Cad/Cam maths required

Question

I am a C++ programmer who is trying to apply for some work. I have recently been invited for an interview at a well known CAD/CAM developer in the UK. I am nervous because I have no idea what kinds of questions they will ask, my math isn't that great as I mostly deal with linear algebra for video game programming.

Can someone who works in that sector please outline what kind of skills are needed? from maths to rendering api.

Thanks

Answer 1

Linear algebra is definitely a good start. Also, you are probably familiar with polygon meshes, that's good too. If I would interview for a CAD job I would read up on other geometry representations. In particular

• NURBS and
• Constructive Solid Geometry (CSG).

I don't think rendering APIs are too important here, but you should have a solid understanding of how ray tracing works and how to use the just mentioned surface types in both a ray tracer and in a rasterization-based pipeline.

Answer 2

Just list out for someone....

Common for CAD and CAM

• vector calculus
  • dot product / cross product / magnitude / normalization / angle calculation
• linear algebra
  • translating / rotating / scaling
• 3D geometry
  • Geometric tools: https://www.geometrictools.com/Source/Mathematics.html
    • curve / surface data structure representation
    • projection / intersection
  • NURBS
    • as mentioned above
  • triangulation
    • Delaunay triangulation
      • http://web.mit.edu/alexmv/Public/6.850-lectures/lecture09.pdf
      • CGAL has the implementation

CAD

important: 3D shape representation and operation for solid shape

• CSG
  • as mentioned above
• BREP (Boundary Representation)
  • another type of solid shape representation
  • OpenCASCADE tutorial: https://www.opencascade.com/doc/occt-7.3.0/overview/html/occt__tutorial.html
• file format
  • neutral file format for data exchange between CAD/CAMs
    • STEP / IGES
      • OpenCASCADe can handle them to read / write with
• FreeCAD is useful to use OpenCASCADE. It has python scripting environment with OpenCASCADE binding.
  • https://www.freecadweb.org/
  • https://wiki.freecadweb.org/Python_scripting_tutorial

CAM

important: mesh operation algorithm

• foundation of tool path generation
  • shape offset operation(minkowski sum)
    • http://acg.cs.tau.ac.il/courses/algorithmic-robotics/spring-2011/slides/ms.pdf
    • CGAL has the implementation
• collision detection
  • to check if workpiece and parts of machining center have invalid collision
    • Narrow-phase / Broad-phase: https://thegeneralsolution.wordpress.com/2011/12/12/collision-detection-broad-phase-vs-narrow-phase/
    • Bounding volume: https://en.wikipedia.org/wiki/Bounding_volume
    • Uniform grid, KD-tree, Octree, BVH, etc
  • video game development resource is also useful for this category