WO2010069269A1

WO2010069269A1 - A method of determining texture map parameters to define a footprint in a graphics processor and device thereof

Info

Publication number: WO2010069269A1
Application number: PCT/CN2009/075707
Authority: WO
Inventors: Qinyu Chen; Ji Zhou
Original assignee: Advanced Micro Devices (Shanghai) Co., Ltd.
Priority date: 2008-12-18
Filing date: 2009-12-18
Publication date: 2010-06-24
Also published as: CN101751687A; CN101751687B

Abstract

The present invention discloses a method of determining texture map parameters to define a footprint representing a projection of a pixel onto a texture map in a graphics processor. The method comprises computing ellipse coefficients based on a pair of specified partial derivative vectors ( U x , V x ) and ( u y , v y ); computing differential value t based on the ellipse coefficients in log scale; determine a range AngleRg within which the direction value of the footprint a lies, and getting reference differential value t' to which the differential value t approximates; and fetching the reference direction value of the footprint a' in the range AngleRg from a LUT corresponding to the reference differential value t'. The present invention results in improved performance compared with exact computation of the texture mapping parameters and favorable image quality compared with simple approximation of the texture mapping parameters.

Description

A METHOD OF DETERMINING TEXTURE MAP

PARAMETERS TO DEFINE A FOOTPRINT IN A GRAPHICS

PROCESSORAND DEVICE THEREOF

TECHNICAL FIELD

The present invention relates to computer graphics. More particularly, the present invention relates to filtering texture map data.

BACKGROUND ART

A texture is a one-, two- or multi-dimensional array of data items used in the calculation of the color or appearance of fragments produced by rasterization of a graphics scene. A texture could be image data, color or transparency data, roughness/smoothness data, reflectivity data, etc. Generally, computing a textured value for a pixel involves projecting a filter from screen space (indexed by x and y coordinates) into texture space (indexed by u and v coordinates). The region in texture space corresponding to a pixel is called the pixel's "footprint". A pixel can be approximated with a circle in screen space. For texture mapping of 2-dimensional pixels, the corresponding footprint in texture space can be approximated by an ellipse.

For low hardware cost and speed, isotropic filtering approximates the ellipse with a circle. Isotropic filtering filters equally in the two texture space dimensions u and v and yields top image quality for pixels whose footprints have major and minor texture axes that are similar in length. However, texture stretching, oblique viewing, and perspective can cause footprints to be very elongated. In such cases, the circle is never a good approximation to the ellipse. An ideal filter would have approximately elliptical shape.

To correct the problem, as mentioned, anisotropic filtering uses a filter that more closely matches the elliptical shape of the ideal filter. It is well known that all ellipses have a largest diameter, which is called the major axis, and a smallest diameter, which is called the minor axis. In contrast to isotropic filtering, anisotropic filtering results in fewer aliasing artifacts for footprints with major and minor axes that are not similar in length. To provide high quality textures, accurate computation of the length of minor axis and major axis is desired.

FIG. IA illustrates Footprint 115 including a Minor Axis 125 that is significantly shorter than a Major Axis 130. Texture samples along Major Axis 130 are read from one or more mipmap levels and are blended to produce a pixel color. The levels the samples are read from are determined using a level of detail (LOD) value which is nominally the log base 2 of the length of Minor Axis 125. An exact computation of the lengths of Major Axis 130 and Minor Axis 125 has proved to be complex and expensive in terms of performance and/or die area.

In order to simplify the computation, several different approaches have been generated to approximate the Major Axis and the Minor Axis. FIG. IB illustrates three vectors within anisotropic Footprint 115. A vector 145 and a vector 150 which are not always perpendicular are used to determine the Major Axis and Minor Axis. According to one of the prior art, the Major Axis is determined by the length of the vector 145 and the vector 150. The longer vector 150 approximates the Major Axis and the vector 155 perpendicular to the Major Axis approximates the Minor Axis. FIG. 1C illustrates four vectors within anisotropic Footprint 115. A vector 145 and a vector 150 which are not always perpendicular are used to determine the Major Axis and Minor Axis. According to another prior art, vector 160 approximates the Major Axis of Footprint 115 and is computed by summing the vector 145 and the vector 150 and dividing the sum by sqrt(2). Likewise, the vector 165 approximates the Minor Axis of Footprint 115 and is computed by subtracting the vector 150 from the vector 145 and dividing the difference by sqrt(2). The computation of the lengths of Major Axis and Minor Axis is simplified. However, the image quality is not satisfactory.

3D texture (Three Dimensional Texture) is a logical extension of the traditional 2D texture. A 3D texture can be thought of as a number of thin pieces of texture used to generate a three dimensional image map. 3D textures are typically represented by 3 coordinates. Similar to 2D textures, the coordinates of a 3D texture range from 0 to 1 in each dimension. The filtering process in a 3D texture is also controlled in the same way as in a 2D texture, that is, with the help of texture parameters.

Currently, the algorithm to apply derivative correction in DX 10/11 is very complicated, involving many division, multiplier, square, and log operations, etc. In the case of 3D texture, more computation operations are included, which is nearly unacceptable. And as a result, it is extremely difficult to implement the algorithm on hardware.

Accordingly, there is a need for a simplified algorithm to save logic area and keep a good balance between the accuracy of computing anisotropic texture mapping parameters and the size of the die area.

SUMMARY OF THE INVENTION

To resolve the existing problems in the prior technology, one object of the present invention is to provide a method of computing texture mapping parameters and a device thereof to reduce the die area and improve, in certain circumstances, the image quality.

In one aspect of the present invention, it provides a method of determining texture map parameters to define a footprint representing a projection of a pixel onto a texture map in a graphics processor, comprising computing differential value t based on a pair of specified partial derivative vectors ( U_x , V_x ) and (u_y ,v_y); determining a range AngleRg within which the direction value of the footprint α lies, and getting reference differential value t' to which the differential value t approximates; and fetching the reference direction value of the footprint α' in the range AngleRg from a LUT corresponding to the reference differential value t'.

