17_custom_coordinate_system.cpp File Reference

Example: Defining custom coordinate systems without modifying OpenPFC. More...

#include <cmath>
#include <iostream>
#include "openpfc/openpfc.hpp"

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Classes
struct	PolarTag
	Tag for polar coordinate system. More...
struct	PolarCoordinateSystem
	Polar coordinate system parameters. More...
struct	SphericalTag
	Tag for spherical coordinate system. More...
struct	SphericalCoordinateSystem
	Spherical coordinate system parameters. More...

Functions
Real3	polar_to_coords (const PolarCoordinateSystem &cs, const Int3 &indices, const Int3 &size)
Int3	polar_to_indices (const PolarCoordinateSystem &cs, const Real3 &coords, const Int3 &size)
	Convert Cartesian coordinates to grid indices (Cartesian → Polar)
Real3	spherical_to_coords (const SphericalCoordinateSystem &cs, const Int3 &indices, const Int3 &size)
	Spherical → Cartesian coordinate transformation.
Int3	spherical_to_indices (const SphericalCoordinateSystem &cs, const Real3 &coords, const Int3 &size)
	Cartesian → Spherical coordinate transformation.
void	example_polar_coordinates ()
	Demonstrate polar coordinate system usage.
void	example_spherical_coordinates ()
	Demonstrate spherical coordinate system usage.
void	show_extension_pattern ()
	Summary of the extension pattern.
int	main ()

Variables
constexpr double	M_PI = 3.14159265358979323846

Detailed Description

Example: Defining custom coordinate systems without modifying OpenPFC.

This example demonstrates OpenPFC's extensibility by showing how to add custom coordinate systems without modifying the library source code.

We implement two complete coordinate systems:

1. Polar coordinates (2D: r, θ) - simpler case
2. Spherical coordinates (3D: r, θ, φ) - complete 3D case

Key Technique: ADL (Argument-Dependent Lookup)

OpenPFC uses ADL to find coordinate transformation functions. You define functions in your namespace (or pfc namespace), and ADL ensures they're found automatically.

Philosophy: Laboratory, Not Fortress

This example proves you can extend OpenPFC without forking or modifying its source code. This is the "laboratory" philosophy in action.

How to Use This Example

1. Read through the polar coordinate implementation (simpler)
2. Study the spherical coordinate implementation (complete)
3. Copy the pattern for your own coordinate system
4. No OpenPFC source code modifications required!

Function Documentation

example_polar_coordinates()

void example_polar_coordinates

(

)

Demonstrate polar coordinate system usage.

Shows:

• Creating polar coordinate system
• Converting grid indices to Cartesian coordinates
• Round-trip transformation (indices → coords → indices)
• Verification of mathematical properties

Examples

/home/runner/work/OpenPFC/OpenPFC/examples/17_custom_coordinate_system.cpp.

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example_spherical_coordinates()

void example_spherical_coordinates

(

)

Demonstrate spherical coordinate system usage.

Shows complete 3D spherical coordinate transformations with verification.

Examples

/home/runner/work/OpenPFC/OpenPFC/examples/17_custom_coordinate_system.cpp.

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polar_to_indices()

Int3 polar_to_indices ( const PolarCoordinateSystem &  cs, const Real3 &  coords, const Int3 &  size  )

inline

Convert Cartesian coordinates to grid indices (Cartesian → Polar)

Inverse transformation of polar_to_coords().

Given Cartesian coordinates (x, y, z):

1. Convert to polar: r = √(x² + y²), θ = atan2(y, x)
2. Map to grid indices: i = round(r), j = round(θ)

Parameters

cs	Polar coordinate system
coords	Cartesian coordinates (x, y, z)
size	Grid dimensions [n_r, n_θ, 1]

Returns

Grid indices (i_r, i_θ, 0)

Note

z coordinate is ignored (2D system)

Warning

Indices may be outside grid range - caller should check bounds

Examples

/home/runner/work/OpenPFC/OpenPFC/examples/17_custom_coordinate_system.cpp.

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show_extension_pattern()

void show_extension_pattern

(

)

Summary of the extension pattern.

Shows the complete recipe for adding custom coordinate systems.

Examples

/home/runner/work/OpenPFC/OpenPFC/examples/17_custom_coordinate_system.cpp.

spherical_to_coords()

Real3 spherical_to_coords ( const SphericalCoordinateSystem &  cs, const Int3 &  indices, const Int3 &  size  )

inline

Spherical → Cartesian coordinate transformation.

Transforms grid indices in spherical coordinates to Cartesian (x,y,z).

Transformation:

• x = r * sin(θ) * cos(φ)
• y = r * sin(θ) * sin(φ)
• z = r * cos(θ)

Parameters

cs	Spherical coordinate system
indices	Grid indices (i_r, i_theta, i_phi)
size	Grid dimensions [n_r, n_θ, n_φ]

Returns

Cartesian coordinates (x, y, z)

Note

Found via ADL - no namespace qualification needed

Special points:

• theta = 0: North pole (0, 0, r)
• theta = pi: South pole (0, 0, -r)
• theta = pi/2, phi = 0: Point on +x axis (r, 0, 0)
• theta = pi/2, phi = pi/2: Point on +y axis (0, r, 0)

Examples

/home/runner/work/OpenPFC/OpenPFC/examples/17_custom_coordinate_system.cpp.

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spherical_to_indices()

Int3 spherical_to_indices ( const SphericalCoordinateSystem &  cs, const Real3 &  coords, const Int3 &  size  )

inline

Cartesian → Spherical coordinate transformation.

Inverse of spherical_to_coords().

Transformation:

• r = √(x² + y² + z²)
• theta = acos(z / r)
• phi = atan2(y, x)

Parameters

cs	Spherical coordinate system
coords	Cartesian coordinates (x, y, z)
size	Grid dimensions [n_r, n_theta, n_phi]

Returns

Grid indices (i_r, i_theta, i_phi)

Warning

Singular at origin (r=0) - undefined theta and phi

Indices may be outside grid - caller should validate

Examples

/home/runner/work/OpenPFC/OpenPFC/examples/17_custom_coordinate_system.cpp.

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