The Cartesian Coordinates System
The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry (from the Classical Greek mathematician Euclid of Alexandria) and algebra (where letters and other general symbols are used to represent numbers and quantities in formulae and equations).
The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry (from the Classical Greek mathematician Euclid of Alexandria) and algebra (where letters and other general symbols are used to represent numbers and quantities in formulae and equations).
Geometric Theory and Polygons
The basic object used in mesh modeling is a vertex, a point in three dimensional space. Two vertices connected by a straight line become an edge. Three vertices, connected to each other by three edges, define a triangle, which is the simplest polygon in Euclidean space. More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Four sided polygons (generally referred to as quads) 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.
In Euclidean geometry, any three non-collinear points determine a plane. For this reason, triangles always inhabit 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.
A group of polygons which are connected by shared vertices is referred to as a mesh, often ferred to as a wireframe model.
Primitives
Polygons can be defined 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.
In 3D applications, pre-made objects can be used to make models out of various shapes, 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 (both triangular and square based) and cones. They are used as the starting point for modelling. They can be edited once created.
Surfaces
Polygons can be defined 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.
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