Struct Hrbf 

pub struct Hrbf<T, K>
where
    T: Real,
    K: Kernel<T>,
{ /* private fields */ }

An HRBF potential field.

The field and its first and second derivatives can be queried at any 3D position. Additionally this field can be reset with a different set of points and normals using one of the fit, fit_to_points, offset_fit, or offset_fit_to_points methods. Some advanced functionality is also exposed (see individual methods for details).

Implementations

impl<T, K> Hrbf<T, K>

where T: Real, K: Kernel<T> + Clone + Default,

pub fn sites(&self) -> &[Point3<T>]

Returns a reference to the vector of site locations used by this HRBF.

pub fn betas(&self) -> &[Vector4<T>]

(Advanced) Returns a reference to the vector of 4D weight vectors, which determine the global HRBF potential.

These are the unknowns computed during fitting. Each 4D vector has the structure [aⱼ; bⱼ] per site j where a is a scalar weighing the contribution from the kernel at site j and b is a 3D vector weighin the contribution from the kernel gradient at site j to the total HRBF potential.

pub fn fit(&mut self, normals: &[Vector3<T>]) -> Result<&mut Self>

Fit the current HRBF to the sites, with which this HRBF was built.

Normals dictate the direction of the HRBF gradient at the specified sites. Return a mutable reference to Self if successful.

pub fn fit_to_points( &mut self, points: &[Point3<T>], normals: &[Vector3<T>], ) -> Result<&mut Self>

Fit the current HRBF to the given data.

Return a mutable reference to Self if successful. NOTE: Currently, points must be the same size as sites.

pub fn offset_fit( &mut self, offsets: &[T], normals: &[Vector3<T>], ) -> Result<&mut Self>

Fit the current HRBF to the sites, with which this HRBF was built, offset by the given offsets.

The resulting HRBF field is equal to offsets at the sites. and has a gradient equal to normals. Return a mutable reference to Self if successful.

pub fn offset_fit_to_points( &mut self, points: &[Point3<T>], offsets: &[T], normals: &[Vector3<T>], ) -> Result<&mut Self>

Fit the current HRBF to the given data.

The resulting HRBF field is equal to offsets at the provided points and has a gradient equal to normals. Return a mutable reference to Self if successful. NOTE: Currently, points must be the same size as sites.

pub fn eval(&self, p: Point3<T>) -> T

Evaluate the HRBF at point p.

pub fn grad(&self, p: Point3<T>) -> Vector3<T>

Gradient of the HRBF function at point p.

pub fn hess(&self, p: Point3<T>) -> Matrix3<T>

Compute the Hessian of the HRBF function.

pub fn fit_block(&self, p: Point3<T>, j: usize) -> Matrix4<T>

(Advanced) Recall that the HRBF fit is done as

∑ⱼ ⎡  𝜙(𝑥ᵢ - 𝑥ⱼ)  ∇𝜙(𝑥ᵢ - 𝑥ⱼ)'⎤ ⎡ 𝛼ⱼ⎤ = ⎡ 0 ⎤
   ⎣ ∇𝜙(𝑥ᵢ - 𝑥ⱼ) ∇∇𝜙(𝑥ᵢ - 𝑥ⱼ) ⎦ ⎣ 𝛽ⱼ⎦   ⎣ 𝑛ᵢ⎦

for every HRBF site i, where the sum runs over HRBF sites j where 𝜙(𝑥) = 𝜑(||𝑥||) for one of the basis kernels we define in kernel If we rewrite the equation above as

∑ⱼ Aⱼ(𝑥ᵢ)bⱼ = rᵢ

this function returns the matrix Aⱼ(p).

This is the symmetric 4x4 matrix block that is used to fit the HRBF coefficients. This is equivalent to stacking the vector from eval_block on top of the 3x4 matrix returned by grad_block. This function is more efficient than evaluating eval_block and grad_block. This is [g ∇g]' = [𝜙 (∇𝜙)'; ∇𝜙 ∇(∇𝜙)'] in MATLAB notation.

pub fn grad_fit_block_prod( &self, p: Point3<T>, b: Vector4<T>, j: usize, ) -> Matrix3x4<T>

(Advanced) Using the same notation as above, this function returns the matrix ∇(Aⱼ(p)b)'

pub fn hess_fit_prod(&self, p: Point3<T>, c: Vector4<T>) -> Matrix3<T>

Sum of hess_fit_prod_block evaluated at all sites.

Trait Implementations

impl<T, K> Clone for Hrbf<T, K>

where T: Real + Clone, K: Kernel<T> + Clone,

fn clone(&self) -> Hrbf<T, K>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T, K> Debug for Hrbf<T, K>

where T: Real + Debug, K: Kernel<T> + Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.