math.qh File Reference

#include "lib/float.qh"

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Macros
#define	MEAN_ACCUMULATE(s, prefix, v, w)
#define	MEAN_DECLARE(prefix, m)
#define	MEAN_EVALUATE(s, prefix)
#define	power2of(e)

Functions
ERASEABLE float	almost_equals (float a, float b)
ERASEABLE float	almost_equals_eps (float a, float b, float times_eps)
ERASEABLE float	almost_in_bounds (float a, float b, float c)
ERASEABLE float	angc (float a1, float a2)
ERASEABLE vector	bezier_quadratic_getderivative (vector a, vector b, vector c, float t)
ERASEABLE vector	bezier_quadratic_getpoint (vector a, vector b, vector c, float t)
ERASEABLE float	cubic_speedfunc (float startspeedfactor, float endspeedfactor, float spd)
ERASEABLE bool	cubic_speedfunc_is_sane (float startspeedfactor, float endspeedfactor)
ERASEABLE float	ExponentialFalloff (float mindist, float maxdist, float halflifedist, float d)
ERASEABLE float	float2range01 (float f)
	continuous function mapping all reals into 0..1
ERASEABLE float	float2range11 (float f)
	continuous function mapping all reals into -1..1
ERASEABLE float	fsnap (float val, float fsize)
ERASEABLE float	lerp (float t0, float f0, float t1, float f1, float t)
ERASEABLE float	lerp3ratio (float f0, float f1, float f2, float ratio)
ERASEABLE float	lerpratio (float f0, float f1, float ratio)
ERASEABLE vector	lerpv (float t0, vector v0, float t1, vector v1, float t)
ERASEABLE vector	lerpv3ratio (vector f0, vector f1, vector f2, float ratio)
ERASEABLE vector	lerpvratio (vector f0, vector f1, float ratio)
ERASEABLE float	log2of (float e)
ERASEABLE float	map_bound_ranges (float value, float src_min, float src_max, float dest_min, float dest_max)
	Same as map_ranges except that values outside the source range are clamped to min or max.
ERASEABLE float	map_ranges (float value, float src_min, float src_max, float dest_min, float dest_max)
	Maps values between the src and dest range: src_min to dest_min, src_max to dest_max, values between them to the corresponding values between and extrapolates for values outside the range.
ERASEABLE void	mean_accumulate (entity e,.float a,.float c, float mean, float value, float weight)
ERASEABLE float	mean_evaluate (entity e,.float a,.float c, float mean)
ERASEABLE float	median (float a, float b, float c)
ERASEABLE vector	solve_quadratic (float a, float b, float c)
	ax^2 + bx + c = 0
ERASEABLE vector	vsnap (vector point, float fsize)

Macro Definition Documentation

MEAN_ACCUMULATE

#define MEAN_ACCUMULATE	(		s,
			prefix,
			v,
			w )

Value:

mean_accumulate(s, prefix##_accumulator, prefix##_count, prefix##_mean, v, w)

Definition at line 22 of file math.qh.

Referenced by anticheat_physics().

MEAN_DECLARE

#define MEAN_DECLARE	(		prefix,
			m )

Value:

float prefix##_mean = m; .float prefix##_count, prefix##_accumulator

Definition at line 24 of file math.qh.

MEAN_EVALUATE

#define MEAN_EVALUATE	(		s,
			prefix )

Value:

mean_evaluate(s, prefix##_accumulator, prefix##_count, prefix##_mean)

Definition at line 23 of file math.qh.

power2of

#define power2of

(

e

)

Value:

(2 ** e)

Definition at line 248 of file math.qh.

Function Documentation

almost_equals()

ERASEABLE float almost_equals	(	float	a,
		float	b )

Definition at line 219 of file math.qh.

{
    float eps = (max(a, -a) + max(b, -b)) * 0.001;
    return a - b < eps && b - a < eps;
}

References max().

Referenced by GetCurrentFov().

almost_equals_eps()

ERASEABLE float almost_equals_eps	(	float	a,
		float	b,
		float	times_eps )

Definition at line 226 of file math.qh.

{
    float eps = max(fabs(a), fabs(b)) * FLOAT_EPSILON * times_eps;
    return a - b < eps && b - a < eps;
}

References fabs(), FLOAT_EPSILON, and max().

Referenced by DamageText::DamageText_update(), and MUTATOR_HOOKFUNCTION().

almost_in_bounds()

ERASEABLE float almost_in_bounds	(	float	a,
		float	b,
		float	c )

Definition at line 233 of file math.qh.

