An Effective Hardware Architecture for Bump Mapping Using Angular Operation

Transcription

1 Graphis Hardware (2003) M. Doggett W. Heidrih W. Mark. Shilling (Editors) n Effetive Hardware rhiteture for Bump Mapping Using ngular peration S. G. Lee W. C. Park W. J. Lee T. D. Han and S. B. Yang Department of Computer Siene Yonsei Universit Seoul Republi of Korea bstrat In this paper we propose an effetive bump mapping algorithm that utilies the referene spae with the polar oordinate sstem and also propose a new hardware arhiteture assoiated with the proposed bump mapping algorithm. The proposed arhiteture redues the omputations to transform the vetors from the objet spae into the referene spae b using a new vetor rotation method. It also redues the omputations for the illumination alulation b using the law of osine. Compared with the previous approahes the proposed arhiteture redues multipliation operations up to 78%. Categories and Subjet Desriptors (aording to CM CCS): I.3.7 [Computer Graphis]: ThreeDimensional Graphis and Realism. Introdution Bump mapping developed b Blinn an represent effetivel the bump parts of the objet surfae suh as a protuberane of the skin of a peanut in detail using geometr mapping without omple modeling The following three steps are required for eah piel to perform the onventional bump mapping In the first step the displaement values or height values are fethed from a 2D bump map. In the seond step both the partial differentiations and the rossproduts are alulated to perturb the normal vetor. In the last step the illumination is alulated with the perturbed normal vetor the light vetor L and the halfwa vetor H after the normaliation of these three vetors. To aomplish the above steps a large amount of perpiel omputations is required. The normal vetor perturbation an be preproessed b defining the surfaeindependent spae alled the referene spae Instead the transformations of the light and the halfwa vetors from the objet spae into the referene spae should be provided for eah piel (or for eah small polgon). For these transformations the definition of a 3 3 matri and a 3 3 matri multipliation are required for eah piel. The rest of this paper is organied as follows. The related work to bump mapping hardware arhiteture is desribed in Setion 2. In Setion 3 we eplain the proposed algorithm for the vetor rotation and the illumination alulation in de In Kim et al. 9 and Kugler the polar oordinate sstem The Eurographis ssoiation is used to represent vetors L and H for bump mapping. Compared with the Cartesian oordinate sstem the polar oordinate sstem is an effetive approah from the viewpoint of hardware requirements. Contrar to three omponents in the Cartesian oordinate sstem onl two angles are suffiient to represent a vetor. The normaliation of the vetors for the illumination alulation an also be eliminated. However the matri multipliation for the transformation or a large map for the normal vetor perturbation are still required. In this paper we propose a new transformation method for both the light vetor L and the halfwa vetor H represented b the polar oordinate sstem and present its hardware arhiteture. The proposed method transforms diretl the vetors L and H in the objet spae into the vetors L and H in the referene spae onl b vetor rotations respetivel. Thus the proposed method does not need an hardware foatri transformation but requires onl a few hardware logis for the vetor rotations. It also redues the illumination alulation hardware b appling the law of osine to the previous illumination alulation equations.

