feat: Solid3D (3DSOLID) ACIS tessellation

Parse SAT geometry directly into GPU MeshModel without going through
the truck B-rep pipeline:
  • plane-surface faces  → fan-triangulate the coedge-loop polygon
  • cone-surface faces   → parametric grid (handles cylinders and cones)
  • sphere-surface faces → UV sphere grid (GRID_U × GRID_V)
  • torus-surface faces  → UV torus grid

Scene integration:
  • add_entity(): tessellates Solid3D on insert, stores in scene.meshes
  • erase_entities(): removes mesh from scene.meshes on delete
  • populate_meshes_from_document(): rebuilds all meshes on file load
    and undo/redo (called alongside populate_hatches/images)

ROADMAP updated: Solid3D tessellation marked ✅ in sections 2.12, 14.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

ROADMAP.md

@@ -40,7 +40,7 @@ Durum simgeleri: ✅ Tamamlandı · 🔧 Kısmen yapıldı · ⬜ Yapılmadı
 | 2.9 | Çizim sırası (draw order / SortEntitiesTable) | ✅ |
 | 2.10 | ViewCube (3D yönelim küpü) | ✅ |
 | 2.11 | UCS simgesi (XYZ tripod) | ✅ |
-| 2.12 | Solid3D / 3DSOLID tessellation (truck pipeline) | 🔧 Altyapı var, tamamlanmadı |
+| 2.12 | Solid3D / 3DSOLID tessellation (truck pipeline) | ✅ |
 | 2.13 | Region / Body / Wire / Silhouette entity render | ⬜ |
 | 2.14 | Anti-aliasing / MSAA seçeneği | ⬜ |
 
@@ -59,7 +59,7 @@ Underlay (PDF/DWF/DGN)
 ### 3.2 Kısmen / Sadece Okunabilir
 | Entity | Durum |
 |--------|-------|
-| Solid3D (3DSOLID) | 🔧 Okunuyor, tessellation eksik |
+| Solid3D (3DSOLID) | ✅ ACIS SAT tessellation |
 | Region | ⬜ Tanınmıyor |
 | Body / Wire / Silhouette | ⬜ Tanınmıyor |
 | Ole2Frame | ⬜ Tanınmıyor |
@@ -291,7 +291,7 @@ Underlay (PDF/DWF/DGN)
 | Truck geometry pipeline entegrasyonu | ✅ |
 | 3D primitive'ler (Box, Sphere, Cylinder) | ✅ |
 | OBJ mesh içe aktarma | ✅ |
-| Solid3D tessellation (acadrust ACIS) | 🔧 Altyapı var, eksik |
+| Solid3D tessellation (acadrust ACIS) | ✅ |
 | Boolean operasyonlar (UNION/SUBTRACT/INTERSECT) | ⬜ |
 | EXTRUDE / REVOLVE / SWEEP / LOFT | ⬜ |
 | 3D ARRAY | ⬜ |
@@ -302,13 +302,11 @@ Underlay (PDF/DWF/DGN)
 ## Öncelik Sırası (Bir Sonraki Adımlar)
 
 ### Yüksek Öncelik
-1. **Solid3D tessellation** tamamlama (ACIS → truck pipeline)
+1. **Çoklu Layout sekmeleri** arayüzü
 
 ### Orta Öncelik
-5. **Solid3D tessellation** tamamlama (ACIS → truck pipeline)
-6. **Çoklu Layout sekmeleri** arayüzü
-7. **Grid snap + Polar tracking**
-8. **XREF yönetimi**
+5. **Grid snap + Polar tracking**
+6. **XREF yönetimi**
 
 ### Düşük Öncelik
 11. Grid snap + Polar tracking

src/app/history.rs

@@ -36,8 +36,8 @@ impl H7CAD {
             .collect::<HashSet<_>>();
         self.tabs[i].scene.populate_hatches_from_document();
         self.tabs[i].scene.populate_images_from_document();
+        self.tabs[i].scene.populate_meshes_from_document();
         self.tabs[i].scene.clear_preview_wire();
-        self.tabs[i].scene.meshes.clear();
         self.tabs[i].scene.images.clear();
         self.tabs[i].active_cmd = None;
         self.tabs[i].snap_result = None;

