Final edits before linking to itch.io page.

Author: adam-rumpf

README.md

@@ -1,26 +1,28 @@
-# GameMaker Scripts
+# GameMaker Studio 2 Mathematical Scripts
 
-A collection of general utility and mathematical functions for GameMaker Studio 2 (Version 2.3).
+A collection of general utility and mathematical functions for [GameMaker Studio 2](https://www.yoyogames.com/) (Version 2.3). These mostly consist of functions that I have found useful during my own game development, and I expect to periodically add more over time.
 
-All scripts are included in the `scripts/` folder of this repository. Each script defines a single function. Most functions are standalone and are meant to be taken à la carte, but some of the more mathematically complicated functions depend on other scripts, indicated in a `@requires` tag. All function names begin with an underscore (`_`) in order to distinguish them from built-in functions. A [local asset package](https://docs2.yoyogames.com/source/_build/2_interface/2_extras/local_asset_packages.html) containing all scripts can be found on the [releases](https://github.com/adam-rumpf/game-maker-scripts/releases) page.
+A [local asset package](https://docs2.yoyogames.com/source/_build/2_interface/2_extras/local_asset_packages.html) containing all scripts can be found for free on the [releases](https://github.com/adam-rumpf/game-maker-scripts/releases) page or as donationware from my [itch.io page](https://adam-rumpf.itch.io/gamemaker-studio-2-mathematical-scripts). I encourage you to download it, use it in your own projects, and modify the source code as much as you like free of charge. If, however, you really, really want to pay for it and it is within your means to do so, I would not say no to your financial support.
+
+Each script defines a single function. Most functions are standalone and are meant to be taken à la carte, but some of the more mathematically complicated functions depend on other scripts, indicated in a `@requires` tag. All function names begin with an underscore (`_`) in order to distinguish them from built-in functions.
 
 The following is a brief description of the included functions, divided into rough categories.
 
 ## Analysis Functions
 
-A variety of scripts dealing with functions and sets, which may have some uses for managing data structures.
+A variety of scripts dealing with sequences, functions, and sets, which may have some uses for managing data structures.
 
-* [`_integer_to_natural`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_integer_to_natural/_integer_to_natural.gml): Converts an integer to a unique natural number using the zig-zagging bijection from _(0, 1, -1, 2, -2, ...)_ to _(0, 1, 2, 3, 4, ...)_. The inverse of `_natural_to_integer`.
-* [`_natural_to_integer`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_natural_to_integer/_natural_to_integer.gml): Converts a natural number to a unique integer using the zig-zagging bijection from _(0, 1, 2, 3, 4, ...)_ to _(0, 1, -1, 2, -2, ...)_. The inverse of `_integer_to_natural`.
-* [`_natural_to_pair`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_natural_to_pair/_natural_to_pair.gml): Converts a natural number to a unique ordered pair of natural numbers using the [inverse Cantor pairing function](https://en.wikipedia.org/wiki/Pairing_function#Inverting_the_Cantor_pairing_function). The inverse of `_pair_to_natural`.
-* [`_pair_to_natural`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_pair_to_natural/_pair_to_natural.gml): Converts an ordered pair of natural numbers to a unique natural number using the [Cantor pairing function](https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function). The inverse of `_natural_to_pair`.
+* [`_integer_to_natural`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_integer_to_natural/_integer_to_natural.gml): Maps an integer to a unique natural number using the zig-zagging bijection from _(0, 1, -1, 2, -2, ...)_ to _(0, 1, 2, 3, 4, ...)_. This is the inverse of `_natural_to_integer`.
+* [`_natural_to_integer`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_natural_to_integer/_natural_to_integer.gml): Maps a natural number to a unique integer using the zig-zagging bijection from _(0, 1, 2, 3, 4, ...)_ to _(0, 1, -1, 2, -2, ...)_. This is the inverse of `_integer_to_natural`.
+* [`_natural_to_pair`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_natural_to_pair/_natural_to_pair.gml): Maps a natural number to a unique ordered pair of natural numbers using the [inverse Cantor pairing function](https://en.wikipedia.org/wiki/Pairing_function#Inverting_the_Cantor_pairing_function). This is the inverse of `_pair_to_natural`.
+* [`_pair_to_natural`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_pair_to_natural/_pair_to_natural.gml): Maps an ordered pair of natural numbers to a unique natural number using the [Cantor pairing function](https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function). This is the inverse of `_natural_to_pair`.
 
