TruForm

ATI TECHNOLOGIES
WHITE PAPER
TRUFORM
Introduction
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The graphical quality of computer games has improved by leaps and bounds from the early days of Doom to
today’s Quake III and is on track to rival the quality of movie special effects in a few years. Despite recent
improvements, most game objects—especially characters—still do not appear very lifelike. They still tend to
look like a collection of geometric blocks with textures painted on them. This blocky computer generated
world is generally a result of limited bus and memory bandwidth.
Objects in virtual worlds, like the head in Figure 1 below, are represented by groups of connected triangles,
which collectively form the surface of a virtual object. Each triangle in a virtual object is defined by 3 vertices
and 3 normals. As developers create more detailed and realistic 3D virtual worlds, the number of triangles
required to represent each scene increases at a tremendous rate. This presents two problems for the
graphics system:
• Increased bandwidth required to transfer the triangles to the GPU
• Increased memory required to store more triangles
TRUFORM, a new technology developed by ATI, overcomes these problems to deliver the smoothest and
most natural images ever seen on a PC. This document describes how TRUFORM works and what benefits
it can provide to application developers and end-users.
3D Model
(represented by
triangles)
TRUFORM capable GPU
Traditional GPU
TRUFORM
Transformed & Lit
Triangles
Figure 1: TRUFORM: On the left is the input triangle geometry, which is compatible with any renderer. On the top right is shown
the result of using TRUFORM; note the realistic highlights and smooth silhouette. On the bottom right, we show that the input
model is still compatible with traditional GPUs.

Bandwidth
In order for the GPU to perform the required vertex shading calculations on this increased number
of triangles, the vertices of every triangle must be read from memory. This vertex data competes
with textures, shaders and other data for space in local graphics memory (on the physical card)
and AGP memory (across the AGP bus in system memory). Graphics memory bandwidth is
limited by memory technology and is often a performance bottleneck. This problem is made even
worse when the GPU has to fetch data from the system memory side of the AGP bus. By
converting 3D models with low polygon counts to smoother, high polygon count versions in the
graphics chip (a process known as tessellation), TRUFORM effectively increases the memory
bandwidth available to the GPU.
Memory Usage
As mentioned above, geometry data competes with other data like textures and shaders for space
in memory. This ultimately limits how much variety can exist in a virtual environment. For
example, to conserve memory, a game developer may have to create one tree model with many
polygons and replicate it in multiple locations to make a forest. This repetition is often visible to
the user and reduces realism. With TRUFORM, the developer can create multiple low-polygon
trees and use N-Patches when rendering to effectively decompress them. This makes better use
of the available memory and increases variety in the world, which enables greater immersion of
the user.
N-Patches (also known as PN Triangles) are a type of Higher Order Surface, a new feature
introduced in DirectX ® 8 and OpenGL ® that allow the transfer of a reduced amount of data across
the AGP bus, while the majority of vertices required for high detail geometry are generated inside
the GPU. As a result of sending a smaller amount of data across the AGP bus, there is also a
saving in graphics memory usage.
HIGHER ORDER SURFACES
Whereas standard polygonal surfaces are made up of flat planes, Higher Order Surfaces are
curved. A first order surface, such as a flat triangle, is based on straight lines defined by the
linear equation y = ax + b. A second order surface contains one bend (parabolic in shape), and is
based upon the quadratic curve equation y = ax 2 + bx + c. A third order surface has two bends
(S-shaped) and is based upon the cubic curve defined by y = ax 3 +bx 2 + cx +d. See Figure 2.
1 st order (linear)
2 nd order (quadratic)
3 rd order (cubic)
Figure 2: Different classes of curves with increasing order.
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A slight variation of these types of curves is the Bezier curve, which provides the basis of many
higher order surface methods. A Bezier curve is a special type of curve described by control
points. A control point has local control over its portion of the curve. If a control point is moved,
the part of the curve closest to the control point is affected the most. A cubic Bezier curve has
four control points: one for each endpoint and 2 inside the curve. See Figure 3.
