HA7 Task 3 - Geometric Theory

3D Geometry
Fundamental Principles


Cartesian Coordinate System

Cartesian Coordinates were invented by a French mathematician René Descartes (or Renatus Cartesius in Latin, hence the name 'Cartesian'). The idea was that everything has an origin from which 3 axis emerge, and the placement of an object/point is signified by the distance and direction of that origin.

Cartesian coordinates allow one to specify the location of a point in the plane, or in three-dimensional space. The Cartesian coordinates (also called rectangular coordinates) of a point are a pair of numbers (in two-dimensions) or a triplet of numbers (in three-dimensions) that specified signed distances from the coordinate axis. http://mathinsight.org/cartesian_coordinates

The system is continued to be used in many programmes, xy axis in 2D software like Adobe Illustrator or Photoshop, xyz axis in 3D software for making 3D models. While making a 3D model out of polygons, the person really signifies that positioning on plane or in space of points, joins them in edged which then create polygons and finally a mesh.

In both of these, the image representation is suggested by the record of the points' co-ordinates in the working area.

Primitives

Primitives are usually (but not restricted to) the most basic 3D shapes, such as spheres, cubes, cones, pyramids, cylinders etc. They are already put into a software and can be created manually as well. Their role is to be a starting point in polygonal 3D modelling, and can be easily modified once created.

Surfaces


Surfaces are the outer layer of a mesh model. They are its topographic representation on a flat 2D surface. It looks like a wrap or as if the object has been skinned. These surfaces are referred to as UV maps and look like a net. They can be coloured, textured and merged with the model again.


Other surfaces are normal and bump maps and allow further distortion of a model without adding to the polygon count.