How to compute a point on a line in CGAL

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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

You can just subtract the points you're interested in to get a slope vector and then walk along it. A MWE is below:

// Compile with: clang++ -DBOOST_ALL_NO_LIB -DCGAL_USE_GMPXX=1 -O2 -g -DNDEBUG -Wall -Wextra -pedantic -march=native -frounding-math main.cpp -lgmpxx -lmpfr -lgmp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
using K = CGAL::Exact_predicates_exact_constructions_kernel;
using Point_3 = K::Point_3;
class InterPointInterpolator {
 public:
  InterPointInterpolator(const Point_3 &a, const Point_3 &b) : a(a), b(b) {}
  // Returns points interpolated from a at t=0 to b at t=1
  Point_3 operator()(const double t) const {
    const auto m = b - a;
    return a + t * m;
  }
 private:
  Point_3 a;
  Point_3 b;
};
int main(){
  InterPointInterpolator ipi(Point_3(0, 0, 0), Point_3(10, 5, 20));
  for(int i=0;i<=10;i++){
    const auto interpolated_point = ipi(i/10.0);
    std::cout<<interpolated_point<<std::endl;
  }
  return 0;
}

Output:

0  0   0
1  0.5 2
2  1   4
3  1.5 6
4  2   8
5  2.5 10
6  3   12
7  3.5 14
8  4   16
9  4.5 18
10 5   20