HomeOperatorsLine/Parlel,L,D

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

SelectorUse When
YLargeHorizontal reference line — picks the upper parallel
YSmallHorizontal reference line — picks the lower parallel
XLargeVertical reference line — picks the right parallel
XSmallVertical 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.