Crash course on CAD data. Part 3.

Precise geometry and tessellation. B-Reps and meshes.

As discussed in part 2, B-Rep (Boundary Representation) and polygonal (mesh) are two key types of representations used in CAD. Let’s consider each one in more details. The former is used to describe precise (exact) geometry whereas the latter — approximated or tessellated one.

  • Solid body — represents a lump of material in 3D space. Examples of a solid body can be a bolt, a piston, a gear or alike. Something which is manufactured using machining (milling, drilling), forging, casting and other processes.
  • Sheet body — a (relatively) thin surface-like body in 3D space. Think of a car body element or a ship hull. Something which is manufactured using molding or bending.
  • Wireframe body — a wire-like body in 3D space. Mainly used as simplification of a body in real-world (e.g. electrical wires).
  • Acorn body — basically a single vertex in 3D space. Again, rather simplification of a a real-world body when precise shape is not important.
From left to right: solid, sheet, wireframe bodies
  • 2D sketching followed by extrusion and rotation
  • Using solid primitives (such as box, sphere, torus, cone, cylinder)
  • Boolean operations (cut, fuse, common)
  • Fillets and chamfers
  • Offsetting and hollowing
  • Sweeping
  • Lofting
  • Extrusions and rotations (extruding/rotating an edge will give you a face; a wire will give you a shell)
  • Offsetting
  • Sweeping and lofting

Gallery

Sketching
Filleting
Hollowing
Sweeping
Lofting
  • Dealing with B-Rep is compute-intensive (e.g. computing a point on a B-Spline surface can take 100x-1000x machine operations comparing to computing a point on a planar triangle).
  • Precise B-Rep definition is not always available. For instance, in reverse-engineering workflows such as 3D scanning (e.g. in dental industry, digital twins / equipment inspection and so on).
Meshes are used in CAE, applying Finite-Element Methods (FEM) in particular.
Siemens Solid Edge ST10 and NX11 feature Convergent Modeling
(image from design-engineering.com)
From left to right: 1700 triangles, 4300 triangles, 6500 triangles

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