Preferably, the differential value t is based on an ellipse coefficients based on said pair of specified partial derivative vectors. The ellipse coefficients can be defined as A=

+ u_y ² , B= 2(u_xv_x + u _yv_y) , and C= v_x ² + v_y ² or

A = Ux¹ + Vx¹, B = 2(UxUy + VxVy), C = Uy¹ + Vy¹. The method of computing texture mapping parameters obtains the direction of the major axis α', sin2α', and cos2α' via looking up a LUT to compute parameters, such as lengths of the major and minor axes and LOD values, for texture mapping.

Specifically, it can be a method of computing anisotropic texture map parameters to define an anisotropic footprint representing a projection of a pixel onto a texture map in a graphics processor, comprising: computing ellipse coefficients A=u_x ² +u²

B= 2(u_xv_x + u_yv_y) , and C= v_x ² + v_y ² based on a pair of specified partial derivative

vectors (u_x ,v_x ) and (u_y ,v_y); computing differential value t between log ( I A-C I ) and log ( I B | ) based on the ellipse coefficients A, B, and C; comparing A-C, B, and 0 to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies, and getting reference differential value t' to which the differential value t approximates; fetching the reference direction value of the anisotropy of the footprint α' in a range AngleRg and corresponding sin2q' and cos2α' from a LUT corresponding to the reference differential value t'; computing the length of the major axis anisotropic texture map parameter and the length of the minor axis anisotropic texture map parameter based on A , B , C, sin2α' , and cos2α'.

Preferably, said pair of specified partial derivative vectors ( ^x , ^x )and ( ^y , ^y ) are separately a partial derivative of texture map coordinates u and v with respect to x and a partial derivative of texture map coordinates with respect to y.

Preferably, if 0<B<A-C or A-C<B<0, the AngleRg is (0, π /S); if 0< A-C <B or B<A-C<0, the AngleRg is (π/$, π IA); if 0< A-C <-B or -B<A-C<0, the AngleRg is ( π /4, 3 π /8); and if A-C <-B<0 or 0<-B<A-C, the AngleRg is (3 ΛΓ /8, π 12).

Preferably, the step of computing the length of the major axis anisotropic texture map parameter and the length of the minor axis anisotropic texture map parameter based on A , B , C, sin2α' , and cos2α' comprises computing (A+C) + [(A-C) cos (2α') + B sin (2α')] and (A+C) - [(A-C) cos (2α') + B sin (2α') ] to produce the first length and the second length; identifying a major axis anisotropic texture map parameter as the longer of the first length and the second length and a minor axis anisotropic texture map parameter as the shorter of the first length and the second length. Preferably, the method further comprises the step of constructing the LUT.

Preferably, the LUT includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α, and reference differential values t' for the direction of the anisotropy of the footprint α<≡ (0, π/2 ) with a specified interval, wherein the reference differential values t' approximates to the differential values t. More preferably, if t=log(|A-C|) - log(|B|), t' is represented by log(|cot(2α)|); if t =log(|B|) - log(|A-C|), t' is represented by log(|tan(2α)|)

Preferably, the LUT includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/8) with a specified interval, wherein the reference differential values t' is represented by log(|tan(2α)|); and includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint ae [π/8, π /4) with the specified interval, wherein the reference differential values t' is represented by log(|cot(2α)|).

Preferably, the method further comprises the step of computing a level of detail anisotropic texture mapping parameter.

Preferably, the method further comprises the step of computing a logratio using the first length and the second length.

Preferably, the step of constructing LUT comprises, for the direction of the anisotropy of the footprint α<≡ (0, π/2) with a specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α,wherein the reference differential values t' represented by log(|cot(2α)|) approximate to differential values t=log(|A-C|)- log(|B|); and organizing the computed values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α and reference differential values to generate the LUT.

Preferably, the step of constructing LUT comprises, for the direction of the anisotropy of the footprint α<≡ (0, π/2) with a specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α, wherein the reference differential values t' represented by log(|tan(2α)|) approximate to differential values t=log ( I B | ) - log ( I A-C I ) ; and organizing the computed values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α and reference differential values to generate the LUT.

Preferably, the step of constructing LUT comprises, for the direction of the anisotropy of the footprint α<≡ (0, π 18) with a specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sinα, cosα, sin2α and cos2α to get a LUTi, wherein the reference differential values t' is represented by log(|tan(2α)|); for the direction of the anisotropy of the footprint α<≡ ( π/8, π IA ) with the specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sinα, cosα, sin2α and cos2α to get a LUT₂ wherein the reference differential values t' is represented by log(|cot(2α)|); and combining the two tables LUTi and LUT₂ , and deleting the redundant columns of sin2α and cos2α to get a LUT₃.

Preferably, the values of sinα and cosα are included in the LUT directly, while the values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α can be obtained from the LUT indirectly.

Preferably, if the range AngleRg is (0, π/8), get reference differential value t' to which the differential value t= log (|B|) - log (|A-C|) approximates; if the range AngleRg is (0, π IA), get reference differential value t' to which the differential value t= log(|A-C|) - log (|B|) approximates.

Preferably, for the direction of the anisotropy of the footprint a<≡(π IA, π 12), the values of sin2α and cos2α can be obtained from the said LUT using the trigonometric function transform formulas.

Preferably, a binary-search is used to get reference differential value t' to which the differential value t approximates.

Preferably, the reference differential value t' corresponds to an Index which is used to fetch the reference direction value of the anisotropy of the footprint α' in the determined range AngleRg and corresponding sin2α' and cos2α' from the LUT.

The matrix of ellipse can be

^~Ux Uy ^~Ux Vx Ux² + Uy² UxVx + UyVy A BI2

M = T * T=

Vx Vy_ Uy Vy_ UxVx + UyVy Vx² + Vy² B/2 C On the other hand, the matrix can also be defined as

Ux² + Vx² UxUy + VxVy

M = r*τ = , that is, wherein the ellipse coefficients

UxUv + VxVv Uy² + Vy

can be defined as A = Ux² + Vx², B = 2(UxUy + Vx Vy), C = Uy² + Vy². By adding a third item W and set

A = Ux² + Vx² + Wx², B = 2(UxUy + VxVy + WxWy), C = Uy² + Vy² + Wy² ,

the above method can also be applied to 3D texture.

In another aspect of the present invention, it provides a computer program product. In one implementation, the computer program product includes, but is not limited to, a medium bearing at least one of one or more programs for executing any one of the above-mentioned methods.

