Partial Torus Mesh

A torus defined parametrically from two angles - one around the tube, one around the ring - and cut short by limiting the second, which turns the same code into an arc, a horseshoe or a full ring without special cases. Normals are computed rather than guessed, because a parametric surface lit with wrong normals looks subtly faceted in a way that is hard to trace back.

The Program.cs file shows how to:

Defining a surface from two angle parameters
Making the shape partial by constraining the bend angle
Computing correct normals for smooth shading
Reusing vertices between adjacent triangles through indexing
Getting triangle winding right so faces are not culled
Using helpers: SceneSetup3D, UseSkybox, CreateMaterial

Partial Torus Mesh

View on GitHub.

using Stride.CommunityToolkit.Bepu;
using Stride.CommunityToolkit.Engine;
using Stride.CommunityToolkit.Rendering;
using Stride.CommunityToolkit.Skyboxes;
using Stride.Core.Mathematics;
using Stride.Engine;
using Stride.Graphics;
using Stride.Rendering;

/*
  A partial torus built vertex by vertex: a parametric surface over two angles, around the tube and
  along the bend, cut short of a full ring by limiting the bend angle. Shows positions, normals,
  triangle winding and vertex reuse through indices. The open ends show back-face culling at work:
  look into one and the tube is see-through, since faces turned away from the camera are not drawn.
*/

// Torus parameters
const float CylinderRadius = 0.3f;
const float TorusAngle = 270.0f;
const float BendRadius = 1.0f;
const int CircumferenceStepsCount = 20;
const int BendSegmentSteps = 40;

using var game = new Game();

game.Run(new SceneSetup3D().UseBepu().UseSkybox(), start: scene =>
{
    CreateMeshEntity(scene, new Vector3(0, 1, 0), b => BuildPartialTorusMesh(b, CylinderRadius, TorusAngle, BendRadius, CircumferenceStepsCount, BendSegmentSteps));
});

Entity CreateMeshEntity(Scene scene, Vector3 position, Action<MeshBuilder> build)
{
    using var meshBuilder = new MeshBuilder();

    build(meshBuilder);

    var model = new Model
    {
        new Mesh { Draw = meshBuilder.ToMeshDraw(game.GraphicsDevice) },
        game.CreateMaterial(new Color(255, 77, 128), metalness: 0f, glossiness: 0.9f),
    };

    var entity = new Entity { Scene = scene, Transform = { Position = position } };

    entity.Add(new ModelComponent { Model = model });

    return entity;
}

void BuildPartialTorusMesh(MeshBuilder meshBuilder, float cylinderRadius, float torusAngle, float bendRadius, int circumferenceStepsCount, int bendSegmentSteps)
{
    // torusAngle is in degrees, up to 360
    meshBuilder.WithIndexType(IndexingType.Int16);
    meshBuilder.WithPrimitiveType(PrimitiveType.TriangleList);

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

    // Vertices: a ring around the tube at every step along the bend
    for (var j = 0; j <= bendSegmentSteps; j++)
    {
        // The bend angle phi starts at 0 on the Z axis and reaches the X axis at 90 degrees
        var phi = j * torusAngle / bendSegmentSteps * Math.PI / 180.0;
        var xc = bendRadius * Math.Sin(phi);
        var zc = bendRadius * Math.Cos(phi);

        for (var i = 0; i < circumferenceStepsCount; i++)
        {
            // The angle theta around the tube
            var theta = i * Math.Tau / circumferenceStepsCount;
            var yr = cylinderRadius * Math.Sin(theta);
            var xr = cylinderRadius * Math.Cos(theta) * Math.Sin(phi);
            var zr = cylinderRadius * Math.Cos(theta) * Math.Cos(phi);

            meshBuilder.AddVertex();
            meshBuilder.SetElement(position, new Vector3((float)(xc + xr), (float)yr, (float)(zc + zr)));
            // Unit length: the direction out from the tube's centre line
            meshBuilder.SetElement(normal, Vector3.Normalize(new Vector3((float)xr, (float)yr, (float)zr)));
        }
    }

    // Triangle indices: two per quad between consecutive rings
    for (var j = 0; j < bendSegmentSteps; j++)
    {
        for (var i = 0; i < circumferenceStepsCount; i++)
        {
            var index = i + j * circumferenceStepsCount;
            var next = (i + 1) % circumferenceStepsCount + j * circumferenceStepsCount;

            meshBuilder.AddIndex(index);
            meshBuilder.AddIndex(next + circumferenceStepsCount);
            meshBuilder.AddIndex(index + circumferenceStepsCount);

            meshBuilder.AddIndex(index);
            meshBuilder.AddIndex(next);
            meshBuilder.AddIndex(next + circumferenceStepsCount);
        }
    }
}

Table of Contents

Partial Torus Mesh