Figure 3: A cubic Bezier curve described by its 4 control points.
The concept of the Bezier curve can be extended to construct a Bezier surface, in which the
surface curvature is also described using control points.
TYPES OF HIGHER ORDER SURFACES
The two types of Higher Order Surface methods supported in DirectX ® 8 are Polynomial Surfaces
and N-Patches. Although, both approaches use Bezier surfaces, they are implemented in
significantly different ways. Polynomial Surfaces require that every patch must be created by the
developer, rather than being generated in the graphics processor. This means that models created
with Polynomial Surfaces will not be compatible with existing hardware. Polynomial Surfaces are
also computationally expensive, which can lead to degradation in performance.
Figure 4: Polynomial surfaces. Note the large number of control points required to define the surface, the additional
driver setup step, and the game art’s lack of compatibility with older graphics processors.
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N-Patches, on the other hand, generate every curved surface in the graphics processor, allowing
for complete compatibility with all existing hardware. As a result, N-Patches offer the most
efficient and practical Higher Order Surface implementation, and form the basis of TRUFORM.
N-PATCHES
N-Patches require only the vertices and normals at the vertices of flat triangles (see Figure 5
below) to create detailed and visually impressive models, while maintaining total backward
compatibility with existing hardware and APIs.
Figure 5: N-Patches. Note how the input data consists of just three vertices and three vertex normals, and how the
game art is compatible with any graphics processor.
As a result, N-Patches allow for a high level of scalability, meaning the number of triangles in a 3D
model can be scaled according to the available graphics hardware. Software developers usually
create low triangle count models so that their games can run well on the low-end systems that
make up the majority of the market, and never create high detail models for users with more
powerful systems. N-Patches can take these low-polygon models and generate smooth, highly
detailed models.
Using the N-Patch technique, the graphics processor converts every flat triangle into a curved
triangular patch. Using the mathematics of Bezier surfaces, a curved triangular surface can be
described with a small amount of data. Once every flat triangle is converted to a curved surface,
the model is then tessellated into triangles again, so that they can be transformed and lit by the
Transform and Lighting engine of the graphics processor. Although the final model is still
described with triangles, for a given input the number of triangles describing a model is greatly
increased, resulting in a major improvement in the model silhouette and model lighting.
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Generating Control Points
The control points along each side of a triangular N-Patch are generated from its vertices and
two additional points evenly spaced along each triangle edge. Each point adjacent to a vertex
is projected into the plane defined by the normal at that vertex, creating a new control point.
The direction of a normal at a vertex is a measure of the curvature of the surface at the vertex.
Figure 6 demonstrates the creation of one these control points.
Figure 6: Construction of an edge control point: a point is
projected into the plane defined by the vertex normal N1
giving us a control point b210
This is then repeated around the original triangle, giving a total of six new control points. So far
we have 9 control points along the edges of the triangular patch. The last control point is placed
in the center of the surface, and is determined through averaging the other nine edge control
points. See Figure 7.
Figure 7: The 10 control points of the N-Patch define the
curvature of the surface.
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Once the 10 control points of the N-Patch are generated, the curved surface is tessellated into a
large number of smaller triangles. Although the curvature of every N-Patch is defined with 10
control points, the developer can easily specify the level of tessellation, which determines the
number of smaller triangles generated. See Figure 8.
Figure 8: Different levels of tessellation as specified by the developer
(top) and the visual effect of tessellation (with two light sources) on an
octahedron (bottom). The number of control points describing the
actual curvature of the surface is always 10, regardless of the level of
tessellation. Also note that the tessellated triangles at the top
represent just one of the eight faces of the octahedron.
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Lighting N-Patches
TRUFORM not only greatly enhances the smoothness of 3D models, but also provides models
with highly detailed lighting effects. This greatly enhances the visual quality of scenes by
providing realistic highlights on the surface of curved objects.
The surface normals of 3D objects are used to mathematically compute the lighting of all surfaces.