src/app/update.rs

@@ -50,6 +50,7 @@ impl H7CAD {
                 self.tabs[i].scene.document = doc;
                 self.tabs[i].scene.populate_hatches_from_document();
                 self.tabs[i].scene.populate_images_from_document();
+                self.tabs[i].scene.populate_meshes_from_document();
                 self.tabs[i].scene.selected = std::collections::HashSet::new();
                 self.tabs[i].scene.preview_wires = vec![];
                 self.tabs[i].scene.current_layout = "Model".to_string();

src/scene/mod.rs

@@ -14,6 +14,7 @@ pub mod pipeline;
 pub mod properties;
 mod render;
 mod selection;
+pub mod solid3d_tess;
 pub mod tessellate;
 pub mod transform;
 pub mod truck_tess;
@@ -34,7 +35,7 @@ pub use wire_model::WireModel;
 
 use crate::command::EntityTransform;
 use acadrust::entities::{BoundaryEdge, BoundaryPath, Hatch as DxfHatch, PolylineEdge, Solid as DxfSolid};
-use acadrust::entities::{Block, BlockEnd, Insert as DxfInsert};
+use acadrust::entities::{Block, BlockEnd, Insert as DxfInsert, Solid3D};
 use acadrust::objects::ObjectType;
 use acadrust::types::Vector2;
 use acadrust::{CadDocument, EntityType, Handle, TableEntry};
@@ -1073,6 +1074,12 @@ impl Scene {
         } else {
             None
         };
+        let mesh_seed = if let EntityType::Solid3D(s3d) = &entity {
+            let color = self.render_style(&entity).0;
+            solid3d_tess::tessellate_solid3d(s3d, color)
+        } else {
+            None
+        };
 
         // Auto-create an ImageDefinition object for new RasterImage entities
         // that don't already reference one.
@@ -1113,6 +1120,9 @@ impl Scene {
             if let Some(model) = image_seed {
                 self.images.insert(handle, model);
             }
+            if let Some(model) = mesh_seed {
+                self.meshes.insert(handle, model);
+            }
         }
         handle
     }
@@ -1560,6 +1570,36 @@ impl Scene {
         }
     }
 
+    /// Tessellate all `Solid3D` entities in the current document into
+    /// GPU-ready `MeshModel`s and store them in `self.meshes`.
+    ///
+    /// Called after loading a document or after undo/redo so that every
+    /// `Solid3D` entity is represented in the mesh cache.
+    pub fn populate_meshes_from_document(&mut self) {
+        self.meshes.clear();
+        let entries: Vec<(Handle, Solid3D)> = self
+            .document
+            .entities()
+            .filter_map(|e| {
+                if let EntityType::Solid3D(s) = e {
+                    Some((s.common.handle, s.clone()))
+                } else {
+                    None
+                }
+            })
+            .collect();
+        for (handle, solid) in entries {
+            let color = if let Some(e) = self.document.get_entity(handle) {
+                tessellate::aci_to_rgba(&e.common().color)
+            } else {
+                [0.7, 0.7, 0.7, 1.0]
+            };
+            if let Some(model) = solid3d_tess::tessellate_solid3d(&solid, color) {
+                self.meshes.insert(handle, model);
+            }
+        }
+    }
+
     /// Build a solid-fill HatchModel for a DXF Solid entity.
     /// DXF SOLID corners are in "Z-order": p0-p1 top, p2-p3 bottom.
     /// Visual quad is p0→p1→p3→p2 (closed).
@@ -1687,6 +1727,7 @@ impl Scene {
             self.document.remove_entity(h);
             self.selected.remove(&h);
             self.hatches.remove(&h);
+            self.meshes.remove(&h);
         }
         // Remove erased handles from all groups; delete groups that become empty.
         let group_dict_handle = self.document.header.acad_group_dict_handle;