2 Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration tail. In Setion 4 we illustrate the proposed bump mapping hardware arhiteture and ompare its hardware ompleit with those of other approahes. Eperimental environments and results are disussed in Setion 5. Conlusions are given in Setion Bakground and related work In the normal vetor perturbation step of the onventional bump mapping as shown in () a perturbed normal vetor is alulated b deviating a normal vetor b the displaement value B stored in the bump map. B u P v B v P u () where B u and B v are the partial derivatives of the bump displaement value B with respet to the bumpmap parameters u and v respetivel. P u and P v are the partial derivatives of the surfae at point P ling in the tangent plane. Then the illumination of the perturbed normal vetor is alulated with L and H using the Phong illumination model as shown in (2). I I ak a I i k d L k s H n (2) where I a is the intensit of ambient light I i is the intensit of inident light and k a k d and k s are ambient diffuse and speular refletion oeffiients respetivel. Peer et al. 8 propose an effiient method to support bump mapping b adding minimal hardware into the Phong shading hardware. B introduing the loal tangent spae (the referene spae) defined b a normal vetor a tangent vetor T and a binormal vetor B the omputation of the perturbed normal is pushed into a preproessor. Ernst et al. 0 simplif the onstrution of the bump map b fiing the value k into where k is a onstant of the equation in Peer et al. 8 for the normal vetor perturbation. In Peer et al. 8 and Ernst et al. 0 a 3 3 matri transformation and a normaliation for the light and the halfwa vetors should be ompleted before the illumination alulation. The polar oordinates of a vetor P are written into ϕ P θ P where ϕ P is an angle between the ais and a vetor generated b projeting P onto the plane and θ P is an angle between P and the ais. The bump mapping methods using the polar oordinate sstem are disussed in Kim et al. 9 Kugler and Ikedo et al Kim et al. 9 gives onl a small redution to the hardware requirements for the illumination alulation b using (3) and (4) whih ompute the inner produts in (2) with the perturbed angles ϕ n θ n obtained from the bump map. n L l L osθ l os θ n sinθ l sinθ n os ϕ l ϕ n (3) n L h L osθ h os θ n sinθ h sinθ n os ϕ h ϕ n (4) Ikedo et al present a high performane Phong shading hardware supporting bump refletion refration and teture mapping in a single LSI hip. s mentioned in 69 Kugler it requires a large amount of logi foatri operations beause it has been implemented with the lassial straightforward method. Moreover it ma not produe the orret refletion angle to alulate the intensit of speular light espeiall in largesied polgons. Kugler integrates the arithmeti units and the referene tables into one dediated memor hip alled the intelligent memor (IMEM) to support teture bump and refletionmapping. In this arhiteture eah normal vetor is transformed from the Cartesian oordinates into the spherial oordinates. Then the transformed normal vetor is perturbed b using three rotations whih are eeuted b two additions and one lookup table (LUT) aess. fter the normal vetor perturbation the illumination is alulated b referring to the diffuse and speular light maps. IMEM redues the amount of omputations b using the preomputed LUTs and maps. However it requires a map of large sie over 3 MBtes. 3. The proposed bump mapping algorithm The proessing flow of the proposed bump mapping algorithm onsists of the Vetor Rotation Stage the Bump Vetor Feth Stage and the Illumination Calulation Stage. In the Vetor Rotation Stage vetors in the 3D objet spae are transformed into the 3D referene spae b the angular rotation operation. This operation generates the light and the halfwa vetors L and H in the referene spae b transforming the vetors L and H in the objet spae. The two angles of the transformed vetors an be alulated b utiliing the projetion onto the plane and the proportion onto the sphere. The detailed eplanation of this method and its hardware arhiteture will be given in Setion 3. and 4. respetivel. In the Bump Vetor Feth Stage the perturbed normal vetors s are fethed from the bump vetoap whih is onstruted in the referene (the tangent) spae and is omputed in the preproess stage b the alulation method in Peer 8 or b the filtering of the bump height map. vetor in the bump vetoap is represented as ϕ θ using the polar oordinate sstem. In the Illumination Calulation Stage after the inner produts L and H are omputed the illumination is alulated b referring to the diffuse and speular tables with the values of the inner produts. The algorithm for the illumination alulation and its hardware arhiteture are disussed in detail in Setion 3.2 and 4.2 respetivel. 3.. The vetor rotation 3... The proposed vetor rotation method In the proposed method the vetors L and H are transformed diretl into the tangent spae b the rotation operations where the polar oordinate (ϕ θ ) of the normal vetor The Eurographis ssoiation 2003.

3 Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration ( =' ) Figure : The first rotation: It rotates ϕ around the ais. ref Figure 3: The geometri information of vetors that are required to find the omponents of the transformed vetor re f. vetor with the ais diretion in the world spae and is in parallel with the normal vetor re f in the referene spae. Similarl is also moved into re f ϕ re f θ re f whih is idential to in the referene spae The information for finding the angles of the vetor after the rotation operation Figure 2: The seond rotation: It rotates θ around the ais. at a point on the objet s surfae are used as the rotation fators (angles) of the vetor. Figures and 2 show these rotation operations; a vetor is transformed into a vetor re f. The polar oordinate (ϕ re f θ re f ) an be found b the projetion onto the plane and the proportion of the angular variation on a sphere respetivel. ϕ θ is an arbitrar vetor on the world spae whih orresponds to a light vetor L ϕ L θ L and a halfwa vetor H ϕ H θ H in ase of performing bump mapping. Figure shows the first rotation that rotates and b ϕ around the ais. Through this rotation and are onverted into and respetivel. This makes it possible to rotate auratel around the ais b moving into on the plane. et as shown in Figure 2 the seond rotation is performed b rotating the transferred vetors and b θ around the ais. s a result is idential to the unit The Eurographis ssoiation Figure 3 shows the geometri information of the vetors that are required to find the polar oordinate (ϕ θ ) of the transformed vetor. More detailed desriptions to the newl defined vetors in Figure 3 are given below. : It is a unit vetor that begins with the origin and ends with a point interseting both the plane and a irle whih passes the end point of and whih is in parallel with the plane. Let an angle between and the ais be θ whih is required to find an angle θ of. : It is a vetor that is generated b projeting onto the plane. The and oordinates of the end point of are sinθ os ϕ ϕ and sinθ sin ϕ ϕ respetivel. re f : It is a unit vetor that begins with the origin and ends with a point interseting both the plane and a irle whih passes the end point of and whih is in parallel with the plane. n angle between re f and the ais is (θ θ ) and the and oordinates of the end point of re f are sin θ θ and os θ θ respetivel. re f : It is a vetor that is generated b projeting onto the plane. The and oordinates of the end point of re f are sin θ θ and sinθ sin ϕ ϕ respetivel.

