math.qh File Reference

#include "lib/float.qh"

Include dependency graph for math.qh:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Macros
#define	crandom()   (2 * (random() - 0.5))
	Returns a random number between -1.0 and 1.0. More...
#define	MEAN_ACCUMULATE(s, prefix, v, w)   mean_accumulate(s, prefix##_accumulator, prefix##_count, prefix##_mean, v, w)
#define	MEAN_DECLARE(prefix, m)   float prefix##_mean = m; .float prefix##_count, prefix##_accumulator
#define	MEAN_EVALUATE(s, prefix)   mean_evaluate(s, prefix##_accumulator, prefix##_count, prefix##_mean)
#define	power2of(e)   (2 ** 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 More...
ERASEABLE float	float2range11 (float f)
	continuous function mapping all reals into -1..1 More...
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. More...
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. More...
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 More...
ERASEABLE vector	vsnap (vector point, float fsize)

Macro Definition Documentation

crandom

#define crandom

(

)

(2 * (random() - 0.5))

Returns a random number between -1.0 and 1.0.

Definition at line 27 of file math.qh.

Referenced by ctf_Handle_Throw(), Item_ScheduleRespawn(), and ka_DropEvent().

MEAN_ACCUMULATE

#define MEAN_ACCUMULATE	(		s,
			prefix,
			v,
			w
	)		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
	)		float prefix##_mean = m; .float prefix##_count, prefix##_accumulator

Definition at line 24 of file math.qh.

MEAN_EVALUATE

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

Definition at line 23 of file math.qh.

power2of

#define power2of

(

e

)

(2 ** e)

Definition at line 251 of file math.qh.

Function Documentation

almost_equals()

ERASEABLE float almost_equals	(	float	a,
		float	b
	)

Definition at line 222 of file math.qh.

References ERASEABLE, and max().

Referenced by GetCurrentFov().

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

Here is the call graph for this function:

Here is the caller graph for this function:

almost_equals_eps()

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

Definition at line 229 of file math.qh.

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

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

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

Here is the call graph for this function:

Here is the caller graph for this function:

almost_in_bounds()

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

Definition at line 236 of file math.qh.

References ERASEABLE, max(), and median().

Referenced by Slider_draw(), Slider_keyDown(), Slider_mouseDrag(), and Slider_valueToText().

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

Here is the call graph for this function:

Here is the caller graph for this function:

angc()

ERASEABLE float angc	(	float	a1,
		float	a2
	)

Definition at line 38 of file math.qh.

References ERASEABLE.

{
    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 122 of file math.qh.

References ERASEABLE.

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

bezier_quadratic_getpoint()

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

Definition at line 114 of file math.qh.

References ERASEABLE.

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

cubic_speedfunc()

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

Definition at line 129 of file math.qh.

References ERASEABLE.

Referenced by SUB_CalcMove_controller_think().

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

Here is the caller graph for this function:

cubic_speedfunc_is_sane()

ERASEABLE bool cubic_speedfunc_is_sane	(	float	startspeedfactor,
		float	endspeedfactor
	)

Definition at line 138 of file math.qh.

References ERASEABLE.

Referenced by set_platmovetype().

{
    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)
    */
}

Here is the caller graph for this function:

ExponentialFalloff()

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

Definition at line 244 of file math.qh.

References bound().

{
    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;
}

Here is the call graph for this function:

float2range01()

ERASEABLE float float2range01

(

float

f

)

continuous function mapping all reals into 0..1

Definition at line 210 of file math.qh.

References ERASEABLE, and float2range11().

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

Here is the call graph for this function:

float2range11()

ERASEABLE float float2range11

(

float

f

)

continuous function mapping all reals into -1..1

Definition at line 203 of file math.qh.

References ERASEABLE, and fabs().

Referenced by float2range01(), and GetCurrentFov().

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

Here is the call graph for this function:

Here is the caller graph for this function:

fsnap()

ERASEABLE float fsnap	(	float	val,
		float	fsize
	)

Definition at line 57 of file math.qh.

References ERASEABLE, and rint().

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

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

Here is the call graph for this function:

Here is the caller graph for this function:

lerp()

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

Definition at line 81 of file math.qh.

References ERASEABLE, and lerpratio().

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

Here is the call graph for this function:

lerp3ratio()

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

Definition at line 87 of file math.qh.

References ERASEABLE, f1, and lerpratio().

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

Here is the call graph for this function:

lerpratio()

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

Definition at line 75 of file math.qh.

References ERASEABLE.

Referenced by lerp(), and lerp3ratio().

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

Here is the caller graph for this function:

lerpv()

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

Definition at line 108 of file math.qh.

References ERASEABLE.

Referenced by antilag_takebackorigin().

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

Here is the caller graph for this function:

lerpv3ratio()

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

Definition at line 101 of file math.qh.

References ERASEABLE, f1, and lerpvratio().

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

Here is the call graph for this function:

lerpvratio()

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

Definition at line 95 of file math.qh.

References ERASEABLE.

Referenced by lerpv3ratio().

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

Here is the caller graph for this function:

log2of()

ERASEABLE float log2of

(

float

e

)

Definition at line 254 of file math.qh.

References ERASEABLE.

{
    // 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 375 of file math.qh.

References map_ranges().

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

                                                                                                  {
    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);
}

Here is the call graph for this function:

Here is the caller graph for this function:

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 366 of file math.qh.

References ERASEABLE.

Referenced by map_bound_ranges().

                                                                                            {
    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;
}

Here is the caller graph for this function:

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.

References ERASEABLE.

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

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));
}

median()

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

Definition at line 216 of file math.qh.

References bound(), and ERASEABLE.

Referenced by almost_in_bounds(), Slider_keyDown(), Slider_mouseDrag(), XonoticSliderCheckBox_configureXonoticSliderCheckBox(), XonoticSliderCheckBox_draw(), and XonoticSliderCheckBox_setChecked().

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

Here is the call graph for this function:

Here is the caller graph for this function:

solve_quadratic()

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

ax^2 + bx + c = 0

Definition at line 307 of file math.qh.

References ERASEABLE, sqrt(), v, and vector().

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

{
    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;
}

Here is the call graph for this function:

Here is the caller graph for this function:

vsnap()

ERASEABLE vector vsnap	(	vector	point,
		float	fsize
	)

Definition at line 63 of file math.qh.

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

{
    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;
}

Here is the call graph for this function: