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Advanced - Geometry · 4:52
Points & Vectors in C++: Dot and Cross Products
Geometry code gets short once a point is treated as a vector: one pt struct with long long coordinates and two products carry the whole chapter. The dot product measures how much two vectors agree, its sign tells acute from right from obtuse, and the points with a fixed dot product against n form a line (a plane in 3D). The cross product is a signed area (a signed volume as the triple product), it tells which side one vector lies on, and two lines meet where a cross product drops to zero.
You will learn
- Write a reusable pt struct with +, -, scaling, dot and cross in long long, and explain why 32-bit int overflows
- Use the sign of the dot product to classify angles and describe a line (or a plane in 3D) as the set r · n = C
- Interpret the 2D cross product as a signed parallelogram area and the 3D triple product as a signed volume
- Intersect two lines with t = ((a2 - a1) × d2) / (d1 × d2) and compute angles robustly with atan2(cross, dot)