worldspawn/libs/math/expression.h

/*
   Copyright (C) 2001-2006, William Joseph.
   All Rights Reserved.

   This file is part of GtkRadiant.

   GtkRadiant 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 2 of the License, or
   (at your option) any later version.

   GtkRadiant 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 GtkRadiant; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */

#if !defined ( INCLUDED_EXPRESSION_H )
#define INCLUDED_EXPRESSION_H

#include <math/matrix.h>

template<typename Value>
class Literal
{
Value m_value;
public:
typedef Value value_type;

Literal( const Value& value )
	: m_value( value ){
}
const value_type& eval() const {
	return m_value;
}
};

template<typename Value>
inline Literal<Value> float_literal( const Value& value ){
	return Literal<Value>( value );
}

template<typename Expression>
inline float float_for_expression( const Expression& expression ){
	return expression.eval();
}


template<typename First, typename Second>
class ScalarDivided
{
First first;
Second second;
public:
typedef typename First::value_type value_type;

ScalarDivided( const First& first_, const Second& second_ ) : first( first_ ), second( second_ ){
}
value_type eval() const {
	return static_cast<value_type>( first.eval() / second.eval() );
}
};

template<typename First, typename Second>
inline ScalarDivided<First, Second> float_divided( const First& first, const Second& second ){
	return ScalarDivided<First, Second>( first, second );
}

template<typename First>
inline ScalarDivided<Literal<typename First::value_type>, First> float_reciprocal( const First& first ){
	typedef typename First::value_type first_value_type;
	return ScalarDivided<Literal<first_value_type>, First>( float_literal( first_value_type( 1.0 ) ), first );
}

template<typename First>
class SquareRoot
{
First first;
public:
typedef typename First::value_type value_type;

SquareRoot( const First& first_ ) : first( first_ ){
}
value_type eval() const {
	return static_cast<value_type>( sqrt( first.eval() ) );
}
};

template<typename First>
inline SquareRoot<First> float_square_root( const First& first ){
	return SquareRoot<First>( first );
}


template<typename Element>
class BasicVector3Literal
{
const BasicVector3<Element> m_value;
public:
typedef Element value_type;
typedef IntegralConstant<3> dimension;

BasicVector3Literal( const BasicVector3<Element>& value )
	: m_value( value ){
}
const value_type& eval( unsigned int i ) const {
	return m_value[i];
}
};

template<typename Element>
inline BasicVector3Literal<Element> vector3_literal( const BasicVector3<Element>& value ){
	return BasicVector3Literal<Element>( value );
}

typedef BasicVector3Literal<float> Vector3Literal;

template<typename Element>
class BasicVector3Identity
{
const BasicVector3<Element>& m_value;
public:
typedef Element value_type;
typedef IntegralConstant<3> dimension;

BasicVector3Identity( const BasicVector3<Element>& value )
	: m_value( value ){
}
const value_type& eval( unsigned int i ) const {
	return m_value[i];
}
};

template<typename Element>
inline BasicVector3Identity<Element> vector3_identity( const BasicVector3<Element>& value ){
	return BasicVector3Identity<Element>( value );
}

typedef BasicVector3Identity<float> Vector3Identity;

template<typename Expression>
inline BasicVector3<typename Expression::value_type> vector3_for_expression( const Expression& expression ){
	return Vector3( expression.eval( 0 ), expression.eval( 1 ), expression.eval( 2 ) );
}


template<typename Operation, typename First, typename Second>
class VectorScalar
{
First first;
Literal<typename Second::value_type> second;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

VectorScalar( const First& first_, const Second& second_ )
	: first( first_ ), second( second_.eval() ){
}
value_type eval( unsigned int i ) const {
	return Operation::apply( first.eval( i ), second.eval() );
}
};



template<typename Operation, typename First, typename Second>
class VectorVector
{
First first;
Second second;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

VectorVector( const First& first_, const Second& second_ )
	: first( first_ ), second( second_ ){
}
value_type eval( unsigned int i ) const {
	return Operation::apply( first.eval( i ), second.eval( i ) );
}
};

template<typename First, typename Second>
class Added
{
public:
typedef First value_type;

static value_type apply( const First& first, const Second& second ){
	return static_cast<value_type>( first + second );
}
};

template<typename First, typename Second>
inline VectorVector<Added<typename First::value_type, typename Second::value_type>, First, Second>
vector_added( const First& first, const Second& second ){
	typedef typename First::value_type first_value_type;
	typedef typename Second::value_type second_value_type;
	return VectorVector<Added<first_value_type, second_value_type>, First, Second>( first, second );
}

template<typename First, typename Second>
class Multiplied
{
public:
typedef First value_type;

