urho3d/Engine/Math/MathDefs.h

//
// Urho3D Engine
// Copyright (c) 2008-2011 Lasse Öörni
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
//

#pragma once

#include <cstdlib>
#include <cmath>

#ifndef M_PI
static const float M_PI = 3.141592653589793238462643f;
#endif

static const int M_MIN_INT = 0x80000000;
static const int M_MAX_INT = 0x7fffffff;
static const unsigned M_MIN_UNSIGNED = 0x00000000;
static const unsigned M_MAX_UNSIGNED = 0xffffffff;

static const float M_EPSILON = 0.000001f;
static const float M_LARGE_EPSILON = 0.00005f;
static const float M_MIN_NEARCLIP = 0.01f;
static const float M_MAX_FOV = 160.0f;
static const float M_LARGE_VALUE = 100000000.0f;
static const float M_INFINITY = (float)HUGE_VAL;
static const float M_DEGTORAD = (float)M_PI / 180.0f;
static const float M_RADTODEG = 1.0f / M_DEGTORAD;

/// Intersection test result.
enum Intersection
{
    OUTSIDE,
    INTERSECTS,
    INSIDE
};

/// Linear interpolation between two float values.
inline float Lerp(float lhs, float rhs, float t) { return lhs * (1.0f - t) + rhs * t; }
/// Return a random float between 0.0 (inclusive) and 1.0 (exclusive.)
inline float Random() { return (rand() & 32767) / 32768.0f; }
/// Return a random float between 0.0 and range, inclusive.
inline float Random(float range) { return (rand() & 32767) * range / 32767.0f; }
/// Return a random integer between 0 and range, inclusive.
inline int Random(int range) { return ((rand() & 32767) * range + 16384) / 32767; }
/// Return the smaller of two floats.
inline float Min(float lhs, float rhs) { return lhs < rhs ? lhs : rhs; }
/// Return the larger of two floats.
inline float Max(float lhs, float rhs) { return lhs > rhs ? lhs : rhs; }

/// Clamp a float to a range.
inline float Clamp(float value, float min, float max)
{
    if (value < min)
        return min;
    else if (value > max)
        return max;
    else
        return value;
}

/// Check whether two floating point values are equal within accuracy.
inline bool Equals(float lhs, float rhs) { return lhs + M_EPSILON >= rhs && lhs - M_EPSILON <= rhs; }
/// Return the smaller of two integers.
inline int Min(int lhs, int rhs) { return lhs < rhs ? lhs : rhs; }
/// Return the larger of two integers.
inline int Max(int lhs, int rhs) { return lhs > rhs ? lhs : rhs; }

/// Clamp an integer to a range.
inline int Clamp(int value, int min, int max)
{
    if (value < min)
        return min;
    else if (value > max)
        return max;
    else
        return value;
}

/// Check whether an unsigned integer is a power of two.
inline bool IsPowerOfTwo(unsigned value)
{
    if (!value)
        return true;
    while (!(value & 1))
        value >>= 1;
    return value == 1;
}

/// Round up to next power of two.
inline unsigned NextPowerOfTwo(unsigned value)
{
    unsigned ret = 1;
    while (ret < value)
        ret <<= 1;
    return ret;
}

/// Fast square root.
inline float FastSqrt(float x)
{
    union
    {
        float f;
        int i;
    } u;
    
    u.f = x;
    u.i -= 1 << 23;
    u.i >>= 1;
    u.i += 1 << 29;
    return u.f;
}

/// Fast inverse square root.
inline float FastInvSqrt(float x)
{
    union
    {
        float f;
        int i;
    } u;
    
    float xHalf = 0.5f * x;
    u.f = x;
    u.i = 0x5f3759df - (u.i >> 1);
    x = u.f * (1.5f - xHalf * u.f * u.f);
    return x;
}

/// Update a hash with the given 8-bit value using the SDBM algorithm.
inline unsigned SDBMHash(unsigned hash, unsigned char c) { return c + (hash << 6) + (hash << 16) - hash; }