Struct SlicingManifold 

pub struct SlicingManifold {
    pub centroid: [f64; 3],
    pub normal: [f64; 3],
    pub basis_u: [f64; 3],
    pub basis_v: [f64; 3],
    pub variance_ratio: f64,
}

A 2D plane fitted through the 3D projected point cloud that captures the maximum variance. Found by PCA on the Cartesian coordinates of the projected embeddings.

The plane is defined by:

• centroid: the mean of all 3D points
• basis_u, basis_v: orthonormal vectors spanning the plane (directions of max variance)
• normal: vector perpendicular to the plane (direction of minimum variance)

Fields

centroid: [f64; 3]

normal: [f64; 3]

basis_u: [f64; 3]

basis_v: [f64; 3]

variance_ratio: f64

Implementations

impl SlicingManifold

pub fn fit(points: &[[f64; 3]]) -> Self

Fit the optimal slicing plane to a set of 3D points. Each point is (x, y, z) in Cartesian coordinates.

pub fn project_2d(&self, point: &[f64; 3]) -> (f64, f64)

Project a 3D point onto the plane, returning (u, v) coordinates.

pub fn distance(&self, point: &[f64; 3]) -> f64

Signed distance from the plane (positive = same side as normal).

pub fn fit_local(query: &[f64; 3], all_points: &[[f64; 3]], k: usize) -> Self

Fit a local manifold around a query point using its k nearest neighbors.

The local plane captures the shape of the semantic neighborhood:

• If variance_ratio ≈ 1.0, the neighborhood is flat (concepts spread in a plane)
• If variance_ratio ≈ 0.67, concepts are uniformly distributed (spherical)
• The normal direction reveals which semantic axis is least relevant locally

This enables directional search narrowing: once you know the local geometry, you can restrict subsequent queries to the dominant plane, cutting the effective search dimensionality from 3D to 2D in that region.

Trait Implementations

impl Clone for SlicingManifold

fn clone(&self) -> SlicingManifold

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SlicingManifold

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

Formats the value using the given formatter.