Point/Intof,L,L
Line / Line Intersection
Creates a point at the intersection of two lines. No selector needed — two non-parallel lines intersect at exactly one point.
What It Does
The Point/Intof,L,L operator creates a point at the exact intersection of two lines. Two non-parallel lines intersect at exactly one point — no selector is required.
No selector needed: Unlike line/circle or circle/circle intersections, two lines produce at most one intersection point. The result is uniquely determined.
Syntax
Point/Intof, L1, L2
Quick Input
L: [first line reference]
L2: [second line reference]
Direction Selector
No direction selector is required. The result is uniquely determined by the input geometry.
Worked Examples
Example 1 — Perpendicular lines:
L0 = Horizontal line at Y=50
L1 = Vertical line at X=75
Point/Intof, L0, L1
→ P15 = (75, 50)
Example 2 — Angled lines:
L0 = Line: y = 2x + 10
L1 = Line: y = -x + 70
Point/Intof, L0, L1
→ P16 = (20, 50)
Example 3 — Diagonal lines:
L0 = Line at 45° through origin
L1 = Line at 135° through (100, 0)
Point/Intof, L0, L1
→ P17 = (50, 50)
Analytic Rule
Two line equations:
L1: a1x + b1y + c1 = 0
L2: a2x + b2y + c2 = 0
Solving simultaneously:
x = (b1*c2 - b2*c1) / (a1*b2 - a2*b1)
y = (a2*c1 - a1*c2) / (a1*b2 - a2*b1)
Result: Exact analytic intersection. No iteration.
FAQ
What if the lines are parallel?
Parallel lines do not intersect. XyzPilot returns an error if the lines are parallel (determinant = 0). Check that the lines are not parallel before using this operator.
What if the lines are the same line?
Identical lines have infinite intersections. XyzPilot returns an error — the operation is geometrically undefined.