Makes the singularity engine actually work stably. (#4068)

* Add GNU Octave script for tuning singularity engine. startsingularityengine is now properly tuned & sets up radiation collectors. FTLize RadiationCollectorComponent.

* Fix bugs with radiation collectors producing infinite power.

* Ensure singularities don't instantly annihilate other singularities (causing new singularities to instantly dissolve)

Technically found by a "bug" where a singularity generator would make multiple singularities, but this renders that bug harmless.

* Tune singularity shield emitters to hopefully randomly fail less, and add an Octave script for looking into that

* Fix singularity shader

* Map in an unfinished PA into Saltern

* Correct PA particles being counted twice by singularity calculations, add singulo food component

* Hopefully stop "level 1 singulo stuck in a corner" issues by freezing it when it goes to level 1 from any other level

* Apply suggestions on 'jazz' PR

Tools/singulo.m

@@ -0,0 +1,95 @@
+# This is a script to be loaded into GNU Octave.
+
+# - Notes -
+# + Be sure to check all parameters are up to date with game before use.
+# + The way things are tuned, only PA level 1 is stable on Saltern.
+# A singularity timestep is one second.
+
+# - Parameters -
+# It's expected that you dynamically modify these if relevant to your scenario.
+global pa_particle_energy_for_level_table pa_level pa_time_between_shots
+pa_particle_energy_for_level_table = [10, 30, 60, 100]
+# Note that level 0 is 1 here.
+pa_level = 1
+pa_time_between_shots = 6
+
+# Horizontal size (interior tiles) of mapped singulo cage
+global cage_area cage_pa1 cage_pa2 cage_pa3
+#  __123__
+# +---+---+
+cage_area = 7
+cage_pa1 = 2.5
+cage_pa2 = 3.5
+cage_pa3 = 4.5
+
+global energy_drain_for_level_table
+energy_drain_for_level_table = [1, 2, 5, 10, 15, 20]
+function retval = level_for_energy (energy)
+  retval = 1
+  if energy >= 1500 retval = 6; return; endif
+  if energy >= 1000 retval = 5; return; endif
+  if energy >= 600 retval = 4; return; endif
+  if energy >= 300 retval = 3; return; endif
+  if energy >= 200 retval = 2; return; endif
+endfunction
+function retval = radius_for_level (level)
+  retval = level - 0.5
+endfunction
+
+# - Simulator -
+
+global singulo_shot_timer
+singulo_shot_timer = 0
+
+function retval = singulo_step (energy)
+  global energy_drain_for_level_table
+  global pa_particle_energy_for_level_table pa_level pa_time_between_shots
+  global cage_area cage_pa1 cage_pa2 cage_pa3
+  global singulo_shot_timer
+  level = level_for_energy(energy)
+  energy_drain = energy_drain_for_level_table(level)
+  energy -= energy_drain
+  singulo_shot_timer += 1
+  if singulo_shot_timer == pa_time_between_shots
+    energy_gain_per_hit = pa_particle_energy_for_level_table(pa_level)
+    # This is the bit that's complicated: the area and probability calculation.
+    # Rather than try to work it out, let's do things by simply trying it.
+    # This is the area of the singulo.
+    singulo_area = radius_for_level(level) * 2
+    # This is therefore the area in which it can move.
+    effective_area = max(0, cage_area - singulo_area)
+    # Assume it's at some random position within the area it can move.
+    # (This is the weak point of the maths. It's not as simple as this really.)
+    singulo_lpos = (rand() * effective_area)
+    singulo_rpos = singulo_lpos + singulo_area
+    # Check each of 3 points.
+    n = 0.5
+    if singulo_lpos < (cage_pa1 + n) && singulo_rpos > (cage_pa1 - n)
+      energy += energy_gain_per_hit
+    endif
+    if singulo_lpos < (cage_pa2 + n) && singulo_rpos > (cage_pa2 - n)
+      energy += energy_gain_per_hit
+    endif
+    if singulo_lpos < (cage_pa3 + n) && singulo_rpos > (cage_pa3 - n)
+      energy += energy_gain_per_hit
+    endif
+    singulo_shot_timer = 0
+  endif
+  retval = energy
+endfunction
+
+# - Scenario -
+
+global scenario_energy
+scenario_energy = 100
+
+function retval = scenario (x)
+  global scenario_energy
+  sce = scenario_energy
+  scenario_energy = singulo_step(sce)
+  retval = scenario_energy
+endfunction
+
+# x is in seconds.
+x = 0:1:960
+plot(x, arrayfun(@scenario, x))