Monday, 20 January 2014

HA4 Task 3 - Geometric Theory

Geometric Theory
3D computer graphics had the same principles which you can find in 2D vector artwork, but use a further axis. When creating 2D vector artwork, the computer draws the image by plotting points on X and Y axes (creating coordinates) and joining these points with paths (lines). The subsequent shapes can be filled with colour and the lines stroked with colour and thickness if required.

Cartesian Coordinates System



All 3D programs operate on a grid of 3D co-ordinates the 3D co-ordinates are pretty much the same as 2D co-ordinates except there’s a third axis known as the Z or ‘depth’ axis you will find this out in the video above and much more will be explained.

Geometric Theory and Polygons

If you were to use Mesh modelling the basic object used is a vertex which is a point in three dimensional space. This is when two vertices are connected by a straight line this is how it becomes an edge. After this When three vertices are connected to each other by three edges it creates a triangle which is the simplest polygon in Euclidean space. There are 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 commonly known shapes used in polygonal modelling. 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.

If you were to look at Euclidean geometry you will find out that any three non-collinear points determine a plane the reason triangles always have a single plane. This is not necessarily true of more complex polygons, however. The flat nature of triangles makes it simple to determine their surface normal, a three-dimensional vector perpendicular to the triangle's surface. Surface normals are useful for determining light transport in ray tracing.

When you look at a group of polygons which are connected by shared vertices they are referred to as a mesh this is often referred to as a wire frame model. 





To make sure a mesh appears attractive when rendered, it is desirable that it be non-self-intersecting this means that no edge passes through a polygon. Another way of looking at this is that the mesh cannot pierce itself. It is also desirable that the mesh not contain any errors such as doubled vertices, edges, or faces. For some purposes it is important that the mesh be a manifold – that is, that it does not contain holes or singularities.

Primitives

During 3D applications you will find that pre-made objects can be used to make models out of various shapes you can find the most basic of this shapes are the Standard Primitive Objects or the Common Primitives, these shapes vary from the basic cube or box to spheres, cylinders, pyramids and cones. They are used as the starting point for modelling. They can be edited once created.



Surfaces

Polygons can be recognized as specific surfaces and then have colour, texture or photographic maps added to them to create the desired look. The example below shows how a map is displayed as if the object has been unwrapped



Bibliography
http://jessgrafton.files.wordpress.com/2010/10/720px-mesh_overview_svg.png
http://jcallisterdesign.files.wordpress.com/2012/09/amnesia2.jpeg
http://docs.autodesk.com/3DSMAX/15/ENU/3ds-Max-Help/images/GUID-551607FE-6AAF-46BE-AA7E-96DECBA45E2A-low.png
http://docs.autodesk.com/ACD/2010/ENU/AutoCAD%202010%20User%20Documentation/images/PTDCPM/Gator-All/English/ill_convert_to_surface_1.png

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