The Invention of the Cartesian Coordinates System was in the 17th century and it revolutionized mathematics by providing the first link between Euclidean Geometry and algebra the Cartesian coordinates system specifies that each point in a plane can be represented by a pair of coordinates these coordinates are found by looking at the two axis (x and y) and then you can find the x and y coordinate of the point on these axis
BBC Coordinates System
When creating 2D Vector artwork the computer draws the image by plotting points on the x and y axis and joining these points with paths the shapes you make with this can be filled with colour and the sides can be given a stroke (border)
3D coordinates exist on a grid of 3D coordinates which is basically the same axis as before but it introduces a z axis this allows you to plot points in 3 dimensions
Geometric Theory and polygons
The simplest object within mesh modelling is known as a point (vertex) these are a single point in a three dimensional space two points connected by a straight line is an edge and 3 edges create the most simple polygon possible which is a triangle more complex polygons can be created out of using 4 triangles or you can create quads which are polygons with 4 vertices however triangles are the most common shapes used in polygonal modelling. a group of polygons connected by shared vertices is known as an element each of the polygons making up an element is known as a face
In Euclidean geometry any three non-collinear points determine a plane therefore triangles are always only on one plane this is not true of more complex polygons however the flat nature of triangles makes it simple to determine there surface as normal a three dimensional vector perpendicular to the triangles surface, object normals are useful for determaning light transport in ray tracing
A group of polygons which are connected by shared vertices is called a mesh it also often reared to as a wire-frame model
In order for a mesh to look attractive when rendered it should non-self-intersecting this means that no edge should pass through a polygon in other words the mesh shouldn't be able to pierce itself unless this is intended it is also desirable that the mesh doesn't have any errors such as double edges, vertices or faces
Primitives
In 3D applications pre made objects can be used to make models out of various shapes the the most simple shapes are the standard primitive shapes these shapes include, boxes, cubes, sphere's, Cylinders, Pyramids, and cones they are used as a starting point for modelling
Surfaces
Polygons can be determined as specific surfaces and then have colour, texture or photographic maps added to them to make them look how you want
Sources:
No comments:
Post a Comment