xmath.h

/* ScummVM - Graphic Adventure Engine
 *
 * ScummVM is the legal property of its developers, whose names
 * are too numerous to list here. Please refer to the COPYRIGHT
 * file distributed with this source distribution.
 *
 * 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://www.gnu.org/licenses/>.
 *
 */
 
#ifndef QDENGINE_XMATH_H
#define QDENGINE_XMATH_H
 
#include "common/scummsys.h"
 
namespace QDEngine {
 
class Archive;
 
class Vect2f;
class Vect2i;
class Vect2s;
class Vect3f;
 
enum eAxis {
    X_AXIS = 0,
    Y_AXIS = 1,
    Z_AXIS = 2,
    W_AXIS = 3
};
 
 
//          Constants
#undef M_PI
#define M_PI  3.14159265358979323846f
#undef M_PI_2
#define M_PI_2 1.57079632679489661923f
#undef M_PI_4
#define M_PI_4 0.785398163397448309616f
 
const double DBL_EPS = 1.e-15;
const double DBL_INF = 1.e+100;
const double DBL_COMPARE_TOLERANCE = 1.e-10;
 
const float FLT_EPS = 1.192092896e-07f; //1.e-7f;
const float FLT_INF = 1.e+30f;
const float FLT_COMPARE_TOLERANCE = 1.e-5f;
 
const int INT_INF = 0x7fffffff;
 
inline float invSqrtFast(float x) {
    x += 1e-7f; // Добавка, устраняющая деление на 0
    float xhalf = 0.5f * x;
 
    uint32 i;
    memcpy(&i, &x, 4);
    i = 0x5f375a86 - (i >> 1); // gives initial guess y0
    memcpy(&x, &i, 4);
    x = x * (1.5f - xhalf * x * x); // Newton step, repeating increases accuracy
    return x;
}
 
inline float cycle(float f, float size) {
    return fmod(fmod(f, size) + size, size);
}
 
inline float getDist(float v0, float v1, float size) {
    float d = fmod(v0 - v1, size);
    float ad = (float)fabs(d);
    float dd = size - ad;
    if (ad <= dd) return d;
    return d < 0 ? d + size : d - size;
}
 
inline float getDeltaAngle(float to, float from) {
    return getDist(to, from, 2 * M_PI);
}
 
inline float cycleAngle(float a) {
    return cycle(a, 2 * M_PI);
}
 
 
//
//          Scalar Functions
//
 
template <class T>
inline T sqr(const T &x) {
    return x*x;
}
 
#define G2R(x) ((x)*M_PI/180.f)
#define R2G(x) ((x)*180.f/M_PI)
 
//
//          class Vect2f
//
 
class Vect2f {
public:
    float x, y;
 
    inline Vect2f()                              { x = y = 0.0; }
    inline Vect2f(float x_, float y_)                 {
        x = x_;
        y = y_;
    }
 
    typedef float float2[2];
    inline Vect2f(const float2 &v) {
        x = v[0];
        y = v[1];
    }
 
    inline Vect2f(const Vect2i &v);
    inline Vect2f(const Vect2s &v);
 
    inline Vect2f &set(float x_, float y_)           {
        x = x_;
        y = y_;
        return *this;
    }
    inline Vect2f operator - () const                {
        return Vect2f(-x, -y);
    }
 
    inline int xi() const {
        return round(x);
    }
    inline int yi() const {
        return round(y);
    }
 
    inline const float &operator[](int i) const          {
        return *(&x + i);
    }
    inline float &operator[](int i)                      {
        return *(&x + i);
    }
 
    inline Vect2f &operator += (const Vect2f &v) {
        x += v.x;
        y += v.y;
        return *this;
    }
    inline Vect2f &operator -= (const Vect2f &v) {
        x -= v.x;
        y -= v.y;
        return *this;
    }
    inline Vect2f &operator *= (const Vect2f &v) {
        x *= v.x;
        y *= v.y;
        return *this;
    }
    inline Vect2f &operator /= (const Vect2f &v) {
        x /= v.x;
        y /= v.y;
        return *this;
    }
    inline Vect2f &operator *= (float f)         {
        x *= f;
        y *= f;
        return *this;
    }
    inline Vect2f &operator /= (float f)         {
        if (f != 0.f) f = 1 / f;
        else f = 0.0001f;
        x *= f;
        y *= f;
        return *this;
    }
 
