djcev.com

//==============================================================================
// math.qc
// Author: Joshua Skelton joshua.skelton@gmail.com
// A collection of helpful math functions.
//==============================================================================

//======================================================================
// forward declarations
//======================================================================

float(float value, float minValue, float maxValue) clamp;
// float(float a, float b) mod;         // available as an engine builtin
float(float x) sign;
float(float value, float minValue, float maxValue) wrap;

float(float a, float b, float mix) lerp;
vector(vector a, vector b, float mix) lerp_vector;
float(float a, float b, float mix) lerp_hermite;
vector(vector a, vector b, float mix) lerp_vector_hermite;

float(float anga, float angb) angledif;
float(vector ang, vector base_ang, vector offset) is_in_angle;

vector(vector ang) normalize_angles;
vector(vector ang) normalize_angles180;

float() crandom;
float(float v) anglemod;

float(float theta) preach_tan;
float(float y, float x) preach_atan2;
float(float theta, vector source, vector dest) preach_iterate_elevation;

//------------------------------------------------------------------------------

//----------------------------------------------------------------------
// clamp
//
// Limits the given value to the given range.
// value: A number
// minValue: The minimum value of the range
// maxValue: The maximum value of the range
// Returns: A number within the given range.
//----------------------------------------------------------------------
float(float value, float minValue, float maxValue) clamp =
{
        if (value < minValue)
        {
                return minValue;
        }
        else if (value > maxValue)
        {
                return maxValue;
        }

        return value;
};

//----------------------------------------------------------------------
// mod
//
// Returns the remainder after the division of a by n
// a: The dividend
// b: The divisor
// Returns: The remainder of a divided by n
//----------------------------------------------------------------------
/*
float(float a, float n) mod =
{
        return a - (n * floor(a / n));
};
*/

//----------------------------------------------------------------------
// sign
//
// Returns an indication of the sign of the given number.
// x: A number
// Returns: -1 if x < 0, 0 if x == 0, 1 if x > 0.
//----------------------------------------------------------------------
float(float x) sign =
{
        if (x > 0)
                return 1;
        else if (x < 0)
                return -1;

        return 0;
};

//----------------------------------------------------------------------
// wrap
//
// Limits the given value to the given range and will wrap the value to the
// the other end of the range if exceeded.
//
// value: A number
// minValue: The minimum value of the range
// maxValue: The maximum value of the range
// Returns: A number within the given range.
//----------------------------------------------------------------------
float(float value, float minValue, float maxValue) wrap =
{
        local float range = maxValue - minValue;
        return mod (value - minValue, range + 1) + minValue;
};

//----------------------------------------------------------------------
float(float a, float b, float mix) lerp =
{
        if (mix <= 0)
                return a;
        if (mix >= 1)
                return b;
        return (b * mix + a * ( 1 - mix ) );
};

//----------------------------------------------------------------------
vector(vector a, vector b, float mix) lerp_vector =
{
        if (mix <= 0)
                return a;
        if (mix >= 1)
                return b;
        return (b * mix + a * ( 1 - mix ) );
};

//----------------------------------------------------------------------
// for a relaxing lerp: hermite lerp.
//----------------------------------------------------------------------
float(float a, float b, float mix) lerp_hermite =
{
        if (mix <= 0)
                return a;
        if (mix >= 1)
                return b;

        local float h01;

        h01 = mix * mix;
        h01 *= 3 - 2 * mix;

        return (b * h01 + a * (1 - h01));
};

//----------------------------------------------------------------------
vector(vector a, vector b, float mix) lerp_vector_hermite =
{
        if (mix <= 0)
                return a;
        if (mix >= 1)
                return b;

        local float h01;

        h01 = mix * mix;
        h01 *= 3 - 2 * mix;

        return (b * h01 + a * (1 - h01));
};

//----------------------------------------------------------------------
float(float anga, float angb) angledif =
{
        local float dif;
        dif = fabs (anga - angb);
        if (dif > 180)
                dif = 360 - dif;
        return dif;
};

