N-Dimensional Hyper-Rectangle Data Structure

ndrect is a library that provides a data structure to work with sequencing hyper-rectangles in an N-dimensional space. We provide some minimally useful tools and syntax to help with sequencing and some handy geometrical calculations.

• Hyper-rectangle (N-Dim Rectangle) is a mathematical term for any rectangular geometry that exists in N dimensions where N >= 1. All of their edges must lie parallel to the global orthogonal axes.
• Sequencing in this case implies placing these Hyper-rectangles flush with each other. For example, in 2D, "flush" hyper-rectangles would have one of their sides intersect each other; in 3D, "flush" hyper-rectangles would have a face intersect with another's face.

The NDRect class

An NDRect is a representation of an atomic hyper-rectangle. Its constructor takes in a mapping of {<DimensionName>: <DimensionLength>} to define its shape.

from ndrect import NDRect

r = NDRect({0: 1, 1: 2})
assert r.shape == {0: 1, 1: 2}

Notice that because the shape is defined as a mapping (dictionary), this is because we do not restrict NDRect to fall in sequential integer dimensions. That is, you can define NDRect like so too:

from ndrect import NDRect

# Dimension 0: Length 1
# Dimension 2: Length 4
NDRect({0: 1, 2: 4})

# Dimension A: Length 1
# Dimension B: Length 4
NDRect({"A": 1, "B": 4})

Sequencing NDRect into Complex Hyper-rectangles

Up to now, this is no more than just a dictionary, its power comes when we sequence them together.

When sequenced with one another, will form a Unaligned Complex Hyper-rectangle. This Unaligned Complex Hyper-rectangle must be aligned along a single axis to resolve into a Complex Hyper-rectangle

• Complex in this case, implies multiple NDRect as a sequence
• Alignment implies a certain axis that the sequence of NDRect objects are aligned along.
• Unaligned would mean there's no axis that the sequence of NDRect objects are aligned along.

For example, given two NDRect rectangles:

R1  R2
┌─┐ ┌───┐    
│ │ │   │    
└─┘ └───┘    

We can sequence them in 2 different axes

R1 + R2 Along Axis 0 (Horizontal)
┌─┬───┐   
│ │   │   
└─┴───┘   

R1 + R2 Along Axis 1 (Vertical)
┌───┐   
│   │   
├─┬─┘   
│ │     
└─┘       

In NDRect, we code it like so:

from ndrect import NDRect

r1 = NDRect({0: 1, 1: 2})
r2 = NDRect({0: 2, 1: 2})

assert r1.then(r2).along(0).shape == {0: 3, 1: 2}
assert r1.then(r2).along(1).shape == {0: 2, 1: 4}

Notice that when we sequence them along axis 1, its shape is the shape of minimal bounding rectangle that contains both R1 and R2.