In another aspect of the present invention, it provides a device for computing texture mapping parameters, comprising: an ellipse coefficients computation unit configured to compute ellipse coefficients based on a pair of specified partial derivative vectors ( U_x V_x ) and ( u_y v_y ); a differential value computation unit configured to compute a differential value t based on the ellipse coefficients in log scale; a comparing unit configured to determine the range AngleRg within which the direction value of the footprint α lies; a reference differential value obtaining unit configured to get reference differential value t' to which the differential value t approximates; and a LUT search unit configured to fetch the reference direction value of the footprint α' in the determined range AngleRg from the LUT corresponding to the reference differential value t'.

Specifically, the present device can be used for computing anisotropic texture mapping parameters by comprising: an ellipse coefficients computation unit configured to compute the ellipse coefficients A=u_x ² +u_y ² , B=2(u_xv_x +u_yv_y) , and C=

^v _x ^{+ v}l based on a pair of specified partial derivative vectors (u_x V_x ) and (u_y v_y); a differential value computation unit configured to compute the differential value t between log (|A-C|) and log(|B|); comparing unit configured to compare A-C, B, and 0 to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies; reference differential value obtaining unit configured to get reference differential value t' to which the differential value t approximates; a LUT search unit configured to fetch the reference direction value of the anisotropy of the footprint α' in a determined range AngleRg, sin2α', and cos2α' from a LUT corresponding to the reference differential value t'; a parameter computation unit configured to compute the length of the major axis anisotropic texture map parameter and the length of the minor axis anisotropic texture map parameter based on A , B , C, sin2α' , and cos2α'.

Preferably, the parameter computation unit further comprises a length computation unit configured to compute (A+C) + [(A-C) cos (2α') + B sin (2α') ] and (A+C) - [(A-C) cos (2α') + Bsin (2α') ] to produce the first length and the second length; and an identification unit configured to identify a major axis anisotropic texture map parameter as the longer of the first length and the second length and a minor axis anisotropic texture map parameter as the shorter of the first length and the second length.

Preferably, said anisotropic device comprises the LUT construction unit used to construct the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α e (0, π/2 ) with a specified interval.

Preferably, said anisotropic device comprises the LUT construction unit used to construct the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/8) with a specified interval, wherein the reference differential values t' is represented by log(|tan(2α)|); and also includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ [;z78, π/4) with the specified interval, wherein the reference differential values t' is represented by log(|cot(2α)|).

Preferably, said parameter computation device is configured to compute a level of detail anisotropic texture mapping parameter.

Preferably, said parameter computation device is configured to compute a logratio using the first length and the second length.

In another aspect of the present invention, it provides a method of computing texture map parameters to define a footprint representing a projection of a pixel onto a texture map in a graphics processor, comprising: computing ellipse coefficients

A = Ux¹ + Vx² + Wx¹, B = 2(UxUy + VxVy + WxWy),C = Uy¹ + Vy¹ + Wy¹ based on a pair of specified partial derivative vectors (u_x ,v_x , W_x) and (u ,v , w_y); computing differential value t based on the ellipse coefficients A, B, and C; determining a range AngleRg within which the direction value of the footprint α lies, and getting reference differential value t' to which the differential value t approximates; and fetching the reference direction value of the footprint α' in the range AngleRg from a LUT corresponding to the reference differential value t'.

It should be understood that the general description above and the detailed description below are all illustrative and descriptive, intended for further describing the present invention.

Other features and advantages of the present invention are given in the following description, partially seen from the description or the implementation of the present invention. Objects and other advantages of the present invention can be learned and obtained from the description, claims and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be understood more easily through the accompanying drawings constituting a part of this specification, which illustrate embodiments of the present invention and serve to explain various principles of embodiments of the present invention together with the description.

FIG. IA illustrate a prior art application of texture samples to surface.

FIG. IB illustrates three vectors within anisotropic Footprint 115 used to determine the major axis and minor axis in a prior art.

FIG. 1C illustrates four vectors within anisotropic Footprint 115 used to determine the major axis and minor axis in a prior art.

FIG. 2 A illustrates texture mapping parameters mapped to adjacent pixels in accordance with aspects of the present invention. FIG. 2B illustrates two vectors within an anisotropic footprint used to determine the major axis and the minor axis of anisotropy in accordance with one or more aspects of the present invention.

FIG.3 illustrates the method of computing texture map parameters in accordance with one or more aspects of the present invention.

FIG.4 shows the first embodiment of a method of computing anisotropic texture mapping parameters according to aspects of the present invention.

FIG.5 shows the third embodiment of a method of computing anisotropic texture mapping parameters according to aspects of the present invention.

FIG.6A shows the fourth embodiment of a method of computing anisotropic texture mapping parameters according to aspects of the present invention.

FIG.6B shows the method of constructing the LUT in the fourth embodiment.

FIG.7A shows the fifth embodiment of a method of computing anisotropic texture mapping parameters according to aspects of the present invention.

FIG.7B shows the method of constructing the LUT in the fifth embodiment.

FIG.8 A shows the sixth embodiment of a method of computing anisotropic texture mapping parameters according to aspects of the present invention.

FIG.8B shows the method of constructing the LUT in the sixth embodiment.

FIG. 9 shows the binary search configuration in the sixth embodiment.

FIGlO shows an anisotropic unit for computing anisotropic texture mapping parameters according to aspects of the present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

In the following description, numerous specific details are set forth to provide a more thorough understanding of aspects of the present invention. However, it will be apparent to one of skill in the art that the present invention may be practiced without one or more of these specific details. In other instances, well-known features have not been described in order to avoid obscuring the present invention.

The major and minor axes of anisotropy determine a footprint that represents the projection of the pixel onto the texture map. In the prior art, exact determination of the major and minor axes requires complex computations which are not cost effective to implement within the die area constraints of graphics processors. In the prior art, the simply approximated major and minor axes used to compute parameters for texture mapping failed to meet the requirement for image quality. In the present embodiment of the invention, the direction of the major axis α', sin2α', and cos2α' can be obtained via looking up LUT (lookup Table), which will be used to compute parameters, such as lengths of the major and minor axes and LOD values, for anisotropic texture mapping. Furthermore, the present embodiment results in improved performance compared with exact computation of the anisotropic texture mapping parameters and favorable image quality compared with simple approximation of the anisotropic texture mapping parameters.

