-#ifndef MATH_H
-#define MATH_H
+#pragma once
void mean_accumulate(entity e, .float a, .float c, float mean, float value, float weight)
{
- if (weight == 0)
- return;
- if (mean == 0)
- e.(a) *= pow(value, weight);
- else
- e.(a) += pow(value, mean) * weight;
+ if (weight == 0) return;
+ if (mean == 0) e.(a) *= pow(value, weight);
+ else e.(a) += pow(value, mean) * weight;
e.(c) += weight;
}
float mean_evaluate(entity e, .float a, .float c, float mean)
{
- if (e.(c) == 0)
- return 0;
- if (mean == 0)
- return pow(e.(a), 1.0 / e.(c));
- else
- return pow(e.(a) / e.(c), 1.0 / mean);
+ if (e.(c) == 0) return 0;
+ if (mean == 0) return pow(e.(a), 1.0 / e.(c));
+ else return pow(e.(a) / e.(c), 1.0 / mean);
}
-#define MEAN_ACCUMULATE(prefix,v,w) mean_accumulate(self,prefix##_accumulator,prefix##_count,prefix##_mean,v,w)
-#define MEAN_EVALUATE(prefix) mean_evaluate(self,prefix##_accumulator,prefix##_count,prefix##_mean)
-#define MEAN_DECLARE(prefix,m) float prefix##_mean = m; .float prefix##_count, prefix##_accumulator
-
-/*
-==================
-crandom
+#define MEAN_ACCUMULATE(s, prefix, v, w) mean_accumulate(s, prefix##_accumulator, prefix##_count, prefix##_mean, v, w)
+#define MEAN_EVALUATE(s, prefix) mean_evaluate(s, prefix##_accumulator, prefix##_count, prefix##_mean)
+#define MEAN_DECLARE(prefix, m) float prefix##_mean = m; .float prefix##_count, prefix##_accumulator
-Returns a random number between -1.0 and 1.0
-==================
-*/
-float crandom (void)
-{
- return 2 * (random () - 0.5);
-}
+/** Returns a random number between -1.0 and 1.0 */
+#define crandom() (2 * (random() - 0.5))
/*
*/
-float angc (float a1, float a2)
+float angc(float a1, float a2)
{
- float a;
-
while (a1 > 180)
- a1 = a1 - 360;
+ a1 -= 360;
while (a1 < -179)
- a1 = a1 + 360;
-
+ a1 += 360;
while (a2 > 180)
- a2 = a2 - 360;
+ a2 -= 360;
while (a2 < -179)
- a2 = a2 + 360;
-
- a = a1 - a2;
+ a2 += 360;
+ float a = a1 - a2;
while (a > 180)
- a = a - 360;
+ a -= 360;
while (a < -179)
- a = a + 360;
-
+ a += 360;
return a;
}
-float fsnap(float val,float fsize)
+float fsnap(float val, float fsize)
{
- return rint(val / fsize) * fsize;
+ return rint(val / fsize) * fsize;
}
-vector vsnap(vector point,float fsize)
+vector vsnap(vector point, float fsize)
{
- vector vret;
+ vector vret;
- vret.x = rint(point.x / fsize) * fsize;
- vret.y = rint(point.y / fsize) * fsize;
- vret.z = ceil(point.z / fsize) * fsize;
+ vret.x = rint(point.x / fsize) * fsize;
+ vret.y = rint(point.y / fsize) * fsize;
+ vret.z = ceil(point.z / fsize) * fsize;
- return vret;
+ return vret;
}
vector lerpv(float t0, vector v0, float t1, vector v1, float t)
return v0 + (v1 - v0) * ((t - t0) / (t1 - t0));
}
-#endif
+vector bezier_quadratic_getpoint(vector a, vector b, vector c, float t)
+{
+ return (c - 2 * b + a) * (t * t)
+ + (b - a) * (2 * t)
+ + a;
+}
+
+vector bezier_quadratic_getderivative(vector a, vector b, vector c, float t)
+{
+ return (c - 2 * b + a) * (2 * t)
+ + (b - a) * 2;
+}
+
+float cubic_speedfunc(float startspeedfactor, float endspeedfactor, float spd)
+{
+ return (((startspeedfactor + endspeedfactor - 2
+ ) * spd - 2 * startspeedfactor - endspeedfactor + 3
+ ) * spd + startspeedfactor
+ ) * spd;
+}
+
+bool 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)
+
+ /*
+ On another note:
+ inflection point is always at (2s + e - 3) / (3s + 3e - 6).
