Complex numerical solution for a simple geometry problem

targeting.m

pkg load linear-algebra

# Initial Conditions
pc = [2,3]; #target pos
pb = [12,-2]; #bullet pos
vc = [7,3].*(1/3); #target vel
sb = 2.8480; #bullet speed
tolerance = 0.1; #search tolerance

# Routines

function n = calculate_n(p_c, p_b, v_c, s_b, t)
  if (s_b * t == 0)
    n = ones(1, 2) * flintmax();
  else
    n = (p_c.-p_b.+(v_c.*t))./(s_b.*t);
  endif
endfunction

score = @(t) abs(1.0 - norm(calculate_n(pc, pb, vc, sb, t)));

# Minimize the score over time space
end_time = fminsearch(score, [0]);
end_score = score(end_time);

if (abs(end_score) <= tolerance)
  printf("Time: %d\n", end_time);
  calculate_n(pc, pb, vc, sb, end_time)
else
  printf("No Solution!");
endif