FIG. 2A shows four pixels in (x, y) screen space with their corresponding texture coordinates u , v , a Pixel 200, a Pixel 201, a Pixel 202, and a Pixel 203, in accordance with one or more aspects of the present invention. Texture coordinate w can be added only for mapping of three dimensional texture.

FIG. 2B shows the footprint of the four pixels, Pixels 200, 201, 202, and 203, in texture space. Points 210, 211, and 212 are the texture coordinates of Pixels 200, 201, and 202, respectively. Texture coordinates for Pixel 200, 0,0 are shown in the FIG. 2B as Point 210. Texture coordinates for Pixel 201, u \, v \ are shown in FIG. 2B as Point 211. Texture coordinates for Pixel 202, M ₂₅V₂ are shown in FIG. 2B as Point 212. Difference Vector 221 is the partial derivative of (u ,v) with respect to x. Difference Vector 222 is the partial derivative of (u , v) with respect to y.

Fig.3 illustrates the method of computing texture map parameters in accordance with one or more aspects of the present invention. In Step 302, ellipse coefficients are computed based on a pair of specified partial derivative vectors (u_x ,v_x) and

In Step 304, a differential value t is computed based on the ellipse coefficients A, B and C in log scale. The differential value t can be log(|A-C|)- log(|B|)or log(|B|)-log(|A-C|).

In step 306, a range AngleRg within which the direction value of the footprint α' lies is determined, and get reference differential value t' to which the differential value t approximates. If 0<B<A-C or A-C<B<0 is true, the AngleRg is (0, π/S); if not, further determining whether 0< A-C <B or B<A-C<0 is true, if it is true, the AngleRg is (π/S, π IA); if it is false, further determining whether 0< A-C <-B or -B<A-C<0 is true, if it is true, the AngleRg is (π IA, 7> πlS), otherwise the AngleRg is (3 πlS, π/2).

In step 308, the reference direction value of the footprint α' in the range AngleRg from a LUT corresponding to the reference differential value t' is fetched.

The value log(|cot(2a)|) or log(|tan(2a)|) may be hardcoded to do a binary-search, while LUT may be preloaded in a ROM.

The LUT can include the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/2 )with a specified interval, wherein the reference differential values t' represented by log(|cot(2α)|) approximate to the differential values t=log(|A-C|) - log (|B|).

The LUT also can include the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/2 )with a specified interval, wherein the reference differential values t' represented by log(|tan(2α)|) approximate to the differential values t=

The LUT also can include the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/S) with a specified interval, wherein the reference differential values t' is represented by log(|tan(2α)|); and include the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint αe [^/8, π IA) with the specified interval, wherein the reference differential values t' is represented by log(|cot(2α)|). First embodiment

Fig. 4 shows the first embodiment of a method of computing texture mapping parameters according to aspects of the present invention.

Table 1 shows the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/2 ) with an interval, wherein the reference differential values t' represented by log(|cot(2α)|) approximates to the differential value t=log(|A-C|) - log (|B|).

As shown in Fig. 4, in Step 402, ellipse coefficients A=u_x ² + u_y ² , B=2(u_xv_x +u_yv_y) ,

and C= v_x + v_y ² are computed based on a pair of specified partial derivative vectors

(M_X , v_x) and (u_y ,v_y ).

Table 1

In Step 404, a differential value t= log(|A-C|)-log(|B|) is computed based on the ellipse coefficients A, B, and C. Suppose A=4, B=-2, and C=I are obtained in step402, then the differential value t= Iog(|4-l|)-log((-2|)=log3-log2=0.17609.

In Step 406, A-C, B, and 0 are compared to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies. Comparing A-C, B, and 0, if 0<B<A-C or A-C<B<0, the AngleRg is (0, π /S); if 0< A-C <B or B<A-C<0, the AngleRg is (π/$, π IA); if 0< A-C <-B or -B<A-C<0, the AngleRg is (π/4, 3 π/S); and if A-C <-B<0 or 0<-B<A-C, the AngleRg is (3 π/8, π/2). For A=4, B=-2, and C=I, 0<-B<A-C, so the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies is (3 π /8, π/2). That is to say, the reference direction value of the anisotropy of the footprint α' φ π/8, π/2).

Subsequently, get the reference differential value t' to which the differential value t approximate, wherein the reference differential values t' is represented by log(|cot(2α)|). For the differential value t=0.17609, comparing 0.17609 with the values in the log(|cot(2α)|) column to obtain the most approximate reference differential value t'=0.138738.

In step 408, the reference direction value of the anisotropy of the footprint α' in the range AngleRg, sin2α' and cos2α' are fetched from the LUT corresponding to the reference differential value t'. The reference differential value t'=0.138738 corresponds to two different groups of α, sin2α, and cos2α in the LUT. One group is that α=6 ;r /60, sin2α=0.587785, and cos2α=0.809017, and the other group is α=24;r/60, sin2α=0.587785, and cos2α— 0.809017. The 24π/60 is in the range AngleRg (3 π/8, n IT), so the reference direction value of the anisotropy of the footprint α' equals to 24 π /60, sin2α' equals to 0.587785, and cos2α' equals to -0.809017.

In step 410, (A+C) + [(A-C) cos (2α') + B sin (2α') ] and (A+C) - [(A-C) cos (2α') + B sin (2α') ] are computed to produce the first length and the second length.

In step 412, a comparison between the first length and the second length is conducted, identifying the longer length and the shorter length as the length of major axis and the length of minor axis, respectively.

In step 414, the base-two logarithm (log) of the major axis length is computed to produce a logmajor value and the base-two log of the minor axis length is computed to produce a logminor value, i.e., LOD.

In step 416, a logratio value is computed by subtracting the logminor value from the logmajor value. The logratio value is equivalent to the base-two log of the ratio value.

Second embodiment

In the embodiment of the present invention, the LUT includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, πll ) with an interval π /60 , wherein the reference differential values t' represented by log(|tan(2α)|) approximates to the differential value t=log ( I A-C I ) - log ( I B | ). The only difference compared with the first embodiment is that in Step 404 a differential value t= log( I B I ) -log( I A-C I ) is computed.

