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docs/lectures/graphics/01_rendering.md

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+# Rendering
+
+**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 
+
+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. 
+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 *fragement* 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.
+
+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.
+2. Vertex Shader
+   - 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.
+
+## Rasterisation
+
+```java
+for each pixel y in Y dimension {
+	for each pixel x in X dimension {
+		for each triangle t {
+ 			if pixel x,y is inside triangle t {
+                Call fragment shader to
+				calculate the fragment colour
+			}
+        }
+	}
+}
+```
+
+#### Barcentric Coordinates
+
+We can use this to calculate if a point is inside a triangle or not.
+
+The barrcentric coordintates are $\alpha, \beta, \gamma$.
+
+$\alpha$ corresponds to the normalised linear distance of P between the line $\alpha$=0 and $\alpha$=1
+
+$\beta$ corresponds to the normalised linear distance of P between the line AC and point B
+
+$\gamma$ corresponds to the normalised linear distance of P between the line AB and point C
+
+If $\alpha, \beta, \gamma$ are all in the range $[0..1]$ then the point is within the triangle.
+
+##### Calculating Barycentric Coordinates
+
+$line(A, B, P) = (B_y-A_y)P_x+(A_x-B_x)P_y+B_xA_y-A_xB_y$
+
+$\alpha = \frac{line(B,C,P)}{line(B,C,A)}$
+
+$\beta = \frac{line(A,C,P)}{line(A,C,B)}$
+
+$\gamma = \frac{line(A,B,P)}{line(A,B,C)}$