4 !!!! Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration sin sin( ) mn C m C n C 0 C m 0 mn ( = ) ' mn 0 sin( ) Figure 4: The alulation of ϕ : This method alulates an angle ϕ between a projeted vetor and the ais b projeting onto the plane. Figure 5: The geometri relationship of the vetors on a sphere. B appling the law of osine to the oordinate of we an find θ whih is epressed as (5). θ Sin sin" 2 Let and Y be θ #%$ ϕ & ϕ ' 2 ( θ #$ ϕ & ϕ ' Y 2 Then θ an be rewritten as θ Sin The alulation of ϕ # sin" θ &%$ ϕ & ϕ ' 2 (*) θ &$ ϕ & ϕ ' 2. sin # siny 2 ). To find an angle ϕ of the projetion of onto the plane is required as shown in Figure 4. In the figure ϕ an be alulated with ϕ Tan sinθ sin$ ϕ & ϕ ' sin$ θ & θ ' ). Let Z θ & θ. Then ϕ an be rewritten as in (9) b appling the law of osine to sinθ sin$ ϕ & ϕ '. ϕ Tan osy & os 2sinZ ) The derivation of an angular equation using the geometri relationship of the vetors on a sphere Compared with the method for finding ϕ it is relativel omple to find the angle θ between and the ais. We will eplain how to alulate the angle θ from this setion through Setion First speifing the geometri relationship of the vetors on a sphere is required to find θ. In this setion the relationship of the vetors on a sphere is (5) (6) (7) (8) (9) 7 speified and the alulation method for finding θ mn of an arbitrar vetor mn is desribed. Figure 5 shows the geometri relationship among a vetor mn the plane and the plane. Detailed desriptions for the irles and the vetors defined in Figure 5 are given below. C m: It is a irle that is in parallel with the plane and passes a point (ϕ mn θ mn ). Let the radius of this irle be. C m : It is a irle that is generated b projeting the irle C m onto the plane. C n: It is a irle that is in parallel with the plane and passes a point (ϕ mn θ mn ). mn : It is a vetor that begins with the origin and ends with a point (0 θ mn ) at whih the irle C m intersets the plane. 0 : It is a vetor that begins with the origin and ends with a point (ϕ 0 θ 0 ) at whih the irle C n intersets the plane. Let the oordinate of the point (ϕ 0 θ 0 ) be 0. mn : It is a vetor that is generated b projeting mn onto the plane. The end point (ϕ mn θ mn ) of mn is on the irle C m. In Figure 5 we assume two arbitrar vetors that begin with the origin and end with points at whih the plane in parallel with the plane intersets the irles C m and C m. Then for C m the variation range of an angle between mn and the ais is from 0 to 90 θ mn. Similarl for C m the variation range is from 0 to 90. When these vetors move on C m and C m under the above assumption the ratio of the angular variation to the variation range of eah vetor for C m is equal to that of C m. Therefore the following epression holds. θ mn & θ mn θ mn (0) 90 & θ mn 90 0 The Eurographis ssoiation 2003.

