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`.