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Lib/Include/CML/quaternion/quaternion_mul.h

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+/* -*- 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 Multiplication of two quaternions, p*q.
+ *
+ * This uses the expression tree, since the result is closed-form and can be
+ * computed by index.
+ */
+
+#ifndef quaternion_mul_h
+#define quaternion_mul_h
+
+#include <cml/mathlib/checking.h>
+#include <cml/quaternion/quaternion_promotions.h>
+
+namespace cml {
+namespace detail {
+
+template < class CrossType, class Real > struct SumOp;
+
+template < class Real > struct SumOp< positive_cross, Real > {
+    Real operator()(Real a, Real b) const {
+        return a + b;
+    }
+};
+
+template < class Real > struct SumOp< negative_cross, Real > {
+    Real operator()(Real a, Real b) const {
+        return a - b;
+    }
+};
+
+template < class Quat1_T, class Quat2_T >
+typename et::QuaternionPromote<
+    typename Quat1_T::temporary_type, typename Quat2_T::temporary_type
+>::temporary_type
+QuaternionMult(const Quat1_T& q1, const Quat2_T& q2)
+{
+    detail::CheckQuat(q1);
+    detail::CheckQuat(q2);
+    
+    typedef typename et::QuaternionPromote<
+        typename Quat1_T::temporary_type, typename Quat2_T::temporary_type
+    >::temporary_type temporary_type;
+
+    typedef typename temporary_type::value_type value_type;
+    typedef typename temporary_type::order_type order_type;
+    typedef typename temporary_type::cross_type cross_type;
+
+    typedef detail::SumOp<cross_type, value_type> sum_op;
+
+    enum {
+        W = order_type::W,
+        X = order_type::X,
+        Y = order_type::Y,
+        Z = order_type::Z
+    };
+    
+    temporary_type result;
+
+    /* s1*s2-dot(v1,v2): */
+    result[W] =
+        q1[W]*q2[W] - q1[X]*q2[X] - q1[Y]*q2[Y] - q1[Z]*q2[Z];
+
+    /* (s1*v2 + s2*v1 + v1^v2) i: */
+    result[X] =
+        sum_op()(q1[W]*q2[X] + q2[W]*q1[X], q1[Y]*q2[Z] - q1[Z]*q2[Y]);
+
+    /* (s1*v2 + s2*v1 + v1^v2) j: */
+    result[Y] =
+        sum_op()(q1[W]*q2[Y] + q2[W]*q1[Y], q1[Z]*q2[X] - q1[X]*q2[Z]);
+
+    /* (s1*v2 + s2*v1 + v1^v2) k: */
+    result[Z] =
+        sum_op()(q1[W]*q2[Z] + q2[W]*q1[Z], q1[X]*q2[Y] - q1[Y]*q2[X]);
+
+    return result;
+}
+
+} // namespace detail
+
+/** Declare mul taking two quaternion operands. */
+template<typename E1, class AT1, typename E2, class AT2, class OT, class CT>
+inline typename et::QuaternionPromote<
+    typename quaternion<E1,AT1,OT,CT>::temporary_type,
+    typename quaternion<E2,AT2,OT,CT>::temporary_type
+>::temporary_type operator*(
+    const quaternion<E1,AT1,OT,CT>& left,
+    const quaternion<E2,AT2,OT,CT>& right)
+{
+    return detail::QuaternionMult(left, right);
+}
+
+/** Declare mul taking a quaternion and a et::QuaternionXpr. */
+template<typename E, class AT, class OT, class CT, class XprT>
+inline typename et::QuaternionPromote<
+    typename quaternion<E,AT,OT,CT>::temporary_type,
+    typename XprT::temporary_type
+>::temporary_type operator*(
+    const quaternion<E,AT,OT,CT>& left,
+    QUATXPR_ARG_TYPE right)
+{
+    return detail::QuaternionMult(left, right);
+}
+
+/** Declare mul taking an et::QuaternionXpr and a quaternion. */
+template<class XprT, typename E, class AT, class OT, class CT>
+inline typename et::QuaternionPromote<
+    typename XprT::temporary_type,
+    typename quaternion<E,AT,OT,CT>::temporary_type
+>::temporary_type operator*(
+    QUATXPR_ARG_TYPE left,
+    const quaternion<E,AT,OT,CT>& right)
+{
+    return detail::QuaternionMult(left, right);
+}
+
+/** Declare mul taking two et::QuaternionXpr operands. */
+template<class XprT1, class XprT2>
+inline typename et::QuaternionPromote<
+    typename XprT1::temporary_type, typename XprT2::temporary_type
+>::temporary_type operator*(
+    QUATXPR_ARG_TYPE_N(1) left,
+    QUATXPR_ARG_TYPE_N(2) right)
+{
+    return detail::QuaternionMult(left, right);
+}
+
+} // namespace cml
+
+#endif
+
+// -------------------------------------------------------------------------
+// vim:ft=cpp