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#ifndef VECTOR_H
#define VECTOR_H
#include <cassert>
#include <cmath>
#include <iostream>
namespace gfx
{
template<class T, int n>
struct Vector
{
// Keep the Vector struct a plain old data (POD) struct by avoiding constructors
static Vector vector(T x)
{
Vector result;
for (int i = 0; i < n; ++i)
result.v[i] = x;
return result;
}
// Use only for 2D vectors
static Vector vector(T x, T y)
{
assert(n == 2);
Vector result;
result.v[0] = x;
result.v[1] = y;
return result;
}
// Use only for 3D vectors
static Vector vector(T x, T y, T z)
{
assert(n == 3);
Vector result;
result.v[0] = x;
result.v[1] = y;
result.v[2] = z;
return result;
}
// Use only for 4D vectors
static Vector vector(T x, T y, T z, T w)
{
assert(n == 4);
Vector result;
result.v[0] = x;
result.v[1] = y;
result.v[2] = z;
result.v[3] = w;
return result;
}
// Pass 'n' arguments to this function.
static Vector vector(T *v)
{
Vector result;
for (int i = 0; i < n; ++i)
result.v[i] = v[i];
return result;
}
T &operator [] (int i) {return v[i];}
T operator [] (int i) const {return v[i];}
#define VECTOR_BINARY_OP(op, arg, rhs) \
Vector operator op (arg) const \
{ \
Vector result; \
for (int i = 0; i < n; ++i) \
result.v[i] = v[i] op rhs; \
return result; \
}
VECTOR_BINARY_OP(+, const Vector &u, u.v[i])
VECTOR_BINARY_OP(-, const Vector &u, u.v[i])
VECTOR_BINARY_OP(*, const Vector &u, u.v[i])
VECTOR_BINARY_OP(/, const Vector &u, u.v[i])
VECTOR_BINARY_OP(+, T s, s)
VECTOR_BINARY_OP(-, T s, s)
VECTOR_BINARY_OP(*, T s, s)
VECTOR_BINARY_OP(/, T s, s)
#undef VECTOR_BINARY_OP
Vector operator - () const
{
Vector result;
for (int i = 0; i < n; ++i)
result.v[i] = -v[i];
return result;
}
#define VECTOR_ASSIGN_OP(op, arg, rhs) \
Vector &operator op (arg) \
{ \
for (int i = 0; i < n; ++i) \
v[i] op rhs; \
return *this; \
}
VECTOR_ASSIGN_OP(+=, const Vector &u, u.v[i])
VECTOR_ASSIGN_OP(-=, const Vector &u, u.v[i])
VECTOR_ASSIGN_OP(=, T s, s)
VECTOR_ASSIGN_OP(*=, T s, s)
VECTOR_ASSIGN_OP(/=, T s, s)
#undef VECTOR_ASSIGN_OP
static T dot(const Vector &u, const Vector &v)
{
T sum(0);
for (int i = 0; i < n; ++i)
sum += u.v[i] * v.v[i];
return sum;
}
static Vector cross(const Vector &u, const Vector &v)
{
assert(n == 3);
return vector(u.v[1] * v.v[2] - u.v[2] * v.v[1],
u.v[2] * v.v[0] - u.v[0] * v.v[2],
u.v[0] * v.v[1] - u.v[1] * v.v[0]);
}
T sqrNorm() const
{
return dot(*this, *this);
}
// requires floating point type T
void normalize()
{
T s = sqrNorm();
if (s != 0)
*this /= sqrt(s);
}
// requires floating point type T
Vector normalized() const
{
T s = sqrNorm();
if (s == 0)
return *this;
return *this / sqrt(s);
}
T *bits() {return v;}