A surface normal is a unit vector that points perpendicular to (i.e. directly outward from) a surface.
The two general types of lighting or shading methods used in 3D graphics are Gouraud shading,
and Phong shading. Gouraud shading uses a normal at each vertex to light a model, while Phong
shading uses a normal for every single pixel to light the model. The increase in the number of
normals in Phong shading gives the lighting equation many more samples to work with, resulting
in much better lighting effects.
The N-Patch lighting technique uses two different algorithms to generate normals. The algorithm
used depends upon the complexity of the curved surface. When the curvature of a patch is
relatively simple, the vertex normals can be linearly interpolated (i.e. blended) across the entire
curved surface. This algorithm is called linear normal generation. When the curvature of a
triangular patch is more complex, a quadratic Bezier surface can be used to describe the variation
of normals across the surface of the patch. A quadratic triangular surface is described with six
control points: three for the vertices, and one for each edge mid-point. Each mid-edge control
point is generated by averaging the vertex normals at either end of the edge, and reflecting the
averaged normal across the plane perpendicular to the edge, as shown in Figure 9. This is
repeated on the other two triangle edges to give three new mid-edge control points, for a total
of 6. These control points (see Figure 10) are then used to determine the normals of any new
vertices created when the N-patch is tessellated.
Figure 9: Generation of mid-edge control points for
quadratically varying normals: the average of N1 and
N2 is reflected across the plane perpendicular to the
edge to obtain n110.
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Figure 10: Control points generated for the
normal component of N-Patches.
As a result of using N-Patch generated normals, the quality of lighting is improved from the
Gouraud shading level (before implementing N-Patches) to a near-Phong shading quality level.
The quadratic normal generation process requires slightly more computation time than the linear
case, but offers even greater improvements in lighting effects. The normal generation method
used by developers will depend on the required performance specifications.
CONCLUSION
Although there are a variety of Higher Order Surface methods available, the N-Patch surfacing
technique provides a great looking solution that for the first time is actually practical for game
developers to use. N-Patches provide developers with the capability to generate smooth and
realistically lit surfaces with a minimal cost in model preparation, code modification and rendering
performance.
With just a triangle’s vertices and vertex normals, the N-Patch surfacing method is able to
generate three-sided cubic Bezier patches, accompanied by a set of varying (linear or quadratic)
normals, giving computer game players smooth, realistically lit models. See Figure 11 for more
examples of image improvements using N-Patches.
The advantages of the N-Patch technique are:
• Improved memory and bandwidth efficiency
• Greatly improved character silhouettes by smoothing out surfaces.
• Highly realistic lighting of model surfaces.
• Complete backward compatibility, even with hardware that does not support N-Patches.
• Easy to implement in both future and current games.
• N-Patches do not require custom model design, unlike polynomial surfaces.
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Figure 11: Models from Quake as provided by id software (left) and their
TRUFORM enhanced counterparts (right). None of these characters were
authored with TRUFORM in mind.
References
1. Alex Vlachos, Jörg Peters, Chas Boyd and Jason L. Mitchell. Curved PN Triangles.
ACM Symposium on Interactive 3D graphics, 2001, pp. 159-166.
2. Brian Sharp. Implementing Curved Surface Geometry. www.gamasutra.com, May 30, 2000.
3. Brian Sharp. Subdivision Surface Theory. www.gamasutra.com, April 11, 2000.
4. Dean Macri. Using NURBS Surfaces in Real-time Applications. www.gamasutra.com, November 17, 1999.
5. Gabe Kruger. Curved Surfaces using Bezier Patches. www.gamasutra.com, June 11, 1999.
6. David Nalasco. DirectX 8.0 and Radeon Graphics Processors White Paper. ATI Technologies, 2001.
TRUFORM White Paper - Page 9

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Copyright 2001, ATI Technologies Inc. All rights reserved. Features, performance and specifications may vary by operating environment and are subject to change without notice. Products may not be exactly
as shown. Features will vary depending on configuration used. Printed in Canada. May 2001.