//----------------------------------------------------------------------
float(vector ang, vector base_ang, vector offset) is_in_angle =
{
        if (angledif(ang_x, base_ang_x) > offset_x ||
                angledif(ang_y, base_ang_y) > offset_y)
        {
                return FALSE;
        }
        else
        {
                return TRUE;
        }
};

//----------------------------------------------------------------------
// normalizes an angle vector to the 0/+359 range
//----------------------------------------------------------------------
vector(vector ang) normalize_angles =
{
    ang_x = ang_x - floor (ang_x / 360) * 360;
    ang_y = ang_y - floor (ang_y / 360) * 360;
    ang_z = ang_z - floor (ang_z / 360) * 360;

    return ang;
};

//----------------------------------------------------------------------
// normalizes an angle vector to the -180/+179 range
//----------------------------------------------------------------------
vector(vector ang) normalize_angles180 =
{
    ang_x = ((ang_x + 180) - floor ((ang_x + 180) / 360) * 360) - 180;
    ang_y = ((ang_y + 180) - floor ((ang_y + 180) / 360) * 360) - 180;
    ang_z = ((ang_z + 180) - floor ((ang_z + 180) / 360) * 360) - 180;

    return ang;
};

//======================================================================
// Below are various math functions copied from elsewhere in the program
// (i.e., the following were not originally in math.qc) -- CEV
//======================================================================

//----------------------------------------------------------------------
// returns -1 to 1 (I think); was in weapons.qc -- CEV
//----------------------------------------------------------------------
float() crandom =
{
        return 2 * (random() - 0.5);
};

//----------------------------------------------------------------------
// was in ai.qc -- CEV
//----------------------------------------------------------------------
float(float v) anglemod =
{
        while (v >= 360)
                v = v - 360;
        while (v < 0)
                v = v + 360;
        return v;
};

//----------------------------------------------------------------------
// the next three functions were in ogre.qc -- CEV
//----------------------------------------------------------------------

//////////////////////////////////////////////////////////////
// start Preach Ogre Marksman tutorial here -- dumptruck_ds //
//////////////////////////////////////////////////////////////

// uses QuakeC builtins to calculate tan of angle
// WARNING: uses makevectors! This overwrites the v_forward... globals
float(float theta) preach_tan =
{
        local vector ang = '0 0 0';     // temp used to calculate trig values

        // assign theta to the yaw to simplify reasoning
        ang_y = theta;
        makevectors (ang);
        return v_forward_y / v_forward_x;
};

// inverse tan function
// takes two parameters, numerator and denominator
// this copes better with denominator 0 and gets quadrant correct
float(float y, float x) preach_atan2 =
{
        // temporary used to calculate trig values
        local vector ang;
        ang = '0 0 0';
        ang_x = x;
        ang_y = y;
        return vectoyaw (ang);
};

float(float theta, vector source, vector dest) preach_iterate_elevation =
{
        // constants in the equation to be solved
        local float a, b, c;
        // displacement we wish the projectile to travel
        local vector ofs;
        // horizontal and vertical components of ofs
        local float y, z;
        // trig values of the angle theta
        local float tan_theta;

        // calculate how far we are firing
        ofs = dest - source;
        z = ofs_z;
        ofs_z = 0;
        y = vlen (ofs);

        // find the coefficients of the quadratic in tan(theta)
        a = 0.5 * world_gravity * y * y / (GRENADE_SPEED * GRENADE_SPEED);
        b = -y;
        c = a + z;

        // check if the destination is too far to reach
        if (b * b < 4 * a * c)
                return OGRE_DEFAULT_ELEVATION;

        // calculate the tan value of the given theta
        tan_theta = preach_tan (theta);

        // reuse ang to create the improved firing direction
        theta = preach_atan2 (a * tan_theta * tan_theta - c,
                2 * a * tan_theta + b);

        // constrain the values to stop anything too mad happening
        while (theta > 90)
                theta = theta - 180;
        return theta;
};
// end Preach tutorial