--- /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 Defines an operator for quaternion inverse.
+ */
+
+#ifndef quaternion_inverse_h
+#define quaternion_inverse_h
+
+#include <cml/quaternion/quaternion_expr.h>
+#include <cml/quaternion/quaternion_functions.h>
+
+namespace cml {
+namespace et {
+
+/** An expression node for inverting a quaternion.
+ *
+ * This internally creates a ConjugateOp node to process the conjugate
+ * of the given expression. The values produced by the ConjugateOp are then
+ * divided by the Cayley norm of the expression on the fly.
+ */
+template<class ExprT>
+class QuaternionInverseOp
+{
+ public:
+
+ typedef QuaternionInverseOp<ExprT> 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;
+
+ /* The subexpression is a ConjugateOp: */
+ typedef et::ConjugateOp<ExprT> subexpression_type;
+ typedef ExprTraits<subexpression_type> expr_traits;
+
+ /* Get traits for the ExprT: */
+ typedef ExprTraits<ExprT> arg_traits;
+ typedef typename arg_traits::const_reference arg_reference;
+
+ typedef typename subexpression_type::value_type value_type;
+ typedef quaternion_result_tag result_tag;
+ typedef typename subexpression_type::size_tag size_tag;
+
+ /* 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 m_expr.real()/m_norm;
+ }
+
+ /** Return the vector part of the expression.
+ *
+ * @todo This could be returned as a VectorXpr also.
+ */
+ imaginary_type imaginary() const {
+ return m_expr.imaginary()/m_norm;
+ }
+
+ /** 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();
+ }
+
+ /** Compute inverse result at index i.
+ *
+ * The inverse of a quaternion p is ~p/norm(p).
+ */
+ value_type operator[](size_t i) const {
+ return m_expr[i]/m_norm;
+ }
+
+
+ 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 an input expression. */
+ explicit QuaternionInverseOp(arg_reference arg)
+ //: m_expr(arg), m_norm(cml::norm(arg)) {}
+ : m_expr(arg), m_norm(arg.norm()) {}
+
+ /** Copy constructor. */
+ QuaternionInverseOp(const expr_type& e)
+ : m_expr(e.m_expr), m_norm(e.m_norm) {}
+
+
+ protected:
+
+ subexpression_type m_expr;
+ value_type m_norm;
+
+
+ private:
+
+ /* Cannot be assigned to: */
+ expr_type& operator=(const expr_type&);
+};
+
+/** Expression traits class for QuaternionInverseOp<>. */
+template<class ExprT>
+struct ExprTraits< QuaternionInverseOp<ExprT> >
+{
+ typedef QuaternionInverseOp<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 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(); }
+};
+
+} // namespace et
+
+/** Inverse of a quaternion. */
+template<typename E, class AT, class OrderT, class CrossT> inline
+et::QuaternionXpr< et::QuaternionInverseOp< quaternion<E,AT,OrderT,CrossT> > >
+inverse(const quaternion<E,AT,OrderT,CrossT>& arg)
+{
+ typedef et::QuaternionInverseOp< quaternion<E,AT,OrderT,CrossT> > ExprT;
+ return et::QuaternionXpr<ExprT>(ExprT(arg));
+}
+
+/** Inverse of a QuaternionXpr. */
+template<class XprT> inline
+et::QuaternionXpr< et::QuaternionInverseOp<XprT> >
+inverse(QUATXPR_ARG_TYPE arg)
+{
+ typedef et::QuaternionInverseOp<XprT> ExprT;
+ return et::QuaternionXpr<ExprT>(ExprT(arg.expression()));
+}
+
+/* NOTE: Quaternion division no longer supported, but I'm leaving the
+ code here for reference (Jesse) */
+
+#if 0
+/** Declare div taking two quaternion operands. */
+template<typename E1, class AT1, typename E2, class AT2, class OT, class CT>
+inline typename et::QuaternionPromote<
+ quaternion<E1,AT1,OT,CT>, quaternion<E2,AT2,OT,CT>
+>::temporary_type
+operator/(
+ const quaternion<E1,AT1,OT,CT>& left,
+ const quaternion<E2,AT2,OT,CT>& right)
+{
+ return left*inverse(right);
+}
+
+/** Declare div taking a quaternion and a et::QuaternionXpr. */
+template<typename E, class AT, class OT, class CT, class XprT>
+inline typename et::QuaternionPromote<
+ quaternion<E,AT,OT,CT>, typename XprT::result_type
+>::temporary_type
+operator/(
+ const quaternion<E,AT,OT,CT>& left,
+ QUATXPR_ARG_TYPE right)
+{
+ return left*inverse(right);
+}
+
+/** Declare div taking an et::QuaternionXpr and a quaternion. */
+template<class XprT, typename E, class AT, class OT, class CT>
+inline typename et::QuaternionPromote<
+ typename XprT::result_type, quaternion<E,AT,OT,CT>
+>::temporary_type
+operator/(
+ QUATXPR_ARG_TYPE left,
+ const quaternion<E,AT,OT,CT>& right)
+{
+ return left*inverse(right);
+}
+
+/** Declare div taking two et::QuaternionXpr operands. */
+template<class XprT1, class XprT2>
+inline typename et::QuaternionPromote<
+ typename XprT1::result_type, typename XprT2::result_type
+>::temporary_type
+operator/(
+ QUATXPR_ARG_TYPE_N(1) left,
+ QUATXPR_ARG_TYPE_N(2) right)
+{
+ return left*inverse(right);
+}
+#endif
+
+} // namespace cml
+
+#endif
+
+// -------------------------------------------------------------------------
+// vim:ft=cpp
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