src/math/func.h

/*
 * This file is part of the Colobot: Gold Edition source code
 * Copyright (C) 2001-2020, Daniel Roux, EPSITEC SA & TerranovaTeam
 * http://epsitec.ch; http://colobot.info; http://github.com/colobot
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * See the GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program. If not, see http://gnu.org/licenses
 */

/**
 * \file math/func.h
 * \brief Common math functions
 */

#pragma once


#include "math/const.h"


#include <cmath>
#include <cstdlib>


// Math module namespace
namespace Math
{


//! Compares \a a and \a b within \a tolerance
inline bool IsEqual(float a, float b, float tolerance = Math::TOLERANCE)
{
    return fabs(a - b) < tolerance;
}

//! Compares \a a to zero within \a tolerance
inline bool IsZero(float a, float tolerance = Math::TOLERANCE)
{
    return Math::IsEqual(a, 0.0f, tolerance);
}

//! Minimum
inline float Min(float a, float b)
{
    if ( a <= b ) return a;
    else          return b;
}

inline float Min(float a, float b, float c)
{
    return Min( Min(a, b), c );
}

inline float Min(float a, float b, float c, float d)
{
    return Math::Min( Math::Min(a, b), Math::Min(c, d) );
}

inline float Min(float a, float b, float c, float d, float e)
{
    return Math::Min( Math::Min(a, b), Math::Min(c, d), e );
}

//! Maximum
inline float Max(float a, float b)
{
    if ( a >= b ) return a;
    else          return b;
}

inline float Max(float a, float b, float c)
{
    return Math::Max( Math::Max(a, b), c );
}

inline float Max(float a, float b, float c, float d)
{
    return Math::Max( Math::Max(a, b), Math::Max(c, d) );
}

inline float Max(float a, float b, float c, float d, float e)
{
    return Math::Max( Math::Max(a, b), Math::Max(c, d), e );
}

//! Clamps the value to a range specified by min and max
template<typename T>
inline T Clamp(T value, T min, T max)
{
    if (value < min) return min;
    else if (value > max) return max;
    else return value;
}

//! Returns the normalized value (0 .. 1)
inline float Norm(float a)
{
    if ( a < 0.0f ) return 0.0f;
    if ( a > 1.0f ) return 1.0f;
    return a;
}

//! Swaps two integers
inline void Swap(int &a, int &b)
{
    int c = a;
    a = b;
    b = c;
}

//! Swaps two real numbers
inline void Swap(float &a, float &b)
{
    float c = a;
    a = b;
    b = c;
}

//! Returns the modulo of a floating point number
/** Mod(8.1, 4) = 0.1
        Mod(n, 1) = fractional part of n */
inline float Mod(float a, float m)
{
    return a - ( static_cast<int>(a / m) ) * m;
}

//! Returns a random value between 0 and 1.
inline float Rand()
{
    return static_cast<float>(rand()) / static_cast<float>(RAND_MAX);
}

//! Returns whether \a x is an even power of 2
inline bool IsPowerOfTwo(unsigned int x)
{
   return x && !(x & (x - 1));
}

//! Returns the next nearest power of two to \a x
inline int NextPowerOfTwo(int x)
{
  double logbase2 = log(static_cast<float>(x)) / Math::LOG_2;
  return static_cast<int>(pow(2, ceil(logbase2)) + 0.5);
}


//! Returns a normalized angle, that is in other words between 0 and 2 * PI
inline float NormAngle(float angle)
{
    angle = Math::Mod(angle, PI*2.0f);
    if ( angle < 0.0f )
        return PI*2.0f + angle;

    return angle;
}

//! Test if a angle is between two terminals
inline bool TestAngle(float angle, float min, float max)
{
    angle = Math::NormAngle(angle);
    min   = Math::NormAngle(min);
    max   = Math::NormAngle(max);

    if ( min > max )
        return ( angle <= max || angle >= min );

    return ( angle >= min && angle <= max );
}

//! Calculates a value (radians) proportional between a and b (degrees)
inline float PropAngle(float a, float b, float p)
{
    float aa = a * DEG_TO_RAD;
    float bb = b * DEG_TO_RAD;

    return aa + p * (bb - aa);
}

//! Calculates the angle to rotate the angle \a a to the angle \a g
/** A positive angle is counterclockwise (CCW). */
inline float Direction(float a, float g)
{
    a = Math::NormAngle(a);
    g = Math::NormAngle(g);

    if ( a < g )
    {
        if ( a+PI*2.0f-g < g-a ) a += PI*2.0f;
    }
    else
    {
        if ( g+PI*2.0f-a < a-g ) g += PI*2.0f;
    }

    return g-a;
}

//! Managing the dead zone of a joystick.
/**
\verbatim
in:   -1            0            1
--|-------|----o----|-------|-->
             <---->
              dead
out:  -1       0         0       1
\endverbatim */
inline float Neutral(float value, float dead)
{
    if ( fabs(value) <= dead )
    {
        return 0.0f;
    }
    else
    {
        if ( value > 0.0f ) return (value-dead)/(1.0f-dead);
        else                return (value+dead)/(1.0f-dead);
    }
}

//! Gently advances a desired value from its current value
/** Over time, the progression is more rapid. */
inline float Smooth(float actual, float hope, float time)
{
    float future = actual + (hope-actual)*time;

    if ( hope > actual )
    {
        if ( future > hope ) future = hope;
    }
    if ( hope < actual )
    {
        if ( future < hope ) future = hope;
    }

    return future;
}

//! Bounces any movement
/**
\verbatim
out
 |
1+------o-------o---
 |    o | o   o |  | bounce
 |   o  |   o---|---
 |  o   |       |
 | o    |       |
-o------|-------+----> progress
0|      |       1
 |<---->|middle
\endverbatim */
inline float Bounce(float progress, float middle = 0.3f, float bounce = 0.4f)
{
    if ( progress < middle )
    {
        progress = progress/middle;    // 0..1
        return 0.5f+sinf(progress*PI-PI/2.0f)/2.0f;
    }
    else
    {
        progress = (progress-middle)/(1.0f-middle);    // 0..1
        return (1.0f-bounce/2.0f)+sinf((0.5f+progress*2.0f)*PI)*(bounce/2.0f);
    }
}


} // namespace Math