Creating

Discrete field with physical coordinate mapping and interpolation.

Discrete field with physical coordinate mapping and interpolationDiscreteField provides a N-dimensional array with physical coordinate system awareness, bridging discrete grid indices and continuous physical space. It supports coordinate transformations, interpolation, and functional operations.

Core Concept:

• Storage: N-dimensional array (via Array<T, D>)
• Geometry: Origin, discretization (spacing), bounding box
• Transformations: Indices ↔ physical coordinates
• Operations: Apply functions, interpolate, access by index/coordinate

Design Philosophy:

• Immutable geometry (const origin, discretization, bounds)
• Direct data access (operator[], get_data())
• Functional operations (apply lambda to all points)
• Simple nearest-neighbor interpolation

Template Parameters

T	Element type (typically double or std::complex<double>)
D	Dimensionality (typically 3)

and initializing a field

// 3D field: 32³ points, spacing 0.5 in each direction
pfc::DiscreteField<double, 3> field(
    {32, 32, 32},           // dimensions
    {0, 0, 0},              // offset (for subdomains)
    {0.0, 0.0, 0.0},        // origin
    {0.5, 0.5, 0.5}         // discretization (spacing)
);
 
// Initialize with mathematical function
field.apply([](double x, double y, double z) {
    return std::sin(x) * std::cos(y) * std::exp(-z/10.0);
});