static value_type apply( const First& first, const Second& second ){
	return static_cast<value_type>( first * second );
}
};

template<typename First, typename Second>
inline VectorVector<Multiplied<typename First::value_type, typename Second::value_type>, First, Second>
vector_multiplied( const First& first, const Second& second ){
	typedef typename First::value_type first_value_type;
	typedef typename Second::value_type second_value_type;
	return VectorVector<Multiplied<first_value_type, second_value_type>, First, Second>( first, second );
}

template<typename First, typename Second>
inline VectorScalar<Multiplied<typename First::value_type, typename Second::value_type>, First, Second>
vector_scaled( const First& first, const Second& second ){
	typedef typename First::value_type first_value_type;
	typedef typename Second::value_type second_value_type;
	return VectorScalar<Multiplied<first_value_type, second_value_type>, First, Second>( first, second );
}

template<typename First>
class Negated
{
public:
typedef First value_type;

static value_type apply( const First& first ){
	return -first;
}
};

template<typename First, typename Operation>
class VectorUnary
{
First first;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

VectorUnary( const First& first_ ) : first( first_ ){
}
value_type eval( unsigned int i ) const {
	return Operation::apply( first.eval( i ) );
}
};

template<typename First>
inline VectorUnary<First, Negated<typename First::value_type> >
vector_negated( const First& first ){
	typedef typename First::value_type first_value_type;
	return VectorUnary<First, Negated<first_value_type> >( first );
}

template<typename First, typename Second>
class VectorCross
{
First first;
Second second;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

VectorCross( const First& first_, const Second& second_ )
	: first( first_ ), second( second_ ){
}
value_type eval( unsigned int i ) const {
	return first.eval( ( i + 1 ) % 3 ) * second.eval( ( i + 2 ) % 3 ) - first.eval( ( i + 2 ) % 3 ) * second.eval( ( i + 1 ) % 3 );
}
};

template<typename First, typename Second>
inline VectorCross<First, Second>
vector_cross( const First& first, const Second& second ){
	return VectorCross<First, Second>( first, second );
}


template<typename First, typename Second>
class VectorDot
{
First first;
Second second;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

VectorDot( const First& first_, const Second& second_ )
	: first( first_ ), second( second_ ){
}

template<typename Index>
struct eval_dot
{
	static value_type apply( const First& first, const Second& second ){
		return static_cast<value_type>(
				   first.eval( Index::VALUE ) * second.eval( Index::VALUE )
				   + eval_dot< IntegralConstant<Index::VALUE - 1> >::apply( first, second )
				   );
	}
};

template<>
struct eval_dot< IntegralConstant<0> >
{
	static value_type apply( const First& first, const Second& second ){
		return first.eval( 0 ) * second.eval( 0 );
	}
};

value_type eval() const {
	return eval_dot< IntegralConstant<dimension::VALUE - 1> >::apply( first, second );
}
};


template<typename First, typename Second>
inline VectorDot<First, Second> vector_dot( const First& first, const Second& second ){
	return VectorDot<First, Second>( first, second );
}

template<typename First>
class VectorLengthSquared
{
First first;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

VectorLengthSquared( const First& first_ )
	: first( first_ ){
}

static value_type squared( const value_type& value ){
	return value * value;
}

template<typename Index>
struct eval_squared
{
	static value_type apply( const First& first ){
		return static_cast<value_type>(
				   squared( first.eval( Index::VALUE ) )
				   + eval_squared< IntegralConstant<Index::VALUE - 1> >::apply( first )
				   );
	}
};

template<>
struct eval_squared< IntegralConstant<0> >
{
	static value_type apply( const First& first ){
		return squared( first.eval( 0 ) );
	}
};

value_type eval() const {
	return eval_squared< IntegralConstant<dimension::VALUE - 1> >::apply( first );
}
};

template<typename First>
inline VectorLengthSquared<First> vector_length_squared( const First& first ){
	return VectorLengthSquared<First>( first );
}

template<typename First>
inline SquareRoot< VectorLengthSquared<First> > vector_length( const First& first ){
	return float_square_root( vector_length_squared( first ) );
}

#if 1
template<typename First>
inline VectorScalar<
	Multiplied<typename First::value_type, typename First::value_type>,
	First,
    // multiple evaulations of subexpression
	ScalarDivided<
		Literal<typename First::value_type>,
		SquareRoot<
			VectorLengthSquared<First>
			>
		>
	> vector_normalised( const First& first ){
	typedef typename First::value_type first_value_type;
	return vector_scaled( first, float_reciprocal( vector_length( first ) ) );
}
#else
template<typename First>
inline VectorScalar<
	Multiplied<typename First::value_type, typename First::value_type>,
	First,
    // single evaluation of subexpression
	Literal<typename First::value_type>
	>
vector_normalised( const First& first ){
	typedef typename First::value_type first_value_type;
	return vector_scaled( first, float_literal( static_cast<first_value_type>( first_value_type( 1.0 ) / vector_length( first ).eval() ) ) );
}
#endif


class Matrix4Literal
{
const Matrix4 m_value;
public:
typedef float value_type;
typedef IntegralConstant<4> dimension0;
typedef IntegralConstant<4> dimension1;