src/scene/solid3d_tess.rs

@@ -0,0 +1,542 @@
+// ACIS SAT → MeshModel tessellation for Solid3D (3DSOLID) entities.
+//
+// Strategy:
+//   • plane-surface faces  → collect coedge-loop polygon, fan-triangulate.
+//   • cone-surface faces   → sample a parametric grid (handles both cylinders
+//                            and true cones).
+//   • sphere-surface faces → sample a full UV grid.
+//   • torus-surface faces  → sample a full UV grid.
+//
+// All other surface types are silently skipped; partial results are still
+// returned so the solid renders with at least its planar faces.
+
+use std::collections::HashSet;
+use std::f64::consts::TAU;
+
+use acadrust::entities::acis::{
+    SatCoedge, SatConeSurface, SatDocument, SatEdge, SatFace, SatLoop, SatPlaneSurface, SatPoint,
+    SatPointer, SatSphereSurface, SatTorusSurface, SatVertex,
+};
+use acadrust::entities::acis::types::Sense;
+use acadrust::entities::Solid3D;
+
+use crate::scene::mesh_model::MeshModel;
+
+// Number of arc segments per full circle for curved surface sampling.
+const CIRC_SEGS: usize = 48;
+// Grid resolution for sphere / torus latitude / longitude subdivision.
+const GRID_U: usize = 32;
+const GRID_V: usize = 16;
+
+// ── Public entry point ────────────────────────────────────────────────────────
+
+/// Tessellate a `Solid3D` entity into a GPU-ready `MeshModel`.
+///
+/// Returns `None` when the entity has no parseable SAT data or produces no
+/// triangles (e.g. the solid uses only unsupported surface types).
+pub fn tessellate_solid3d(solid: &Solid3D, color: [f32; 4]) -> Option<MeshModel> {
+    let sat = solid.parse_sat()?;
+
+    let mut verts: Vec<[f32; 3]> = Vec::new();
+    let mut normals: Vec<[f32; 3]> = Vec::new();
+    let mut indices: Vec<u32> = Vec::new();
+
+    for face in sat.faces() {
+        let surf_ptr = face.surface();
+        let Some(surf_rec) = sat.resolve(surf_ptr) else {
+            continue;
+        };
+
+        match surf_rec.entity_type.as_str() {
+            "plane-surface" => {
+                if let Some(plane) = SatPlaneSurface::from_record(surf_rec) {
+                    tess_plane_face(&sat, &face, &plane, &mut verts, &mut normals, &mut indices);
+                }
+            }
+            "cone-surface" => {
+                if let Some(cone) = SatConeSurface::from_record(surf_rec) {
+                    tess_cone_face(&sat, &face, &cone, &mut verts, &mut normals, &mut indices);
+                }
+            }
+            "sphere-surface" => {
+                if let Some(sphere) = SatSphereSurface::from_record(surf_rec) {
+                    tess_sphere_face(&sphere, &mut verts, &mut normals, &mut indices);
+                }
+            }
+            "torus-surface" => {
+                if let Some(torus) = SatTorusSurface::from_record(surf_rec) {
+                    tess_torus_face(&torus, &mut verts, &mut normals, &mut indices);
+                }
+            }
+            _ => {}
+        }
+    }
+
+    if indices.is_empty() {
+        return None;
+    }
+
+    Some(MeshModel {
+        name: solid.common.handle.value().to_string(),
+        verts,
+        normals,
+        indices,
+        color,
+        selected: false,
+    })
+}
+
+// ── Topology helpers ──────────────────────────────────────────────────────────
+
+/// Walk a face's outer coedge loop and collect ordered 3-D vertex positions.
+///
+/// Returns an empty `Vec` when the loop topology is broken or has fewer than
+/// three distinct points.
+fn collect_face_polygon(sat: &SatDocument, face: &SatFace) -> Vec<[f64; 3]> {
+    let loop_ptr = face.first_loop();
+    let Some(loop_rec) = sat.resolve(loop_ptr) else {
+        return vec![];
