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Computer Graphics: Polygonal Representation and Rendering, Slides of Multimedia Applications

Amity University - BiharMultimedia Applications

An overview of computer graphics, focusing on the polygonal representation and rendering of three-dimensional objects. It covers the advantages and disadvantages of using polygons, the main steps in rendering a polygonal object, and various coordinate systems and transformations used in the rendering process. Additionally, it discusses screen space, homogeneous coordinates, and pixel-level processes such as rasterization and hidden surface removal.

Typology: Slides

2012/2013

Uploaded on 04/23/2013

sarasvatir
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Computer Graphics
•One of the central components of three-dimensional
graphics has been a basic system that renders objects
represented by a set of polygons
•One approach to rendering three-dimensional objects is to
build a basic renderer then add on enhancements
•The basic renderer may be one which incorporates a local
reflection model, such as the Phong model, into a Phong
incremental shader
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Download Computer Graphics: Polygonal Representation and Rendering and more Slides Multimedia Applications in PDF only on Docsity!

Computer Graphics

  • One of the central components of three-dimensional graphics has been a basic system that renders objects represented by a set of polygons
  • One approach to rendering three-dimensional objects is to build a basic renderer then add on enhancements
  • The basic renderer may be one which incorporates a local reflection model, such as the Phong model, into a Phong incremental shader

Computer Graphics

  • Advantages gained by this approach include:
    • Modeling objects using polygons is straighforward
      • Piecewise linearities are rendered invisible by the shading technique
    • Geometric information is only stored at the polygonal vertices - information required for the reflection model that evaluates a shade at each pixel is interpolated from this information - This allows fast, hardware-based shading

Computer Graphics

  • The main steps in rendering a polygonal object are:
      1. Polygons representing an object are extracted from the database and transformed into the world coordinate system using linear transformations such as translation and scaling
      1. A scene constructed in this way is transformed into a coordinate system based on a view point or view direction.
      1. The polygons are then subjected to a visibility test. This is called ‘backface elimination’ or ‘culling’ and removes those polygons that face away from the viewer.

Computer Graphics

  • The main steps in rendering a polygonal object are:
      1. Unculled polygons are clipped against a three-dimensional view volume.
      1. Clipped polygons are then projected onto a view plane or image plane
      1. Projected polygons are then shaded by an incremental shading algorithm. First, the polygon is rasterized, or those pixels that the edges of the polygon contain are determined. Second, a depth for each pixel is evaluated and a hidden surface calculation is performed. Third, the polygon is shaded.

Polygonal Representation of

Curved Objects

Polygonal representation of three-

dimensional objects

  • For complex objects, a number of polygons in excess of 100,000 is not uncommon
  • Another problem occurs when objects are scaled up
  • An object adequately represented at one size may degrade when the object is enlarged - This has been called ‘geometric aliasing’

Coordinate systems and rendering

  • One view of the geometric part of the rendering process is that it consists of the application of a series of coordinate transformations that takes an object database through a series of coordinate systems
  • For ease of modeling and application of local transformations, it makes sense to store the vertices of an object with respect to some point conveniently located in or near the the object - This is called the local coordinate system

Coordinate systems and rendering

  • Once an object has been modeled, the next stage is to place it in the scene that we wish to render
  • The global coordinate system of the scene is known as the world coordinate system
  • All the objects have to be placed into this common space in order to have their relative spatial relationships defined - The act of placing an object in a scene defines the transformation required to take the object from local space to global space - If this object is being animated, then the animation provides a time-varying transformation that takes the object into world space on a frame-by-frame basis

Backface elimination and culling

  • This operation removes entire polygons that face away from the viewer - When dealing with a single convex object, culling completely solves the hidden surface problem - If an object contains a concavity, or if we have multiple objects in a scene, a general hidden surface removal algorithm is needed as well as culling
  • We can determine whether a polygon is visible from a view point by a simple geometric test - The geometric normal to the polygon is calculated and the angle between this and the line-of-sight vector is determined. (The line-of-sight vector is the vector from the polygon to the view point) - If this angle is greater than 90 degrees, then the polygon is invisible.

Screen space

  • The fundamental transformation that takes us into screen space is the perspective transformation which takes a point in the scene and projects it onto a view plane positioned at disance D away from the view point and oriented normal to the viewing direction

Screen Space

  • Screen space is defined to act within a closed volume called the viewing frustum that delineates the volume of space which is to be rendered
  • Objects that lie outside the viewing frustum are not rendered

View Frustum

Homogeneous Coordinates

  • The transformations we are most interested in are scaling, translation and rotation
  • These can be defined as follows

Scaling Transformation