Matrix4Literal( const Matrix4& value )
	: m_value( value ){
}
const value_type& eval( unsigned int r, unsigned int c ) const {
	return m_value[r * 4 + c];
}
};

inline Matrix4Literal matrix4_literal( const Matrix4& value ){
	return Matrix4Literal( value );
}

class Matrix4Identity
{
const Matrix4& m_value;
public:
typedef float value_type;
typedef IntegralConstant<4> dimension0;
typedef IntegralConstant<4> dimension1;

Matrix4Identity( const Matrix4& value )
	: m_value( value ){
}
const value_type& eval( unsigned int r, unsigned int c ) const {
	return m_value[r * 4 + c];
}
};

inline Matrix4Identity matrix4_identity( const Matrix4& value ){
	return Matrix4Identity( value );
}

template<typename Expression>
inline Matrix4 matrix4_for_expression( const Expression& expression ){
	return Matrix4(
			   expression.eval( 0, 0 ), expression.eval( 0, 1 ), expression.eval( 0, 2 ), expression.eval( 0, 3 ),
			   expression.eval( 1, 0 ), expression.eval( 1, 1 ), expression.eval( 1, 2 ), expression.eval( 1, 3 ),
			   expression.eval( 2, 0 ), expression.eval( 2, 1 ), expression.eval( 2, 2 ), expression.eval( 2, 3 ),
			   expression.eval( 3, 0 ), expression.eval( 3, 1 ), expression.eval( 3, 2 ), expression.eval( 3, 3 )
			   );
}

template<typename Expression>
inline Matrix4 matrix4_affine_for_expression( const Expression& expression ){
	return Matrix4(
			   expression.eval( 0, 0 ), expression.eval( 0, 1 ), expression.eval( 0, 2 ), 0,
			   expression.eval( 1, 0 ), expression.eval( 1, 1 ), expression.eval( 1, 2 ), 0,
			   expression.eval( 2, 0 ), expression.eval( 2, 1 ), expression.eval( 2, 2 ), 0,
			   expression.eval( 3, 0 ), expression.eval( 3, 1 ), expression.eval( 3, 2 ), 1
			   );
}


template<typename First, typename Second>
class PointMultiplied
{
const First& first;
const Second& second;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension dimension;

PointMultiplied( const First& first_, const Second& second_ )
	: first( first_ ), second( second_ ){
}
value_type eval( unsigned int i ) const {
	return static_cast<value_type>( second.eval( 0, i ) * first.eval( 0 )
									+ second.eval( 1, i ) * first.eval( 1 )
									+ second.eval( 2, i ) * first.eval( 2 )
									+ second.eval( 3, i ) );
}
};

template<typename First, typename Second>
inline PointMultiplied<First, Second> point_multiplied( const First& point, const Second& matrix ){
	return PointMultiplied<First, Second>( point, matrix );
}

template<typename First, typename Second>
class Matrix4Multiplied
{
const First& first;
const Second& second;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension0 dimension0;
typedef typename First::dimension1 dimension1;

Matrix4Multiplied( const First& first_, const Second& second_ )
	: first( first_ ), second( second_ ){
}

value_type eval( unsigned int r, unsigned int c ) const {
	return static_cast<value_type>(
			   second.eval( r, 0 ) * first.eval( 0, c )
			   + second.eval( r, 1 ) * first.eval( 1, c )
			   + second.eval( r, 2 ) * first.eval( 2, c )
			   + second.eval( r, 3 ) * first.eval( 3, c )
			   );
}
};

template<typename First, typename Second>
inline Matrix4Multiplied<First, Second> matrix4_multiplied( const First& first, const Second& second ){
	return Matrix4Multiplied<First, Second>( first, second );
}

template<typename First>
class MatrixTransposed
{
const First& first;
public:
typedef typename First::value_type value_type;
typedef typename First::dimension0 dimension0;
typedef typename First::dimension1 dimension1;

MatrixTransposed( const First& first_ )
	: first( first_ ){
}

value_type eval( unsigned int r, unsigned int c ) const {
	return first.eval( c, r );
}
};

template<typename First>
inline MatrixTransposed<First> matrix_transposed( const First& first ){
	return MatrixTransposed<First>( first );
}

#endif