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