HA7 - Task 3: Geometric Theory

Cartesian Co-ordinate System
The Cartesian Co-ordinate System was invented in the 17th century by René Descartes, and it revolutionized maths by providing the first proper link between Euclidean geometry and algebra.

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Computers draw 2D vector artwork by plotting points on the X and Y axis, and then joining the points with lines. The shapes can then be filled with colours and the lines made thicker, or given colours. 3D programs do the same, but have an addition axis called Z.

                     

Geometric Theory & Polygons
The basic object that is used in modeling is called a vertex, which is a point in a 3D space. Two vertices are connected by a line, and it becomes an edge. 3 connected vertices form a triangle, which is the simplest polygon that can be made in the eulcidean space. Triangles together can form more complex shapes, such as 'quads' like squares. 

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A group of polygons that are connected by vertices are called 'meshes', also known as a wireframe model. 
To make it look better, none of the polygons must cross over each other. It should also not include any doubled vertices or edges. It's also preferred that a mesh doesn't have any errors in it, like doubled edges, vertices, etc. Sometimes it is important for meshes to not have any holes in them.

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
Once polygons are created, they can be made into surfaces, so they can be coloured or textured to create the right look.