# Crate construct [−] [src]

A library for higher order functional programming with homotopy maps to construct 3D geometry.

### What is a homotopy map?

A homotopy is a continuous deformation between two functions. Think about combining two functions `f` and `g` with a parameter in the range between 0 and 1 such that setting the parameter to 0 gives you `f` and setting it to 1 gives you `g`. With other words, it lets you interpolate smoothly between functions.

This library uses a simplified homotopy version designed for constructing 3D geometry:

```/// A function of type `1d -> 3d`.
pub type Fn1<T> = Arc<Fn(T) -> [T; 3] + Sync + Send>;
/// A function of type `2d -> 3d`.
pub type Fn2<T> = Arc<Fn([T; 2]) -> [T; 3] + Sync + Send>;
/// A function of type `3d -> 3d`.
pub type Fn3<T> = Arc<Fn([T; 3]) -> [T; 3] + Sync + Send>;```

In this library, these functions are called homotopy maps and usually satisfies these properties:

• All inputs are assumed to be normalized, starting at 0 and ending at 1. This means that `Fn1` forms a curved line, `Fn2` forms a curved quad, and `Fn3` forms a curved cube.
• The `Arc` smart pointer makes it possible to clone closures.
• The `Sync` and `Send` constraints makes it easier to program with multiple threads.
• Basic geometric shapes are continuous within the range from 0 to 1.

A curved cube does not mean it need to look like a cube. Actually, you can create a variety of shapes that do not look like cubes at all, e.g. a sphere. What is meant by a "curved cube" is that there are 3 parameters between 0 and 1 controlling the generation of points. If you used an identity map, you would get a cube shape. The transformation to other shapes is the reason it is called a "curved cube".

### Motivation

Constructing 3D geometry is an iterative process where the final design/need can be quite different from the first draft. In game engines there are additional needs like generating multiple models of various detail or adjusting models depending on the capacity of the target platform. This makes it desirable to have some tools where one can work with an idea without getting slowed down by a lot of technical details.

Homotopy maps have the property that the geometry can be constructed by need, without any additional instructions. This makes it a suitable candidate for combining them with higher order functional programming. Functions give an accurate representation while at the same time being lazy, such that one can e.g. intersect a curved cube to get a curved quad.

This library is an experiment to see how homotopy maps and higher order functional programming can be used to iterate on design. Function names are very short to provide good ergonomics.

## Reexports

 `pub use vecmath::traits::*;`

## Functions

 add2 Adds two vectors. add3 Adds two vectors. cast2 Converts to another vector type. cast3 Converts to another vector type. cbez Cubic bezier curve. circle Creates a circle located at a center and with a radius. con Concatenates two `1d -> 3d` functions returning a new function. contour Gets the contour line of a curved quad. conx2 Concatenates two `2d -> 3d` functions at x-weight. conx3 Concatenates two `3d -> 3d` functions at x-weight. cony2 Concatenates two `2d -> 3d` functions at y-weight. cony3 Concates two `3d -> 3d` functions at y-weight. conz3 Concates two `3d -> 3d` functions at z-weight. cquad Constructs a curved quad by smoothing between boundary functions. ext1 Extends a 1d shape into 2d by adding a vector to the result generated by a 1d shape. ext2 Extends a 2d shape into 3d by adding a vector to the result generated by a 1d shape. len2 Computes the length of vector. len3 Computes the length of vector. lin Returns a linear function. lin2 Creates a linear interpolation between two functions. margin1 Adds a margin to input of a `1d -> 3d` function. margin2 Adds a margin to input of a `2d -> 3d` function. margin3 Adds a margin to input of a `3d -> 3d` function. mirx2 Bake mirror `2d -> 3d` around yz-plane at x coordinate. mirx3 Bake mirror `3d -> 3d` around yz-plane at x coordinate. miry2 Bake mirror `2d -> 3d` around xz-plane at y coordinate. miry3 Bake mirror `3d -> 3d` around xz-plane at y coordinate. mirz3 Bake mirror `3d -> 3d` around xy-plane at z coordinate. mx Mirror shape `1d -> 3d` around yz-plane at x coordinate. my Mirror shape `1d -> 3d` around xz-plane at y coordinate. mz Mirror shape `1d -> 3d` around xy-plane at z coordinate. off Offsets `3d -> 3d` at position. qbez Quadratic bezier curve. rev Reverses input direction. scale2 Multiplies the vector with a scalar. scale3 Multiplies the vector with a scalar. seg1 Uses a range to pick a segment of a curve. sphere Creates a sphere located at a center and with a radius. sub2 Subtracts 'b' from 'a'. sub3 Subtracts 'b' from 'a'. x2 Intersects a curved quad at x-line. x3 Intersects a curved cube at x-plane. y2 Intersects a curved quad at y-line. y3 Intersects a curved cube at y-plane. z3 Intersects a curved cube at z-plane.

## Type Definitions

 Fn1 A function of type `1d -> 3d`. Fn2 A function of type `2d -> 3d`. Fn3 A function of type `3d -> 3d`.