add links to post

collections/projects/Arduino Libraries/_posts/2020-09-20-3d_datatypes.md

@@ -3,7 +3,7 @@ layout: post
 title: "Datatypes for 3D vectors and quaternions"
 ---
 
-While developing an algorithm to perform [sensor fusion](/projects/arduino libraries/2020/03/14/imu_sensor_fusion.html) between the gyroscope and accelerometer of an inertial measurement unit, I needed a way to execute basic [vector](https://es.wikipedia.org/wiki/Vector) operations and manipulate a [quaternion](https://en.wikipedia.org/wiki/Quaternion) to encode the gyroscope's heading. Although it was possible to hard-code these operations directly into the sensor fusion, it seemed prudent to separate this functionality in case it needed to be reused. This was especially relevant for spatial navigation, which requires manipulating vectors in different frames of reference.
+While developing an algorithm to perform [sensor fusion](/projects/arduino libraries/2020/03/14/imu_sensor_fusion.html) between the gyroscope and accelerometer of an inertial measurement unit, I needed a way to execute basic [vector](https://es.wikipedia.org/wiki/Vector) operations and manipulate a [quaternion](https://en.wikipedia.org/wiki/Quaternion) to encode the gyroscope's heading. Although it was possible to hard-code these operations directly into the sensor fusion, it seemed prudent to separate this functionality in case it needed to be reused. This was especially relevant for spatial [navigation](https://en.wikipedia.org/wiki/Navigation), which requires manipulating vectors in different [frames of reference](https://en.wikipedia.org/wiki/Frame_of_reference). 
 
 To create data types for vectors and quaternions, I first needed to understand the [operations](https://en.wikipedia.org/wiki/Operation_(mathematics)) they can perform. These operations, defined through mathematical notation, had to be converted into functions. By using [operator overloading](https://www.geeksforgeeks.org/operator-overloading-cpp/), I was able to employ these functions in a way that closely resembled mathematical notation. This is because an operation is simply a different way of writing a function that takes one or more parameters. This approach was applied to most of the operations possible for vectors and quaternions. For more information on vector and quaternion operations, see these links:
 
@@ -12,7 +12,7 @@ To create data types for vectors and quaternions, I first needed to understand t
 - [Vector operations](http://emweb.unl.edu/Math/mathweb/vectors/vectors.html)
 
 <br>
-For example, the addition of two vectors can be written as **V1 + V2**. The **+** sign serves as shorthand for the function that takes two vectors and returns a new vector of their added values. When it came time to actually use these data types in code, it was straightforward because the corresponding operations could be written just as they would be in mathematical notation. This simplicity made the code easier to read, as operations reduced to a symbol rather than a function call.
+For example, the addition of two vectors can be written as **V1 + V2**. The **+** sign serves as shorthand for the function that takes two vectors and returns a new vector of their added values. When it came time to actually use these data types in code, it was straightforward because the corresponding operations could be written just as they would be in mathematical notation. This simplicity made the code easier to read, as operations reduced to a symbol rather than a _function call_. 
 
 Inside the library, vectors and quaternions were declared as [structs](https://cplusplus.com/doc/tutorial/structures/) to define their [data types](https://en.wikipedia.org/wiki/Data_type). Both vectors and quaternions could perform basic operations such as _addition, subtraction, multiplication, division, increment, decrement_, and their analogs for _multiplication and division_. Vectors and quaternions were also compatible with each other through operations such as the vector [dot product](https://en.wikipedia.org/wiki/Dot_product) and [cross product](https://en.wikipedia.org/wiki/Cross_product). Quaternions could be constructed as unit quaternions to represent rotations, allowing them to be directly used to rotate vectors. Additionally, both data types were made compatible with [arrays](https://cplusplus.com/doc/tutorial/arrays/), meaning that a length-3 array could be added, subtracted, etc, from a vector. This compatibility also extended to quaternions.