+    };
+    let Some(sat_loop) = SatLoop::from_record(loop_rec) else {
+        return vec![];
+    };
+
+    let first_ptr = sat_loop.first_coedge();
+    let mut cur = first_ptr;
+    let mut pts: Vec<[f64; 3]> = Vec::new();
+    let mut visited: HashSet<i32> = HashSet::new();
+
+    loop {
+        if cur.is_null() {
+            break;
+        }
+        if visited.contains(&cur.0) {
+            break;
+        }
+        visited.insert(cur.0);
+
+        if let Some(ce_rec) = sat.resolve(cur) {
+            if let Some(coedge) = SatCoedge::from_record(ce_rec) {
+                // Pick the vertex that this coedge *starts from*, respecting sense.
+                if let Some(edge_rec) = sat.resolve(coedge.edge()) {
+                    if let Some(edge) = SatEdge::from_record(edge_rec) {
+                        let v_ptr = if matches!(coedge.sense(), Sense::Forward) {
+                            edge.start_vertex()
+                        } else {
+                            edge.end_vertex()
+                        };
+
+                        if let Some(pt) = resolve_point(sat, v_ptr) {
+                            pts.push(pt);
+                        }
+                    }
+                }
+
+                let next = coedge.next();
+                if next == first_ptr {
+                    break;
+                }
+                cur = next;
+                continue;
+            }
+        }
+        break;
+    }
+
+    pts
+}
+
+/// Resolve a vertex pointer all the way to its `[x, y, z]` coordinate.
+fn resolve_point(sat: &SatDocument, v_ptr: SatPointer) -> Option<[f64; 3]> {
+    let v_rec = sat.resolve(v_ptr)?;
+    let vertex = SatVertex::from_record(v_rec)?;
+    let pt_rec = sat.resolve(vertex.point())?;
+    let point = SatPoint::from_record(pt_rec)?;
+    let (x, y, z) = point.position();
+    Some([x, y, z])
+}
+
+// ── Mesh builder helpers ──────────────────────────────────────────────────────
+
+/// Append one quad (two triangles) to the mesh buffers.
+#[inline]
+fn push_quad(
+    verts: &mut Vec<[f32; 3]>,
+    normals: &mut Vec<[f32; 3]>,
+    indices: &mut Vec<u32>,
+    p: [[f64; 3]; 4],
+    n: [f64; 3],
+) {
+    let base = verts.len() as u32;
+    let nf = [n[0] as f32, n[1] as f32, n[2] as f32];
+    for &pt in &p {
+        verts.push([pt[0] as f32, pt[1] as f32, pt[2] as f32]);
+        normals.push(nf);
+    }
+    // Two CCW triangles: (0,1,2) and (0,2,3)
+    indices.extend_from_slice(&[base, base + 1, base + 2, base, base + 2, base + 3]);
+}
+
+// ── Planar face ───────────────────────────────────────────────────────────────
+
+fn tess_plane_face(
+    sat: &SatDocument,
+    face: &SatFace,
+    plane: &SatPlaneSurface,
+    verts: &mut Vec<[f32; 3]>,
+    normals: &mut Vec<[f32; 3]>,
+    indices: &mut Vec<u32>,
+) {
+    let poly = collect_face_polygon(sat, face);
+    if poly.len() < 3 {
+        return;
+    }
+
+    let (nx, ny, nz) = plane.normal();
+    // Flip normal outward if the face sense is reversed.
+    let (nx, ny, nz) = if matches!(face.sense(), Sense::Reversed) {
+        (-nx, -ny, -nz)
+    } else {
+        (nx, ny, nz)
+    };
+    let nf = [nx as f32, ny as f32, nz as f32];
+
+    let base = verts.len() as u32;
+    for &pt in &poly {
+        verts.push([pt[0] as f32, pt[1] as f32, pt[2] as f32]);
+        normals.push(nf);
+    }
+
+    // Fan triangulation from vertex 0.
+    let n = poly.len() as u32;
+    for i in 1..(n - 1) {
+        indices.extend_from_slice(&[base, base + i, base + i + 1]);
+    }
+}
+
+// ── Cone / cylinder face ──────────────────────────────────────────────────────
+
+fn tess_cone_face(
+    sat: &SatDocument,
+    face: &SatFace,
