Partial Torus Mesh in F#

The parametric partial torus, written in F#. The geometry is identical to the C# version; what differs is the shape of the code - the vertex generation is nested for loops with their results piped to ignore, and mutable engine state has to be assigned with the left arrow rather than plain equals.

The Program.fs file shows how to:

Generating parametric geometry in F#
Expressing vertex generation with nested for loops
Assigning to engine properties with the <- operator
Computing correct normals for smooth shading
Interoperating with the C# MeshBuilder API from F#
Using helpers: SceneSetup3D, UseBepu, UseSkybox

View on GitHub.

open Stride.CommunityToolkit.Bepu;
open Stride.CommunityToolkit.Engine;
open Stride.CommunityToolkit.Skyboxes;
open Stride.Core.Mathematics;
open Stride.Engine;
open Stride.CommunityToolkit.Rendering
open Stride.Graphics
open System
open Stride.Rendering
open Stride.Rendering.Materials
open Stride.Rendering.Materials.ComputeColors

let game = new Game()

let CreateMaterial (game: Game) : Material =
    Material.New(
        game.GraphicsDevice,
        MaterialDescriptor(
            Attributes = MaterialAttributes(
                    MicroSurface =  MaterialGlossinessMapFeature(GlossinessMap = ComputeFloat(0.9f)),
                    Diffuse = MaterialDiffuseMapFeature(DiffuseMap = ComputeColor(Color4(1.0f, 0.3f, 0.5f, 1.0f))),
                    DiffuseModel = MaterialDiffuseLambertModelFeature(),
                    Specular = MaterialMetalnessMapFeature(MetalnessMap = ComputeFloat(0.0f)),
                    SpecularModel = MaterialSpecularMicrofacetModelFeature(
                            Environment = MaterialSpecularMicrofacetEnvironmentGGXPolynomial()
                        )
                )
        )
    )

let CreateMeshEntity (graphicsDevice:GraphicsDevice) (scene:Scene) (position:Vector3) (build:MeshBuilder -> unit) =
    use meshBuilder = new MeshBuilder()

    build(meshBuilder)

    let model = new Model()
    model.Add(MaterialInstance(Material = CreateMaterial(game)))
    model.Add(Mesh(
        Draw = meshBuilder.ToMeshDraw(graphicsDevice),
        MaterialIndex = 0
    ))

    let entity = new Entity()
    entity.Scene <- scene
    entity.Transform.Position <- position
    entity.Add(ModelComponent(Model = model))
    entity

let BuildPartialTorusMesh (meshBuilder:MeshBuilder) cylinderRadius torusAngle bendRadius circumferenceStepsCount bendSegmentSteps =
    // torusAngle is in degrees, up to 360
    meshBuilder.WithIndexType(IndexingType.Int16) |> ignore
    meshBuilder.WithPrimitiveType(PrimitiveType.TriangleList)  |> ignore

    let position = meshBuilder.WithPosition<Vector3>()
    let normal = meshBuilder.WithNormal<Vector3>()

    //vertices
    for j in 0..bendSegmentSteps do
      // The bend angle tPhi starts at 0 on the Z axis and reaches the X axis at Pi/2
      let tPhi = (float j) * torusAngle / (float bendSegmentSteps) * Math.PI / 180.0
      let xc = bendRadius * Math.Sin(tPhi)
      let zc = bendRadius * Math.Cos(tPhi)

      for i in 0..(circumferenceStepsCount - 1) do
      //circumference angle tTheta
        let tTheta = float i * Math.Tau / float circumferenceStepsCount
        let yr = cylinderRadius * Math.Sin(tTheta)

        let xr = cylinderRadius * Math.Cos(tTheta) * Math.Sin(tPhi)
        let zr = cylinderRadius * Math.Cos(tTheta) * Math.Cos(tPhi)

        // Unit length: the direction out from the tube's centre line
        let tNorm = Vector3.Normalize(Vector3(float32 xr, float32 yr, float32 zr))
        let tPos = Vector3(float32 (xc + xr), float32 yr, float32 (zc + zr))

        meshBuilder.AddVertex() |> ignore
        meshBuilder.SetElement(position, tPos)
        meshBuilder.SetElement(normal, tNorm)

    //triangle indices
    for j in 0..(bendSegmentSteps - 1) do
      for i in 0..(circumferenceStepsCount - 1) do

        let i_tot = i + j * circumferenceStepsCount
        let i_next = (i + 1) % circumferenceStepsCount + j * circumferenceStepsCount

        //triangle 1
        meshBuilder.AddIndex(i_tot)
        meshBuilder.AddIndex(i_next + circumferenceStepsCount)
        meshBuilder.AddIndex(i_tot + circumferenceStepsCount)


        //triangle 2
        meshBuilder.AddIndex(i_tot)
        meshBuilder.AddIndex(i_next)
        meshBuilder.AddIndex(i_next + circumferenceStepsCount)

let Start rootScene =
    game.AddProfiler() |> ignore

    // Torus parameters
    let cylinderRadius = 0.3f
    let torusAngle = 270.0f
    let bendRadius = 1.0f
    let circumferenceStepsCount = 20
    let bendSegmentSteps = 40

    CreateMeshEntity
        game.GraphicsDevice
        rootScene
        (Vector3(0.0f, 1.0f, 0.0f))
        (fun b -> BuildPartialTorusMesh b (float cylinderRadius) (float torusAngle) (float bendRadius) circumferenceStepsCount bendSegmentSteps)
    |> ignore

[<EntryPoint>]
let main argv =
    game.Run(SceneSetup3D().UseBepu().UseSkybox(), start = Start)
    0

Table of Contents

Partial Torus Mesh in F#