Float3d.h

/*
This Source Code Form is subject to the
terms of the Mozilla Public License, v.
2.0. If a copy of the MPL was not
distributed with this file, You can
obtain one at
http://mozilla.org/MPL/2.0/.
*/

#ifndef float3dH
#define float3dH
#include <math.h>
//---------------------------------------------------------------------------

class float3
{ // wapó³rzêdne wiercho³ka 3D o pojedynczej precyzji
  public:
    float x, y, z;
    float3(void){};
    float3(float a, float b, float c)
    {
        x = a;
        y = b;
        z = c;
    };
    double inline Length() const;
};

inline bool operator==(const float3 &v1, const float3 &v2)
{
    return (v1.x == v2.x && v1.y == v2.y && v1.z == v2.z);
};
inline float3 &operator+=(float3 &v1, const float3 &v2)
{
    v1.x += v2.x;
    v1.y += v2.y;
    v1.z += v2.z;
    return v1;
};
inline float3 operator-(const float3 &v)
{
    return float3(-v.x, -v.y, -v.z);
};
inline float3 operator-(const float3 &v1, const float3 &v2)
{
    return float3(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z);
};
inline float3 operator+(const float3 &v1, const float3 &v2)
{
    return float3(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z);
};
double inline float3::Length() const
{
    return sqrt(x * x + y * y + z * z);
};
inline float3 operator/(const float3 &v, double k)
{
    return float3(v.x / k, v.y / k, v.z / k);
};
inline float3 SafeNormalize(const float3 &v)
{ // bezpieczna normalizacja (wektor d³ugoœci 1.0)
    double l = v.Length();
    float3 retVal;
    if (l == 0)
        retVal.x = retVal.y = retVal.z = 0;
    else
        retVal = v / l;
    return retVal;
};
inline float3 CrossProduct(const float3 &v1, const float3 &v2)
{
    return float3(v1.y * v2.z - v1.z * v2.y, v2.x * v1.z - v2.z * v1.x, v1.x * v2.y - v1.y * v2.x);
}

class float4
{ // kwaternion obrotu
  public:
    float x, y, z, w;
    float4()
    {
        x = y = z = 0.f;
        w = 1.f;
    };
    float4(float a, float b, float c, float d)
    {
        x = a;
        y = b;
        z = c;
        w = d;
    };
    double inline float4::LengthSquared() const
    {
        return x * x + y * y + z * z + w * w;
    };
    double inline float4::Length() const
    {
        return sqrt(x * x + y * y + z * z + w * w);
    };
};
inline float4 operator*(const float4 &q1, const float4 &q2)
{ // mno¿enie to prawie jak mno¿enie macierzy
    return float4(q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y,
                  q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z,
                  q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x,
                  q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z);
}
inline float4 operator-(const float4 &q)
{ // sprzê¿ony; odwrotny tylko dla znormalizowanych!
    return float4(-q.x, -q.y, -q.z, q.w);
};
inline float4 operator-(const float4 &q1, const float4 &q2)
{ // z odejmowaniem nie ma lekko
    return (-q1) * q2; // inwersja tylko dla znormalizowanych!
};
inline float4 operator+(const float4 &v1, const float4 &v2)
{
    return float4(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z, v1.w + v2.w);
};
inline float4 operator/(const float4 &v, double k)
{
    return float4(v.x / k, v.y / k, v.z / k, v.w / k);
};
inline float4 Normalize(const float4 &v)
{ // bezpieczna normalizacja (wektor d³ugoœci 1.0)
    double l = v.LengthSquared();
    if (l == 1.0)
        return v;
    if (l == 0.0)
        return float4(); // wektor zerowy, w=1
    else
        return v / sqrt(l); // pierwiastek liczony tylko jeœli trzeba wykonaæ dzielenia
};
float Dot(const float4 &q1, const float4 &q2)
{ // iloczyn skalarny
    return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
}
inline float4 &operator*=(float4 &v1, double d)
{ // mno¿enie przez skalar, jaki ma sens?
    v1.x *= d;
    v1.y *= d;
    v1.z *= d;
    v1.w *= d;
    return v1;
};
inline float4 Slerp(const float4 &q0, const float4 &q1, float t)
// void Slerp(QUATERNION *Out, const QUATERNION &q0, const QUATERNION &q1, float t)
{ // interpolacja sweryczna
    float cosOmega = Dot(q0, q1);
    float4 new_q1(q1);
    if (cosOmega < 0.0f)
    { // je¿eli s¹ niezgodne kierunki, jeden z nich trzeba zanegowaæ
        new_q1.x = -new_q1.x;
        new_q1.y = -new_q1.y;
        new_q1.z = -new_q1.z;
        new_q1.w = -new_q1.w;
        cosOmega = -cosOmega;
    }
    double k0, k1;
    if (cosOmega > 0.9999f)
    { // jeœli jesteœmy z (t) na maksimum kosinusa, to tam prawie liniowo jest
        k0 = 1.0f - t;
        k1 = t;
    }
    else
    { // a w ogólnym przypadku trzeba liczyæ na trygonometriê
        double sinOmega = sqrt(1.0f - cosOmega * cosOmega); // sinus z jedynki tryg.
        double omega = atan2(sinOmega, cosOmega); // wyznaczenie k¹ta
        double oneOverSinOmega = 1.0f / sinOmega; // odwrotnoϾ sinusa, bo sinus w mianowniku
        k0 = sin((1.0f - t) * omega) * oneOverSinOmega;
        k1 = sin(t * omega) * oneOverSinOmega;
    }
    return float4(q0.x * k0 + new_q1.x * k1, q0.y * k0 + new_q1.y * k1, q0.z * k0 + new_q1.z * k1,
                  q0.w * k0 + new_q1.w * k1);
}