    inline Vect2f operator + (const Vect2f &v) const     {
        return Vect2f(*this) += v;
    }
    inline Vect2f operator - (const Vect2f &v) const     {
        return Vect2f(*this) -= v;
    }
    inline Vect2f operator * (const Vect2f &v) const     {
        return Vect2f(*this) *= v;
    }
    inline Vect2f operator / (const Vect2f &v) const     {
        return Vect2f(*this) /= v;
    }
    inline Vect2f operator * (float f)   const       {
        return Vect2f(*this) *= f;
    }
    inline Vect2f operator / (float f)   const       {
        return Vect2f(*this) /= f;
    }
 
    inline bool eq(const Vect2f &v, float delta = FLT_COMPARE_TOLERANCE) const {
        return fabsf(v.x - x) < delta && fabsf(v.y - y) < delta;
    }
 
    inline float dot(const Vect2f &v) const {
        return x * v.x + y * v.y;
    }
    inline friend float dot(const Vect2f &u, const Vect2f &v) {
        return u.dot(v);
    }
 
    inline float operator % (const Vect2f &v) const {
        return x * v.y - y * v.x;
    }
 
    inline Vect2f &scaleAdd(const Vect2f &u, float lambda) {
        x += lambda * u.x;
        y += lambda * u.y;
        return *this;
    }
 
    inline Vect2f &interpolate(const Vect2f &u, const Vect2f &v, float lambda); // (1-lambda)*u + lambda*v
 
    inline float norm()  const                       {
        return sqrtf(x * x + y * y);
    }
    inline float norm2() const                       {
        return x * x + y * y;
    }
    inline Vect2f &normalize(float norma)                {
        float f = norma * invSqrtFast(x * x + y * y);
        x *= f;
        y *= f;
        return *this;
    }
    inline float distance(const Vect2f &v) const {
        return sqrtf(distance2(v));
    }
    inline float distance2(const Vect2f &v) const    {
        float dx = x - v.x, dy = y - v.y;
        return dx * dx + dy * dy;
    }
 
    inline void swap(Vect2f &v)                  {
        Vect2f tmp = v;
        v = *this;
        *this = tmp;
    }
};
 
 
//
//          class Vect2i
//
 
class Vect2i {
public:
    int x, y;
 
    inline Vect2i()                              { x = y = 0; }
    inline Vect2i(int x_, int y_)                        {
        x = x_;
        y = y_;
    }
    inline Vect2i(float x_, float y_)                    {
        x = round(x_);
        y = round(y_);
    }
 
    inline Vect2i(const Vect2f &v)           {
        x = round(v.x);
        y = round(v.y);
    }
    inline Vect2i(const Vect2s &v);
 
    inline void set(int x_, int y_)                  {
        x = x_;
        y = y_;
    }
    inline void set(float x_, float y_)              {
        x = round(x_);
        y = round(y_);
    }
    inline Vect2i operator - () const                {
        return Vect2i(-x, -y);
    }
 
    inline const int &operator[](int i) const            {
        return *(&x + i);
    }
    inline int &operator[](int i)                        {
        return *(&x + i);
    }
 
    inline Vect2i &operator += (const Vect2i &v) {
        x += v.x;
        y += v.y;
        return *this;
    }
    inline Vect2i &operator -= (const Vect2i &v) {
        x -= v.x;
        y -= v.y;
        return *this;
    }
    inline Vect2i &operator *= (const Vect2i &v) {
        x *= v.x;
        y *= v.y;
        return *this;
    }
    inline Vect2i &operator /= (const Vect2i &v) {
        x /= v.x;
        y /= v.y;
        return *this;
    }
 
    inline Vect2i operator + (const Vect2i &v) const     {
        return Vect2i(*this) += v;
    }
    inline Vect2i operator - (const Vect2i &v) const     {
        return Vect2i(*this) -= v;
    }
    inline Vect2i operator * (const Vect2i &v) const     {
        return Vect2i(*this) *= v;
    }
 
