--- /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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