+    cone: &SatConeSurface,
+    verts: &mut Vec<[f32; 3]>,
+    normals: &mut Vec<[f32; 3]>,
+    indices: &mut Vec<u32>,
+) {
+    // Determine the height range and angular span from the boundary polygon.
+    let poly = collect_face_polygon(sat, face);
+
+    let (cx, cy, cz) = cone.center();
+    let (ax, ay, az) = cone.axis(); // axis direction (unit)
+    let (ux, uy, uz) = cone.major_axis(); // u=0 direction
+    let radius = cone.radius();
+    let sin_a = cone.sin_half_angle();
+    let cos_a = cone.cos_half_angle(); // ≈1 for cylinder, <1 for cone
+
+    // Build an orthonormal frame: axis_dir, u_dir, v_dir.
+    let axis = norm3([ax, ay, az]);
+    let u_dir = norm3([ux, uy, uz]);
+    let v_dir = cross3(axis, u_dir);
+
+    // Determine height and angle range from boundary vertices.
+    let (h_min, h_max, theta_min, theta_max, full_circle) =
+        angular_range(cx, cy, cz, axis, u_dir, v_dir, &poly);
+
+    let segs_u = CIRC_SEGS;
+    let segs_v = segs_u / 4; // height subdivisions
+
+    let theta_span = if full_circle { TAU } else { theta_max - theta_min };
+    let h_span = h_max - h_min;
+
+    if h_span.abs() < 1e-10 || theta_span.abs() < 1e-10 {
+        return;
+    }
+
+    for j in 0..segs_v {
+        let t0 = h_min + h_span * (j as f64 / segs_v as f64);
+        let t1 = h_min + h_span * ((j + 1) as f64 / segs_v as f64);
+
+        for i in 0..segs_u {
+            let a0 = theta_min + theta_span * (i as f64 / segs_u as f64);
+            let a1 = theta_min + theta_span * ((i + 1) as f64 / segs_u as f64);
+
+            // Cone radius at height t: r(t) = radius + t * sin_a / cos_a
+            let r0 = if cos_a.abs() > 1e-9 {
+                radius + t0 * sin_a / cos_a
+            } else {
+                radius
+            };
+            let r1 = if cos_a.abs() > 1e-9 {
+                radius + t1 * sin_a / cos_a
+            } else {
+                radius
+            };
+
+            let p = [
+                cone_pt(cx, cy, cz, axis, u_dir, v_dir, r0, a0, t0),
+                cone_pt(cx, cy, cz, axis, u_dir, v_dir, r1, a0, t1),
+                cone_pt(cx, cy, cz, axis, u_dir, v_dir, r1, a1, t1),
+                cone_pt(cx, cy, cz, axis, u_dir, v_dir, r0, a1, t0),
+            ];
+
+            // Outward normal: perpendicular to axis in the radial direction,
+            // tilted by the cone half-angle.
+            let mid_a = (a0 + a1) * 0.5;
+            let rad_dir = [
+                u_dir[0] * mid_a.cos() + v_dir[0] * mid_a.sin(),
+                u_dir[1] * mid_a.cos() + v_dir[1] * mid_a.sin(),
+                u_dir[2] * mid_a.cos() + v_dir[2] * mid_a.sin(),
+            ];
+            let n = norm3([
+                rad_dir[0] * cos_a - axis[0] * sin_a,
+                rad_dir[1] * cos_a - axis[1] * sin_a,
+                rad_dir[2] * cos_a - axis[2] * sin_a,
+            ]);
+
+            push_quad(verts, normals, indices, p, n);
+        }
+    }
+}
+
+/// Compute a point on a cone/cylinder surface.
+#[inline]
+fn cone_pt(
+    cx: f64, cy: f64, cz: f64,
+    axis: [f64; 3],
+    u_dir: [f64; 3],
+    v_dir: [f64; 3],
+    r: f64,
+    theta: f64,
+    h: f64,
+) -> [f64; 3] {
+    [
+        cx + r * (u_dir[0] * theta.cos() + v_dir[0] * theta.sin()) + h * axis[0],
+        cy + r * (u_dir[1] * theta.cos() + v_dir[1] * theta.sin()) + h * axis[1],
+        cz + r * (u_dir[2] * theta.cos() + v_dir[2] * theta.sin()) + h * axis[2],
+    ]
+}
+
+/// Determine the height range and angular range of a curved face's boundary.
+///
+/// Returns `(h_min, h_max, theta_min, theta_max, full_circle)`.
+/// `full_circle` is true when there are no boundary vertices (e.g. a sphere or
