1. HA4 – Geometric Theory
Geometry - Cartesian Coordinates System
Cartesian coordinates, also called rectangular coordinates, provide a method of rendering graphs
and indicating the positions of points on a two-dimensional (2D) surface or in three-dimensional ( 3D
) space. The scheme gets its name from one of the first people known to have used it, the French
mathematician and philosopher René Descartes (1596-1650). The Cartesian coordinate system is
used to define positions on computer displays and in virtual reality (VR) renderings. The system is
also employed in mathematics, physics, engineering, navigation, robotics, economics, and other
sciences.
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Vector
A vector is a quantity or phenomenon that has t...
(WhatIs.com)
Co-ordinates
Coordinates are distances or angles.
The Cartesian plane consists of two perpendicular axes that cross at a central point called the origin.
Positions or coordinates are determined according to the east/west and north/south displacements
from the origin. The east/west axis is often called the x axis, and the north/south axis is called the y
axis. For this reason, the Cartesian plane is also known as the xy -plane. The x and y axes are linear
number lines, meaning that each division on a given axis always represents the same increment.
However, the increments on different axes can differ. For example, in the illustration at left below,
each increment on the x axis might represent 2 units, while each increment on the y axis represents
5 units. Points or coordinates are indicated by writing an opening parenthesis, the x value, a comma,
the y value, and a closing parenthesis in that order. An example is (x,y) = (2,-5). The origin is usually,
but not always, assigned the value (0,0).
Cartesian three-space, also called xyz -space, has a third axis, oriented at right angles to the xy -
plane. This axis, usually called the z axis, passes through the origin of the xy -plane. Positions or
coordinates are determined according to the east/west (x), north/south ( y ), and up/down ( z )
displacements from the origin. As is the case with the x and y axes, the z axis is a linear number line.
For example, in the illustration at right above, each increment on the x axis might represent 5 units,
each increment on the y axis 10 units, and each increment on the z axis 2 units. Points or coordinates
are indicated by writing an opening parenthesis, the x value, a comma, the y value, another comma,
the z value, and a closing parenthesis in that order. An example is ( x,y, z ) = (5,-10,-4). The origin is
usually, but not always, assigned the value (0, 0, 0).

2. http://www.basic-mathematics.com/cartesian-coordinate-system.html
http://whatis.techtarget.com/definition/Cartesian-coordinates-rectangular-coordinates
Polygon in video games
- Wireframes are an important design tool used in Web
development. It is a visualization tool for presenting proposed functions, structure and content of a
Web page or Web site. A wireframe separates the graphic elements of a Web site from the
functional elements in such a way that Web teams can easily explain how users will interact with the
Web site. A typical wireframe includes:
(1) key page elements and their location, such as header, footer, navigation, content objects,
branding elements, (2) grouping of elements, such as side bars, navigation bars, content
areas, (3) labelling, page title, navigation links, headings to content objects, and (4) place
holders, content text and images.http://www.webopedia.com/TERM/W/wireframe.html
(2) Image - http://cgcookie.com/unity/2013/04/29/modeling-and-texturing-polygon-hair-for-
game-characters/
Primitives
A low-level object or operation from which higher-level, more complex objects and operations can
be constructed. In graphics, primitives are basic elements, such as lines, curves, and polygons, which
you can combine to create more complex graphical images. In programming, primitives are the basic
operations supported by the programming language. A programmer combines these primitives to
create more complex operations, which are packaged as functions, procedures, and methods.
http://www.webopedia.com/TERM/P/primitive.html

3. Polygons and Shading - Suface
The vast majority of 3-D objects created for computer games are made up of polygons. A polygon is
an area defined by lines. To have a polygon, you must have at least three lines. The lines connect a
series of coordinates in the three-dimensional "space" the computer creates. The point where the
lines connect is known as a vertex. Each vertex has X, Y and Z coordinates.
•X determines the position relative to right or left in the virtual space
•Y determines the position relative to top or bottom in the virtual space
•Z determines the position relative to front or back in the virtual space
Once each polygon has a set of vertices to define its shape, it needs information that tells it what to
look like. There are four common ways to do this:
•Flat shading
•Gouraud shading
•Phong shading
•Texture mapping
Flat shading simply assigns a single colour to a polygon. It is very simple and fast, but makes the
object look artificial. Gouraud shading is more complex. Colours are assigned to each vertex and
then are blended across the face of the polygon. Since each vertex is typically associated with at
least three distinct polygons, this makes the object look natural instead of faceted.
http://www.slideshare.net/upload?from_source=loggedin_newsfeed
http://forums.eidosgames.com/showthread.php?t=108926