615 lines
17 KiB
C++
615 lines
17 KiB
C++
/* -*- C++ -*- ------------------------------------------------------------
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Copyright (c) 2007 Jesse Anders and Demian Nave http://cmldev.net/
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The Configurable Math Library (CML) is distributed under the terms of the
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Boost Software License, v1.0 (see cml/LICENSE for details).
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*-----------------------------------------------------------------------*/
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/** @file
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* @brief
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*/
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#ifndef quaternion_expr_h
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#define quaternion_expr_h
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#include <cml/et/size_checking.h>
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#include <cml/mathlib/epsilon.h>
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#include <cml/quaternion/quaternion_traits.h>
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#include <cml/quaternion/quaternion_promotions.h>
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#include <cml/util.h>
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#define QUATXPR_ARG_TYPE const et::QuaternionXpr<XprT>&
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#define QUATXPR_ARG_TYPE_N(_N_) const et::QuaternionXpr<XprT##_N_>&
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namespace cml {
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namespace et {
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/** A placeholder for a quaternion expression in an expression tree. */
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template<class ExprT>
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class QuaternionXpr
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{
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public:
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typedef QuaternionXpr<ExprT> expr_type;
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/* Record ary-ness of the expression: */
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typedef typename ExprT::expr_ary expr_ary;
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/* Copy the expression by value into higher-up expressions: */
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typedef expr_type expr_const_reference;
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typedef typename ExprT::value_type value_type;
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typedef quaternion_result_tag result_tag;
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typedef typename ExprT::size_tag size_tag;
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/* Store the expression traits: */
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typedef ExprTraits<ExprT> expr_traits;
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/* Get the reference type: */
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typedef typename expr_traits::const_reference expr_reference;
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/* Get the result type: */
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typedef typename expr_traits::result_type result_type;
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/* Get the vector type: */
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typedef typename result_type::vector_type vector_type;
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/* Get the imaginary part type: */
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typedef typename vector_type::subvector_type imaginary_type;
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/* For matching by assignability: */
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typedef cml::et::not_assignable_tag assignable_tag;
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/* Get the temporary type: */
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typedef typename result_type::temporary_type temporary_type;
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/* Record the order type: */
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typedef typename result_type::order_type order_type;
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/* Record the cross type: */
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typedef typename result_type::cross_type cross_type;
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public:
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/** Record result size as an enum. */
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enum { array_size = ExprT::array_size };
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public:
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/** Return the real part of the expression. */
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value_type real() const {
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return m_expr.real();
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}
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/** Return the vector part of the expression. */
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imaginary_type imaginary() const {
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return m_expr.imaginary();
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}
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/** Return the Cayley norm of the expression. */
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value_type norm() const {
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return m_expr.length_squared();
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}
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/** Return square of the quaternion length. */
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value_type length_squared() const {
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return m_expr.length_squared();
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}
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/** Return the quaternion length. */
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value_type length() const {
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return m_expr.length();
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}
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/** Return the result as a normalized quaternion. */
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temporary_type normalize() const {
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return m_expr.normalize();
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}
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/** Return the log of the expression. */
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temporary_type log(
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value_type tolerance = epsilon<value_type>::placeholder()) const
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{
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return m_expr.log(tolerance);
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}
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/**
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* Return the result of the exponential function as applied to
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* this expression.
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*/
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temporary_type exp(
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value_type tolerance = epsilon<value_type>::placeholder()) const
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{
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return m_expr.exp(tolerance);
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}
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/** Compute value at index i of the result quaternion. */
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value_type operator[](size_t i) const {
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return m_expr[i];
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}
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public:
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/** Return size of this expression (same as subexpression's size). */
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size_t size() const {
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return m_expr.size();
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}
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/** Return reference to contained expression. */
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expr_reference expression() const { return m_expr; }
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public:
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/** Construct from the subexpression to store. */
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explicit QuaternionXpr(expr_reference expr) : m_expr(expr) {}
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/** Copy constructor. */
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QuaternionXpr(const expr_type& e) : m_expr(e.m_expr) {}
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protected:
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expr_reference m_expr;
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private:
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/* Cannot be assigned to: */
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expr_type& operator=(const expr_type&);
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};
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/** Expression traits class for QuaternionXpr<>. */
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template<class ExprT>
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struct ExprTraits< QuaternionXpr<ExprT> >
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{
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typedef QuaternionXpr<ExprT> expr_type;
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typedef ExprT arg_type;
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typedef typename expr_type::value_type value_type;
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typedef typename expr_type::expr_const_reference const_reference;
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typedef typename expr_type::result_tag result_tag;
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typedef typename expr_type::size_tag size_tag;
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typedef typename expr_type::result_type result_type;
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typedef typename expr_type::assignable_tag not_assignable_tag;
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typedef expr_node_tag node_tag;
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value_type get(const expr_type& v, size_t i) const { return v[i]; }
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size_t size(const expr_type& e) const { return e.size(); }
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};
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/** A unary quaternion expression.