    inline Vect2i &operator *= (int f)               {
        x *= f;
        y *= f;
        return *this;
    }
    inline Vect2i operator * (int f) const       {
        return Vect2i(*this) *= f;
    }
 
    inline Vect2i &operator >>= (int n)              {
        x >>= n;
        y >>= n;
        return *this;
    }
    inline Vect2i operator >> (int n) const      {
        return Vect2i(*this) >>= n;
    }
 
    inline Vect2i &operator *= (float f)             {
        x = round(x * f);
        y = round(y * f);
        return *this;
    }
    inline Vect2i &operator /= (float f)             {
        return *this *= 1.f / f;
    }
    inline Vect2i operator * (float f) const         {
        return Vect2i(*this) *= f;
    }
    inline Vect2i operator / (float f) const         {
        return Vect2i(*this) /= f;
    }
 
    inline int dot(const Vect2i &v) const {
        return x * v.x + y * v.y;
    }
    inline friend int dot(const Vect2i &u, const Vect2i &v) {
        return u.dot(v);
    }
 
    inline int operator % (const Vect2i &v) const {
        return x * v.y - y * v.x;
    }
 
    inline int norm() const                      {
        return round(sqrtf(float(x * x + y * y)));
    }
    inline int norm2() const                     {
        return x * x + y * y;
    }
 
    inline void normalize(int norma)             {
        float f = (float)norma * invSqrtFast((float)(x * x + y * y));
        x = round(x * f);
        y = round(y * f);
    }
    inline int distance2(const Vect2i &v) const  {
        return sqr(x - v.x) + sqr(y - v.y);
    }
 
    inline int operator == (const Vect2i &v) const   {
        return x == v.x && y == v.y;
    }
    inline int operator != (const Vect2i &v) const   {
        return x != v.x || y != v.y;
    }
 
    inline void swap(Vect2i &v)                  {
        Vect2i tmp = v;
        v = *this;
        *this = tmp;
    }
};
 
 
//
//          class Vect2s
//
 
class Vect2s {
public:
    int16 x, y;
 
    inline Vect2s()                                      { x = y = 0; }
    inline Vect2s(int x_, int y_)                         {
        x = x_;
        y = y_;
    }
 
    inline Vect2s(const Vect2f &v)           {
        x = round(v.x);
        y = round(v.y);
    }
    inline Vect2s(const Vect2i &v)           {
        x = v.x;
        y = v.y;
    }
 
    inline void set(int x_, int y_)                  {
        x = x_;
        y = y_;
    }
    inline Vect2s operator - () const                {
        return Vect2s(-x, -y);
    }
 
    inline const int16 &operator[](int i) const          {
        return *(&x + i);
    }
    inline int16 &operator[](int i)                      {
        return *(&x + i);
    }
 
    inline Vect2s &operator += (const Vect2s &v) {
        x += v.x;
        y += v.y;
        return *this;
    }
    inline Vect2s &operator -= (const Vect2s &v) {
        x -= v.x;
        y -= v.y;
        return *this;
    }
    inline Vect2s &operator *= (const Vect2s &v) {
        x *= v.x;
        y *= v.y;
        return *this;
    }
    inline Vect2s &operator *= (float f)         {
        x = round(x * f);
        y = round(y * f);
        return *this;
    }
    inline Vect2s &operator /= (float f)         {
        if (f != 0.f) f = 1 / f;
        else f = 0.0001f;
        x = round(x * f);
        y = round(y * f);
        return *this;
    }
    inline Vect2s operator - (const Vect2s &v) const {
        return Vect2s(x - v.x, y - v.y);
    }
    inline Vect2s operator + (const Vect2s &v) const {
        return Vect2s(x + v.x, y + v.y);
    }
    inline Vect2s operator * (const Vect2s &v) const {
        return Vect2s(x * v.x, y * v.y);
    }
    inline Vect2s operator * (float f) const             {
        Vect2s tmp(round(x * f), round(y * f));
        return tmp;
    }
    inline Vect2s operator / (float f) const             {
        if (f != 0.f) f = 1 / f;
        else f = 0.0001f;
        Vect2s tmp(round(x * f), round(y * f));
        return tmp;
    }
 
