Page 119 - DCAP504_Computer Graphics

Computer Graphics

5. Each edge table contains indicators to their respective polygons and every edge pointed by the
polygon indicator has an indicator which is indicating back to its polygon or not.
Plane Equation and Visible Points

The input data that defines the representation of the 3-D object must be processed by the computer to
display the object. The steps to be included in the processing are the following:
1. Transforming the model and descriptions of coordinates to device coordinates.

2. Identifying the surfaces that are visible.
3. Applying the procedures of surface rendering.
In some cases the information regarding the spatial orientation of individual surface components are
required. The vertex coordinate values and the equations that describe a polygon plane provide the
geometrical information.
Quadratic Surface
The quadratic polynomials define quadratic surfaces in 3-D. A quadratic object is created and rendering
state is set with one or more state setting functions. The object is specified when drawing one of its
surfaces, and its state determines the way the object is rendered. These surfaces include spheres,
ellipsoids, etc.

The above ellipsoid can be mathematically written as,
f(p)=(x-x c)2/a +(y-y c) /b +(z-z c) /c -1=0
2
2
2
2
2
Bezier Surface
The Bezier surfaces were first described by Pierre Bezier. The Bezier surface is defined by a set of
control points. Here, the surface does not pass through the control points that are positioned in between
the surface. They can be of any degree but the popularly used are the cubic Bezier surfaces. They are the
most common parametric surfaces implemented for modeling.

Bezier equation
For a 2-D Bezier surface,

Here, P= function of parametric coordinates u, v
Bezier surface is of the order (n, m)

Control points are (n+1) (m+1) =ki,j

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