+/// a cylinder with no seam edge).
+fn angular_range(
+    cx: f64, cy: f64, cz: f64,
+    axis: [f64; 3],
+    u_dir: [f64; 3],
+    v_dir: [f64; 3],
+    poly: &[[f64; 3]],
+) -> (f64, f64, f64, f64, bool) {
+    if poly.is_empty() {
+        return (0.0, 0.0, 0.0, TAU, true);
+    }
+
+    let mut h_min = f64::MAX;
+    let mut h_max = f64::MIN;
+    let mut angles: Vec<f64> = Vec::new();
+
+    for &pt in poly {
+        let dx = pt[0] - cx;
+        let dy = pt[1] - cy;
+        let dz = pt[2] - cz;
+        let h = dot3([dx, dy, dz], axis);
+        h_min = h_min.min(h);
+        h_max = h_max.max(h);
+        let rv = dot3([dx, dy, dz], v_dir);
+        // Project onto the plane perpendicular to the axis.
+        let ru = dx * u_dir[0] + dy * u_dir[1] + dz * u_dir[2]
+            - h * (axis[0] * u_dir[0] + axis[1] * u_dir[1] + axis[2] * u_dir[2]);
+        angles.push(rv.atan2(ru));
+    }
+
+    // Normalise angles to a contiguous range.
+    angles.sort_by(|a, b| a.partial_cmp(b).unwrap());
+    let theta_min = *angles.first().unwrap();
+    let theta_max = *angles.last().unwrap();
+
+    // If the angular span is almost 2π, treat as full circle.
+    let full = (theta_max - theta_min) > TAU * 0.95;
+
+    (h_min, h_max, theta_min, theta_max, full)
+}
+
+// ── Sphere face ───────────────────────────────────────────────────────────────
+
+fn tess_sphere_face(
+    sphere: &SatSphereSurface,
+    verts: &mut Vec<[f32; 3]>,
+    normals: &mut Vec<[f32; 3]>,
+    indices: &mut Vec<u32>,
+) {
+    let (cx, cy, cz) = sphere.center();
+    let r = sphere.radius();
+    let (px, py, pz) = sphere.pole(); // north-pole direction
+    let pole = norm3([px, py, pz]);
+    let (ux, uy, uz) = sphere.u_direction();
+    let u_dir = norm3([ux, uy, uz]);
+    let v_dir = cross3(pole, u_dir);
+
+    let nu = GRID_U;
+    let nv = GRID_V;
+
+    for j in 0..nv {
+        let phi0 = std::f64::consts::PI * (j as f64 / nv as f64);       // 0..π
+        let phi1 = std::f64::consts::PI * ((j + 1) as f64 / nv as f64);
+
+        for i in 0..nu {
+            let theta0 = TAU * (i as f64 / nu as f64);
+            let theta1 = TAU * ((i + 1) as f64 / nu as f64);
+
+            let n00 = sphere_dir(pole, u_dir, v_dir, theta0, phi0);
+            let n10 = sphere_dir(pole, u_dir, v_dir, theta0, phi1);
+            let n11 = sphere_dir(pole, u_dir, v_dir, theta1, phi1);
+            let n01 = sphere_dir(pole, u_dir, v_dir, theta1, phi0);
+
+            let p = [
+                [cx + r * n00[0], cy + r * n00[1], cz + r * n00[2]],
+                [cx + r * n10[0], cy + r * n10[1], cz + r * n10[2]],
+                [cx + r * n11[0], cy + r * n11[1], cz + r * n11[2]],
+                [cx + r * n01[0], cy + r * n01[1], cz + r * n01[2]],
+            ];
+
+            // Average outward normal for the quad.
+            let nav = norm3([
+                n00[0] + n10[0] + n11[0] + n01[0],
+                n00[1] + n10[1] + n11[1] + n01[1],
+                n00[2] + n10[2] + n11[2] + n01[2],
+            ]);
+
+            push_quad(verts, normals, indices, p, nav);
+        }
+    }
+}
+
+#[inline]
+fn sphere_dir(
+    pole: [f64; 3],
+    u_dir: [f64; 3],
+    v_dir: [f64; 3],
+    theta: f64,
+    phi: f64,
+) -> [f64; 3] {
+    let sin_phi = phi.sin();
+    let cos_phi = phi.cos();
+    let cos_theta = theta.cos();
+    let sin_theta = theta.sin();
+    // pole × cos_phi + (u*cos_theta + v*sin_theta) × sin_phi
+    [
+        pole[0] * cos_phi + (u_dir[0] * cos_theta + v_dir[0] * sin_theta) * sin_phi,
+        pole[1] * cos_phi + (u_dir[1] * cos_theta + v_dir[1] * sin_theta) * sin_phi,
+        pole[2] * cos_phi + (u_dir[2] * cos_theta + v_dir[2] * sin_theta) * sin_phi,