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*
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* The operator's operator() method must take exactly one argument.
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*/
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template<class ExprT, class OpT>
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class UnaryQuaternionOp
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{
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public:
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typedef UnaryQuaternionOp<ExprT,OpT> expr_type;
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/* Record ary-ness of the expression: */
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typedef unary_expression expr_ary;
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/* Copy the expression by value into higher-up expressions: */
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typedef expr_type expr_const_reference;
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typedef typename OpT::value_type value_type;
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typedef quaternion_result_tag result_tag;
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typedef typename ExprT::size_tag size_tag;
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/* Store the expression traits for the subexpression: */
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typedef ExprTraits<ExprT> expr_traits;
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/* Reference type for the subexpression: */
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typedef typename expr_traits::const_reference expr_reference;
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/* Get the result type (same as for subexpression): */
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typedef typename expr_traits::result_type result_type;
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/* For matching by assignability: */
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typedef cml::et::not_assignable_tag assignable_tag;
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/* Get the temporary type: */
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typedef typename result_type::temporary_type temporary_type;
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/* Get the vector type: */
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typedef typename result_type::vector_type vector_type;
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/* Get the imaginary part type: */
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typedef typename vector_type::subvector_type imaginary_type;
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/* Record the order type: */
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typedef typename result_type::order_type order_type;
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public:
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/** Record result size as an enum. */
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enum { array_size = ExprT::array_size };
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/** Localize the ordering as an enum. */
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enum {
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W = order_type::W,
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X = order_type::X,
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Y = order_type::Y,
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Z = order_type::Z
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};
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public:
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/** Return the real part of the expression. */
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value_type real() const {
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return (*this)[W];
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}
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/** Return the vector part of the expression. */
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imaginary_type imaginary() const {
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imaginary_type v;
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v[0] = (*this)[X]; v[1] = (*this)[Y]; v[2] = (*this)[Z];
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return v;
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}
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/** Return the Cayley norm of the expression. */
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value_type norm() const {
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return length_squared();
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}
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/** Return square of the quaternion length. */
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value_type length_squared() const {
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return dot(
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QuaternionXpr<expr_type>(*this),
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QuaternionXpr<expr_type>(*this));
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}
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/** Return the quaternion length. */
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value_type length() const {
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return std::sqrt(length_squared());
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}
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/** Return the result as a normalized quaternion. */
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temporary_type normalize() const {
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temporary_type q(QuaternionXpr<expr_type>(*this));
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return q.normalize();
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}
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/** Return the log of this expression. */
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temporary_type log(
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value_type tolerance = epsilon<value_type>::placeholder()) const
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{
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value_type a = acos_safe(real());
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value_type s = std::sin(a);
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if (s > tolerance) {
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return temporary_type(value_type(0), imaginary() * (a / s));
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} else {
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return temporary_type(value_type(0), imaginary());
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}
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}
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/**
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* Return the result of the exponential function as applied to
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* this expression.
