Computer graphics processing and selective visual display system – Computer graphics processing – Attributes
Reexamination Certificate
1999-06-08
2002-07-30
Brier, Jeffery (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Attributes
Reexamination Certificate
active
06426756
ABSTRACT:
TECHNICAL FIELD
The present claimed invention relates to the field of computer controlled graphics display systems. Specifically, the present claimed invention relates to an apparatus and a method for linearly filtering data using the phase angle of the texture data to render an interactive graphics display.
BACKGROUND ART
Computer controlled graphics systems are used for displaying graphics objects on a display screen. A graphics object is composed of graphics primitive elements (“graphics primitives”) that include points, lines, polygons, etc. that render a two-dimensional (2D) image of a three dimensional (3D) object on a display screen. Each graphics primitive element within the graphics object is represented by a data structure. By linking all the graphics primitive elements and their respective data structures, a linked data structure is stored in computer memory. Each graphics primitive in the geometrical model is, in turn, associated with the proper attributes to give it the desired color, texture, etc.
Prior Art
FIG. 1A
presents an illustration of texture maps
102
a
and
102
b.
Each of the two maps covers the ‘X’ and ‘Y’ spatial dimension as indicated by the coordinate axes
104
. Multiple texture maps
102
a
and
102
b
can be used to provide another aspect to texture data. Texture maps are used to create a more realistic looking 2D image of a 3D object by digitally ‘covering’ the surface of an object with a texture. Texture map
102
a
is comprised of one or more texels, or tiles, e.g.
106
. Texels are essentially a pixel with a texture attribute. In Prior Art
FIG. 1
, the tiles, a.k.a. texels, in the lower left corner of texture map
102
a
have been labeled t(
0
,
0
), t(
0
,
1
), t(
1
,
0
), and t(
1
,
1
) and of texture map 102
b
have been labeled with the primed equivalent. These texels usually represent a texture pattern (e.g. a texture having a constant, a pattern, a gradient, etc. appearance of color, intensity, etc.).
Referring now to Prior Art
FIG. 1B
, an illustration of a conventional display device
112
having a field to which a conventional texture map will be projected is presented. The texture of the tile is in the form of data that can be mathematically stretched, shrunk, or flexed to cover a given 2D or 3D object, e.g. the rectangular surface
112
projected on conventional display device
110
. If the 2-dimensional texel map
102
a
from Prior Art
FIG. 1
A was used to map rectangular surface
112
projected in conventional display device
110
, then texel map
102
a
would have to be digitally stretched to cover the surface due to the difference in indexes, e.g. a 4×4 matrix to an 8×8 matrix.
The process of mapping a texture onto a geometry can be defined as a function that maps a texel (s,t) or a set of texels {(s
0
, t
0
), (s
1
, t
1
) . . . (sn, tn)} to a point (u,v) of the geometry. The function defining the resulting texture on the geometry f(u, v) is defined by, or equivalent to, a function that manipulates the texel values, g(s, t). There are three conventional functions, or ‘filters,’ that are typically used for mapping. The first is a ‘nearest’ filter, the second is a ‘linear’ filter, and the third is a ‘weighted’ filter. These three filters will be described below with an example. The example will stretch a 4×4 texture into an 8×8 image. The set of texels is made up of four points, using s, t={0, 1, 2, 3}, in two directions. The image to receive the texture is made up of eight points, using u, v={0, 1, 2, 3, 4, 5, 6, 7}, in two dimensions.
The first filter is a nearest filter. For a linear filter, the texels are scaled to the geometry in a mapping function similar to:
f
(
u
)=floor (2
*s
)
f
(
v
)=floor (2
*
0
t
)
T
(
u,v
)=
f
(
u,v
)
The function T(u, v) represents the resulting texel color value at f(u, v). The mapping function described above is the nearest filter because only the texel point (s, t) closest to a given geometry point (u, v) is chosen as the texel value for the given geometry point.
In the second filter, the linear filter, the mapping function uses the four nearest texels, for a two-dimensional field, to obtained the resulting filtered texel. Thus, for example, one possible mapping function can be defined as:
f
(
u
)=floor (2
*s
)
f
(
v
)=floor (2
*t
)
T
(
u
,
v
)
=
f
(
u
,
v
)
+
f
(
u
,
(
v
+
1
)
)
+
f
(
(
u
+
1
)
,
v
)
+
f
(
(
u
+
1
)
,
(
v
+
1
)
)
4
The mapping described by T(u, v) sums the four nearest texels, then divides by four to normalize the result.
In the third filter, the weighted filter, the mapping function applies a weighting function to the linear filter to bias the texel values depending on their relative closeness to the geometry point. Hence, the mapping function could be:
T
(
u, v
)=Fraction_of [(1−
A
)
*T
0 +
A*T
1]
where:
T
0=Fraction_of [(1−
A
)
*f
(
u, v
)]+[
A *f
(
u,
(
v+
1))]
T
1=Fraction_of [(1−
A
)
*f
((
u+
1),
v
)]+[
A *f
((
u+
1), (
v+
1))]
and where A=the weighted coefficient to be used. Note that this weighted filter function simplifies to the linear filter used above if A=0.5. The weighting function can be further refined by specifying different values for A, the weighting coefficient, for each equation of T
0
, T
1
and T(u, v).
While all these prior art filters provide different functions for computing a resulting texel value from a set of texels, they are constrained to a rectangular coordinate system. However, some applications, such as ultrasound data, represent their texel values using a polar coordinate system. That is, the texel values represent the phase or angular position. For example, ultrasound data can measure echo amplitude, frequency and phase throughout an image. The phase and frequency changes are used to indicate motion and relative velocities. That is, the measured differences in phase and frequency is used to study, for example blood flow. In the example of medical ultrasound, motion or blood flow is assigned a color value that represents velocity and flow direction. More specifically, flow toward the transducer can be assigned , for example, the color red, with a shift toward yellow at higher velocities. Similarly, flow away from the transducer is assigned the color blue with a shift toward green for higher velocities. No motion or flow is assigned the color black. It is precisely this angular form of data that is inadequately filtered using rectangular coordinate system filter functions.
An exemplary prior art normalized scale
150
for attribute data is presented in prior art FIG.
1
C. The normalized scale
150
necessarily has a range from 0.0 to 1.0. This figure illustrates the averaging method used in the conventional filters. In this example, if two texels being averaged from texture map
100
have values of 0.8 and 0.2, their weighted average will be somewhere between 0.2-0.8, and their simple average will be 0.5. Neither the weighted average nor the simple average will be between 0.0-0.2 or 0.8-1.0.
Likewise, if the two texels being averaged have values of 0.4 and 0.6, their weighted average will be somewhere between 0.4 and 0.6, and their simple average will be 0.5. Again, neither the weighted average nor the simple average for this set of numbers will be between 0.0-0.4 or 0.6-1.0. This is assuming that the attribute data has been normalized to a maximum value of 1. Unfortunately, with this form of averaging, the averaged value must always be greater than the smallest attribute value and less than the largest attribute value. Consequently, the averaged value can be drastically different than the two nearest values. For example, an averaged value of 0.5 is clearly very proximate to attribute values of 0.4 and 0.6. However, an averaged value of 0.5 is very distant from either attribute values of 0.1 and 0.9. That is, the average of 0.5 is located 0.4 units away from 0.1 an
Cam Winget Nancy
Silkebakken Richard
Brier Jeffery
Washburn Woodcock LLP
LandOfFree
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