Third embodiment

Fig. 5 shows the third embodiment of a method of computing texture mapping parameters according to the present invention.

Table 2 shows another LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π /8) with a specified interval, wherein the reference differential values t' is represented by log(|tan(2α)|). The LUT also includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ [ π /8 , π 14) with the specified interval, wherein the reference differential values t' represented by log(|cot(2α)|) approximate to differential values t.

As shown in Fig. 5, in Step 502, ellipse coefficients A=u_x ² + u_y ² , B=2(u_xv_x +u_yv_y) ,

and C= v_x ² + v² are computed based on a pair of specified partial derivative vectors

("_{x >}O and (u_y ,v_y ).

In Step 504 differential value t between log(|A-C|) and log(|B|) are computed based on the ellipse coefficients A, B, and C. Suppose A=4, B=2, and C=I are computed in step 502, the differential value t= log(|4-l|)-log(|2|)⁼log3-log2 =0.17609, or the differential value t= log(|2|) -log(|4-l|) =-0.17609

In Step 506, A-C, B, and 0 are compared to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies. Comparing A-C, B, and 0, if 0<B<A-C or A-C<B<0, the AngleRg is (0, π/S); if 0< A-C <B or B<A-C<0, the AngleRg is (π/S, π IA); if 0< A-C <-B or -B<A-C<0, the AngleRg is (π/4, 3 π/S); and if A-C <-B<0 or 0<-B<A-C, the AngleRg is (3 π/S, π/2). For A=4, B=2, and C=I, 0<B<A-C, so the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies is (0, π/S). That is to say, the reference direction value of the anisotropy of the footprint α' <≡ (0, π/S).

Table 2

Subsequently, get the reference differential value t' to which the differential value t approximates. For the differential value t=0.17609, comparing 0.17609 with the reference differential values to obtain the reference differential value t'=0.138738. For the differential value t— 0.17609, comparing -0.17609 with the reference differential values to obtain the reference differential value t'=-0.138738.

In step 508 the reference direction value of the anisotropy of the footprint α' in the range AngleRg, sin2α', and cos2α' are fetched from the LUT corresponding to the reference differential value t'. The reference differential value t'=0.138738 corresponds to one group of α, sin2α, and cos2α in the LUT. The group is that α=9π/60, sin2α=0.809017, and cos2α=0.587785.

The reference differential value t'=-0.138738 corresponds to one group of α, sin2α, and cos2α in the LUT. The group is that α=6;r/60, sin2α=0.587785, and cos2α=0.809017.

Only 6π 160 is in the range AngleRg (0, π/8), so the reference direction value of the anisotropy of the footprint α' =6 π /60, sin2α=0.587785, and cos2α=0.809017.

In step 510, the (A+C) + [(A-C) cos (2α') + B sin (2α') ] and (A+C) - [(A-C) cos (2α') + B sin (2α') ] are computed to produce the first length and the second length.

In step 512, a comparison between the first length and the second length is conducted, identifying the longer length and the shorter length as the length of major axis and the length of minor axis, respectively.

In step 514 the base-two logarithm (log) of the major axis length is computed to produce a logmajor value and the base-two log of the minor axis length is computed to produce a logminor value i.e. LOD. In step 516 a logratio value is computed by subtracting the logminor value from the logmajor value. The logratio value is equivalent to the base-two log of the ratio value.

Fourth embodiment

FIG.6A shows the fourth embodiment of a method of computing texture mapping parameters according to an aspect of the present invention. FIG.6B shows the method of constructing LUT in the fourth embodiment.

As shown in FIG.6A, in Step 600 the LUT is constructed. As shown in FIG.6B, the step further comprises the following substeps:

Step 6001: for the direction of the anisotropy of the footprint α<≡ (0, π/2) with a specified interval, compute the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α, wherein the reference differential values t' represented by log(|cot(2α)|) approximates to differential values;

Step 6003: organize the computed values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α and reference differential values to generate the LUT, wherein the reference differential value t' approximates to the differential value t=log (|A-C|) - log (|B|).

In Step 602, ellipse coefficients

+u_yv_y) , and C=

+ v_y ² are

computed based on a pair of specified partial derivative vectors (u_x , v_x) and (« , v ).

In Step 604, a differential value t= log( I A-C I )-log( I B | ) is computed based on the ellipse coefficients A, B, and C.

In Step 606, A-C, B, and 0 are compared to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies. Subsequently, get the reference differential value t' to which the differential value t approximates in the LUT.

In step 608, the reference direction value of the anisotropy of the footprint α' in the range AngleRg, sin2α', and cos2α' are fetched from the LUT corresponding to the reference differential value t'. In step 610, (A+C) + [(A-C) cos (2α') + B sin (2α')] and (A+C) - [(A-C) cos (2α') + B sin (2α')] are computed to produce the first length and the second length;

In step 612, a comparison between the first length and the second length is conducted, identifying the longer length and the shorter length as the length of major axis and the length of minor axis, respectively.

In step 614, the base-two logarithm (log) of the major axis length is computed to produce a logmajor value and the base-two log of the minor axis length is computed to produce a logminor value i.e. LOD.

In step 616, a logratio value is computed by subtracting the logminor value from the logmajor value. The logratio value is equivalent to the base-two log of the ratio value.

Fifth embodiment

FIG.7A shows the fifth embodiment of a method of computing anisotropic texture mapping parameters according to an aspect of the present invention. FIG.7B shows the method of constructing LUT in the fifth embodiment.

As shown in FIG.7A, in Step 700, LUT is constructed. As shown in FIG.7B, the step further comprises the following substeps:

Step 7001 : for the direction of the anisotropy of the footprint α<≡ ( 0, π 12 ) with a specified interval, compute the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α, wherein the reference differential values t' is represented by log(|tan(2α)|)approximate to differential values t;

Step 7003: organize the computed values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α, and reference differential values to generate the LUT, wherein the reference differential value t' approximates to the differential value t=log ( I B | ) - log ( I A-C I ).

In Step 702, ellipse coefficients

+u_yv_y) , and C= v_x ² + v_y ² are

computed based on a pair of specified partial derivative vectors (u_x , v_x ) and (u v ). In Step 704, a differential value t= log ( I B | ) - log ( I A-C I ) is computed based on the ellipse coefficients A, B, and C.

