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I have a line L in the Euclidean plane and a scalar D, and I want to find the 2 lines that are parallel to L and is at a distance of D from L. How can I do that in CGAL? The api CGAL::parallel is for comparing if two lines/segments/rays are parallel, not for returning a parallel line. The api Line_2< Kernel > perpendicular (const Point_2< Kernel > &p) const can be used to get the equation of a line N normal to the line L, but I can't seem to find a way to get the point at a distance D from L on the normal N. (If I can get such a point P, I can generate the line parallel to L passing through P to get my desired line equation).

Thoughts? I'm sure there is a way using some other API's, but I can't seem to find it (I've looked pretty thoroughly through 2D and 3D Linear Geometry Kernel API list, and have checked the APIs whose names sound promising).

TCSGrad
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1 Answers1

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You can get a, b, c parameters of general line equation

a * x + b * y + c = 0

Then normalize it dividing by 

d = Sqrt(a * a + b * b)

obtaining

A * x + B * y + C = 0, where
A = a / d 
B = b / d 
C = c / d

and make parallel lines equations with parameters (A, B, C + D) and (A, B, C - D) (where D is your distance)

If Line_2.direction is normalized, it would simpler to use another approach:

dir = L.direction
p = L.point
p1  = Point(p.x + dir.y * D, p.y - dir.x * D)
p2  = Point(p.x - dir.y * D, p.y + dir.x * D)
L1 = Line_2(p1, dir)
L2 = Line_2(p2, dir)
MBo
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