    inline int operator == (const Vect2s &v) const   {
        return x == v.x && y == v.y;
    }
 
    inline int norm() const                              {
        return round(sqrtf((float)(x * x + y * y)));
    }
    inline int norm2() const                             {
        return x * x + y * y;
    }
    inline int distance(const Vect2s &v) const           {
        int dx = v.x - x, dy = v.y - y;
        return round(sqrtf((float)(dx * dx + dy * dy)));
    }
    inline void normalize(int norma)             {
        float f = (float)norma * invSqrtFast((float)((int)x * x + (int)y * y));
        x = round(x * f);
        y = round(y * f);
    }
 
    inline void swap(Vect2s &v)                  {
        Vect2s tmp = v;
        v = *this;
        *this = tmp;
    }
};
 
//
//          class Vect3f
//
 
class Vect3f {
 
public:
    typedef float float3[3];
 
    float x, y, z;
 
    // constructors //////////////////////////////////////////////////////////////
 
    inline Vect3f() { x = y = z = 0.0;}
    inline Vect3f(float x_, float y_, float z_) {
        x = x_;
        y = y_;
        z = z_;
    }
    explicit inline Vect3f(const Vect2f &v, float z_ = 0) {
        x = v.x;
        y = v.y;
        z = z_;
    }
 
    inline Vect3f(const float3 &v) {
        x = v[0];
        y = v[1];
        z = v[2];
    }
 
    inline operator const Vect2f &() const {
        return *reinterpret_cast<const Vect2f *>(this);
    }
 
    // setters / accessors / translators /////////////////////////////////////////
 
    inline Vect3f &set(float x_, float y_, float z_) {
        x = x_;
        y = y_;
        z = z_;
        return *this;
    }
 
    inline Vect3f &setSpherical(float psi, float theta, float radius);
 
    // index-based access:  0=x, 1=y, 2=z.
    inline const float &operator[](int i) const {
        return *(&x + i);
    }
    inline float &operator[](int i)       {
        return *(&x + i);
    }
 
    // Fortran index-based access:  1=x, 2=y, 3=z.
    inline const float &operator()(int i) const {
        return *(&x + i - 1);
    }
    inline float &operator()(int i)       {
        return *(&x + i - 1);
    }
 
    // Conversion to int ///////
    inline int xi() const {
        return round(x);
    }
    inline int yi() const {
        return round(y);
    }
    inline int zi() const {
        return round(z);
    }
 
    //  Negate  ////////////////////////////////////
    inline Vect3f operator- () const;
    inline Vect3f &negate(const Vect3f &v);
    inline Vect3f &negate();
 
    //  Logical operations  ////////////////////////////////
    inline bool eq(const Vect3f &v, float delta = FLT_COMPARE_TOLERANCE) const;
 
    //  Addition and substruction  ////////////////////
    inline Vect3f &add(const Vect3f &u, const Vect3f &v);
    inline Vect3f &add(const Vect3f &v);
    inline Vect3f &sub(const Vect3f &u, const Vect3f &v);
    inline Vect3f &sub(const Vect3f &v);
    inline Vect3f &operator+= (const Vect3f &v) {
        return add(v);
    }
    inline Vect3f &operator-= (const Vect3f &v) {
        return sub(v);
    }
    inline Vect3f operator+ (const Vect3f &v) const {
        Vect3f u;
        return u.add(*this, v);
    }
    inline Vect3f operator- (const Vect3f &v) const {
        Vect3f u;
        return u.sub(*this, v);
    }
 