In Step 706, A-C, B, and 0 are compared to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies. Subsequently, get the reference differential value t' to which the differential value t approximates in the LUT.

In step 708 the reference direction value of the anisotropy of the footprint α' in the range AngleRg, sin2α', and cos2α' are fetched from the LUT corresponding to the reference differential value t'.

In step 710, (A+C) + [(A-C) cos (2α') + B sin (2α')] and (A+C) - [(A-C) cos (2α') + B sin (2α')] are computed to produce the first length and the second length;

In step 712, a comparison between the first length and the second length is conducted, identifying the longer length and the shorter length as the length of major axis and the length of minor axis, respectively.

In step 714 the base-two logarithm (log) of the major axis length is computed to produce a logmajor value and the base-two log of the minor axis length is computed to produce a logminor value i.e. LOD.

In step 716 a logratio value is computed by subtracting the logminor value from the logmajor value. The logratio value is equivalent to the base-two log of the ratio value.

Sixth embodiment

Fig. 8A shows the sixth embodiment of a method of computing anisotropic texture mapping parameters according to aspects of the present invention. FIG.8B shows the method of constructing LUT in the sixth embodiment.

As shown in FIG.8 A, in Step 800 LUT is constructed. As shown in FIG.8B, the step further comprises the following substeps:

Step 8001: for the direction of the anisotropy of the footprint α<≡ (0, π /8) with a specified interval, compute the values of every direction of the anisotropy of the footprint α and corresponding sinα, cosα, sin2α, and cos2α to get LUTi, wherein the reference differential values t' is represented by log(|tan(2α)|);

Step 8002: for the direction of the anisotropy of the footprint α<≡ ( π/8, π IA ) with the specified interval, compute the values of every direction of the anisotropy of the footprint α and corresponding sinα, cosα, sin2α, and cos2αto get LUT₂, wherein the reference differential values t' is represented by log(|cot(2α)|);

Step 8003: combine the tables LUTi with LUT₂, and delete the redundant columns of sin2α and cos2α to get LUT;

Table 3 shows the LUTi in the sixth embodiment. Table 4 shows the LUT₂ in the sixth embodiment. Table 5 shows the LUT obtained by combining LUTi with LUT₂. The values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α are included in the LUT indirectly, while the values of sinα and cosα are included in the LUT directly.

Table 3 LUTi (α e (0, π/S))

Table 4 LUT₂ (α e C π/S, π/4))

Table5 LUT Combination of LUTiand LUT₂

In Step 802 ellipse coefficients

C= + v_y ² are

computed based on a pair of specified partial derivative vectors (u_x , v_x) and (u_y ,v_y ).

In Step 804 differential value t between log(|A-C|) and log(|B|) are computed based on the ellipse coefficients A, B, and C. Suppose A=4, B=3, and C=2 are computed in step 802, then the differential value t= Iog₂(|4-2|)-log₂(|3|) ⁼log22-log23

=-0.477121

In Step 806, A-C, B, and 0 are compared to determine the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies. Comparing A-C, B, and 0, if 0<B<A-C or A-C<B<0, the AngleRg is (0, π/S); if 0< A-C <B or B<A-C<0, the AngleRg is (π/S, π IA); if 0< A-C <-B or -B<A-C<0, the AngleRg is (π/4, 3 π/S); and if A-C <-B<0 or 0<-B<A-C, the AngleRg is (3 π/S, π/2). For A=4, B=3, and C=2, 0< A-C <B, so the range AngleRg within which the reference direction value of the anisotropy of the footprint α' lies is (π/S, π/4). That is to say, the reference direction value of the anisotropy of the footprint α' e(π/8, π/4).

Subsequently, get the reference differential value t' to which the differential value t approximates in the LUT. The reference differential values correspond with indexes which are integers. Therefore, the index corresponding to the reference differential value t' can be obtained.

For the differential value t=-0.477121, via binary search, the reference differential value t' and the corresponding Index can be obtained. FIG.9 shows the binary search configuration. The binary search is implemented according to FIG.9. In the embodiment, the midpoints between the fitting nodes are separating points to achieve rounding effect. Totally three comparisons can determine an index. The reference differential values t=-4.60881 corresponds to the Index 6.

In step 808 the reference direction value of the anisotropy of the footprint α' in the range AngleRg, sin2α', and cos2α' are fetched from the LUT corresponding to the Index. The Index 6 is used to look up the LUT according to the relationship between the Index and the position of the reference direction value of the anisotropy of the footprint α' in the range AngleRg, sin2α', and cos2α'. In the embodiment, α'=9^/60, sin2α'=0.809017, and cos2α'=0.587785. In step 810 (A+C) + [(A-C) cos (2α') + B sin (2α') ] and (A+C) - [(A-C) cos (2α') + B sin (2α') ] are computed to produce the first length and the second length.

In step 812, a comparison between the first length and the second length is conducted, identifying the longer length and the shorter length as the length of major axis and the length of minor axis, respectively.

In step 814, the base-two logarithm (log) of the major axis length is computed to produce a logmajor value and the base-two log of the minor axis length is computed to produce a logminor value i.e. LOD.

In step 816, a logratio value is computed by subtracting the logminor value from the logmajor value. The logratio value is equivalent to the base-two log of the ratio value.

Fig.10 shows a device for computing texture mapping parameters according to one aspect of the present invention. The device comprises:

an ellipse coefficients computation unit 1001 configured to compute the ellipse coefficients based on a pair of specified partial derivative vectors ( U_x V_x ) and

a differential value computation unit 1003 configured to compute the differential value t based on the ellipse coefficients in log scale;

comparing unit 1005 configured to determine a range AngleRg within which the direction value of the footprint α' lies;

reference differential value obtaining unit 1007 configured to get reference differential value t' to which the differential value t approximates, wherein the differential value t comes from a differential value computation unit 1003;

a LUT search unit 1009 configured to fetch the reference direction value of the footprint α' in a determined range AngleRg from a LUT corresponding to the reference differential value t';

a parameter computation unit 1011 configured to compute texture parameters. In another embodiment of the present invention, the parameter computation unit 1011 comprises length computation unit configured to computing (A+C) + [(A-C) cos (2α') + B sin (2α') ] and (A+C) - [(A-C) cos (2α') + Bsin (2α') ] to produce the first length and the second length; and an identification unit configured to identify a major axis anisotropic texture map parameter as the longer of the first length and the second length and a minor axis anisotropic texture map parameter as the shorter of the first length and the second length.

