Introduction to Three dimensional geometry |TutorVista.com
4,083 views · Published 1 April 2010 · 1:12 · Indexed 28 September 2026
Channel: Educational Videos · 2010 · Education
Check us out at http://math.tutorvista.com/geometry/3d-shapes.html Three Dimensional Geometry In computer graphics, we are constantly describing both the shapes and positions of three dimensional objects. For example, one simple way to describe a 3D object is to approimate its shape as a mesh of triangles. Each triangle is defined by three vertices, and the positions of each of these vertices will have to be described by three coordinates [x, y, z]t. When modeling a 3D environment, one often needs to apply various transformations to these 3D objects. We may wish to translate or rotate the object to position some object in a scene. Alternatively one may wish to apply a non-rigid transformation to object; this allows us to change its shape. For example, one may wish to create an egg shape by starting with a sphere, and squashing it in one direction. When one is creating an animation, one very often wants to have the position and orientation of some object to be continually changing over time. In this case, one wants to apply a time-varying rigid transformation. To create a 2D image of the 3D environment, one places a virtual camera at some postion in the scene. a projection operation is then applied to turn the 3d scene description into a 2d image. This too needs to be represented as some type of transformation. It is for these reasons, it is essential that we understand how to manipulate the coordinates that describe 3D objects. We must also understand how to manipulate and apply transformations. We will pay special attention to the role that the order of tranformaion applications play. When we study things like rotations, we will pay special attention to the role of the coordinate system with respect to which we will be applying the rotation. In this chapter, we will begin by looking at linear transformations; these can represent rotations, but they can also represent scaling, and shearing. Later we will investigate affine transformations, which add the ability to translate objects. Finally we will look at projective transformations, which are essential in the imaging process.to Three dimensional geometry. Please like our facebook page http://www.facebook.com/tutorvista Follow us at: https://plus.google.com/+tutorvista/
