Modeling

Shift from polygon meshes to precise boundary representations (B-reps).
Although both meshes and B-reps use vertices, edges, and faces, they describe geometry in completely different ways.


Meshes approximate shape using flat pieces:

  • Vertices: points in 3D space
  • Edges: straight line segments
  • Faces: flat polygons (usually triangles)

A mesh sphere, cylinder, or fillet is always a faceted approximation (represented using many small flat faces).


B-reps store the exact analytic geometry of a solid:

  • Vertices: points in 3D space
  • Edges: mathematical curves (lines, arcs, splines, NURBS)
  • Faces: analytic surfaces (planes, cylinders, spheres, NURBS patches)
  • Solids: closed collections of faces forming true watertight bodies

With B-reps, a circle is a true circle, a sphere is a perfect sphere, and fillets/blends are smooth by definition—not approximated by polygons.

This is the representation used by major CAD kernels:
Parasolid (SolidWorks, Onshape, NX), ACIS/ShapeManager (Inventor), CGM (CATIA), and others.



Why use B-reps?

B-reps (Boundary Representations) are used in CAD because they preserve the exact geometry of a solid.
Unlike polygon meshes—which approximate surfaces with many small flat facets—B-reps retain the true analytic curves and surfaces that define engineered parts.

Advantages of B-reps:

  • Exact mathematical curves and surfaces
    Lines, arcs, circles, splines, NURBS, cylinders, spheres—no approximation.

  • Dimension-driven modeling
    Features can be defined by precise measurements (radius, thickness, angle, sweep distance).

  • Smooth surfaces by definition
    Fillets, blends, and revolved surfaces are perfectly smooth, not faceted.

  • Export to neutral CAD formats (STEP, IGES)
    These formats require analytic geometry; meshes cannot represent them accurately.

  • Clean conversion to meshes for rendering or simulation
    Tessellated meshes inherit exact topology from the B-rep, producing cleaner normals and fewer artifacts.

Truck includes a complete B-rep system that you will use throughout Chapter 3.

Project layout for Chapter 3

Keep your Chapter 2 mesh crate as-is, and add a sibling B-rep crate. Target workspace layout:

truck-workspace/
├─ truck_meshes/   # Chapter 2 mesh crate (unchanged)
└─ truck_brep/     # Chapter 3 B-rep crate you’ll create below

Add a sibling crate dedicated to B-rep modeling

  • Create a sibling crate named truck_brep in the parent directory that already contains truck_meshes:
# run from the parent dir that already has truck_meshes/
cargo new --lib truck_brep
mkdir -p truck_brep/examples truck_brep/output
  • src/lib.rs holds the shared OBJ/STEP helpers and exports the per-shape modules.
  • Per-shape modules (cube.rs, torus.rs, cylinder.rs, bottle.rs) sit directly in src/ next to lib.rs.
  • examples/ holds runnable samples that call into truck_brep::*.
  • output/ collects OBJ/STEP exports so they do not clutter source control.
truck_brep/
├─ Cargo.toml      # add truck-modeling, truck-meshalgo, truck-stepio deps
├─ src/
│  ├─ lib.rs       # helpers + re-exports
│  └─              # add torus.rs, cylinder.rs, bottle.rs as you go
│ 
├─ examples/
│  └─              # calls truck_brep::cube(), etc.
└─ output/         # generated OBJ/STEP files

Update truck_brep/Cargo.toml

Add the Truck crates (match the versions you used in truck_meshes so everything stays in sync):

[dependencies]
# modeling API
truck-modeling = "0.6.0"
# meshing modeled shape
truck-meshalgo = "0.4.0"
# output STEP
truck-stepio = "0.3.0"
# topology helpers (compression)
truck-topology = "0.6.0"

Tessellate B-reps to Meshes

To render or export, B-rep solids must be tessellated into polygon meshes.
Truck’s meshing layer truck-meshalgo provides core traits for this process:

  • MeshableShape
    Converts an analytic B-rep shape into a polygon mesh using default tessellation settings.

  • RobustMeshableShape
    A more defensive version of MeshableShape that adds numerical tolerances and safety checks for difficult or complex shapes (CSG trees, tiny edges, near-degenerate surfaces).

  • MeshedShape
    Represents the final tessellated result — a PolygonMesh paired with the metadata used during tessellation.

Truck also includes a tessellation demo, examples/tessellate-shape, which converts analytic shapes and full CSG trees into OBJ meshes.

Typical workflow:

  1. Build or finish the analytic (B-rep) solid.
  2. Tessellate it into a polygon mesh.
  3. Run mesh filters (normals, smoothing, optimization).
  4. Export or view the cleaned mesh in your preferred viewer.

This ensures the final mesh accurately reflects the B-rep geometry while remaining efficient for rendering.

What you will learn in Chapter 3

  • 3.1 Cube: build an exact cube; see how B-rep solids are assembled.
  • 3.2 Torus: work with rotational sweeps to create curved surfaces.
  • 3.3 Cylinder: combine rotational, planar, and translational sweeps for a solid.
  • 3.4 Higher Level Modeling: model with NURBS; build solids from exact curved surfaces instead of approximations.

By the end of this chapter, you’ll understand how Truck represents CAD-quality shapes—far more precise than meshes.

Reference: full truck_brep snapshot

Directory tree:

truck_brep/
├─ Cargo.toml      # add truck-modeling, truck-meshalgo, truck-stepio deps
├─ src/
│  ├─ lib.rs       # helpers + re-exports
│  └─              # add torus.rs, cylinder.rs, bottle.rs as you go
│ 
├─ examples/
│  └─              # calls truck_brep::cube(), etc.
└─ output/         # generated OBJ/STEP files

Cargo.toml dependencies:

[dependencies]
# modeling API
truck-modeling = "0.6.0"
# meshing modeled shape
truck-meshalgo = "0.4.0"
# output STEP
truck-stepio = "0.3.0"
# topology helpers (compression)
truck-topology = "0.6.0"