+
+ s + e - 2 == 0: no inflection
+
+ s + e > 2:
+ 0 < inflection < 1 if:
+ 0 < 2s + e - 3 < 3s + 3e - 6
+ 2s + e > 3 and 2e + s > 3
+
+ s + e < 2:
+ 0 < inflection < 1 if:
+ 0 > 2s + e - 3 > 3s + 3e - 6
+ 2s + e < 3 and 2e + s < 3
+
+ Therefore: there is an inflection point iff:
+ e outside (3 - s)/2 .. 3 - s*2
+
+ in other words, if (s,e) in triangle (1,1)(0,3)(0,1.5) or in triangle (1,1)(3,0)(1.5,0)
+ */
+}
+
+/** continuous function mapping all reals into -1..1 */
+float float2range11(float f)
+{
+ return f / (fabs(f) + 1);
+}
+
+/** continuous function mapping all reals into 0..1 */
+float float2range01(float f)
+{
+ return 0.5 + 0.5 * float2range11(f);
+}
+
+float median(float a, float b, float c)
+{
+ return (a < c) ? bound(a, b, c) : bound(c, b, a);
+}
+
+float almost_equals(float a, float b)
+{
+ float eps = (max(a, -a) + max(b, -b)) * 0.001;
+ return a - b < eps && b - a < eps;
+}
+
+float almost_in_bounds(float a, float b, float c)
+{
+ float eps = (max(a, -a) + max(c, -c)) * 0.001;
+ if (a > c) eps = -eps;
+ return b == median(a - eps, b, c + eps);
+}
+
+float ExponentialFalloff(float mindist, float maxdist, float halflifedist, float d)
+{
+ if (halflifedist > 0) return pow(0.5, (bound(mindist, d, maxdist) - mindist) / halflifedist);
+ else if (halflifedist < 0) return pow(0.5, (bound(mindist, d, maxdist) - maxdist) / halflifedist);
+ else return 1;
+}
+
+float power2of(float e)
+{
+ return pow(2, e);
+}
+
+float log2of(float e)
+{
+ // NOTE: generated code
+ if (e > 2048)
+ if (e > 131072)
+ if (e > 1048576)
+ if (e > 4194304) return 23;
+ else
+ if (e > 2097152) return 22;
+ else return 21;
+ else
+ if (e > 524288) return 20;
+ else
+ if (e > 262144) return 19;
+ else return 18;
+ else
+ if (e > 16384)
+ if (e > 65536) return 17;
+ else
+ if (e > 32768) return 16;
+ else return 15;
+ else
+ if (e > 8192) return 14;
+ else
+ if (e > 4096) return 13;
+ else return 12;
+ else
+ if (e > 32)
+ if (e > 256)
+ if (e > 1024) return 11;
+ else
+ if (e > 512) return 10;
+ else return 9;
+ else
+ if (e > 128) return 8;
+ else
+ if (e > 64) return 7;
+ else return 6;
+ else
+ if (e > 4)
+ if (e > 16) return 5;
+ else
+ if (e > 8) return 4;
+ else return 3;
+ else
+ if (e > 2) return 2;
+ else
+ if (e > 1) return 1;
+ else return 0;
+}
+
+/** ax^2 + bx + c = 0 */
+vector solve_quadratic(float a, float b, float c)
+{
+ vector v;
+ float D;
+ v = '0 0 0';
+ if (a == 0)
+ {
+ if (b != 0)
+ {
+ v.x = v.y = -c / b;
+ v.z = 1;
+ }
+ else
+ {
+ if (c == 0)
+ {
+ // actually, every number solves the equation!
+ v.z = 1;
+ }
+ }
+ }
+ else
+ {
+ D = b * b - 4 * a * c;
+ if (D >= 0)
+ {
+ D = sqrt(D);
+ if (a > 0) // put the smaller solution first
+ {
+ v.x = ((-b) - D) / (2 * a);
+ v.y = ((-b) + D) / (2 * a);
+ }
+ else
+ {
+ v.x = (-b + D) / (2 * a);
+ v.y = (-b - D) / (2 * a);
+ }
+ v.z = 1;
+ }
+ else
+ {
+ // complex solutions!
+ D = sqrt(-D);
+ v.x = -b / (2 * a);
+ if (a > 0) v.y = D / (2 * a);
+ else v.y = -D / (2 * a);
+ v.z = 0;
+ }
+ }
+ return v;
+}
projects / xonotic / xonotic-data.pk3dir.git / blobdiff