?Input

Source code

V ← °1≍"Mesh"ID

RenderConfig

RenderConfig module

A RenderConfig defines some parameters for rendering a mesh, which aren’t specific to the mesh. Using the same RenderConfig with multiple meshes should result in a set of renders which can be composed into a single scene, as though they were rendered from the same camera.

RenderConfig~ data boxed

SizeV~Vec₂

ZoomV~Num

CameraTransform~V

FOVV~Num

LightV~Vec₃

AmbientColorV~Color

RenderConfig~AspectRatio function

|1Output?Input

Source code

AspectRatio ← /÷Size

RenderConfig~HalfwayVec function

|1Output?Input

Source code

HalfwayVec  ← ÷⊸⩜⌵+⊃(¯Light|Camera≈Forward)

RenderConfig~V function

|1.0?Input

Source code

V ← °1≍"RenderConfig"ID

RenderOutput

RenderOutput module

RenderOutput~ data boxed

IndexV~GreyscaleImg

DepthV~GreyscaleImg

MaterialIndexV~GreyscaleImg

NormalV~ColorImg

LightV~GreyscaleImg

TriCoordsV~AlphaImg

AmbientV~ColorImg

UVsV~AlphaImg

PosV~ColorImg

MaterialMaterial~V

RenderOutput~ApplyTexture‼ index macro

Source code

ApplyTexture‼ ← °⊸^0^1˜⬚0⊡⟜(⌊⧋×△₂)⊙⊸⊃(UVs|^0)

RenderOutput~ApplyTexture! index macro

Source code

ApplyTexture! ← ApplyTexture‼^⊙◌

RenderOutput~GenUVs function

|2Output?Input1Input2

Source code

GenUVs ← (
    ⬚NaN GenMeshProp‼Mesh~UVs UVs
  )

RenderOutput~GenPos function

|2Output?Input1Input2

Source code

GenPos ← (
    ⬚∞GenMeshProp‼Mesh~Triangles Pos⊙Mesh~ApplyTransform
  )

RenderOutput~GenMaterials function

|2Output?Input1Input2

Source code

GenMaterials ← (
    ⤚⊓(⊃MaterialIndex UVs|⍚⊃(Material~Albedo|Material~Roughness|Material~Reflectivity) Mesh~Materials)
    ⊞=⇡◡⋅⋅⧻
    ⨬NaN_NaN∘⊙¤
    ∩₃⌞(/+≡◇(⬚0⊡⌊⧋×⊸⊙△₂))
    °⊸⊃(Material≈Albedo|Material≈Roughness|Material≈Reflectivity)
  )

RenderOutput~ApplyTexFromSet‼ index macro

Source code

ApplyTexFromSet‼ ← (
    ∪⌞∘(°□⊡)⊙⊙Mesh~TextureSet
    ˜ApplyTexture‼^0^1
  )

RenderOutput~ApplyTexFromSet! index macro

Source code

ApplyTexFromSet! ← (
    ∪⌞∘(°□⊡)⊙⊙Mesh~TextureSet
    ˜ApplyTexture‼^⊙◌
  )

RenderOutput~ConvertTanNormals function

|2Output?Input1Input2

Source code

ConvertTanNormals ← (
    ⊙(⊃(⍜⍉(-⌞°⊂)Mesh~Triangles|⍜⍉(Inv₂-⌞°⊂)Mesh~UVs|Mesh~Normals)Mesh~ApplyTransform
      ÷⊸⧋(√/+˙×)≡(⊂˜Mmp))
    ⍉⧋˜Mvp Normal⟜⤚(⬚0⊏Index)
    °⊸Normal
  )

RenderOutput~Call function

|7Output?Input1Input2Input3Input4Input5Input6Input7

Source code

Call ← °⊸UVs˜↯0△ ⊸TriCoords New

RenderOutput~V function

|1.0?Input

Source code

V ← °1≍"RenderOutput"ID

ImageAndDepth

ImageAndDepth module

ImageAndDepth~ data boxed

ImageV~ColorImg

DepthV~GreyscaleImg

ImageAndDepth~Combine function

|2Output?Input1Input2

Source code

Combine ← ImageAndDepth CombineByDepth ∩°ImageAndDepth

Constants

Suzanne constant

Suzanne is a constant containing the “Suzanne” mesh used by Blender as a Mesh instance. The Suzanne constant does not have a UV map.

Monadic functions

TriNorm function

|1Vector?Triangle

Find the normal vector for a triangle

Source code

TriNorm ← ÷⊸⩜⌵Cross°⊟-¤°⊂

DrawTri function

|1Output?Input

Rasterize a triangle PixelLocs ? 2DTriangle

Source code

DrawTri ← (
  ⊓⌊⌈⊸⊃/↧/↥
  ⧋⤙+⇡⤚-
  ⊙(⊚˜InTri°⍉)
  +°¤
)

STL function

|1Output?Input

Import an STL file as a Mesh. STL files do not contain UV coordinates. There are two types of STL, ASCII and binary. The inverse of this function can decode either, just make sure to &fras or &frab appropriately. The STL function always generates binary STL.

