Crate hexasphere

Library for subdividing shapes made of triangles.

This library defines Subdivided<T, S>. This struct allows one to define a base shape using S and the BaseShape trait, and to subdivide it using the interpolation functions defined as part of S.

This includes a few base shapes:

• Icosahedron
• Tetrahedron
• Square
• Triangle

Example usage

use hexasphere::IcoSphere;

fn main() {
    // Create a new sphere with 20 subdivisions
    // an no data associated with the vertices.
    let sphere = IcoSphere::new(20, |_| ());

    let points = sphere.raw_points();
    for p in points {
        println!("{:?} is a point on the sphere!", p);
    }
    let indices = sphere.get_all_indices();
    for triangle in indices.chunks(3) {
        println!(
            "[{}, {}, {}] is a triangle on the resulting shape",
            triangle[0],
            triangle[1],
            triangle[2],
        );
    }
}

Features

• adjacency allows the user to create neighbour maps from the indices provided by the Subdivided struct.

Structs

IcoSphereBase	Implements an icosahedron as the base shape.
SquareBase	Implements a square as the base shape.
Subdivided	A progressively subdivided shape which can record the indices of the points and list out the individual triangles of the resulting shape.
TetraSphereBase	Implements a tetrahedron as the base shape.
Triangle	A main triangle on the base shape of a subdivided shape.
TriangleBase	Implements a single triangle as the base shape.

Traits

BaseShape	Defines the setup for a base shape, and the functions used in interpolation.
EquilateralBaseShape	Implemented in the case where the triangles on the shape are both equilateral and identifiable from their normal.

Functions

geometric_slerp	Implements spherical interpolation along the great arc created by the initial points. This returns a new point p percent of the way along that arc.
geometric_slerp_half	This is an optimization for the geometric_slerp in the case where p is 0.5 or 50%.
geometric_slerp_multiple	This is an optimization for the case where multiple points require the calculation of varying values of p for the same start and end points.
lerp	Simple linear interpolation. No weirdness here.
lerp_half	Gives the average of the two points.
lerp_multiple	This is provided as a plug in for people who need it, but this implements essentially the same algorithm as BaseShape would without ever being reimplemented.
normalized_lerp	Performs normalized linear interpolation. This creates distortion when compared with spherical interpolation along an arc, however this is most likely faster, as though this avoids expensive sin and acos calculations.
normalized_lerp_half	This is an optimization of normalized_lerp which avoids a multiplication.
normalized_lerp_multiple	This is provided as a plug in for people who need it, but this implements essentially the same algorithm as BaseShape would without ever being reimplemented.

Type Definitions

Hexasphere	Icosphere.
IcoSphere	Icosphere.
SquarePlane	A square.
TetraSphere	Tetrasphere (Sphere from tetrahedron).
TrianglePlane	A triangle.