Question

Given a 3D line in CGAL, how do I compute a point on that line that is some known distance from an endpoint?

Answer 1

If you have two points P₀ and P₁, you can make a vector V = P₁ – P₀.

Given distance D from P₀, you can get the resulting point R = P₀ + (D ÷ ||V||) ⋅ V.

(Linearly interpolate between the lines, changing D into a percentage by dividing by the full length of the line.)

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I don’t know CGAL (and the documentation kind of sucks), but I assume it’d be something like this:

Line_3<K> l = /* ... */;
Vector_3<K> v = l.to_vector();
Point_3<K> r = l.p + (d * d / v.squared_length()) * v;

Note I can’t even find a way to get the starting point of a line, so that one is up to you. (The l.p part is made up.)