3D Geometric theory Introduction
3D geometry is probably one of the most important things that an artist has to consider whilst modeling. 3D geometry include a lot steps/Rules which I am going to explain because if an artist fails to follow the 3D geometry then that could result in a unsuccessful asset which may look or texture wrong. 3D Geometry basically effects any shapes including lines or even curves. The most simplest shapes can still be effected by 3D geometry because if the artists fails to stick to the 3D Geometry correctly the object could not render probably or effect the temperance of the object.
The first step is the Cartesian coordinates system. The Cartesian Coordinates system is a method which helps render and indicate points of a 2D surface or in a 3D Space For instance it is used to define positions on a computer display and in virtual reality renderings.The system is also used in mathematics, physics, engineering, navigation, robotics , economics, and other sciences. Although Its name just simply came from one of the first people known to have used it, the French mathematician and philosopher René Descartes (1596-1650)
The Cartesian plane has two perpendicular axes that cross at a central point called the origin (The middle of the axes). Positions or coordinates are determined according to the east/west and north/south sides from the origin. The east/west axis is often called the x axis, and the north/south axis is called the y axis. 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.
This is very important to a game developer simply because in a game you will be telling the game where to move an object using coordinates. Another reason this is important to video game developers is because whilst creating 2D vector artwork. 3D programs operate on a grid of 3D co-ordinates. 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. For instance here is a image of a cube in a 3D model
2D and 3D
As you can see there is a cube in the middle which is my object. If I wanted to scale the object along the Z axis (Blue line) then it will make the box go up the blue axis and make it a lot taller. If I scaled it along the Y axis it will then go across the green line and the same with the X axis with the Red line. (As labelled.) You can also see in the bottom left corner what the vector is saying (circled) how far the object is on each axis for instance the cube is on 1.000 along each axis but if I move the cube somewhere else in the grid the vector will the re-locate the cube and note down the new co-ordinates.
Here is a video explaining the basic concepts and terminology of one dimensional, and two dimensional coordinate systems.
Explaining the 3D Geometric theory & Polygons
The Geometric Theory has a design progress which basically involves an initial mesh which is made up of combined polygons. Polygons are just a simple 2D shape although they involve the most important three key components needed for the geometric theory. These include vertices, edge and a face. Polygons have two vertices which is joined up by a line which then creates a face.Polygons are the most basic triangle with a face although these most basic shapes can help create the most complicated objects and shapes. In order to do this before the shape is created extra vertices can be added or different shaped polygons can be combined to help create a new shape. Once the 2D polygons have all been joined together into their desired shape with no vertices left detached, the shape that is created becomes a 3D model composed entirely of 2D polygons.
Vertices: Are points which are at the corner of geometric shapes. When in 3D modeling it is easy to adjust a vertices on a polygon which makes it an easier progress to modify new shapes. Although you can also add a new vertices to make the shape more smooth or delete a vertices to create an new entire shape all together.
Face: The face of a polygon or any other object is basically complete side. This usually happens when a shape has complete sides for instance if a square has 4 sides it will create a face in the center.
Primitives
3D primitives are the most basic geometric forms which can be used to modify, transform or use to help a Boolean. The most common 3D primitives is a cube, cylinder, tube, sphere, torus and cone. Although Primitives are not just restricted to the most basic shapes as it is possible to use more complex shapes to modify or transform. The most common primitives are usually already pre-made and placed in to software for instance I am personally using blender for my 3D modelling and these shapes have already been placed within the software however you are also able to create the shapes your self. The main idea of using a primitives is usually because the most common primitives are usually the easiest to edit and modify.
Surfaces
Surfaces are the outer layer of a mesh model and can be used to make any model look more attractive, detailed and look exactly how imagined to be. Although there is several different ways which can make a surface look more unique and sometimes look a lot more better than another surface. For instance there is a UV Map, Normal Maps, Transparency Maps, Baking, Specularity, and shaders. To create a surface which resembles the object in real life it is important to use the correct texture mapping so the object will have more age and appeal to it. For instance if you have a car as a object it will want to have a shiny metal materiel to make the car look a lot more realistic which specularity helps to achieve whilst a flat texture will not. Links
http://whatis.techtarget.com/definition/Cartesian-coordinates-rectangular-coordinates
http://www.basic-mathematics.com/cartesian-coordinate-system.html
https://jcallisterdesign.wordpress.com/year-1/unit-66-3d-modelling/assignment-one/task-one/introduction-to-3d-modelling/explaining-geometric-theory/
https://jessgrafton.wordpress.com/3d/geometric-theory/
http://www.peachpit.com/articles/article.aspx?p=30594&seqNum=5
http://www.acme-3d.com/3d_3/3d3_large/3d-lush-primitives.html
http://blog.digitaltutors.com/cover-bases-common-3d-texturing-terminology/