You can use a Hilbert Curve to map from a finite (bounded) 2D square area of size (L * L) onto a 1D line of length (L * L), however, in a separate step, the shape and size of the square can be transformed with an afine transformation function and the line can be scaled to any size.

To start with the simplest case consider a point projected onto a two dimensional line. If we want to map the two dimensional space shown here onto the one dimensional space of the line we can use: P2 = line • P1. where: P1 = vector representing a point to be transformed; P2 = scalar representing point in terms of its distance along line ...

May 21, 2012 · I have 2D elements distributed in a space of [-4, +4] and want to convert any point in the 2D space to a 1D real-valued number 0~1.0 such that 1st quadrant...

May 7, 2019 · Yes, there are mappings from 2D to 1D for natural numbers, known as Pairing functions. For example, the Cantor pairing function: defun 2d->1d (x, y): return (1 / 2) * (x + y) * (x + y + 1) + y; For the reverse function see the link above, it is a little more complex.

Nov 15, 2019 · You can map your 3D space onto a 1D line via a 3D Hilbert Curve, then map the 1D line into 2D via a 2D Hilbert Curve.

Mar 27, 2014 · I have a array of [width, height, x, y] vectors, like so: [[width_1, height_1, x_1, y_1],...,[width_n, height_n, x_n, y_n]] representing a 2D plane of blocks. This vector is potentially long (n > 10k). An example: must be projected like:

Nov 18, 2022 · Take your average globe of the earth and project it onto a 2D image, essentially flattening it but keep the same diameter. You loose an entire half of the globe in the process, and the remaining image is also deformed with everything crushed towards the center point.

Take a look at this post, this might give you some direction. The best approach depends on what you want to do with it. The Cantor Pairing function as linked by @AugustoQ is definitely a good option. Hilbert curves or other space-filling curves (most notably the Z-curve due to its computational simplicity) are other good options.

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Feb 6, 2020 · I would like to convert a 2D line into a 1D polyline with the same length. How can I do it, please?