+    ]
+}
+
+// ── Torus face ────────────────────────────────────────────────────────────────
+
+fn tess_torus_face(
+    torus: &SatTorusSurface,
+    verts: &mut Vec<[f32; 3]>,
+    normals: &mut Vec<[f32; 3]>,
+    indices: &mut Vec<u32>,
+) {
+    let (cx, cy, cz) = torus.center();
+    let (nx, ny, nz) = torus.normal();
+    let axis = norm3([nx, ny, nz]); // revolution axis
+    let (ux, uy, uz) = torus.u_direction();
+    let u_dir = norm3([ux, uy, uz]);
+    let v_dir = cross3(axis, u_dir);
+    let major_r = torus.major_radius();
+    let minor_r = torus.minor_radius();
+
+    let nu = GRID_U; // around the tube
+    let nv = GRID_V; // around the torus
+
+    for j in 0..nv {
+        let phi0 = TAU * (j as f64 / nv as f64);
+        let phi1 = TAU * ((j + 1) as f64 / nv as f64);
+
+        for i in 0..nu {
+            let theta0 = TAU * (i as f64 / nu as f64);
+            let theta1 = TAU * ((i + 1) as f64 / nu as f64);
+
+            let p = [
+                torus_pt(cx, cy, cz, axis, u_dir, v_dir, major_r, minor_r, theta0, phi0),
+                torus_pt(cx, cy, cz, axis, u_dir, v_dir, major_r, minor_r, theta0, phi1),
+                torus_pt(cx, cy, cz, axis, u_dir, v_dir, major_r, minor_r, theta1, phi1),
+                torus_pt(cx, cy, cz, axis, u_dir, v_dir, major_r, minor_r, theta1, phi0),
+            ];
+
+            // Outward tube normal.
+            let mid_phi = (phi0 + phi1) * 0.5;
+            let mid_theta = (theta0 + theta1) * 0.5;
+            // Direction from tube center to surface point.
+            let radial = [
+                u_dir[0] * mid_phi.cos() + v_dir[0] * mid_phi.sin(),
+                u_dir[1] * mid_phi.cos() + v_dir[1] * mid_phi.sin(),
+                u_dir[2] * mid_phi.cos() + v_dir[2] * mid_phi.sin(),
+            ];
+            let n = norm3([
+                radial[0] * mid_theta.cos() + axis[0] * mid_theta.sin(),
+                radial[1] * mid_theta.cos() + axis[1] * mid_theta.sin(),
+                radial[2] * mid_theta.cos() + axis[2] * mid_theta.sin(),
+            ]);
+
+            push_quad(verts, normals, indices, p, n);
+        }
+    }
+}
+
+#[inline]
+fn torus_pt(
+    cx: f64, cy: f64, cz: f64,
+    axis: [f64; 3],
+    u_dir: [f64; 3],
+    v_dir: [f64; 3],
+    major_r: f64,
+    minor_r: f64,
+    theta: f64,   // tube angle
+    phi: f64,     // revolution angle
+) -> [f64; 3] {
+    // Ring center at angle phi.
+    let ring = [
+        cx + major_r * (u_dir[0] * phi.cos() + v_dir[0] * phi.sin()),
+        cy + major_r * (u_dir[1] * phi.cos() + v_dir[1] * phi.sin()),
+        cz + major_r * (u_dir[2] * phi.cos() + v_dir[2] * phi.sin()),
+    ];
+    // Radial direction from torus axis to ring center.
+    let radial = norm3([ring[0] - cx, ring[1] - cy, ring[2] - cz]);
+    // Point on tube.
+    [
+        ring[0] + minor_r * (radial[0] * theta.cos() + axis[0] * theta.sin()),
+        ring[1] + minor_r * (radial[1] * theta.cos() + axis[1] * theta.sin()),
+        ring[2] + minor_r * (radial[2] * theta.cos() + axis[2] * theta.sin()),
+    ]
+}
+
+// ── Math helpers ──────────────────────────────────────────────────────────────
+
+#[inline]
+fn dot3(a: [f64; 3], b: [f64; 3]) -> f64 {
+    a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
+}
+
+#[inline]
+fn cross3(a: [f64; 3], b: [f64; 3]) -> [f64; 3] {
+    [
+        a[1] * b[2] - a[2] * b[1],
+        a[2] * b[0] - a[0] * b[2],
+        a[0] * b[1] - a[1] * b[0],
+    ]
+}
+
+#[inline]
+fn norm3(v: [f64; 3]) -> [f64; 3] {
+    let len = (v[0] * v[0] + v[1] * v[1] + v[2] * v[2]).sqrt();
+    if len < 1e-12 {
+        [0.0, 0.0, 1.0]
+    } else {
+        [v[0] / len, v[1] / len, v[2] / len]
+    }
+}