    // Component-wise multiplication and division  ////////////////
    inline Vect3f &mult(const Vect3f &u, const Vect3f &v);
    inline Vect3f &mult(const Vect3f &v);
    inline Vect3f &div(const Vect3f &u, const Vect3f &v);
    inline Vect3f &div(const Vect3f &v);
    inline Vect3f &operator*= (const Vect3f &v) {
        return mult(v);
    }
    inline Vect3f &operator/= (const Vect3f &v) {
        return div(v);
    }
    inline Vect3f operator* (const Vect3f &v) const {
        Vect3f u;
        return u.mult(*this, v);
    }
    inline Vect3f operator/ (const Vect3f &v) const {
        Vect3f u;
        return u.div(*this, v);
    }
 
    //  Cross product  //////////////////////
    inline Vect3f &cross(const Vect3f &u, const Vect3f &v);// u x v  [!]
    inline Vect3f &precross(const Vect3f &v);      // v x this  [!]
    inline Vect3f &postcross(const Vect3f &v);     // this x v  [!]
    inline Vect3f &operator%= (const Vect3f &v) {
        return postcross(v);    // this x v  [!]
    }
    inline Vect3f operator% (const Vect3f &v) const {
        Vect3f u;
        return u.cross(*this, v);
    }
 
    //  Dot product  //////////////////////
    inline float dot(const Vect3f &other) const;
    inline friend float dot(const Vect3f &u, const Vect3f &v) {
        return u.dot(v);
    }
 
    // Multiplication & division by scalar ///////////
    inline Vect3f &scale(const Vect3f &v, float s);
    inline Vect3f &scale(float s);
 
    inline Vect3f &operator*= (float s) {
        return scale(s);
    }
    inline Vect3f &operator/= (float s) {
        return scale(1 / s);
    }
    inline Vect3f operator* (float s) const {
        Vect3f u;
        return u.scale(*this, s);
    }
    inline Vect3f operator/ (float s) const {
        Vect3f u;
        return u.scale(*this, 1 / s);
    }
    inline friend Vect3f operator* (float s, const Vect3f &v) {
        Vect3f u;
        return u.scale(v, s);
    }
 
    //  Normalize  ///////////////////////////
    inline Vect3f &normalize(float r = 1.0f);
    inline Vect3f &normalize(const Vect3f &v, float r = 1.0f);
 
    //  Operation returning scalar  ////////////
    inline float norm()  const;
    inline float norm2() const;  // norm^2
    inline float distance(const Vect3f &other) const;
    inline float distance2(const Vect3f &other) const;  // distance^2
 
    inline float psi() const;
    inline float theta() const;
 
    inline float min() const;
    inline float max() const;
    inline float minAbs() const;
    inline float maxAbs() const;
    inline float sumAbs() const;  // |x| + |y| + |z|
 
 
    //  Composite functions  ////////////////////////////////
    inline Vect3f &crossAdd(const Vect3f &u, const Vect3f &v, const Vect3f &w); // u x v + w [!]  this must be distinct from u and v, but not necessarily from w.
    inline Vect3f &crossAdd(const Vect3f &u, const Vect3f &v); // u x v + this [!]
    inline Vect3f &scaleAdd(const Vect3f &v, const Vect3f &u, float lambda); // v + lambda * u
    inline Vect3f &scaleAdd(const Vect3f &u, float lambda);// this + lambda * u
    inline Vect3f &interpolate(const Vect3f &u, const Vect3f &v, float lambda); // (1-lambda)*u + lambda*v
 
    //  Swap  /////////////////////////
    inline void swap(Vect3f &other);
    inline friend void swap(Vect3f &u, Vect3f &v) {
        u.swap(v);
    }
};
 
 
//
//          Miscellaneous functions
//
//  Decomposition  ////////////////////////////////
inline void decomposition(const Vect3f &axis, const Vect3f &v, Vect3f &v_normal, Vect3f &v_tangent) {
    // axis - axis of decomposition, v_normal - collinear to axis, v_tangent - perpendicular to axis
    v_normal.scale(axis, dot(axis, v) / ((axis).norm2()));
    v_tangent.sub(v, v_normal);
}
 
 
 
 
//
//      Vect2 definitions
//
inline Vect2i::Vect2i(const Vect2s &v)   {
    x = v.x;
    y = v.y;
}
inline Vect2f::Vect2f(const Vect2i &v)   {
    x = float(v.x);
    y = float(v.y);
}
inline Vect2f::Vect2f(const Vect2s &v)   {
    x = v.x;
    y = v.y;
}
 