const T *bits() const {return v;}
T v[n];
};
#define SCALAR_VECTOR_BINARY_OP(op) \
template<class T, int n> \
Vector<T, n> operator op (T s, const Vector<T, n>& u) \
{ \
Vector<T, n> result; \
for (int i = 0; i < n; ++i) \
result[i] = s op u[i]; \
return result; \
}
SCALAR_VECTOR_BINARY_OP(+)
SCALAR_VECTOR_BINARY_OP(-)
SCALAR_VECTOR_BINARY_OP(*)
SCALAR_VECTOR_BINARY_OP(/)
#undef SCALAR_VECTOR_BINARY_OP
template<class T, int n>
std::ostream &operator << (std::ostream &os, const Vector<T, n> &v)
{
assert(n > 0);
os << "[" << v[0];
for (int i = 1; i < n; ++i)
os << ", " << v[i];
os << "]";
return os;
}
typedef Vector<float, 2> Vector2f;
typedef Vector<float, 3> Vector3f;
typedef Vector<float, 4> Vector4f;
template<class T, int rows, int cols>
struct Matrix
{
// Keep the Matrix struct a plain old data (POD) struct by avoiding constructors
static Matrix matrix(T x)
{
Matrix result;
for (int i = 0; i < rows; ++i) {
for (int j = 0; j < cols; ++j)
result.v[i][j] = x;
}
return result;
}
static Matrix matrix(T *m)
{
Matrix result;
for (int i = 0; i < rows; ++i) {
for (int j = 0; j < cols; ++j) {
result.v[i][j] = *m;
++m;
}
}
return result;
}
T &operator () (int i, int j) {return v[i][j];}
T operator () (int i, int j) const {return v[i][j];}
Vector<T, cols> &operator [] (int i) {return v[i];}
const Vector<T, cols> &operator [] (int i) const {return v[i];}
// TODO: operators, methods
Vector<T, rows> operator * (const Vector<T, cols> &u) const
{
Vector<T, rows> result;
for (int i = 0; i < rows; ++i)
result[i] = Vector<T, cols>::dot(v[i], u);
return result;
}
template<int k>
Matrix<T, rows, k> operator * (const Matrix<T, cols, k> &m)
{
Matrix<T, rows, k> result;
for (int i = 0; i < rows; ++i)
result[i] = v[i] * m;
return result;
}
T* bits() {return reinterpret_cast<T *>(this);}
const T* bits() const {return reinterpret_cast<const T *>(this);}
// Simple Gauss elimination.
// TODO: Optimize and improve stability.
Matrix inverse(bool *ok = 0) const
{
assert(rows == cols);
Matrix rhs = identity();
Matrix lhs(*this);
T temp;
// Down
for (int i = 0; i < rows; ++i) {
// Pivoting
int pivot = i;
for (int j = i; j < rows; ++j) {
if (qAbs(lhs(j, i)) > lhs(pivot, i))
pivot = j;
}
// TODO: fuzzy compare.
if (lhs(pivot, i) == T(0)) {
if (ok)
*ok = false;
return rhs;
}
if (pivot != i) {
for (int j = i; j < cols; ++j) {
temp = lhs(pivot, j);
lhs(pivot, j) = lhs(i, j);
lhs(i, j) = temp;
}
for (int j = 0; j < cols; ++j) {
temp = rhs(pivot, j);
rhs(pivot, j) = rhs(i, j);
rhs(i, j) = temp;
}
}
// Normalize i-th row
rhs[i] /= lhs(i, i);
for (int j = cols - 1; j > i; --j)
lhs(i, j) /= lhs(i, i);
// Eliminate non-zeros in i-th column below the i-th row.
