Graphics Reference
In-Depth Information
This can be extended to computer graphics in the general sense of using many smaller
pieces of geometry to create, without gaps or overlaps, a larger complete surface. At its
simplest, a common closed mesh of triangles satisfies this definition.
A number of other related terms are used within the field of computer graphics to for-
malize tessellation as a means of representing non-linear mathematical surfaces. Triangles
are typically the preferred unit of raster-based computer graphics, due to their very useful
properties of being convex and having coplanar vertices, but this convenience also limits
them to representing flat geometric surfaces. Many small triangles may be used to approxi-
mate a smooth surface, but the basic unit of the triangle is still fiat.
Two of the better known techniques for representing a curved surface are non-uniform
rational basis splines (NURBS ) and SubDivision surfaces (often abbreviated as SubDs).
The former is a generalized mathematical form (Weisstein] for smooth, curved surfaces; it
has been a staple feature in graphics software for decades. The latter is a general framework
for mesh refinement, recursively adding triangles until it better represents the ideal sur-
face. Catmull-Clark subdivision surfaces (Catmull & Clark, 1978) are a commonly used
example. The crucial difference is that subdivision surfaces don't require a mathematical
basis, whereas using NURBS does.
Mathematically defined surfaces are often referred to as higher-order surfaces be-
cause their underlying equations are defined in terms of their order—quadratic and cubic
are most common—and because this order is above linear.
Various tessellation algorithms allow developers or artists to create idealized surface
of curves and smooth surfaces to be mapped to conventional triangle-based raster hardware.
The individual triangles are the small stone fragments of the final curved-surface mosaic.
4.1.2 Why Is Tessellation Useful?
As previously discussed, a large number of small triangles can be used to approximate a
higher-order smooth surface. It is therefore useful to understand why we need additional
complexity and hardware when we could simply stick with existing techniques.
This new technology available in Direct3D 1 1 solves real technical, artistic, and busi-
ness problems in the domain of real-time computer graphics.
The demand for increasing image quality imposes a significant strain by greatly
increasing the volume of data required to define high-resolution models. This increased
volume of data requires a correspondingly large increase in on-disk and in-memory stor-
age, I/O bandwidth, and number of calculations. A mathematical definition for a surface
requires storage of only the coefficients or inputs into the appropriate function, much less
than needed to store raw triangles. Being able to dynamically scale output based on fixed inputs
also offers convenience for developers looking to scale image quality across multiple grades
of hardware, thus reducing problems involved in targeting different hardware configurations.
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