HA7 Task 3 - Geometric Theory

Geometric theory is how a developer can transform a 3D object using vertices, edges, and faces. This is done by first creating a basic mesh such as a plane, cube, or circle which can be edited and made into more complex shapes.

https://jcallisterdesign.wordpress.com/year-1/unit-66-3d-modelling/assignment-one/task-one/introduction-to-3d-modelling/explaining-geometric-theory/

The mesh is constructed in 3D space using 2D polygons such as the triangle above. To create depth polygons are joined together to create 3D objects, such as below.

http://www.real3dtutorials.com/tut00007.php

The Z axis above represents depth in 3D space, while the X and Y axis are what we use to measure 2D shapes. As shown above 6 2D square polygons are created next to each other, passing through the Z axis to create a 3D shape called a cube.

The cube is a primitive shape supplied by most 3D modeling software. Other primitives exist which can be quickly created by the software for manipulation by the developer. Common primitive shapes are: spheres, cubes, torus, cylinders and pyramids.

http://flylib.com/books/en/4.423.1.23/1/

Primitives are useful as a starting point in creating an object, sometimes offering many polygons which would take a long time to create manually, such as with a torus, cylinder or sphere.

The mesh is made more complex by manipulating the object's vertices, edges and faces and finally becomes a finished object to be implemented into a game world. Curves can be achieved by moving vertices through the 3D plane, which is useful for creating a smooth surface which isn't flat such as the ground.

This is necessary when using geometric theory to create a 3D environment because a game character is going to need to move across this surface, if it isn't smooth enough the surface will not only look wrong but the character will get stuck when moving across it.

This is important in all aspects of geometric theory, not just in curved objects. The appropriate mesh should be chosen at the beginning of development to reduce work load as well as give the developer a good starting point to work with. For example if someone wants to create a simple table they should start with a cube object, since it has 8 vertices. This shape can then be edited by reducing or increasing the size of he edges to create a rectangle. Then extrusions can be made to create the legs. This would be easier than starting with, for example, a circle.

http://www.cmap.polytechnique.fr/~peyre/geodesic_computations/

This mesh is has been created using geometric theory, going from left to right they become more advanced and detailed as more polygons are added. The mesh is made out of many triangles because a triangle is the most simple shape which can be used to create 3D objects. As more polygons are added the rabbit becomes more smooth, and smaller details ca be made out. The first rabbit barely has a tail for example, while the second and third have clearly visible tails.

A middle ground must be found between low polygon count and detail. Not having enough detail is bad since the rabbit doesn't look good. However having too many polygons is bad as it will take a lot of computational power to render it.