Initial commit

Lib/Include/CML/mathlib/coord_conversion.h

@@ -0,0 +1,162 @@
+/* -*- 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 coord_conversion_h
+#define coord_conversion_h
+
+#include <cml/mathlib/checking.h>
+#include <cml/mathlib/epsilon.h>
+#include <cml/mathlib/helper.h>
+
+/* Functions for converting between Cartesian, polar, cylindrical and
+ * spherical coordinates.
+ *
+ * The 3D conversion functions take an integer axis index argument. For
+ * cylindrical coordinates this determines the axis of the cylinder, and for
+ * spherical it determines which cardinal axis is normal to the azimuth plane.
+ *
+ * For spherical coordinates the option of whether to treat phi as latitude
+ * or colatitude is also available. The 'type' argument takes either of the
+ * enumerants cml::latitude and cml::colatitude to reflect this.
+ */
+
+namespace cml {
+
+//////////////////////////////////////////////////////////////////////////////
+// Conversion to Cartesian coordinates
+//////////////////////////////////////////////////////////////////////////////
+
+/* Convert cylindrical coordinates to Cartesian coordinates in R3 */
+template < typename E, class A > void
+cylindrical_to_cartesian(
+    E radius, E theta, E height, size_t axis, vector<E,A>& v)
+{
+    typedef vector<E,A> vector_type;
+    typedef typename vector_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckVec3(v);
+    detail::CheckIndex3(axis);
+
+    size_t i, j, k;
+    cyclic_permutation(axis, i, j, k);
+    
+    v[i] = height;
+    v[j] = std::cos(theta) * radius;
+    v[k] = std::sin(theta) * radius;
+}
+
+/* Convert spherical coordinates to Cartesian coordinates in R3 */
+template < typename E, class A > void
+spherical_to_cartesian(E radius, E theta, E phi, size_t axis,
+    SphericalType type, vector<E,A>& v)
+{
+    typedef vector<E,A> vector_type;
+    typedef typename vector_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckVec3(v);
+    detail::CheckIndex3(axis);
+    
+    if (type == latitude) {
+        phi = constants<value_type>::pi_over_2() - phi;
+    }
+
+    value_type sin_phi = std::sin(phi);
+    value_type cos_phi = std::cos(phi);
+    value_type sin_phi_r = sin_phi * radius;
+
+    size_t i, j, k;
+    cyclic_permutation(axis, i, j, k);
+
+    v[i] = cos_phi * radius;
+    v[j] = sin_phi_r * std::cos(theta);
+    v[k] = sin_phi_r * std::sin(theta);
+}
+
+/* Convert polar coordinates to Cartesian coordinates in R2 */
+template < typename E, class A > void
+polar_to_cartesian(E radius, E theta, vector<E,A>& v)
+{
+    /* Checking handled by set() */
+    v.set(std::cos(theta) * radius, std::sin(theta) * radius);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// Conversion from Cartesian coordinates
+//////////////////////////////////////////////////////////////////////////////
+
+/* Convert Cartesian coordinates to cylindrical coordinates in R3  */
+template < class VecT, typename Real > void
+cartesian_to_cylindrical(const VecT& v, Real& radius, Real& theta,
+    Real& height, size_t axis, Real tolerance = epsilon<Real>::placeholder())
+{
+    typedef Real value_type;
+
+    /* Checking */
+    detail::CheckVec3(v);
+    detail::CheckIndex3(axis);
+
+    size_t i, j, k;
+    cyclic_permutation(axis, i, j, k);
+    
+    radius = length(v[j],v[k]);
+    theta = radius < tolerance ? value_type(0) : std::atan2(v[k],v[j]);
+    height = v[i];
+}
+
+/* Convert Cartesian coordinates to spherical coordinates in R3 */
+template < class VecT, typename Real > void
+cartesian_to_spherical(const VecT& v, Real& radius, Real& theta, Real& phi,
+    size_t axis, SphericalType type,
+    Real tolerance = epsilon<Real>::placeholder())
+{
+    typedef Real value_type;
+
+    /* Checking */
+    detail::CheckVec3(v);
+    detail::CheckIndex3(axis);
+
+    size_t i, j, k;
+    cyclic_permutation(axis, i, j, k);
+
+    value_type len = length(v[j],v[k]);
+    theta = len < tolerance ? value_type(0) : std::atan2(v[k],v[j]);
+    radius = length(v[i], len);
+    if (radius < tolerance) {
+        phi = value_type(0);
+    } else {
+        phi = std::atan2(len,v[i]);
+        //phi = type.convert(phi);
+        if (type == latitude) {
+            phi = constants<value_type>::pi_over_2() - phi;
+        }
+    }
+}
+
+/* Convert Cartesian coordinates to polar coordinates in R2 */
+template < class VecT, typename Real > void
+cartesian_to_polar(const VecT& v, Real& radius, Real& theta,
+    Real tolerance = epsilon<Real>::placeholder())
+{
+    typedef Real value_type;
+
+    /* Checking */
+    detail::CheckVec2(v);
+
+    radius = v.length();
+    theta = radius < tolerance ? value_type(0) : std::atan2(v[1],v[0]);
+}
+
+} // namespace cml
+
+#endif