Vect2f &Vect2f::interpolate(const Vect2f &u, const Vect2f &v, float lambda) {
    float lambda2 = 1.0f - lambda;
 
    x = lambda2 * u.x + lambda * v.x;
    y = lambda2 * u.y + lambda * v.y;
    return *this;
}
 
//
//      Vect3f inline definitions
//
 
//  Dot product  //////////////////////
//inline double dot(const Vect3d& u, const Vect3f& v) { return u.dot(v); }
//inline float dot(const Vect3f& u, const Vect3d& v) { return u.dot(v); }
 
bool Vect3f::eq(const Vect3f &other, float delta) const {
    return fabs(x - other.x) < delta &&
           fabs(y - other.y) < delta &&
           fabs(z - other.z) < delta;
}
 
Vect3f Vect3f::operator- () const {
    return Vect3f(-x, -y, -z);
}
 
//  Norm operations /////////
float Vect3f::sumAbs() const {
    return (float)(fabs(x) + fabs(y) + fabs(z));
}
 
 
//  Descart - spherical function  //////////////
float Vect3f::psi() const {
    return (float)atan2(y, x);
}
float Vect3f::theta() const {
    return (float)acos(z / (norm() + FLT_EPS));
}
Vect3f &Vect3f::setSpherical(float psi, float theta, float radius) {
    x = radius * (float)sin(theta);
    y = x * (float)sin(psi);
    x = x * (float)cos(psi);
    z = radius * (float)cos(theta);
    return *this;
}
 
float Vect3f::dot(const Vect3f &other) const {
    return x * other.x + y * other.y + z * other.z;
}
 
 
float Vect3f::norm() const {
    return (float)sqrt(x * x + y * y + z * z);
}
 
 
float Vect3f::norm2() const {
    return (x * x + y * y + z * z);
}
 
 
float Vect3f::distance(const Vect3f &other) const {
    Vect3f w;
 
    w.sub(other, *this);
    return w.norm();
}
 
 
float Vect3f::distance2(const Vect3f &other) const {
    Vect3f w;
 
    w.sub(other, *this);
    return w.norm2();
}
 
 
float Vect3f::min() const {
    return (x <= y) ? ((x <= z) ? x : z) : ((y <= z) ? y : z);
}
 
 
float Vect3f::max() const {
    return (x >= y) ? ((x >= z) ? x : z) : ((y >= z) ? y : z);
}
 
 
float Vect3f::minAbs() const {
    float ax, ay, az;
 
    ax = (float)fabs(x);
    ay = (float)fabs(y);
    az = (float)fabs(z);
    return (ax <= ay) ? ((ax <= az) ? ax : az) : ((ay <= az) ? ay : az);
}
 
 
float Vect3f::maxAbs() const {
    float ax, ay, az;
 
    ax = (float)fabs(x);
    ay = (float)fabs(y);
    az = (float)fabs(z);
    return (ax >= ay) ? ((ax >= az) ? ax : az) : ((ay >= az) ? ay : az);
}
 
 
void Vect3f::swap(Vect3f &other) {
    Vect3f tmp;
 
    tmp = *this;
    *this = other;
    other = tmp;
}
 
 
Vect3f &Vect3f::normalize(const Vect3f &v, float r) {
    float s = r * invSqrtFast(v.x * v.x + v.y * v.y + v.z * v.z);
    x = s * v.x;
    y = s * v.y;
    z = s * v.z;
    return *this;
}
 
 
Vect3f &Vect3f::normalize(float r) {
    float s = r * invSqrtFast(x * x + y * y + z * z);
    x *= s;
    y *= s;
    z *= s;
    return *this;
}
 
Vect3f &Vect3f::negate(const Vect3f &v) {
    x = - v.x;
    y = - v.y;
    z = - v.z;
    return *this;
}
 
 
Vect3f &Vect3f::negate() {
    x = - x;
    y = - y;
    z = - z;
    return *this;
}
 
