Why BIM software runs on maths

Open a model in any BIM tool and you see walls, doors, slabs and pipes. The file does not store pictures of them. A straight wall is stored as little more than two points (its location line), a thickness, a height and a few settings. Everything else you see is calculated from those numbers, again and again, every time something changes.

Drag the two ends of the wall below. Every value in the panel, including the four corners of the outline, is computed from just the two points and the thickness.

The corners come from a small piece of vector maths: take the wall’s direction, turn it 90° to get the perpendicular, and step half the thickness to each side. You will write exactly that code in the Vectors module. For now, notice how much the software derives from so little data.

What a BIM tool computes all day

A wall as data

Here is the same idea in C#. A wall is two points, a thickness and a height. Its length, face area and volume are not stored; they are computed.

1using Pt = (double X, double Y);2 3Pt start = (0, 0);4Pt end = (6, 8);5double thickness = 0.2, height = 3.0;6 7double dx = end.X - start.X, dy = end.Y - start.Y;8double length = Math.Sqrt(dx * dx + dy * dy);9 10Console.WriteLine($"Length: {length} m");11Console.WriteLine($"Face area: {length * height} square metres");12Console.WriteLine($"Volume: {length * thickness * height} cubic metres");

Length: 10 m
Face area: 30 square metres
Volume: 6 cubic metres

Math.Sqrt(dx * dx + dy * dy) is Pythagoras: the wall runs 6 m in X and 8 m in Y, so its length is √(36 + 64) = 10 m. If the model changes either end, the length, area and volume all follow automatically. That is the core idea of parametric modelling: store the few numbers that define an element and compute the rest.

Why learn it if the software already does it?

• Automation: as soon as you write a plug-in, a Dynamo or Grasshopper script, or an IFC tool, the software stops doing the geometry for you. You get points and vectors and have to work out the rest.
• Debugging: “the wall join is off by half a millimetre” or “the family rotates the wrong way when mirrored” are maths bugs. Knowing the maths turns them from mysteries into five-minute fixes.
• Performance: a clash check over a large model is millions of geometric tests. Knowing which test is cheap (a box overlap) and which is expensive (a full solid intersection) is the difference between seconds and hours.
• Interviews: BIM and AEC software roles routinely ask about vectors, transforms and intersections.

How this course is organised

1using Pt = (double X, double Y);2 3static double Length(Pt a, Pt b)4{5    double dx = b.X - a.X, dy = b.Y - a.Y;6    return Math.Sqrt(dx * dx + dy * dy);7}8 9static double WallVolume(Pt a, Pt b, double thickness, double height)10    => Length(a, b) * thickness * height;11 12Pt a = (2, 1), b = (2, 7);13Console.WriteLine($"Length: {Length(a, b):F2} m");14Console.WriteLine($"Volume: {WallVolume(a, b, 0.3, 2.7):F2} cubic metres");

Length: 6.00 m
Volume: 4.86 cubic metres