 ## Array Functions
 
 Common array functions (such as searching and counting).
 
 * [`_array_count`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_array_count/_array_count.gml): Counts the number of occurrences of a specified value in an array.
-* [`_array_index`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_array_index/_array_index.gml): Finds the first index at which a specified value occurs in an array (or -1 if not found). An optional argument allows the search to begin with a specified index.
+* [`_array_index`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_array_index/_array_index.gml): Finds the first index at which a specified value occurs in an array (or -1 if not found). An optional argument allows the search to begin from a specified index.
 * [`_array_max`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_array_max/_array_max.gml): Returns the maximum value (or the index of the maximum value) in an array.
 * [`_array_min`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_array_min/_array_min.gml): Returns the minimum value (or the index of the minimum value) in an array.
 * [`_invert_permutation`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_invert_permutation/_invert_permutation.gml): Generates a permutation array to invert a given permutation array.
@@ -34,14 +36,14 @@ Numerical algorithms for computational mathematics.
 
 * [`_cubic_spline_coefficients`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_cubic_spline_coefficients/_cubic_spline_coefficients.gml): Calculates vectors of polynomial coefficients for the natural [cubic spline](https://en.wikipedia.org/wiki/Spline_interpolation) interpolating a given data set.
 * [`_cubic_spline_evaluate`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_cubic_spline_evaluate/_cubic_spline_evaluate.gml): Evaluates a piecewise cubic polynomial at a specific value given a given set of coefficient vectors and intervals.
-* [`_root_bisection`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_root_bisection/_root_bisection.gml): Finds a function root on a specified interval using the [bisection method](https://en.wikipedia.org/wiki/Bisection_method).
-* [`_root_newton`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_root_newton/_root_newton.gml): Finds a function root given a derivative and an initial guess using [Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method).
+* [`_root_bisection`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_root_bisection/_root_bisection.gml): Finds the root of a continuous function on a specified interval using the [bisection method](https://en.wikipedia.org/wiki/Bisection_method). This requires that the function change sign over the interval.
+* [`_root_newton`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_root_newton/_root_newton.gml): Finds the root of a differentiable function using [Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method). This requires an initial guess and a derivative function.
 
 ## Linear Algebra Functions
 
 Common linear algebra algorithms for dealing with matrices and vectors. In all functions, _vectors_ are considered to be 1D arrays while _matrices_ are 2D arrays (i.e. arrays of arrays).
 
-* [`_linear_solve`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_linear_solve/_linear_solve.gml): Solves a linear system given a coefficient matrix and righthand vector (using [Gaussian elimination with partial pivoting](https://en.wikipedia.org/wiki/Pivot_element)).
+* [`_linear_solve`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_linear_solve/_linear_solve.gml): Solves a linear system of the form _Ax = b_ (using [Gaussian elimination with partial pivoting](https://en.wikipedia.org/wiki/Pivot_element)).
 * [`_matrix_multiply`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_matrix_multiply/_matrix_multiply.gml): Performs matrix-matrix, matrix-vector, and vector-vector multiplication.
 * [`_matrix_transpose`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_matrix_transpose/_matrix_transpose.gml): Transposes a 2D matrix.
 * [`_tridiagonal_solve`](https://github.com/adam-rumpf/game-maker-scripts/blob/master/scripts/_tridiagonal_solve/_tridiagonal_solve.gml): Solves a tridiagonal system (using the [Thomas algorithm](https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm)).