bullet3/examples/TinyRenderer/geometry.h

#ifndef __GEOMETRY_H__
#define __GEOMETRY_H__
#include <cmath>
#include <cassert>
#include <stdlib.h>

template <size_t DimCols, size_t DimRows, typename T>
class mat;

template <size_t DIM, typename T>
struct vec
{
	vec()
	{
		for (size_t i = DIM; i--; data_[i] = T())
			;
	}
	T& operator[](const size_t i)
	{
		assert(i < DIM);
		return data_[i];
	}
	const T& operator[](const size_t i) const
	{
		assert(i < DIM);
		return data_[i];
	}

private:
	T data_[DIM];
};

/////////////////////////////////////////////////////////////////////////////////

template <typename T>
struct vec<2, T>
{
	vec() : x(T()), y(T()) {}
	vec(T X, T Y) : x(X), y(Y) {}
	template <class U>
	vec<2, T>(const vec<2, U>& v);
	T& operator[](const size_t i)
	{
		assert(i < 2);
		return i <= 0 ? x : y;
	}
	const T& operator[](const size_t i) const
	{
		assert(i < 2);
		return i <= 0 ? x : y;
	}

	T x, y;
};

/////////////////////////////////////////////////////////////////////////////////

template <typename T>
struct vec<3, T>
{
	vec() : x(T()), y(T()), z(T()) {}
	vec(T X, T Y, T Z) : x(X), y(Y), z(Z) {}
	template <class U>
	vec<3, T>(const vec<3, U>& v);
	T& operator[](const size_t i)
	{
		assert(i < 3);
		return i <= 0 ? x : (1 == i ? y : z);
	}
	const T& operator[](const size_t i) const
	{
		assert(i < 3);
		return i <= 0 ? x : (1 == i ? y : z);
	}
	float norm() { return std::sqrt(x * x + y * y + z * z); }
	vec<3, T>& normalize(T l = 1)
	{
		*this = (*this) * (l / norm());
		return *this;
	}

	T x, y, z;
};

/////////////////////////////////////////////////////////////////////////////////

template <size_t DIM, typename T>
T operator*(const vec<DIM, T>& lhs, const vec<DIM, T>& rhs)
{
	T ret = T();
	for (size_t i = DIM; i--; ret += lhs[i] * rhs[i])
		;
	return ret;
}

template <size_t DIM, typename T>
vec<DIM, T> operator+(vec<DIM, T> lhs, const vec<DIM, T>& rhs)
{
	for (size_t i = DIM; i--; lhs[i] += rhs[i])
		;
	return lhs;
}

template <size_t DIM, typename T>
vec<DIM, T> operator-(vec<DIM, T> lhs, const vec<DIM, T>& rhs)
{
	for (size_t i = DIM; i--; lhs[i] -= rhs[i])
		;
	return lhs;
}

template <size_t DIM, typename T, typename U>
vec<DIM, T> operator*(vec<DIM, T> lhs, const U& rhs)
{
	for (size_t i = DIM; i--; lhs[i] *= rhs)
		;
	return lhs;
}

template <size_t DIM, typename T, typename U>
vec<DIM, T> operator/(vec<DIM, T> lhs, const U& rhs)
{
	for (size_t i = DIM; i--; lhs[i] /= rhs)
		;
	return lhs;
}

template <size_t LEN, size_t DIM, typename T>
vec<LEN, T> embed(const vec<DIM, T>& v, T fill = 1)
{
	vec<LEN, T> ret;
	for (size_t i = LEN; i--; ret[i] = (i < DIM ? v[i] : fill))
		;
	return ret;
}

template <size_t LEN, size_t DIM, typename T>
vec<LEN, T> proj(const vec<DIM, T>& v)
{
	vec<LEN, T> ret;
	for (size_t i = LEN; i--; ret[i] = v[i])
		;
	return ret;
}

template <typename T>
vec<3, T> cross(vec<3, T> v1, vec<3, T> v2)
{
	return vec<3, T>(v1.y * v2.z - v1.z * v2.y, v1.z * v2.x - v1.x * v2.z, v1.x * v2.y - v1.y * v2.x);
}
#if 0
template <size_t DIM, typename T> std::ostream& operator<<(std::ostream& out, vec<DIM,T>& v) {
    for(unsigned int i=0; i<DIM; i++) {
        out << v[i] << " " ;
    }
    return out ;
}
#endif
/////////////////////////////////////////////////////////////////////////////////

template <size_t DIM, typename T>
struct dt
{
	static T det(const mat<DIM, DIM, T>& src)
	{
		T ret = 0;
		for (size_t i = DIM; i--; ret += src[0][i] * src.cofactor(0, i))
			;
		return ret;
	}
};

template <typename T>
struct dt<1, T>
{
	static T det(const mat<1, 1, T>& src)
	{
		return src[0][0];
	}
};

