Tidy up

docs/lectures/graphics/01_rendering.md

@@ -2,17 +2,17 @@
 
 **Rendering** is the process of drawing images on the computer display. In this course we will focus on images which are made up of triangles.
 
-Rendering in 2-Dimensions involves the following 
+Rendering in 2-Dimensions involves the following
 
-1. The graphics programmer specifies vertices which make up some triangles to be drawn. 
-2. The API assembles triangles from the vertices. 
+1. The graphics programmer specifies vertices which make up some triangles to be drawn.
+2. The API assembles triangles from the vertices.
 3. The API rasterises the triangles to calculate which pixels are inside each triangle.
-4. The pixels inside triangles, called fragments, are shaded to calculate the colour. 
+4. The pixels inside triangles, called fragments, are shaded to calculate the colour.
 5. The colours are displayed at the appropriate pixels.
 
-A **vertex** is a point in space and is used to model geometry. A vertex can be presented using a vector, which is like an arrow. Can be written as $v=(3,2,0)$ 
+A **vertex** is a point in space and is used to model geometry. A vertex can be presented using a vector, which is like an arrow. Can be written as $v=(3,2,0)$
 
-A *fragement* is a piece of a triangle which will be drawn to a pixel.
+A *fragment* is a piece of a triangle which will be drawn to a pixel.
 
 A section of memory called a **frame buffer** (or colour buffer) stores the colour values that will be used at each pixel.
 
@@ -21,15 +21,15 @@ A shader is a program. Shaders are run on the GPU.
 #### Rendering Stages
 
 1. Vertex Specification
-   - In the application the vertices making up the triangles are specified, that is, given positions. The application is a software program which might be a Computer Aided Design (CAD), some kind of simulation, a visualisation, or a videogame. The graphics programmer specifies the location of vertices which make up the triangles to be rendered. These vertices are passed to the vertex shaders.
+    - In the application the vertices making up the triangles are specified, that is, given positions. The application is a software program which might be a computer-aided design (CAD) program, some kind of simulation, a visualisation, or a video game. The graphics programmer specifies the location of vertices which make up the triangles to be rendered. These vertices are passed to the vertex shaders.
 2. Vertex Shader
-   - Vertex processing by the vertex shader moves the vertices around. . The Vertices are used to construct triangles.
+    - Vertex processing by the vertex shader moves the vertices around. The vertices are used to construct triangles.
 3. Rasterisation
-   - There may be empty space around the triangles. Rasterisation is the process of taking all of the triangles and figuring out which pixels are inside each of the triangles.
-   - Each of these pixels inside the triangles is called a fragment.
-   - Rasterisation will generate a fragment for each pixel which is inside a triangle. The fragments are passed to the fragment shaders.
-4.  Fragment Shader
-   - The colour of Fragments is calculated by the fragment shader.
+    - There may be empty space around the triangles. Rasterisation is the process of taking all of the triangles and figuring out which pixels are inside each of the triangles.
+    - Each of these pixels inside the triangles is called a fragment.
+    - Rasterisation will generate a fragment for each pixel which is inside a triangle. The fragments are passed to the fragment shaders.
+4. Fragment Shader
+    - The colour of fragments is calculated by the fragment shader.
 
 ## Rasterisation
 
@@ -46,11 +46,11 @@ for each pixel y in Y dimension {
 }
 ```
 
-#### Barcentric Coordinates
+#### Barycentric Coordinates
 
 We can use this to calculate if a point is inside a triangle or not.
 
-The barrcentric coordintates are $\alpha, \beta, \gamma$.
+The barycentric coordinates are $\alpha, \beta, \gamma$.
 
 $\alpha$ corresponds to the normalised linear distance of P between the line $\alpha$=0 and $\alpha$=1