Source code

STL ← ⌅(GenSTL|DecodeSTL)

OBJ function

|1Output?Input

Import an OBJ file as a Mesh. OBJ files should be read with &fras. For use with this library, the OBJ file must only contain triangles, and must contain UV coordinates.

Source code

OBJ ← ⌅(GenOBJ|DecodeOBJ)

Dyadic functions

WorldToView function

|2.2MeshRenderConfig?MeshRenderConfig

Convert from World-space coordinates to View-space coordinates

Source code

WorldToView ← (
  ◡⊓Mesh~Triangles (⊃(Camera~Position|Camera~Rotation|Camera~Scale)RC~Camera)
  ⧋˜-
  ˜(QRot ⍜(↘1°⍉)¯)
  ⧋˜÷
  ⧋(⊏0_2_1)
  °⊸Mesh~Triangles
)

CullBackfaces function

|2Mesh?MeshRenderConfig

Filter out faces by direction facing relative to camera

Source code

CullBackfaces ← (
  ˜⤚⊓(¯RC~Camera≈Up|⊃(Mesh~Normals|Mesh~Triangles|Mesh~UVs|Mesh~MaterialIndex))
  ∩₄⌞▽⊸≡⌞(>0Dot)
  °⊸⊃(Mesh~Normals|Mesh~Triangles|Mesh~UVs|Mesh~MaterialIndex)
)

InTri function

|2Output?Input1Input2

Check if a point is within a triangle Boolean ? 2DTriangle Point

Source code

InTri ← (
  °⊟⤚-⌞°⊂
  ∩⌞÷Det₂⟜₂(¯∩˜-∩⌟₂∩⌞Det₂)
  ×⊃(×∩≥₀|≤₁+)
)

RenderPreview function

|2Render?MeshRenderConfig

Fast render that does not output a depth map for compositing. Use for real-time rendering or scene previewing.

Source code

RenderPreview ← (
  Mesh!(
    ApplyTransform
    InitNormals
  )
  ◡⊓(⊃(Mesh~Triangles|Mesh~Normals)|RC~Camera≈Forward)
  ∩⌟˜▽⊙⟜(<₀⧋Dot)
  °⊸⊃Mesh~Triangles Mesh~Normals
  WorldToView
  ⊃↓(
    /↧⤙˜↯0 ⋅RC~Size
  | °(-⊸¬)¯⧋Dot⊓(Mesh~Normals|RC~Light)
  | ⍖÷₃≡/+⧋⊃↘₂↙₂Mesh~Triangles)
  ∩⌞⊏
  ÷₂+₁
  ∪⌟×∘
  ∧(˜⍜⊙⬚0⊡≡⊙◌⊙¤ DrawTri)
  ⇌°⍉
)

Tetradic functions

CombineByDepth function

|4.2ValueDepth?ValueDepthValueDepth

Pick the closer of two depth-value pairs

Source code

CombineByDepth ← ˜(⍜-×⊙⊙⊃<↧)

Hexadic functions

RenderMesh function

|6RenderOutput?MeshRenderConfigInput3Input4Input5Input6

Full-featured renderer. Performs the core steps of the full rendering process.

Source code

RenderMesh ← (
  Mesh!(
    ApplyTransform
    InitNormals
    InitMaterialIndex
  )
  WorldToView
  ◡⊓(⊃Mesh~Triangles Mesh~Normals|⊃(RC~Camera≈Forward|⤙˜↯∞ RC~Size))
  ⊃(÷₃⧋(/+⊣)|⧋↙₂)
  ⟜∩₃⌟˜▽⊙⊙(°⊏<₀⧋Dot)
  ⊙(∪⌞∘(+×⊙(⊃/↧(¤¤)÷₂))∩⌞⊏⍖)
  ⤚⋅(⇌°⍉∧(⍜⊙⬚0⊡≡⊙◌¤ ⊙DrawTri))
  ⊙⊙⊃↓(
  | ↯⋅⊃(˜⊂3RC~Size|RC~AmbientColor)
  | ⍜(°⊂⍉)⟜(Inv₂-⌞)+×⊙(⊃/↧(¤¤)÷₂)⊓(⧋↙₂Mesh~Triangles|RC~Size)
  | ↥₀¯⧋Dot⊓(Mesh~Normals|RC~Light)
  | Mesh~Normals
  | Mesh~MaterialIndex
  )
  ⟜⊓⌞(
    ⬚∞⊏ | ⬚NaN⊏ | ⬚0⊏ | ⬚0⊏
  | ⇌⤸₁⍉⧋˜Mvp⊙(⤸0_1_3_2⍉)˜-⇡⊸△₂°⊂⤸₂⬚NaN⊏⍉⇌
  )
  RO
)