In another embodiment of the present invention, the device for computing texture mapping parameters further comprises a LUT construction unit used to construct the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α, and cos2α for the direction of the anisotropy of the footprint α e (0, π/2 ) with a specified interval.

In another embodiment of the present invention, the device for computing texture mapping parameters further comprises a LUT construction unit used to construct the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π /8) with a specified interval, wherein the reference differential values t' represented by log(|tan(2α)|) approximate to differential values t; and includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α, and cos2α for the direction of the anisotropy of the footprint αe[^/8, π IA) with the specified interval, wherein the reference differential values t' represented by log(|cot(2α)|) approximate to differential values t.

In another embodiment of the present invention, a parameter computation unit 1011 is configured to compute a level of detail anisotropic texture mapping parameter.

In another embodiment of the present invention, a parameter computation unit 1011 is configured to compute a logratio using the first length and the second length.

Obviously, the present invention can be applied to both anisotropic and isotropic filtering. The difference is that anisotropic filtering needs the length of minor axis/ratio/direction, while only the length of major axis is needed for isotropic filtering. It is apparent to those skilled in the art that if the ellipse matrix is defined as

Ux² + Vx² UxUy + VxVy

M = T'*T = , that is, wherein the ellipse coefficients is

UxUy + VxVy Uy¹ + Vf

defined as A = Ux² + Vx², B = 2(UxUy + VxVy), C = Uy² + Vy². By adding a third item

W and set A = Ux² + Vx² + Wx², B = 2(UxUy + VxVy + WxWy), C = Uy² + Vy² + Wy² ,

the above methods can also be applied to 3D texture.

In addition, the various illustrative logical blocks, flowcharts, windows, and steps described in connection with the embodiments disclosed herein may be implemented or performed in hardware or software with an application-specific integrated circuit (ASIC), a programmable logic device, discrete gate or transistor logic, discrete hardware components, such as, e.g., registers and FIFO, a processor executing a set of firmware instructions, any conventional programmable software and a processor, or any combination thereof. Such hardware components may be manufactured based on hardware description language (HDL) instructions stored on a computer readable medium. Such HDL instructions may be used for mask works and the like and ultimately configure a manufacturing process so as to manufacture a hardware device (such as a processor, for example) capable of operating in accordance with aspects of the invention. The processor may advantageously be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. The software could reside in RAM memory, flash memory, ROM memory, registers, hard disk, a removable disk, or any other form of storage medium known in the art.

Described above are only the preferred embodiments of the present invention which do not limit the present invention. Rather, as for those skilled in the art, the present invention may have various changes and alternations. All such modifications, substitutions, improvements etc. within the spirit and principle of the present invention should be all covered in the scope of the affixed claims of the present invention.

Claims

1. A method of determining texture map parameters to define a footprint representing a projection of a pixel onto a texture map in a graphics processor, comprising: computing differential value t based on a pair of specified partial derivative vectors (u_x ,v_x ) and (u_y ,v_y );

determining a range AngleRg within which the direction value of the footprint α lies, and getting reference differential value t' to which the differential value t approximates; and fetching the reference direction value of the footprint α' in the range AngleRg from a LUT corresponding to the reference differential value t'.

2. The method of claim 1, wherein the differential value is based on an ellipse coefficients based on said pair of specified partial derivative vectors.

3. The method of Claim 2, wherein

the ellipse coefficients are defined as A=u_x ² + u_y ² , B= 2(u_xv_x +u_yv_y) , and C=

4. The method of Claim 2, wherein the ellipse coefficients are defined as

A = Ux¹ + Vx¹, B = 2(UxUy + VxVy), C = Uy¹ + Vy¹.

5. The method of Claims 3 or 4, wherein the value t is the difference between log (|A-C|) and log(|B|); and the range AngleRg is determined by comparing A-C, B, and 0.

6. The method of Claim 5, further comprising: computing the length of a major axis anisotropic texture map parameter and the length of a minor axis anisotropic texture map parameter based on A , B , C, sin2α' and cos2α'.

7. The method of Claim 6, wherein the pair of specified partial derivative vectors ( U_x , V_x ) and ( u_y , v_y ) are separately a partial derivative of texture map coordinates u and v with respect to x and a partial derivative of texture map coordinates with respect to y.

8. The method of Claim 6, wherein if 0<B<A-C or A-C<B<0, the AngleRg is (0, π/S); if 0< A-C <B or B<A-C<0, the AngleRg is (π/S, π IA); if 0< A-C <-B or -B<A-C<0, the AngleRg is (π IA, 3 π IS); and if A-C <-B<0 or 0<-B<A-C, the AngleRg is (3 π /8, π 12).

9. The method of Claim 6, wherein computing the length of the major axis anisotropic texture map parameter and the length of the minor axis anisotropic texture map parameter based on A , B , C, sin2α' and cos2α', comprising, computing (A+C) + [(A-C) cos (2α') + B sin (2α')] and (A+C) - [(A-C) cos (2α') + B sin (2α') ] to produce the first length and the second length; identifying a major axis anisotropic texture map parameter as the longer of the first length and the second length and a minor axis anisotropic texture map parameter as the shorter of the first length and the second length.

10. The method of Claim 6, further comprising the step of constructing the LUT.

11. The method of any one of Claims 6-10, wherein the LUT includes the values of every reference direction of the anisotropy of the footprint α and corresponding sin2α, cos2α, and reference differential value t' for the direction of the anisotropy of the footprint α e (0, π/2 ) with a specified interval, wherein reference differential value t' are reference differential values which approximate to the differential values t.

12. The method of Claim 11, wherein if t=log(|A-C|) - log(|B|), t' represents log(|cot(2α)|); if t =log(|B|) - log(|A-C|), t' represents log(|tan(2α)|).