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*/
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temporary_type exp(
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value_type tolerance = epsilon<value_type>::placeholder()) const
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{
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imaginary_type v = imaginary();
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value_type a = cml::length(v);
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if (a > tolerance) {
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return temporary_type(std::cos(a), v * (std::sin(a) / a));
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} else {
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return temporary_type(std::cos(a), v);
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}
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}
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/** Compute value at index i of the result quaternion. */
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value_type operator[](size_t i) const {
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/* This uses the expression traits to figure out how to access the
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* i'th index of the subexpression:
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*/
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return OpT().apply(expr_traits().get(m_expr,i));
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}
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public:
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/** Return size of this expression (same as argument's size). */
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size_t size() const {
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return m_expr.size();
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}
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/** Return reference to contained expression. */
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expr_reference expression() const { return m_expr; }
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public:
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/** Construct from the subexpression. */
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explicit UnaryQuaternionOp(expr_reference expr) : m_expr(expr) {}
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/** Copy constructor. */
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UnaryQuaternionOp(const expr_type& e) : m_expr(e.m_expr) {}
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protected:
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expr_reference m_expr;
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private:
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/* Cannot be assigned to: */
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expr_type& operator=(const expr_type&);
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};
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/** Expression traits class for UnaryQuaternionOp<>. */
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template<class ExprT, class OpT>
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struct ExprTraits< UnaryQuaternionOp<ExprT,OpT> >
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{
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typedef UnaryQuaternionOp<ExprT,OpT> expr_type;
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typedef ExprT arg_type;
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typedef typename expr_type::value_type value_type;
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typedef typename expr_type::expr_const_reference const_reference;
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typedef typename expr_type::result_tag result_tag;
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typedef typename expr_type::size_tag size_tag;
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typedef typename expr_type::result_type result_type;
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typedef typename expr_type::assignable_tag not_assignable_tag;
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typedef expr_node_tag node_tag;
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value_type get(const expr_type& v, size_t i) const { return v[i]; }
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size_t size(const expr_type& e) const { return e.size(); }
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};
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/** A binary quaternion expression.
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*
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* The operator's operator() method must take exactly two arguments.
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*/
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template<class LeftT, class RightT, class OpT>
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class BinaryQuaternionOp
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{
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public:
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typedef BinaryQuaternionOp<LeftT,RightT,OpT> expr_type;
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/* Record ary-ness of the expression: */
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typedef binary_expression expr_ary;
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/* Copy the expression by value into higher-up expressions: */
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typedef expr_type expr_const_reference;
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typedef typename OpT::value_type value_type;
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typedef quaternion_result_tag result_tag;
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/* Store the expression traits types for the two subexpressions: */
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typedef ExprTraits<LeftT> left_traits;
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typedef ExprTraits<RightT> right_traits;
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/* Reference types for the two subexpressions: */
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typedef typename left_traits::const_reference left_reference;
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typedef typename right_traits::const_reference right_reference;
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/* Figure out the expression's resulting (quaternion) type: */
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typedef typename left_traits::result_type left_result;
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typedef typename right_traits::result_type right_result;
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typedef typename QuaternionPromote<left_result,right_result>::type
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result_type;
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typedef typename result_type::size_tag size_tag;
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/* For matching by assignability: */
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typedef cml::et::not_assignable_tag assignable_tag;
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/* Get the temporary type: */
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typedef typename result_type::temporary_type temporary_type;
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/* Get the vector type: */
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typedef typename result_type::vector_type vector_type;
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/* Get the imaginary part type: */
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typedef typename vector_type::subvector_type imaginary_type;
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/* Record the order type: */
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typedef typename result_type::order_type order_type;
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/* Define a size checker: */
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typedef GetCheckedSize<LeftT,RightT,size_tag> checked_size;
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public:
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/** Record result size as an enum. */
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enum { array_size = 4 };
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/** Localize the ordering as an enum. */
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enum {
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W = order_type::W,
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X = order_type::X,
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Y = order_type::Y,
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Z = order_type::Z
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};
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public:
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/** Return the real part of the expression. */
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value_type real() const {
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return (*this)[W];
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}
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/** Return the vector part of the expression. */
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imaginary_type imaginary() const {
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imaginary_type v;
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v[0] = (*this)[X]; v[1] = (*this)[Y]; v[2] = (*this)[Z];
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return v;
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}
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/** Return the Cayley norm of the expression. */
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value_type norm() const {
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return length_squared();
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}
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/** Return square of the quaternion length. */
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value_type length_squared() const {
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return dot(
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QuaternionXpr<expr_type>(*this),
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QuaternionXpr<expr_type>(*this));
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}
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/** Return the quaternion length. */
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value_type length() const {
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return std::sqrt(length_squared());
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}
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/** Return the result as a normalized quaternion. */
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temporary_type normalize() const {
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temporary_type q(QuaternionXpr<expr_type>(*this));
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return q.normalize();
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}
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/** Return the log of this expression. */
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temporary_type log(
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value_type tolerance = epsilon<value_type>::placeholder()) const
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{
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value_type a = acos_safe(real());
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value_type s = std::sin(a);
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if (s > tolerance) {
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return temporary_type(value_type(0), imaginary() * (a / s));
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} else {
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return temporary_type(value_type(0), imaginary());
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}
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}
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/**
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* Return the result of the exponential function as applied to
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* this expression.
