An API (application programming interface) allows software components to interact and is usually a library specifying routines, data structures, and more. Direct3D is part of Microsoft's DirectX API used for 3D graphics on Windows and Xbox, exposing capabilities like z-buffering and texture mapping. OpenGL is a cross-platform 3D graphics API managed by Khronos used widely in gaming, VR, and more. The graphics pipeline involves transforming 3D images through stages like projection to produce a 2D screen image from vertex properties.

1. Displaying 3D polygon Animations
API
Generally speaking, an application programming interface (API) specifies how some software
components should interact with each other. In practice in most of the cases an API is a library that
usually includes specification for routines, data structures, object classes, and variables. An API
specification can take many forms, including an International Standard such as POSIX, vendor
documentation such as the Microsoft Windows API, the libraries of a programming language, e.g.,
Standard Template Library in C++ or Java API. An API differs from an application binary interface
(ABI) in that an API is source code based while an ABI is a binary interface. For instance POSIX is an
API, while the Linux Standard Base is an ABI.
http://en.wikipedia.org/wiki/Application_programming_interface
Direct 3D
Direct3D is part of Microsoft's DirectX application programming interface (API). Direct3D is available
for Microsoft Windows operating systems (Windows 95 and above), and for other platforms through
the open source software Wine. It is the base for the graphics API on the Xbox and Xbox 360 console
systems. Direct3D is used to render three dimensional graphics in applications where performance is
important, such as games. Direct3D also allows applications to run full screen instead of embedded
in a window, though they can still run in a window if programmed for that feature. Direct3D uses
hardware acceleration if it is available on the graphics card, allowing for hardware acceleration of
the entire 3D rendering pipeline or even only partial acceleration. Direct3D exposes the advanced
graphics capabilities of 3D graphics hardware, including z-buffering, spatial anti-aliasing, alpha
blending, mipmapping, atmospheric effects, and perspective-correct texture mapping. Integration
with other DirectX technologies enables Direct3D to deliver such features as video mapping,
hardware 3D rendering in 2D overlay planes, and even sprites, providing the use of 2D and 3D
graphics in interactive media titles.
http://en.wikipedia.org/wiki/Microsoft_Direct3D
Open GL
OpenGL (Open Graphics Library) is a cross-language, multi-platform API for rendering 2D and 3D
computer graphics. The API is typically used to interact with a GPU, to achieve hardware-accelerated
rendering. OpenGL was developed by Silicon Graphics Inc. (SGI) from 1991 and released in January
1992[4] and is widely used in CAD, virtual reality, scientific visualization, information visualization,
flight simulation, and video games. OpenGL is managed by the non-profit technology consortium
Khronos Group.
http://en.wikipedia.org/wiki/OpenGL

2. Graphic Pipeline
In 3D graphics rendering, the stages required to transform a three-dimensional image into a two-
dimensional screen. The stages are responsible for processing information initially provided just as
properties at the end points (vertices) or control points of the geometric primitives used to describe
what is to be rendered. The typical primitives in 3D graphics are lines and triangles. The type of
properties provided per vertex includes x-y-z coordinates, RGB values, translucency, texture,
reflectivity and other characteristics.
http://www.pcmag.com/encyclopedia/term/43933/graphics-pipeline
Per vertex lighting and shading
In computer graphics, per-pixel lighting refers to any technique for lighting an image or scene that
calculates illumination for each pixel on a rendered image. This is in contrast to other popular
methods of lighting such as vertex lighting, which calculates illumination at each vertex of a 3D
model and then interpolates the resulting values over the model's faces to calculate the final per-
pixel colour values.
Per-pixel lighting is commonly used with techniques like normal mapping, bump mapping, secularity,
and shadow volumes. Each of these techniques provides some additional data about the surface
being lit or the scene and light sources that contributes to the final look and feel of the surface.
Projection Transformation
After the viewing transformation we have everything oriented as we would like them to appear in
the final image. All that remains is to project out the depth, or z-dimension, so that the the three-
dimensional view-space primitives are reduced to two-dimensional screen-space primitives.
There are many different types of projection. The simplest, is to simply ignore the z-dimension. This
form of projection is called orthographic or parallel. It is the common form of projection used by
drafts people for top, bottom, and side views. The advantage of parallel projection is that the you
can make accurate measurements of image features in the two dimensions that remain. The
disadvantage is that the images don't appear natural (i.e. they lack perspective fore shorting).
http://groups.csail.mit.edu/graphics/classes/6.837/F98/Lecture12/projection.html
Scan conversion or Rasterisation
Scan conversion or scan rate converting is a video processing technique for changing the vertical /
horizontal scan frequency of video signal for different purposes and applications. The device which
performs this conversion is called a scan converter.
The application of scan conversion is wide and covers video projectors, cinema equipment, TV and
video capture cards, standard and HDTV televisions, LCD monitors and many different aspects of
picture processing.

3. http://en.wikipedia.org/wiki/Scan_conversion
Rasterisation (or Rasterisation) is the task of taking an image described in a vector graphics format
(shapes) and converting it into a raster image (pixels or dots) for output on a video display or printer,
or for storage in a bitmap file format.
http://en.wikipedia.org/wiki/Rasterisation