support functions: cubic speed function for "whatever use" :P

diff --git a/qcsrc/common/util.qc b/qcsrc/common/util.qc
index b973850cc9f23393062a1b60a781e6ead3052d3f..6e534ffc19464a92777b956353b926f48ddd578e 100644 (file)
--- a/qcsrc/common/util.qc
+++ b/qcsrc/common/util.qc
@@ -2364,3 +2364,55 @@ void queue_to_execute_next_frame(string s)
        }
        to_execute_next_frame = strzone(s);
 }
+
+float cubic_speedfunc(float startspeedfactor, float endspeedfactor, float x)
+{
+       return
+               (((     startspeedfactor + endspeedfactor - 2
+               ) * x - 2 * startspeedfactor - endspeedfactor + 3
+               ) * x + startspeedfactor
+               ) * x;
+}
+
+float cubic_speedfunc_is_sane(float startspeedfactor, float endspeedfactor)
+{
+       if(startspeedfactor < 0 || endspeedfactor < 0)
+               return FALSE;
+
+       /*
+       // if this is the case, the possible zeros of the first derivative are outside
+       // 0..1
+       We can calculate this condition as condition 
+       if(se <= 3)
+               return TRUE;
+       */
+
+       // better, see below:
+       if(startspeedfactor <= 3 && endspeedfactor <= 3)
+               return TRUE;
+
+       // if this is the case, the first derivative has no zeros at all
+       float se = startspeedfactor + endspeedfactor;
+       float s_e = startspeedfactor - endspeedfactor;
+       if(3 * (se - 4) * (se - 4) + s_e * s_e <= 12) // an ellipse
+               return TRUE;
+
+       // Now let s <= 3, s <= 3, s+e >= 3 (triangle) then we get se <= 6 (top right corner).
+       // we also get s_e <= 6 - se
+       // 3 * (se - 4)^2 + (6 - se)^2
+       // is quadratic, has value 12 at 3 and 6, and value < 12 in between.
+       // Therefore, above "better" check works!
+
+       return FALSE;
+
+       // known good cases:
+       // (0, [0..3])
+       // (0.5, [0..3.8])
+       // (1, [0..4])
+       // (1.5, [0..3.9])
+       // (2, [0..3.7])
+       // (2.5, [0..3.4])
+       // (3, [0..3])
+       // (3.5, [0.2..2.3])
+       // (4, 1)
+}

diff --git a/qcsrc/common/util.qh b/qcsrc/common/util.qh
index c409de3544578c00acc39b6b4e0c2248fabe65f3..3ce173bf638e95d705a70042fc6bfae62f4838aa 100644 (file)
--- a/qcsrc/common/util.qh
+++ b/qcsrc/common/util.qh
@@ -320,3 +320,17 @@ void queue_to_execute_next_frame(string s);
 
 // for marking written-to values as unused where it's a good idea to do this
 noref float unused_float;
+
+
+
+// a function f with:
+// f(0) = 0
+// f(1) = 1
+// f'(0) = startspeedfactor
+// f'(1) = endspeedfactor
+float cubic_speedfunc(float startspeedfactor, float endspeedfactor, float x);
+
+// checks whether f'(x) = 0 anywhere from 0 to 1
+// because if this is the case, the function is not usable for platforms
+// as it may exceed 0..1 bounds, or go in reverse
+float cubic_speedfunc_is_sane(float startspeedfactor, float endspeedfactor);