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BIM Math

BIM Math

The maths behind 3D and BIM software: coordinates, vectors, lines, planes, transforms, rotations and solids, up to clash detection and georeferencing. Every idea drawn interactively and coded in C#.

0 of 44 lessons completed · 44 topics in the full course Start learning: Why BIM software runs on maths

Beginner

1. Foundations

5 topics

Why BIM software runs on mathsLesson
Coordinate systems: 2D, 3D, right-handed, Z-upLesson
Units, precision and toleranceLesson
Angles: degrees, radians and Atan2Lesson
Trigonometry on site: slopes, pitches, rise and runLesson

Beginner

2. Vectors

6 topics

Points vs vectorsLesson
Adding, subtracting and scaling vectorsLesson
Length, distance and unit vectorsLesson
The dot product: angles, projection, facingLesson
The cross product: normals, area, left or rightLesson
Building a Vec3 struct in C#Lesson

Intermediate

3. Lines and curves

6 topics

Lines, rays and segments in parametric formLesson
Closest point and distance to a line or segmentLesson
Line intersections in 2D, and skew lines in 3DLesson
Circles and arcs: 3-point arcs and tangentsLesson
Polylines: length, offsetting and filletsLesson
Bézier curves and splinesLesson

Intermediate

4. Planes and polygons

6 topics

Planes: point and normal, ax + by + cz + dLesson
Point-to-plane distance and projectionLesson
Line–plane and plane–plane intersectionLesson
Polygon area, normal and windingLesson
Point in polygon and triangulationLesson
Polygon offsets and boolean operationsLesson

Advanced

5. Matrices and transforms

6 topics

Matrices and matrix multiplicationLesson
Rotation in 2D, 3D and about any axisLesson
Homogeneous coordinates and 4×4 transformsLesson
Composing transforms: order and inversesLesson
Local vs world: families, instances and nested placementLesson
Mirroring and handednessLesson

Advanced

6. Rotations in depth

3 topics

Euler angles and gimbal lockLesson
Quaternions without fearLesson
Interpolating rotations: lerp vs slerpLesson

Advanced

7. 3D geometry and solids

6 topics

Bounding boxes: AABB and OBBLesson
Meshes: vertices, faces and normalsLesson
Ray–triangle intersectionLesson
Clash detection and the separating-axis theoremLesson
Volumes and surface areas of solidsLesson
Sections: cutting a mesh with a planeLesson

Master

8. Master level

6 topics

Robust geometry: epsilons, snapping and exact predicatesLesson
Survey points, true north and georeferencingLesson
Cameras: view matrices, perspective and section boxesLesson
B-rep and NURBS: how BIM kernels store solidsLesson
Spatial queries at scaleLesson
Putting it together: a mini room-and-wall geometry engineLesson