 
Vect3f &Vect3f::add(const Vect3f &u, const Vect3f &v) {
    x = u.x + v.x;
    y = u.y + v.y;
    z = u.z + v.z;
    return *this;
}
 
 
Vect3f &Vect3f::add(const Vect3f &v) {
    x += v.x;
    y += v.y;
    z += v.z;
    return *this;
}
 
 
Vect3f &Vect3f::sub(const Vect3f &u, const Vect3f &v) {
    x = u.x - v.x;
    y = u.y - v.y;
    z = u.z - v.z;
    return *this;
}
 
 
Vect3f &Vect3f::sub(const Vect3f &v) {
    x -= v.x;
    y -= v.y;
    z -= v.z;
    return *this;
}
 
 
Vect3f &Vect3f::mult(const Vect3f &u, const Vect3f &v) {
    x = u.x * v.x;
    y = u.y * v.y;
    z = u.z * v.z;
    return *this;
}
 
 
Vect3f &Vect3f::mult(const Vect3f &v) {
    x *= v.x;
    y *= v.y;
    z *= v.z;
    return *this;
}
 
Vect3f &Vect3f::div(const Vect3f &u, const Vect3f &v) {
    x = u.x / v.x;
    y = u.y / v.y;
    z = u.z / v.z;
    return *this;
}
 
 
Vect3f &Vect3f::div(const Vect3f &v) {
    x /= v.x;
    y /= v.y;
    z /= v.z;
    return *this;
}
 
 
 
Vect3f &Vect3f::scale(const Vect3f &v, float s) {
    x = s * v.x;
    y = s * v.y;
    z = s * v.z;
    return *this;
}
 
 
Vect3f &Vect3f::scale(float s) {
    x *= s;
    y *= s;
    z *= s;
    return *this;
}
 
 
 
Vect3f &Vect3f::cross(const Vect3f &u, const Vect3f &v) {
    x = u.y * v.z - u.z * v.y;
    y = u.z * v.x - u.x * v.z;
    z = u.x * v.y - u.y * v.x;
    return *this;
}
 
 
Vect3f &Vect3f::precross(const Vect3f &v) {
    float ox, oy;
 
    ox = x;
    oy = y;
    x = v.y * z - v.z * oy;
    y = v.z * ox - v.x * z;
    z = v.x * oy - v.y * ox;
    return *this;
}
 
 
Vect3f &Vect3f::postcross(const Vect3f &v) {
    float ox, oy;
 
    ox = x;
    oy = y;
    x = oy * v.z - z * v.y;
    y = z * v.x - ox * v.z;
    z = ox * v.y - oy * v.x;
    return *this;
}
 
 
Vect3f &Vect3f::crossAdd(const Vect3f &u, const Vect3f &v, const Vect3f &w) {
    x = u.y * v.z - u.z * v.y + w.x;
    y = u.z * v.x - u.x * v.z + w.y;
    z = u.x * v.y - u.y * v.x + w.z;
    return *this;
}
 
 
Vect3f &Vect3f::crossAdd(const Vect3f &u, const Vect3f &v) {
    x += u.y * v.z - u.z * v.y;
    y += u.z * v.x - u.x * v.z;
    z += u.x * v.y - u.y * v.x;
    return *this;
}
 
 
Vect3f &Vect3f::scaleAdd(const Vect3f &v, const Vect3f &u, float lambda) {
    x = v.x + lambda * u.x;
    y = v.y + lambda * u.y;
    z = v.z + lambda * u.z;
    return *this;
}
 
 
Vect3f &Vect3f::scaleAdd(const Vect3f &u, float lambda) {
    x += lambda * u.x;
    y += lambda * u.y;
    z += lambda * u.z;
    return *this;
}
 
 
Vect3f &Vect3f::interpolate(const Vect3f &u, const Vect3f &v, float lambda) {
    float lambda2 = 1.0f - lambda;
 
    x = lambda2 * u.x + lambda * v.x;
    y = lambda2 * u.y + lambda * v.y;
    z = lambda2 * u.z + lambda * v.z;
    return *this;
}
 
} // namespace QDEngine
 
#endif // QDENGINE_XMATH_H