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*/
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temporary_type exp(
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value_type tolerance = epsilon<value_type>::placeholder()) const
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{
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imaginary_type v = imaginary();
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value_type a = cml::length(v);
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if (a > tolerance) {
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return temporary_type(std::cos(a), v * (std::sin(a) / a));
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} else {
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return temporary_type(std::cos(a), v);
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}
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}
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/** Compute value at index i of the result quaternion. */
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value_type operator[](size_t i) const {
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/* This uses the expression traits to figure out how to access the
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* i'th index of the two subexpressions:
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*/
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return OpT().apply(
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left_traits().get(m_left,i),
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right_traits().get(m_right,i));
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}
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public:
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/** Return the size of the quaternion result.
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*
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* @throws std::invalid_argument if the expressions do not have the same
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* size.
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*/
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size_t size() const {
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/* Note: This actually does a check only if
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* CML_CHECK_VECTOR_EXPR_SIZES is set:
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*/
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CheckedSize(m_left,m_right,size_tag());
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/* The size is always 4: */
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return 4;
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}
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/** Return reference to left expression. */
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left_reference left_expression() const { return m_left; }
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/** Return reference to right expression. */
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right_reference right_expression() const { return m_right; }
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public:
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/** Construct from the two subexpressions. */
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explicit BinaryQuaternionOp(left_reference left, right_reference right)
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: m_left(left), m_right(right) {}
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/** Copy constructor. */
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BinaryQuaternionOp(const expr_type& e)
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: m_left(e.m_left), m_right(e.m_right) {}
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protected:
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left_reference m_left;
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right_reference m_right;
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private:
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/* This ensures that a compile-time size check is executed: */
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typename checked_size::check_type _dummy;
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private:
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/* Cannot be assigned to: */
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expr_type& operator=(const expr_type&);
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};
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/** Expression traits class for BinaryQuaternionOp<>. */
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template<class LeftT, class RightT, class OpT>
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struct ExprTraits< BinaryQuaternionOp<LeftT,RightT,OpT> >
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{
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typedef BinaryQuaternionOp<LeftT,RightT,OpT> expr_type;
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typedef LeftT left_type;
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typedef RightT right_type;
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typedef typename expr_type::value_type value_type;
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typedef typename expr_type::expr_const_reference const_reference;
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typedef typename expr_type::result_tag result_tag;
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typedef typename expr_type::size_tag size_tag;
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typedef typename expr_type::result_type result_type;
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typedef typename expr_type::imaginary_type imaginary_type;
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typedef typename expr_type::assignable_tag not_assignable_tag;
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typedef expr_node_tag node_tag;
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value_type get(const expr_type& v, size_t i) const { return v[i]; }
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size_t size(const expr_type& e) const { return e.size(); }
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};
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/* Helper struct to verify that both arguments are quaternion expressions: */
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template<class LeftTraits, class RightTraits>
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|
struct QuaternionExpressions
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|
{
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|
/* Require that both arguments are quaternion expressions: */
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typedef typename LeftTraits::result_tag left_result;
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typedef typename RightTraits::result_tag right_result;
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enum { is_true = (same_type<left_result,et::quaternion_result_tag>::is_true
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&& same_type<right_result,et::quaternion_result_tag>::is_true) };
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};
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|
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} // namespace et
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} // namespace cml
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|
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#endif
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// -------------------------------------------------------------------------
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// vim:ft=cpp
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