struct float8
{ // wiercho³ek 3D z wektorem normalnym i mapowaniem, pojedyncza precyzja
  public:
    float3 Point;
    float3 Normal;
    float tu, tv;
};

class float4x4
{ // macierz transformacji pojedynczej precyzji
    float e[16];

  public:
    float4x4(void){};
    float4x4(float f[16])
    {
        for (int i = 0; i < 16; ++i)
            e[i] = f[i];
    };
    float *__fastcall operator()(int i)
    {
        return &e[i << 2];
    }
    const float *__fastcall readArray(void)
    {
        return e;
    }
    void Identity()
    {
        for (int i = 0; i < 16; ++i)
            e[i] = 0;
        e[0] = e[5] = e[10] = e[15] = 1.0f;
    }
    const float *operator[](int i) const
    {
        return &e[i << 2];
    };
    void InitialRotate()
    { // taka specjalna rotacja, nie ma co ci¹gaæ trygonometrii
        float f;
        for (int i = 0; i < 16; i += 4)
        {
            e[i] = -e[i]; // zmiana znaku X
            f = e[i + 1];
            e[i + 1] = e[i + 2];
            e[i + 2] = f; // zamiana Y i Z
        }
    };
    inline float4x4 &Rotation(double angle, float3 axis);
    inline bool IdentityIs()
    { // sprawdzenie jednostkowoœci
        for (int i = 0; i < 16; ++i)
            if (e[i] != ((i % 5) ? 0.0 : 1.0)) // jedynki tylko na 0, 5, 10 i 15
                return false;
        return true;
    }
    void Quaternion(float4 *q);
    inline float3 *TranslationGet()
    {
        return (float3 *)(e + 12);
    }
};

inline float3 operator*(const float4x4 &m, const float3 &v)
{ // mno¿enie wektora przez macierz
    return float3(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0],
                  v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1],
                  v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]);
}

inline float4x4 &float4x4::Rotation(double angle, float3 axis)
{
    double c = cos(angle);
    double s = sin(angle);
    // One minus c (short name for legibility of formulai)
    double omc = (1 - c);
    if (axis.Length() != 1.0f)
        axis = SafeNormalize(axis);
    double x = axis.x;
    double y = axis.y;
    double z = axis.z;
    double xs = x * s;
    double ys = y * s;
    double zs = z * s;
    double xyomc = x * y * omc;
    double xzomc = x * z * omc;
    double yzomc = y * z * omc;
    e[0] = x * x * omc + c;
    e[1] = xyomc + zs;
    e[2] = xzomc - ys;
    e[3] = 0;
    e[4] = xyomc - zs;
    e[5] = y * y * omc + c;
    e[6] = yzomc + xs;
    e[7] = 0;
    e[8] = xzomc + ys;
    e[9] = yzomc - xs;
    e[10] = z * z * omc + c;
    e[11] = 0;
    e[12] = 0;
    e[13] = 0;
    e[14] = 0;
    e[15] = 1;
    return *this;
};

inline float4x4 operator*(const float4x4 &m1, const float4x4 &m2)
{ // iloczyn macierzy
    float4x4 retVal;
    for (int x = 0; x < 4; ++x)
        for (int y = 0; y < 4; ++y)
        {
            retVal(x)[y] = 0;
            for (int i = 0; i < 4; ++i)
                retVal(x)[y] += m1[i][y] * m2[x][i];
        }
    return retVal;
};

// From code in Graphics Gems; p. 766
inline float Det2x2(float a, float b, float c, float d)
{ // obliczenie wyznacznika macierzy 2×2
    return a * d - b * c;
};

inline float Det3x3(float a1, float a2, float a3, float b1, float b2, float b3, float c1, float c2,
                    float c3)
{ // obliczenie wyznacznika macierzy 3×3
    return +a1 * Det2x2(b2, b3, c2, c3) - b1 * Det2x2(a2, a3, c2, c3) + c1 * Det2x2(a2, a3, b2, b3);
};

float Det(const float4x4 &m)
{ // obliczenie wyznacznika macierzy 4×4
    float a1 = m[0][0], a2 = m[1][0], a3 = m[2][0], a4 = m[3][0];
    float b1 = m[0][1], b2 = m[1][1], b3 = m[2][1], b4 = m[3][1];
    float c1 = m[0][2], c2 = m[1][2], c3 = m[2][2], c4 = m[3][2];
    float d1 = m[0][3], d2 = m[1][3], d3 = m[2][3], d4 = m[3][3];
    return +a1 * Det3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4) -
           b1 * Det3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4) +
           c1 * Det3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4) -
           d1 * Det3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
};

#endif