math2dcomputational-geometry
Calculating paralel lines coordinates with arbitrary angle
We have 2 parallel lines in the 2D space separated by 5 units:
Black - 0,0 -> 20,0
Red - 0,5 -> 20,5
The angle is 0 degrees. We always know the coordinates of the black line and the angle in degrees. The coordinates of the red line needs to be calculated given arbitrary angle.
Is there any formula for such calculation?
Solution
Find direction vector for the first line
dx = x2 - x1
dy = y2 - y1
Normalize it
len = sqrt(dx*dx + dy*dy)
dx = dx / len
dy = dy / len
Get perpendicular vector (note it is "right" normal, for "left" one change signs)
nx = dy
ny = -dx
Get parallel segment ends with d = parallel distance
x3 = x1 + d * nx
y3 = y1 + d * ny
x4 = x2 + d * nx
y4 = y2 + d * ny
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