Point/Intof,L,A
Line / Arc Intersection
Creates a point at the intersection of a line and an arc. Direction selector required — two solutions may exist.
What It Does
The Point/Intof,L,A operator creates a point at the intersection of a line and an arc. Unlike a full circle, an arc has defined start and end angles — only intersections within the arc sweep are valid.
Selector required: Two intersections may exist. The direction selector specifies which one to create.
Syntax
Point/XLarge|XSmall|YLarge|YSmall, Intof, L, A
Quick Input
L: [line reference]
A: [arc reference]
Z: 0
Dir: ○ XL ○ XS ● YL ○ YS
Direction Selector
| Selector | Picks |
|---|---|
XLarge | Intersection with largest X coordinate |
XSmall | Intersection with smallest X coordinate |
YLarge | Intersection with largest Y coordinate |
YSmall | Intersection with smallest Y coordinate |
Worked Examples
Setup:
L0 = Horizontal line at Y=10
A0 = Arc: centre (0,0), r=20, 0° to 180° CCW
Point/XLarge, Intof, L0, A0
→ P0 = (17.321, 10) ← right intersection
Point/XSmall, Intof, L0, A0
→ P1 = (-17.321, 10) ← left intersection
Analytic Rule
Line equation: ax + by + c = 0
Circle equation: (x-cx)² + (y-cy)² = r²
Substitute line into circle → quadratic → two roots.
Filter roots: only keep points within arc sweep angles.
Direction selector picks which valid root to use.
Result: Exact analytic coordinates.
FAQ
What if the line intersects the full circle but not the arc?
If the intersection points fall outside the arc sweep angles, XyzPilot returns an error. The line does not intersect the arc within its defined extent.
How is this different from Point/Intof,L,C?
Point/Intof,L,C works with full circles. Point/Intof,L,A respects the arc start and end angles — only intersections within the arc sweep are valid results.