Monday, 20 January 2014

HA4 Task 3 - Geometric Theory

In this segment of my assignment, I will be reviewing the fundamental principles behind the creation of virtual 3D space and 3D geometry.

What are the fundamental principles behind the creation of virtual 3D space?

The basic object used in mesh modeling is a vertex, a point in three dimensional space.

One point is represented on the X axis.

Two vertices connected by a straight line become an edge, the second point is represented on the z axis.

Three vertices, connected to each other by three edges, define a triangle, which is the simplest polygon in Euclidean space, the third point is represented on the Y axis.

 More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Four sided polygons and triangles are the most common shapes used in polygonal modeling. A group of polygons, connected to each other by shared vertices, is generally referred to as an element. Each of the polygons making up an element is called a face.

Any three non-col-linear points determine a plane, triangles always inhabit a single plane. This is not necessarily true of more complex polygons, the flat nature of triangles makes it simple to determine their surface normal, a three-dimensional vector parallel to the triangle's surface.

A group of polygons which are connected by shared vertices is referred to as a mesh. In order for a mesh to appear attractive when rendered, it is desirable that it be non-self-intersecting, meaning that no edge passes through a polygon.


http://mathworld.wolfram.com/images/eps-gif/XAxis_1000.gif

The X axis represents the first dimension, 1-dimensional items can be most easily related to a line. Picture an x-y axis. The x-axis which is a line, is one dimensional. Anything that stays within just the x-axis, only has one dimension. If you were to draw one line in any direction on a sheet of paper, that would be a 1 dimensional line.

The Y axis represents the second dimension, 2 dimensional objects consist of more than one line that exist on a plane. They have measurable dimensions when placed on an x-y axis. It must have no thickness to it. If you were to draw a rectangle, a circle, a triangle, or any other shape on a sheet of paper, this would be two dimensional.

The Z axis represents the third dimension, 3 dimensional objects consist of 3 or more dimensional planes joined together, they have measurable dimensions on the X, Y and z axis, three dimensional shapes have depth, width and height, although on paper, three dimensional objects are represented in 2D, they can be used to create a real 3D model.


http://illustrations.marin.ntnu.no/structures/analysis/FEM/theory/2.gif

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