{
    float eps = (max(a, -a) + max(c, -c)) * 0.001;
    if (a > c) eps = -eps;
    return b == median(a - eps, b, c + eps);
}

References max(), and median().

Referenced by Slider::mousePress(), Slider_draw(), Slider_keyDown(), and Slider_valueToText().

angc()

ERASEABLE float angc	(	float	a1,
		float	a2 )

Definition at line 35 of file math.qh.

{
    while (a1 > 180)
        a1 -= 360;
    while (a1 < -179)
        a1 += 360;
    while (a2 > 180)
        a2 -= 360;
    while (a2 < -179)
        a2 += 360;
    float a = a1 - a2;
    while (a > 180)
        a -= 360;
    while (a < -179)
        a += 360;
    return a;
}

bezier_quadratic_getderivative()

ERASEABLE vector bezier_quadratic_getderivative	(	vector	a,
		vector	b,
		vector	c,
		float	t )

Definition at line 119 of file math.qh.

{
    return (c - 2 * b + a) * (2 * t)
           + (b - a) * 2;
}

References vector.

bezier_quadratic_getpoint()

ERASEABLE vector bezier_quadratic_getpoint	(	vector	a,
		vector	b,
		vector	c,
		float	t )

Definition at line 111 of file math.qh.

{
    return (c - 2 * b + a) * (t * t)
           + (b - a) * (2 * t)
           + a;
}

References vector.

Referenced by Draw_ArcBeam(), and W_Arc_Beam_Think().

cubic_speedfunc()

ERASEABLE float cubic_speedfunc	(	float	startspeedfactor,
		float	endspeedfactor,
		float	spd )

Definition at line 126 of file math.qh.

{
    return (((startspeedfactor + endspeedfactor - 2
             ) * spd - 2 * startspeedfactor - endspeedfactor + 3
            ) * spd + startspeedfactor
           ) * spd;
}

Referenced by SUB_CalcMove_controller_think().

cubic_speedfunc_is_sane()

ERASEABLE bool cubic_speedfunc_is_sane	(	float	startspeedfactor,
		float	endspeedfactor )

Definition at line 135 of file math.qh.

{
    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)
    */
}

Referenced by set_platmovetype().

ExponentialFalloff()

ERASEABLE float ExponentialFalloff	(	float	mindist,
		float	maxdist,
		float	halflifedist,
		float	d )

Definition at line 241 of file math.qh.

{
    if (halflifedist > 0) return (0.5 ** ((bound(mindist, d, maxdist) - mindist) / halflifedist));
    else if (halflifedist < 0) return (0.5 ** ((bound(mindist, d, maxdist) - maxdist) / halflifedist));
    else return 1;
}

References bound().

Referenced by fireBullet_falloff(), and W_Arc_Beam_Think().

float2range01()

ERASEABLE float float2range01

(

float

f

)

continuous function mapping all reals into 0..1

Definition at line 207 of file math.qh.

{
    return 0.5 + 0.5 * float2range11(f);
}

References float2range11().

float2range11()

ERASEABLE float float2range11

(

float

f

)

continuous function mapping all reals into -1..1

Definition at line 200 of file math.qh.

{
    return f / (fabs(f) + 1);
}

References fabs().

Referenced by float2range01(), and GetCurrentFov().

fsnap()

ERASEABLE float fsnap	(	float	val,
		float	fsize )

Definition at line 54 of file math.qh.

{
    return rint(val / fsize) * fsize;
}

References rint().

Referenced by pathlib_astar(), pathlib_flynode(), pathlib_nodeatpoint(), pathlib_swimnode(), pathlib_walknode(), and pathlib_wateroutnode().

lerp()

ERASEABLE float lerp	(	float	t0,
		float	f0,
		float	t1,
		float	f1,
		float	t )

Definition at line 78 of file math.qh.

{
    return lerpratio(f0, f1, (t - t0) / (t1 - t0));
}

References f1, and lerpratio().

lerp3ratio()

ERASEABLE float lerp3ratio	(	float	f0,
		float	f1,
		float	f2,
		float	ratio )

Definition at line 84 of file math.qh.

{
    float mid = 0.5;
    return ratio < mid ? lerpratio(f0, f1, ratio / mid) : ratio > mid ? lerpratio(f1, f2, (ratio - mid) / mid) : f1;
}

References f1, f2, and lerpratio().

lerpratio()

ERASEABLE float lerpratio	(	float	f0,
		float	f1,
		float	ratio )

Definition at line 72 of file math.qh.

{
    return f0 * (1 - ratio) + f1 * ratio;
}

References f1.

Referenced by lerp(), and lerp3ratio().

lerpv()

ERASEABLE vector lerpv	(	float	t0,
		vector	v0,
		float	t1,
		vector	v1,
		float	t )

Definition at line 105 of file math.qh.

