Struct hrbf::HRBF

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

Methods

impl<T, K> HRBF<T, K> where
    T: Real,
    K: Kernel<T> + LocalKernel<T>, 

pub fn radius(self, radius: T) -> Self

pub fn radii(self, radii: Vec<T>) -> Self

impl<T, K> HRBF<T, K> where
    T: Real,
    K: Kernel<T> + Default, 

pub fn new(sites: Vec<Point3<T>>) -> Self

Main constructor. Assigns the degrees of freedom used by this HRBF in a form of 3D points at which the kernel will be evaluated.

pub fn with_kernel(self, kernel: KernelType<K>) -> Self

Builder that assigns a particular kernel to this HRBF.

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

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

pub fn betas(&self) -> &Vec<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, points: &[Point3<T>], normals: &[Vector3<T>]) -> bool

Fit the current HRBF to the given data. Return true if successful. NOTE: Currently, points must be the same size as as sites.

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

Fit the current HRBF to the given data. The resulting HRBF field is equal to offsets and has a gradient equal to normals. Return true if successful. NOTE: Currently, points must be the same size as as sites.

pub fn fit_system(
    &self,
    points: &[Point3<T>],
    potential: &[T],
    normals: &[Vector3<T>]
) -> (DMatrix<T>, DVector<T>)

Advanced. Returns the fitting matrix A and corresponding right-hand-side b. b is a stacked vector of 4D vectors representing the desired HRBF potential and normal at data point i, so A.inverse()*b gives the betas (or weights) defining the HRBF potential.

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.rs 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> HRBFTrait<T> for HRBF<T, K> where
    T: Real,
    K: Kernel<T> + Default, 

fn fit(&mut self, points: &[Point3<T>], normals: &[Vector3<T>]) -> bool

fn fit_offset(
    &mut self,
    points: &[Point3<T>],
    offsets: &[T],
    normals: &[Vector3<T>]
) -> bool

fn fit_system(
    &self,
    points: &[Point3<T>],
    potential: &[T],
    normals: &[Vector3<T>]
) -> (DMatrix<T>, DVector<T>)

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

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

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

impl<T, K> Default for HRBF<T, K> where
    T: Real,
    K: Kernel<T> + Default, 

fn default() -> Self

Returns the "default value" for a type.

impl<T: Clone, K: Clone> Clone for HRBF<T, K> where
    T: Real,
    K: Kernel<T>, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug, K: Debug> Debug for HRBF<T, K> where
    T: Real,
    K: Kernel<T>, 

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

Formats the value using the given formatter.