Fundamentals
Intersection is the basis of descriptive geometry. We always look for common elements (points or lines).
1. Line–plane intersection (general method)
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Setup
We want to find the point I where line r crosses plane Alpha.
2. Plane–plane intersection
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Concept
The intersection is a line defined by two points: V (where the vertical traces meet) and H (where the horizontal traces meet).
3. Intersection of 3 planes (A, B, C)
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Setup
We have 3 planes defined by their traces. We look for the common point P. It is the intersection of the 3 surfaces.
Special cases
- If the matching traces are parallel (α₁ ∥ β₁ and α₂ ∥ β₂), the planes are parallel and there is no intersection.
- If only the vertical traces meet (α₁ ∥ β₁), the intersection is a line parallel to the PH.
- If only the horizontal traces meet (α₂ ∥ β₂), the intersection is a line parallel to the PV.
- If the line is parallel to the plane there is no intersection point: check it with an auxiliary line of the plane.