{
    return v0 + (v1 - v0) * ((t - t0) / (t1 - t0));
}

References vector.

Referenced by antilag_takebackorigin().

lerpv3ratio()

ERASEABLE vector lerpv3ratio	(	vector	f0,
		vector	f1,
		vector	f2,
		float	ratio )

Definition at line 98 of file math.qh.

{
    float mid = 0.5;
    return ratio < mid ? lerpvratio(f0, f1, ratio / mid) : ratio > mid ? lerpvratio(f1, f2, (ratio - mid) / mid) : f1;
}

References f1, f2, lerpvratio(), and vector.

lerpvratio()

ERASEABLE vector lerpvratio	(	vector	f0,
		vector	f1,
		float	ratio )

Definition at line 92 of file math.qh.

{
    return f0 * (1 - ratio) + f1 * ratio;
}

References f1, and vector.

Referenced by lerpv3ratio().

log2of()

ERASEABLE float log2of

(

float

e

)

Definition at line 251 of file math.qh.

{
    // 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;
}

map_bound_ranges()

ERASEABLE float map_bound_ranges	(	float	value,
		float	src_min,
		float	src_max,
		float	dest_min,
		float	dest_max )

Same as map_ranges except that values outside the source range are clamped to min or max.

Definition at line 372 of file math.qh.

                                                                                                  {
    if (value <= src_min) return dest_min;
    if (value >= src_max) return dest_max;
    return map_ranges(value, src_min, src_max, dest_min, dest_max);
}

References map_ranges().

Referenced by bobmodel_ofs(), DamageText::DamageText_update(), determine_force(), Handicap_UpdateHandicapLevel(), and HUD_Panel_HlCenterLine().

map_ranges()

ERASEABLE float map_ranges	(	float	value,
		float	src_min,
		float	src_max,
		float	dest_min,
		float	dest_max )

Maps values between the src and dest range: src_min to dest_min, src_max to dest_max, values between them to the corresponding values between and extrapolates for values outside the range.

src_min and src_max must not be the same or division by zero occurs.

dest_max can be smaller than dest_min if you want the resulting range to be inverted, all values can be negative.

Definition at line 363 of file math.qh.

                                                                                            {
    float src_diff = src_max - src_min;
    float dest_diff = dest_max - dest_min;
    float ratio = (value - src_min) / src_diff;
    return dest_min + dest_diff * ratio;
}

Referenced by map_bound_ranges().

mean_accumulate()

ERASEABLE void mean_accumulate	(	entity	e,
		.float	a,
		.float	c,
		float	mean,
		float	value,
		float	weight )

Definition at line 6 of file math.qh.

{
    if (weight == 0) return;
    if (mean == 0) e.(a) *= (value ** weight);
    else e.(a) += (value ** mean) * weight;
    e.(c) += weight;
}

References entity().

mean_evaluate()

ERASEABLE float mean_evaluate	(	entity	e,
		.float	a,
		.float	c,
		float	mean )

Definition at line 15 of file math.qh.

{
    if (e.(c) == 0) return 0;
    if (mean == 0) return (e.(a) ** (1.0 / e.(c)));
    else return ((e.(a) / e.(c)) ** (1.0 / mean));
}

References entity().

median()

ERASEABLE float median	(	float	a,
		float	b,
		float	c )

Definition at line 213 of file math.qh.

{
    return (a < c) ? bound(a, b, c) : bound(c, b, a);
}

References bound().

Referenced by almost_in_bounds(), Slider::mousePress(), Slider_keyDown(), XonoticSliderCheckBox_configureXonoticSliderCheckBox(), XonoticSliderCheckBox_draw(), and XonoticSliderCheckBox_setChecked().

solve_quadratic()

ERASEABLE vector solve_quadratic	(	float	a,
		float	b,
		float	c )

ax^2 + bx + c = 0

Definition at line 304 of file math.qh.

{
    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;
}

References sqrt(), and vector.

Referenced by get_shotvelocity(), solve_shotdirection(), spiberbot_calcartillery(), StartFrame(), trigger_push_calculatevelocity(), and W_Devastator_SteerTo().

vsnap()

ERASEABLE vector vsnap	(	vector	point,
		float	fsize )

Definition at line 60 of file math.qh.

{
    vector vret;
 
    vret.x = rint(point.x / fsize) * fsize;
    vret.y = rint(point.y / fsize) * fsize;
    vret.z = ceil(point.z / fsize) * fsize;
 
    return vret;
}

References ceil(), rint(), and vector.