for (int j = i + 1; j < rows; ++j) {
rhs[j] -= lhs(j, i) * rhs[i];
for (int k = i + 1; k < cols; ++k)
lhs(j, k) -= lhs(j, i) * lhs(i, k);
}
}
// Up
for (int i = rows - 1; i > 0; --i) {
for (int j = i - 1; j >= 0; --j)
rhs[j] -= lhs(j, i) * rhs[i];
}
if (ok)
*ok = true;
return rhs;
}
Matrix<T, cols, rows> transpose() const
{
Matrix<T, cols, rows> result;
for (int i = 0; i < rows; ++i) {
for (int j = 0; j < cols; ++j)
result.v[j][i] = v[i][j];
}
return result;
}
static Matrix identity()
{
Matrix result = matrix(T(0));
for (int i = 0; i < rows && i < cols; ++i)
result.v[i][i] = T(1);
return result;
}
Vector<T, cols> v[rows];
};
template<class T, int rows, int cols>
Vector<T, cols> operator * (const Vector<T, rows> &u, const Matrix<T, rows, cols> &m)
{
Vector<T, cols> result = Vector<T, cols>::vector(T(0));
for (int i = 0; i < rows; ++i)
result += m[i] * u[i];
return result;
}
template<class T, int rows, int cols>
std::ostream &operator << (std::ostream &os, const Matrix<T, rows, cols> &m)
{
assert(rows > 0);
os << "[" << m[0];
for (int i = 1; i < rows; ++i)
os << ", " << m[i];
os << "]";
return os;
}
typedef Matrix<float, 2, 2> Matrix2x2f;
typedef Matrix<float, 3, 3> Matrix3x3f;
typedef Matrix<float, 4, 4> Matrix4x4f;
template<class T>
struct Quaternion
{
// Keep the Quaternion struct a plain old data (POD) struct by avoiding constructors
static Quaternion quaternion(T s, T x, T y, T z)
{
Quaternion result;
result.scalar = s;
result.vector[0] = x;
result.vector[1] = y;
result.vector[2] = z;
return result;
}
static Quaternion quaternion(T s, const Vector<T, 3> &v)
{
Quaternion result;
result.scalar = s;
result.vector = v;
return result;
}
static Quaternion identity()
{
return quaternion(T(1), T(0), T(0), T(0));
}
// assumes that all the elements are packed tightly
T& operator [] (int i) {return reinterpret_cast<T *>(this)[i];}
T operator [] (int i) const {return reinterpret_cast<const T *>(this)[i];}
#define QUATERNION_BINARY_OP(op, arg, rhs) \
Quaternion operator op (arg) const \
{ \
Quaternion result; \
for (int i = 0; i < 4; ++i) \
result[i] = (*this)[i] op rhs; \
return result; \
}
QUATERNION_BINARY_OP(+, const Quaternion &q, q[i])
QUATERNION_BINARY_OP(-, const Quaternion &q, q[i])
QUATERNION_BINARY_OP(*, T s, s)
QUATERNION_BINARY_OP(/, T s, s)
#undef QUATERNION_BINARY_OP
Quaternion operator - () const
{
return Quaternion(-scalar, -vector);
}
Quaternion operator * (const Quaternion &q) const
{
Quaternion result;
result.scalar = scalar * q.scalar - Vector<T, 3>::dot(vector, q.vector);
result.vector = scalar * q.vector + vector * q.scalar + Vector<T, 3>::cross(vector, q.vector);
return result;
}
Quaternion operator * (const Vector<T, 3> &v) const
{
Quaternion result;
result.scalar = -Vector<T, 3>::dot(vector, v);
result.vector = scalar * v + Vector<T, 3>::cross(vector, v);
return result;
}
friend Quaternion operator * (const Vector<T, 3> &v, const Quaternion &q)
{
Quaternion result;
result.scalar = -Vector<T, 3>::dot(v, q.vector);
result.vector = v * q.scalar + Vector<T, 3>::cross(v, q.vector);
return result;
}
#define QUATERNION_ASSIGN_OP(op, arg, rhs) \
