Merge remote-tracking branch 'origin/master' into samual/spawn_weapons

[xonotic/xonotic-data.pk3dir.git] / qcsrc / server / g_damage.qc

diff --git a/qcsrc/server/g_damage.qc b/qcsrc/server/g_damage.qc
index 65bde938db5bb47cbb67b184b539eeca1ec4fe29..710c7d4e2a88e7e7fa5ca4fdeb019c5e84ab5d96 100644 (file)
--- a/qcsrc/server/g_damage.qc
+++ b/qcsrc/server/g_damage.qc
@@ -1273,43 +1273,59 @@ float Fire_AddDamage(entity e, entity o, float d, float t, float dt)
 
                if(maxtime > mintime || maxdps > mindps)
                {
+                       // Constraints:
+                       
+                       // damage we have right now
                        mindamage = mindps * mintime;
-                       maxdamage = mindamage + d;
-
-                       // interval [mintime, maxtime] * [mindps, maxdps]
-                       // intersected with
-                       // [mindamage, maxdamage]
-                       // maximum of this!
-
-                       if(maxdamage >= maxtime * maxdps)
-                       {
-                               totaltime = maxtime;
-                               totaldamage = maxtime * maxdps;
 
-                               // this branch increases totaldamage if either t > mintime, or dps > mindps
-                       }
-                       else
-                       {
-                               // maxdamage is inside the interval!
-                               // first, try to use mindps; only if this fails, increase dps as needed
-                               totaltime = min(maxdamage / mindps, maxtime); // maxdamage / mindps >= mindamage / mindps = mintime
-                               totaldamage = maxdamage;
-                               // can totaldamage / totaltime be >= maxdps?
-                               // max(mindps, maxdamage / maxtime) >= maxdps?
-                               // we know maxdamage < maxtime * maxdps
-                               // so it cannot be
-
-                               // this branch ALWAYS increases totaldamage, but requires maxdamage < maxtime * maxdps
-                       }
+                       // damage we want to get
+                       maxdamage = mindamage + d;
 
-                       // total conditions for increasing:
-                       //     maxtime > mintime OR maxdps > mindps OR maxtime * maxdps > maxdamage
-                       // however:
-                       //     if maxtime = mintime, maxdps = mindps
-                       // then:
-                       //     maxdamage = mindamage + d
-                       //     mindamage = mindps * mintime = maxdps * maxtime < maxdamage!
-                       // so the last condition is not needed
+                       // but we can't exceed maxtime * maxdps!
+                       totaldamage = min(maxdamage, maxtime * maxdps);
+
+                       // LEMMA:
+                       // Look at:
+                       // totaldamage = min(mindamage + d, maxtime * maxdps)
+                       // We see:
+                       // totaldamage <= maxtime * maxdps
+                       // ==> totaldamage / maxdps <= maxtime.
+                       // We also see:
+                       // totaldamage / mindps = min(mindamage / mindps + d, maxtime * maxdps / mindps)
+                       //                     >= min(mintime, maxtime)
+                       // ==> totaldamage / maxdps >= mintime.
+
+                       /*
+                       // how long do we damage then?
+                       // at least as long as before
+                       // but, never exceed maxdps
+                       totaltime = max(mintime, totaldamage / maxdps); // always <= maxtime due to lemma
+                       */
+
+                       // alternate:
+                       // at most as long as maximum allowed
+                       // but, never below mindps
+                       totaltime = min(maxtime, totaldamage / mindps); // always >= mintime due to lemma
+
+                       // assuming t > mintime, dps > mindps:
+                       // we get d = t * dps = maxtime * maxdps
+                       // totaldamage = min(maxdamage, maxtime * maxdps) = min(... + d, maxtime * maxdps) = maxtime * maxdps
+                       // totaldamage / maxdps = maxtime
+                       // totaldamage / mindps > totaldamage / maxdps = maxtime
+                       // FROM THIS:
+                       // a) totaltime = max(mintime, maxtime) = maxtime
+                       // b) totaltime = min(maxtime, totaldamage / maxdps) = maxtime
+
+                       // assuming t <= mintime:
+                       // we get maxtime = mintime
+                       // a) totaltime = max(mintime, ...) >= mintime, also totaltime <= maxtime by the lemma, therefore totaltime = mintime = maxtime
+                       // b) totaltime = min(maxtime, ...) <= maxtime, also totaltime >= mintime by the lemma, therefore totaltime = mintime = maxtime
+
+                       // assuming dps <= mindps:
+                       // we get mindps = maxdps.
+                       // With this, the lemma says that mintime <= totaldamage / mindps = totaldamage / maxdps <= maxtime.
+                       // a) totaltime = max(mintime, totaldamage / maxdps) = totaldamage / maxdps
+                       // b) totaltime = min(maxtime, totaldamage / mindps) = totaldamage / maxdps
 
                        e.fire_damagepersec = totaldamage / totaltime;
                        e.fire_endtime = time + totaltime;