Enum RadialBasisFunction

Defined in File mls_interpolation.hpp

Enum Documentation

enum class pcms::RadialBasisFunction

Enumeration of supported radial basis functions (RBFs) for MLS interpolation.

Specifies the kernel type used for computing weights in Moving Least Squares (MLS) interpolation. Each RBF defines a different spatial weighting behavior, influencing locality, smoothness, and conditioning of the interpolant.

Values:

RBF_GAUSSIAN (0) \( \phi(r) = \exp\left(-\left(\frac{a r}{r_c}\right)^2\right) \) Infinitely smooth and compactly supported. a is the shape (decay) parameter — smaller values give wider influence. Good for smooth interpolants; may cause ill-conditioning for large a.
RBF_C4 (1) Compactly supported, \( C^4\)-continuous polynomial kernel. Does not require a shape parameter. Efficient, stable, and good for local approximations.
RBF_CONST (2) Uniform weights within support: \( \phi(r) = 1 \text{ for } r < r_c \), otherwise 0. Equivalent to averaging.
NO_OP (3) Disables internal RBF weighting logic. Always returns \( \phi = 1 \) regardless of distance. Useful for methods like SPR patching
RBF_MULTIQUADRIC (4) \( \phi(r) = \sqrt{1 + \left(\frac{a r}{r_c}\right)^2} \) Smooth and locally supported. a controls the width; higher values increase conditioning issues.
RBF_INVMULTIQUADRIC (5) \( \phi(r) = \frac{1}{\sqrt{1 + \left(\frac{a r}{r_c}\right)^2}} \) Compactly supported and generally more stable than MQ. a adjusts the decay; larger a leads to faster fall-off.
RBF_THINPLATESPLINE (6)\( \phi(r) = \left(\frac{a r}{r_c}\right)^2 \log\left(\frac{a r}{r_c}\right) \) Classic 2D surface fitting kernel. No explicit shape parameter is required, but a can scale smoothness.
RBF_CUBIC (7) \( \phi(r) = \left(\frac{a r}{r_c}\right)^3 \) Smooth with compact support. Simple and effective for local interpolation.