Enum SheetMethod 

#[non_exhaustive]
pub enum SheetMethod {
    Geodesic,
    LeastDistortion {
        resolution: f64,
    },
    AsRigidAsPossible {
        resolution: f64,
        stretch: f64,
    },
}

How the flat sheet is carried away from its origin.

Variants (Non-exhaustive)

Non-exhaustive enums could have additional variants added in future. Therefore, when matching against variants of non-exhaustive enums, an extra wildcard arm must be added to account for any future variants.

Geodesic

Geodesic polar coordinates: the sheet point at distance r and angle t from the origin lands where the geodesic leaving the origin at angle t from the sheet’s +x is after length r (the exponential map). Lengths along lines through the origin are kept.

LeastDistortion

The conformal flattening of the geodesic disc the sheet covers that stretches nothing along the disc’s rim, pinned at the origin with its +x along the sheet’s, and scaled to keep the disc’s area as a whole. On a sphere it is the stereographic projection from the origin’s antipode.

It is conformal, not area-keeping: angles are kept, and lengths stretch alike in every direction at a point but by different amounts from point to point, so a region’s area on the surface is not its area on the sheet. On a sphere of radius 10 with reach 5 the stretch runs from 1.031 at the origin to 0.968 at the reach, and a 6 x 4 rectangle at the origin covers 25.07 rather than 24.

The flattening is computed on a mesh, and SurfaceSheet::flattening_error is an estimate, not a bound, of how far the laid map stands from the smooth one; see there for the assumption it rests on. On a plane, a cylinder and a cone it is their exact development, as Geodesic is.

Fields

resolution: f64

The estimated departure from the smooth flattening to refine down to, as a length on the sheet.

AsRigidAsPossible

The as-rigid-as-possible flattening of the geodesic disc the sheet covers: each triangle of a mesh of the disc as near a rotation of itself on the surface as the whole allows, so lengths stretch as little as they can in every direction at once, and areas with them. Pinned at the origin with its +x along the sheet’s, and not scaled.

The flattening is a minimum of a non-convex energy, settled from the conformal flattening, and not unique: nothing is said of how far it stands from any smooth map. The sheet is judged by what it does. Its length ratio, against the surface’s own metric, is measured at every vertex and triangle centroid of the flattened mesh within the reach, and the sheet is refused where any falls outside 1 / (1 + stretch) to 1 + stretch, or where it folds over. These are measurements at those points, not a bound between them. SurfaceSheet::distortion starts from the range measured. SurfaceSheet::flattening_error is the miss of the smooth map carried, a polynomial, against the mesh’s own map, within half of resolution at the same points. On a plane, a cylinder and a cone it is their exact development.

Fields

resolution: f64

How closely the smooth map carried follows the flattened mesh, as a length on the sheet.

stretch: f64

How far the length ratio may stand from one, as a fraction.

Trait Implementations

impl Clone for SheetMethod

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for SheetMethod

impl Debug for SheetMethod

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

Formats the value using the given formatter.

impl PartialEq for SheetMethod

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for SheetMethod