HA7 Task 3 - Geometric Theory

Cartesian Co-ordinate System
The Cartesian co-ordinate system was invented by Rene Descartes during the 17th century which provided the first link between Euclidean geometry and algebra revolutionizing maths. 

Computers are able to draw 2D vectors by plotting points on the X and Y axis and then they can  create art by joining the points with lines and then filling the shapes created with colours and the lines made thicker. 3D programs can also perform this task but with an added axis named Z. 

Geometric Theory & Polygons
A basic object is used to model and is called the Vertex, this is a point in a 3D space. When two vertices are connected by a line they will create an edge and when 3 connected vertices create a triangle it becomes the simplest polygon that can be made in the Euclidean space. Also when you form together more than one triangle they can create more complex shapes such as quads also known as squares and rectangles.

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Polygons that form a group and are connected by vertices are called meshes, hich can also be called a wireframe model. To make these look a lot better none of the polygons are allowed to cross over each other, it is also preferable to not include doubled vertices or edges. No errors should be allowed and it is sometimes important for meshes not to have any gaps or holes. 

Primitives
Within 3D applications, some objects are pre-made, and can be used to make models out of them. The most basic shapes are called the Common Primitive, and can be anything from a basic cube to a pyramid. These shapes are used as the beginning points of modelling.

Surfaces
After polygons are made, they can be turned into surfaces which allows them to be coloured or even textured to give them the right look.