/////////////////////////////////////////////////////////////////////////////////

template <size_t DimRows, size_t DimCols, typename T>
class mat
{
	vec<DimCols, T> rows[DimRows];

public:
	mat() {}

	vec<DimCols, T>& operator[](const size_t idx)
	{
		assert(idx < DimRows);
		return rows[idx];
	}

	const vec<DimCols, T>& operator[](const size_t idx) const
	{
		assert(idx < DimRows);
		return rows[idx];
	}

	vec<DimRows, T> col(const size_t idx) const
	{
		assert(idx < DimCols);
		vec<DimRows, T> ret;
		for (size_t i = DimRows; i--; ret[i] = rows[i][idx])
			;
		return ret;
	}

	void set_col(size_t idx, vec<DimRows, T> v)
	{
		assert(idx < DimCols);
		for (size_t i = DimRows; i--; rows[i][idx] = v[i])
			;
	}

	static mat<DimRows, DimCols, T> identity()
	{
		mat<DimRows, DimCols, T> ret;
		for (size_t i = DimRows; i--;)
			for (size_t j = DimCols; j--; ret[i][j] = (i == j))
				;
		return ret;
	}

	T det() const
	{
		return dt<DimCols, T>::det(*this);
	}

	mat<DimRows - 1, DimCols - 1, T> get_minor(size_t row, size_t col) const
	{
		mat<DimRows - 1, DimCols - 1, T> ret;
		for (size_t i = DimRows - 1; i--;)
			for (size_t j = DimCols - 1; j--; ret[i][j] = rows[i < row ? i : i + 1][j < col ? j : j + 1])
				;
		return ret;
	}

	T cofactor(size_t row, size_t col) const
	{
		return get_minor(row, col).det() * ((row + col) % 2 ? -1 : 1);
	}

	mat<DimRows, DimCols, T> adjugate() const
	{
		mat<DimRows, DimCols, T> ret;
		for (size_t i = DimRows; i--;)
			for (size_t j = DimCols; j--; ret[i][j] = cofactor(i, j))
				;
		return ret;
	}

	mat<DimRows, DimCols, T> invert_transpose()
	{
		mat<DimRows, DimCols, T> ret = adjugate();
		T tmp = ret[0] * rows[0];
		return ret / tmp;
	}

	mat<DimRows, DimCols, T> invert()
	{
		return invert_transpose().transpose();
	}

	mat<DimCols, DimRows, T> transpose()
	{
		mat<DimCols, DimRows, T> ret;
		for (size_t i = DimCols; i--; ret[i] = this->col(i))
			;
		return ret;
	}
};

/////////////////////////////////////////////////////////////////////////////////

template <size_t DimRows, size_t DimCols, typename T>
vec<DimRows, T> operator*(const mat<DimRows, DimCols, T>& lhs, const vec<DimCols, T>& rhs)
{
	vec<DimRows, T> ret;
	for (size_t i = DimRows; i--; ret[i] = lhs[i] * rhs)
		;
	return ret;
}

template <size_t R1, size_t C1, size_t C2, typename T>
mat<R1, C2, T> operator*(const mat<R1, C1, T>& lhs, const mat<C1, C2, T>& rhs)
{
	mat<R1, C2, T> result;
	for (size_t i = R1; i--;)
		for (size_t j = C2; j--; result[i][j] = lhs[i] * rhs.col(j))
			;
	return result;
}

template <size_t DimRows, size_t DimCols, typename T>
mat<DimCols, DimRows, T> operator/(mat<DimRows, DimCols, T> lhs, const T& rhs)
{
	for (size_t i = DimRows; i--; lhs[i] = lhs[i] / rhs)
		;
	return lhs;
}

#if 0
template <size_t DimRows,size_t DimCols,class T> std::ostream& operator<<(std::ostream& out, mat<DimRows,DimCols,T>& m) {
    for (size_t i=0; i<DimRows; i++) out << m[i] << std::endl;
    return out;
}
#endif
/////////////////////////////////////////////////////////////////////////////////

typedef vec<2, float> Vec2f;
typedef vec<2, int> Vec2i;
typedef vec<3, float> Vec3f;
typedef vec<3, int> Vec3i;
typedef vec<4, float> Vec4f;
typedef mat<4, 4, float> Matrix;
#endif  //__GEOMETRY_H__