Line/Parlel,L,D
Parallel Line at Distance
Creates a line parallel to an existing line at a specified perpendicular distance D. Direction selector required.
What It Does
The Line/Parlel,L,D operator creates a line parallel to an existing line at a specified perpendicular distance D. Two solutions exist — one on each side of the reference line. The direction selector specifies which side.
Syntax
Line/XLarge|XSmall|YLarge|YSmall, Parlel, L, D
Quick Input
L: [reference line]
D: [perpendicular distance]
Dir: ○ XL ○ XS ● YL ○ YS
Direction Selector
| Selector | Use When |
|---|---|
YLarge | Horizontal reference line — picks the upper parallel |
YSmall | Horizontal reference line — picks the lower parallel |
XLarge | Vertical reference line — picks the right parallel |
XSmall | Vertical reference line — picks the left parallel |
Use the selector on the axis where the two solutions differ. For a horizontal line, use YLarge/YSmall. For a vertical line, use XLarge/XSmall.
Worked Examples
Setup:
L0 = Horizontal line at Y=0
Line/YLarge, Parlel, L0, D=25
→ L1: Y=+25 (above L0)
Line/YSmall, Parlel, L0, D=25
→ L2: Y=-25 (below L0)
Setup:
L1 = Vertical line at X=50
Line/XLarge, Parlel, L1, D=20
→ L3: X=70 (right of L1)
Line/XSmall, Parlel, L1, D=20
→ L4: X=30 (left of L1)
Analytic Rule
Offset line parallel to L at perpendicular distance D.
Two solutions: one each side of L.
Direction selector picks which offset to use.
For line ax + by + c = 0:
Offset lines: ax + by + (c ± D*|n|) = 0
where |n| = sqrt(a² + b²)
Result: Exact analytic parallel line.
FAQ
What is the difference between Line/Parlel,L,D and Line/P,Parlel,L?
Line/Parlel,L,D creates a parallel at a fixed distance — selector required. Line/P,Parlel,L creates a parallel through a specific point — no selector needed because the point uniquely determines the line.
Can D be zero?
D=0 creates a line coincident with the reference line. This is valid but rarely useful.