Game Development Reference
In-Depth Information
1.3.3 Shape
A shape refers not only to primitive geometrics such as circles, squares, and
triangles, but also to freeform and nonstandard formations. In computer
graphics, polygons are treated as they are in geometry; a series of points
called vertices connected by straight edges . By storing the coordinates of the
vertices the edges can be reconstructed using straight line algorithms. A circle
is often represented by as a regular polygon with many edges. As the number
of edges increases, a regular polygon approaches the shape of a circle.
Freeform objects involve the use of curves. To be stored and manipulated
by the computer efficiently, these need to be stored in a mathematical
format. Two common types of curves used include Bezier and nonuniform
rational basis spline (NURBS).
A Bezier curve is constructed from a number of control points. The first and
last points specify the start and end of the curve and the other points act as
attractors, drawing the line toward them and forming a curve, as shown in
Figure 1.8 . A NURBS curve is similar to a Bezier curve in that it has a number
of control points; however, the control points can be weighted such that
some may attract more than others.
In computer graphics, a polygon is the basic building block for objects,
whether in 2D or 3D. A single polygon defines a flat surface onto which
texture can be applied. The most efficient way to define a flat surface is
through the use of three points; therefore, triangles are the polygon of choice
for constructing models, although sometimes you will find square polygons
used in some software packages. Fortunately for the artist, modeling software
such as Autodesk's 3DS Studio Max and Blender do not require models to be
handcrafted from triangles; instead they automatically construct any objects
using triangles as a base as shown in Figure 1.9 .
Fig 1.8 A Bezier and a NURBS curve.
Bezier Curve
NURBS Curve
P3
P2
X
X
P3
X
P2
P4
X
X
P5
X
X
X
P4
P1
X
P1
X
P6