Quaternion &operator op (arg) \
{ \
for (int i = 0; i < 4; ++i) \
(*this)[i] op rhs; \
return *this; \
}
QUATERNION_ASSIGN_OP(+=, const Quaternion &q, q[i])
QUATERNION_ASSIGN_OP(-=, const Quaternion &q, q[i])
QUATERNION_ASSIGN_OP(=, T s, s)
QUATERNION_ASSIGN_OP(*=, T s, s)
QUATERNION_ASSIGN_OP(/=, T s, s)
#undef QUATERNION_ASSIGN_OP
Quaternion& operator *= (const Quaternion &q)
{
Quaternion result;
result.scalar = scalar * q.scalar - Vector<T, 3>::dot(vector, q.vector);
result.vector = scalar * q.vector + vector * q.scalar + Vector<T, 3>::cross(vector, q.vector);
return (*this = result);
}
Quaternion& operator *= (const Vector<T, 3> &v)
{
Quaternion result;
result.scalar = -Vector<T, 3>::dot(vector, v);
result.vector = scalar * v + Vector<T, 3>::cross(vector, v);
return (*this = result);
}
Quaternion conjugate() const
{
return quaternion(scalar, -vector);
}
T sqrNorm() const
{
return scalar * scalar + vector.sqrNorm();
}
Quaternion inverse() const
{
return conjugate() / sqrNorm();
}
// requires floating point type T
Quaternion normalized() const
{
T s = sqrNorm();
if (s == 0)
return *this;
return *this / sqrt(s);
}
void matrix(Matrix<T, 3, 3>& m) const
{
T bb = vector[0] * vector[0];
T cc = vector[1] * vector[1];
T dd = vector[2] * vector[2];
T diag = scalar * scalar - bb - cc - dd;
T ab = scalar * vector[0];
T ac = scalar * vector[1];
T ad = scalar * vector[2];
T bc = vector[0] * vector[1];
T cd = vector[1] * vector[2];
T bd = vector[2] * vector[0];
m(0, 0) = diag + 2 * bb;
m(0, 1) = 2 * (bc - ad);
m(0, 2) = 2 * (ac + bd);
m(1, 0) = 2 * (ad + bc);
m(1, 1) = diag + 2 * cc;
m(1, 2) = 2 * (cd - ab);
m(2, 0) = 2 * (bd - ac);
m(2, 1) = 2 * (ab + cd);
m(2, 2) = diag + 2 * dd;
}
void matrix(Matrix<T, 4, 4>& m) const
{
T bb = vector[0] * vector[0];
T cc = vector[1] * vector[1];
T dd = vector[2] * vector[2];
T diag = scalar * scalar - bb - cc - dd;
T ab = scalar * vector[0];
T ac = scalar * vector[1];
T ad = scalar * vector[2];
T bc = vector[0] * vector[1];
T cd = vector[1] * vector[2];
T bd = vector[2] * vector[0];
m(0, 0) = diag + 2 * bb;
m(0, 1) = 2 * (bc - ad);
m(0, 2) = 2 * (ac + bd);
m(0, 3) = 0;
m(1, 0) = 2 * (ad + bc);
m(1, 1) = diag + 2 * cc;
m(1, 2) = 2 * (cd - ab);
m(1, 3) = 0;
m(2, 0) = 2 * (bd - ac);
m(2, 1) = 2 * (ab + cd);
m(2, 2) = diag + 2 * dd;
m(2, 3) = 0;
m(3, 0) = 0;
m(3, 1) = 0;
m(3, 2) = 0;
m(3, 3) = 1;
}
// assumes that 'this' is normalized
Vector<T, 3> transform(const Vector<T, 3> &v) const
{
Matrix<T, 3, 3> m;
matrix(m);
return v * m;
}
// assumes that all the elements are packed tightly
T* bits() {return reinterpret_cast<T *>(this);}
const T* bits() const {return reinterpret_cast<const T *>(this);}
// requires floating point type T
static Quaternion rotation(T angle, const Vector<T, 3> &unitAxis)
{
T s = sin(angle / 2);
T c = cos(angle / 2);
return quaternion(c, unitAxis * s);
}
T scalar;
Vector<T, 3> vector;
};
template<class T>
Quaternion<T> operator * (T s, const Quaternion<T>& q)
{
return Quaternion<T>::quaternion(s * q.scalar, s * q.vector);
}
typedef Quaternion<float> Quaternionf;
} // end namespace gfx
#endif