Computer graphics processing and selective visual display system – Computer graphics processing – Three-dimension
Reexamination Certificate
1997-04-23
2001-01-16
Zimmerman, Mark (Department: 2772)
Computer graphics processing and selective visual display system
Computer graphics processing
Three-dimension
C345S426000
Reexamination Certificate
active
06175367
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of computer controlled graphics display systems. More specifically, the present invention relates to a method and system for real time illumination of computer generated images.
2. Background Art
With the advent of graphics based operating systems, graphical user interfaces have become the dominant mode of interacting with computers. Such a progress was made possible due in large part to the innovations in computer graphics. Computer graphics, in a practical sense, concerns the representation of real or imaginary objects based on their computer-based models for interaction with computer users.
In the evolution of computer graphics, rendering a realistic image of a real or imaginary object has been a prime goal for researchers and users alike. At the cutting edge in this quest for realism in computer graphics lies three dimensional (3D) graphics systems. However, rendering realistic 3D images in a graphics system has been slow in coming because it requires enormous and costly computing resources.
One of the most important factors in rendering realistic 3D graphics images is shading. Specifically, rendering realistic 3D graphics requires accurate and efficient modeling of 3D surfaces based upon the position, orientation, and characteristics of the surfaces and the light sources illuminating them. In computer graphics, illumination or lighting model refers to factors determining a surface's color at a given point, usually a pixel, and is typically represented by a lighting equation. Shading, on the other hand, refers to systematic utilization of the illumination or lighting model to render an image. Well known lighting and shading models are discussed in detail in
Computer Graphics: Principles and Practice
by James D. Foley, et al., Addison-Wesley (1996).
In order to produce realistically shaded 3D images in computer graphics systems, the interaction between lights and surface must be modeled for replication. However, due to complexities of such interactions which are based on rules of optics and thermal dynamics, traditional modeling has been based largely on approximations and simplifications. To this date, two shading methods have been popular with computer graphics professionals.
In 1971, Gouraud first proposed a shading method (“Gouraud shading”) using intensity interpolation. Under Gouraud shading, intensity is determined at each vertex of a polygon, typically a triangle. Then, each polygon is shaded by linear interpolation of vertex intensities along each edge and then between edges. However, since this method did not determine intensities at individual pixels, it did not provide realistic shading of images.
A few years later, Phong Bui-Tuong proposed a shading method for determining colors at each individual pixel. He formulated a lighting model derived largely from empirical observations. Bui-Tuong, Phong, “Illumination for Computer Generated Pictures,” CACM, 18(6), June 1975, 311-317. The original Phong model used a reflection vector to compute the position and extent of specular highlights on objects. J. Blinn simplified the Phong equation by using a half-angle vector between the light vector and the eye vector. In both cases, 3D surfaces were shaded by computing a color value at each pixel. Hence, Phong shading was more accurate and realistic than Gouraud shading. At the same time Phong shading was more difficult to implement because it required far more computer graphics resources than Gouraud shading.
A modified Phong lighting equation (“modified Phong lighting equation”), incorporating color wavelength dependent components and the half-angle vector, computes the color (i.e., intensity) of a pixel according to the following formulation:
I
&lgr;
=I
a&lgr;
k
a
O
a&lgr;
+f
att
I
p&lgr;
[k
d
O
d&lgr;
(N•L)+k
s
O
s&lgr;
(N•H)
n
]
where,
I
&lgr;
=Intensity or color of a light at a pixel;
I
a&lgr;
=Intensity of ambient light;
k
a
=Ambient-reflection coefficient with range between 0 to 1;
O
a&lgr;
=Object's ambient color;
f
att
=Light source attenuation factor;
I
p&lgr;
=point light source intensity;
k
d
=Material's diffuse-reflection coefficient (a constant with a value between 0 and 1);
O
d&lgr;
=Object's diffuse color;
k
s
=Material's specular-reflection coefficient set as a constant between 0 and 1;
O
s&lgr;
=Object's specular color;
n=specular exponent (i.e., shininess of the material);
N=surface normal vector at the pixel;
L=light-source vector (pointing from pixel to light) at the pixel; and
H=half-angle vector between light-source vector and eye vector at the pixel.
Another variation of the Phong lighting equation is the Phong-Blinn equation (“Phong-Blinn lighting equation”). This equation computes the color (i.e., intensity) of a pixel according to the following formulation:
C=Sa+Attn×(Ca+Cd×(N•L)+Cs×(N•H)
s
)
where,
C=color of the pixel,
Sa=ambient color of the scene,
Attn=attenuation of light intensity due to distance (local and spot lights),
Ca=ambient color of light*ambient color of material,
Cd=diffuse color of light*diffuse color of material,
Cs=specular color of light*specular color of material,
s=specular exponent (i.e., shininess of the material),
N=surface normal vector at the pixel,
L=light-source vector (pointing from pixel to light) at the pixel, and
H=half-angle vector between light-source vector and eye vector at the pixel.
Although the modified Phong lighting equation and the Phong-Blinn equation (hereinafter collectively referred to as “Phong lighting equation”) differ in some aspects, they produce similar lighting values. The implementation of the Phong lighting equation requires considerable computing resources to evaluate due mainly to the two dot product terms N•L and (N•H)
s
. The dot product N•L is a diffuse term which accounts for reflection of light from dull surfaces. Specular term, represented by (N•H)
s
, accounts for reflection of light from shiny surfaces as in a highlight off a shiny surface. The dot product N•H is part of the specular term.
The relationship between the vectors, N, L, and H are illustrated in Prior Art FIG.
1
. Vector L is a light direction vector pointing from a point P on a 3D surface
100
to a light source, such as a lamp. Vector N is a surface normal vector at point P. Eye vector is a vector pointing from point P to a viewer's eye. Vector H is a half-angle vector bisecting the light vector L and the eye vector. Vector R is a reflection vector that was used in determining a specular term in the original Phong lighting equation.
In the Phong shading method, the N vector at a point (i.e. pixel) is typically interpolated between the three vertices of a triangle. The light vector L and the half-angle vector H at a given pixel are constant over a triangle for lights and viewer at infinity. However, for local lights, the L vector at the pixel is also interpolated in a similar manner. Likewise, for a local viewer, the H vector at the pixel is similarly interpolated. Hence, at a given pixel, for a local light and a local viewer, all three vectors N, L, and H are linearly interpolated based on the N, L, and H vectors of the vertices of a polygon. In an exemplary triangle, linear interpolation of N, L, and H vectors at a given pixel would involve 9 vectors: three vectors N, L, and H at each of the three vertices.
The linear interpolation of N, L, and H vectors at a given pixel yields vectors whose orientations (i.e. directions) are accurate interpolations, but whose lengths (i.e. magnitudes) depart from the interpolation scheme. Hence, the interpolated vectors N, L, and H must be normalized before being used in the Phong equation above. The normalization involves an inverse square-root operation. After normalization
Gossett Carroll Philip
Parikh Vimal
Padmanabhan Mano
Siligon Graphics, Inc.
Wagner , Murabito & Hao LLP
Zimmerman Mark
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