13. The method of any one of Claims 6-10, wherein the LUT includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α e (0, π/8) with a specified interval, wherein the reference differential values t' is represented by log(|tan(2α)|); and includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ [ π/8 , π/4)] with the specified interval, wherein the reference differential values t' is represented by log(|cot(2α)|).

14. The method of any one of Claims 6-10, further comprising the step of computing a level of detail anisotropic texture mapping parameter.

15. The method of any one of Claims 6-10, further comprising the step of computing a logratio using the first length and the second length.

16. The method of Claim 10, wherein the step of constructing the LUT comprises: for the direction of the anisotropy of the footprint α<≡ (0, π/2) with a specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α, wherein the reference differential values t' represented by log(|cot(2α)|) approximate to differential values t=log (|A-C|) - log (|B|); organizing the computed values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α and reference differential values t' to generate the LUT.

17. The method of Claim 10, wherein the step of constructing the LUT comprises: for the direction of the anisotropy of the footprint α<≡ (0, π/2) with a specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α, wherein the reference differential values t' represented by log(|tan(2α)|) approximate to differential values t=log (|B|) - log ( A-C|); and organizing the computed values of every direction of the anisotropy of the footprint α and corresponding sin2α, cos2α and reference differential values t' to generate the LUT.

18. The method of Claim 10, wherein the step of constructing the LUT comprises: for the direction of the anisotropy of the footprint α<≡ (0, π 18) with a specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sinα, cosα, sin2α, and cos2α to get LUTi, wherein the reference differential values t' is represented by log(|tan(2α)|); for the direction of the anisotropy of the footprint α<≡ ( π/8, π IA ) with the specified interval, computing the values of every direction of the anisotropy of the footprint α and corresponding sinα, cosα, sin2α, and cos2α to get LUT₂, wherein the reference differential values t' is represented by log(|cot(2α)|); combining LUTi with LUT₂ , and deleting the redundant columns of sin2α and cos2α to get LUT.

19. The method of Claim 13, wherein the values of sinα and cosα are included in the LUT directly, while the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α can be obtained from the LUT indirectly.

20. The method of Claim 13, wherein if the range AngleRg is (0, π 18), get reference differential value t' to which the differential value t= log (|B|) - log (|A-C|) approximates; if the range AngleRg is (π/8 > π IA), get reference differential value t' to which the differential value t= log (|A-C|) - log (|B|) approximates.

21. The method of Claim 13, wherein for the direction of the anisotropy of the footprint αe(π/4, π 12), the values of sin2α and cos2α can be found from the said LUT using the trigonometric function transform formulas.

22. The method of Claim 20, wherein a binary-search is used to get reference differential value t' to which the differential value t approximates in the LUT.

23. The method of Claim 22, wherein the reference differential value t' corresponds to an Index which is used to fetch the reference direction value of the anisotropy of the footprint α' in a determined range AngleRg and corresponding sin2α' and cos2α' from the LUT.

24. A computer program product, comprising:

computer program for executing the methods according to any one of Claims 1-23.

25. The computer program product of claim 24, wherein the computer program is based on hardware description language instructions.

26. A device for determining texture map parameters to define a footprint, comprising: an ellipse coefficients computation unit configured to compute ellipse coefficients based on a pair of specified partial derivative vectors (u_x V_x ) and (u_y v_y);

a differential value computation unit configured to compute a differential value t based on the ellipse coefficients; a comparing unit configured to determine the range AngleRg within which the direction value of the footprint α lies; a reference differential value obtaining unit configured to get reference differential value t' to which the differential value t approximates; and a LUT search unit configured to fetch the reference direction value of the footprint α' in the determined range AngleRg from a LUT corresponding to the reference differential value t'.

27. The device of Claim 26, wherein the ellipse coefficients are defined as A=u_x ² + u_y ² , B= 2(u_xv_x +u_yv_y) , and C=

28. The device of Claim 26, wherein the ellipse coefficients are defined as

A = Ux¹ + Vx¹, B = 2(UxUy + VxVy), C = Uy¹ + Vy¹ .

29. The device of Claims 27 or 28, wherein : the value t is the difference between log (|A-C|) and log(|B|); and the range AngleRg is determined by comparing A-C, B, and 0.

30. The device of Claim 29, further comprising: a parameter computation unit configured to compute the length of the major axis texture map parameter and the length of the minor axis anisotropic texture map parameter based on A , B , C, sin2α', and cos2α'.

31. The device of Claim 30, further comprising the LUT construction unit used to construct the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α e (0, π 12) with a specified interval.

32. The device of Claim 30, further comprising the LUT construction unit used to construct the LUT which includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint α<≡ (0, π/8) with a specified interval, wherein the reference differential values t' is represented by log(|tan(2α)|); and includes the values of every direction of the anisotropy of the footprint α and corresponding sin2α and cos2α for the direction of the anisotropy of the footprint αe[^/8, π /4) with the specified interval, wherein the reference differential values t' is represented by log(|cot(2α)|).

33. The device of Claim 30, wherein the parameter computation unit comprises: a length computation unit configured to compute (A+C) + [(A-C) cos (2α') + B sin (2α') ] and (A+C) - [(A-C) cos (2α') + Bsin (2α') ] to produce the first length and the second length; and an identification unit configured to identify a major axis texture map parameter as the longer of the first length and the second length and a minor axis texture map parameter as the shorter of the first length and the second length.

34. The device of Claim 30, wherein the parameter computation unit is configured to compute a level of detail texture mapping parameter.

35. The device of Claim 34, wherein the parameter computation unit is configured to compute a logratio using the first length and the second length.

36. A method of determining texture map parameters to define a footprint representing a projection of a pixel onto a texture map in a graphics processor, comprising:

computing ellipse coefficients A = Ux¹ + Vx² + Wx¹, B = 2(UxUy + VxVy + WxWy),C = Uy¹ + Vy¹ + Wy¹ based on a pair of specified partial derivative vectors (u_x ,v_x , W_x) and (u_y ,v_y , w_y);

computing differential value t based on the ellipse coefficients A, B, and C; determining a range AngleRg within which the direction value of the footprint α lies, and getting reference differential value t' to which the differential value t approximates; and

fetching the reference direction value of the footprint α' in the range AngleRg from a LUT corresponding to the reference differential value t'.