Task 3 - Geometric Theory

The Cartesian Coordinates System

The Cartesian coordinate system is a coordinate system created in the 17th century by René Descartes, the system specifies each point uniquely by a pair of numerical coordinates. The Cartesian Coordinates system was important and still is because it revolutionized mathematics by providing proof that the link between Euclidean geometry and algebra is real and means something.

Source: http://www.basic-mathematics.com/images/coordinate2.gif

The points are named X,Y,Z in its basic form and they are a equal distance apart in perpendicular lines. The point the lines meet is called the origin and the coordinates are referred to being on an axis. You can specify the position of any point in the three dimensional space using the Cartesian coordinates.

Source for facts: https://en.wikipedia.org/wiki/Cartesian_coordinate_system

Coordinate Introduction

2D Vector artwork is created through a computer connecting points, plotting them on an X and Y axes, joining these points with lines also called paths you will create an image. The shapes can be colored and filled and the lines can be changed making them thinner,fatter and much more, you can easily do all of this within the illustrator application. Programs that work in 3D operate on a 3D grid of coordinates which are very similar to the 2D coordinates except there is a third axis known as the Z or also known as the depth axis on the 3D grid.

Examples of this process:

source: https://m1.behance.net/rendition/pm/9158837/disp/814f80f209560cd18cedb2210ec86b7e.png

As you can see in the image above this is a vector image created in adobe illustrator using points and lines then its colored and filled to create a beautiful piece of artwork. The vector artwork is of David Beckham.

Geometric Theory and Polygons

basic objects used in mesh modeling are called vertex's which are a point in the three dimensional space. A mesh is basically a group of polygons which are connected together by shared vertices. A mesh is often referred to as a wire frame model. two vertices connect by straight lines become an edge and three connected become a triangle which is the simplest form of a polygon. 

In the Euclidean geometry any three non collinear points determine a plane, and because of this any triangle will always inhabit a single plane. The geometric theorem is an area in mathematics and basically the connections between algebraic properties such as the groups and topological and geometric properties of spaces on which these groups act.

source of facts: https://en.wikipedia.org/wiki/Geometric_group_theory

Surfaces are the faces BOOM. Surfaces are the areas on objects that you see.