Struct splashsurf_lib::kernel::DiscreteSquaredDistanceCubicKernel

pub struct DiscreteSquaredDistanceCubicKernel<R: Real> { /* fields omitted */ }

Accelerator for efficient evaluation of a precomputed cubic kernel

This structure is used to pre-compute a discrete representation of the cubic kernel function. In some computations that require many evaluations of the kernel, it is more efficient to evaluate the kernel using a squared distance to avoid taking the square root. To produce an appropriate quantization of the kernel for this use case, the compact support radius of the kernel is divided into n segments with quadratically increasing width. To be more precise, on a quadratic scale, the compact support [0, h*h] is divided into n equally sized segments of width dr. For the actual pre-computation, the exact kernel k(r) is evaluated at the midpoint m_i of every segment given by m_i = sqrt(i * dr) for i ∈ [0, n]. This results in an array of kernel values K that can be evaluated at runtime using a squared radius s by just mapping this radius back to the corresponding segment index i followed by a lookup in the value array, i.e. k(sqrt(s)) ≈ K[s/dr] (while taking care of rounding and clamping to the allowed index range).

Implementations

impl<R: Real> DiscreteSquaredDistanceCubicKernel<R>

pub fn new(n: usize, h: R) -> Self

Precomputes the discrete cubic kernel with compact support radius h, the squared radius h * h is divided into n segments for the quantization

pub fn evaluate(&self, r_squared: R) -> R

Evaluates the precomputed kernel function at the specified squared radius, i.e. returns an approximate cubic kernel value at the radius sqrt(r_squared)