5 Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration C0 C m 0 θ (= θ re f ) of is (θ (8). θ θ ) thus (7) is rewritten into θ θ θ θ 76 θ prop (8) mn θ an be rewritten as follows. θ Z 90 Z θ prop (9) 0 mn 0 0 θ prop that an be alulated b the method presented in Setion 3..4 is represented as (20). θ prop 90 Cos3 sinθ sin ϕ ϕ (20) os θ θ Figure 6: The projetion of mn and its related omponents onto the plane. Hene θ mn an be written as θ mn θ mn θ mn θ mn () We will define the etent to the angular variation θ prop as in (2) whose alulation method will be desribed in detail in Setion Finall θ mn an be rewritten as (3). θ mn θ prop (2) 90 θ mn θ mn θ prop 90 θ mn (3) The alulation of θ prop depending on the loation of vetors θ prop an be alulated b using an angle θ mn of mn as shown in Figure 5. Figure 6 shows the projetion of mn and its related omponents onto the plane. s shown in Figure 6 the oordinate of a point at whih the etension line of mn intersets a unit irle C 0 in the plane is 02. The osine of an angle between mn and the ais is alulated as in (4). 0 os 90 θ mn (4) θ mn 90 Cos3 0 (5) s a result θ prop is alulated b (6) where both 0 and are alread alulated and θ prop ranges from 0 to. θ prop 90 Cos3 0 (6) The alulation of θ The angle θ of the transformed vetor is alulated b using the methods derived from Setions 3..4 and From (3) θ an be alulated as follows. θ The Eurographis ssoiation θ 90 θ θprop (7) 72 Through the use of the law of osine along with Y and Z (20) an be rewritten into (2). Finall θ an be determined b using (9) and (2). θ prop 90 Cos3 osy os (2) 2osZ 3.2. The illumination alulation In the Illumination Calulation Stage the intensit of a piel is omputed with the light and the halfwa vetors L = (ϕ L θ L ) and H = (ϕ H θ H ) and the perturbed normal vetor = (ϕ θ ). In order to alulate the inner produts of the vetors in (2) the appropriate vetors represented b the polar oordinates should be transformed into the vetors in the Cartesian oordinates. The inner produts of the transformed vetors L and H are alulated as follows. L osθ L osθ sinθ L sinθ os ϕ L ϕ (22) H osθ H osθ sinθ H sinθ os ϕ H ϕ (23) (22) and (23) are idential to (3) and (4) in Kim et al. 9 respetivel. However appling the law of osine to these equations makes it possible to redue the amount of omputations for the inner produts. (24) and (25) are the final equations of the inner produts in whih the numbers of multipliations and osines required in the inner produts of the vetors represented b the polar oordinates are redued from 6 and 0 to 2 and 6 respetivel. L 2 4 os θ L θ os θ L θ 6 2 4os θ L θ 8 os θ L θ 6 os ϕ L ϕ (24) H 2 4 os θ H θ os θ H θ 6 2 4os θ H θ os θ H θ 6 os ϕ H ϕ (25) The intensities of the diffuse and the speular lights are omputed b multipling these inner produts b the light parameters. Then the final olor of a bumpmapped piel is determined b adding these intensities together.

6 Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration Right Y Right sin & os sin & os sin sin os os Right Right SI 90 Z sin & os os sin T Tprop ' ' Figure 7: The hardware arhiteture for the proposed vetor rotation method. 4. The hardware arhiteture for the proposed bump mapping algorithm L L H H 4.. The vetor rotation unit The hardware arhiteture for the proposed vetor rotation method is shown in Figure 7. It requires si tables three multipliers and eight adderssubtrators to implement (9) and (9). For the sine and osine alulations we use the sin & os LUTs to redue the omputations for perpiel operations. The reiproals of the sine and osine are alulated b ombining the sine and osine alulation step and the reiproal alulation step not b two separate steps. For arbitrar values of k s θ prop s are preomputed b (26) and are stored in the proportion table T prop. Cos3 θ prop k (26) 90 ote that k s in the above equation are alulated b (27) whih is obtained from (2). Therefore θ prop s are fethed from T prop with the indies of k s. osy os k (27) 2osZ 4.2. The illumination alulation unit Figure 8 shows the whole bump mapping hardware arhiteture inluding both the vetor rotation unit and the illumination alulation unit. The illumination alulation unit onsists of two parts that alulate the intensities of the diffuse and the speular light. The intensities of lights are obtained from the light tables referred to b the values of the inner produts. The proposed illumination alulation unit an be implemented with si osine tables one diffuse table one speular table two multipliers and thirteen adderssubtrators. Compared with Kim s arhiteture 9 requiring twelve tables si multipliers and five adderssubtrators the proposed arhiteture is more effiient in terms of hardware ompleit. More detailed omparisons of the proposed arhiteture with other arhitetures are made in Setion 4.3. The light table method for the illumination alulation 73 u B v B The Bump Vetor Map ' ' The Illumination Calulation Unit The Vetor Rotation Unit Diffuse Table The Vetor Rotation Unit os os os os os os Right L' L' H H ' ' Right Right I Bumpmapped Figure 8: The proposed bump mapping hardware. used in Kim et al. 9 finds the intensities of a piel b referring to the diffuse and the speular light tables whih are preomputed. In this method the table entries are indeed b salar values i.e. inner produt values. Therefore the sie of the table is : bits whih is quite small. However in the light map method the map s entries are indeed b vetor values with two or three oordinates. Thus the sie of the map is at least bits whih is muh larger sie than that of the light table method The omparison of other eisting approahes Table shows the omparison of the proposed arhiteture with other arhitetures based on the hardware ompleit. For the omparison we split the proess of bump mapping into two parts the illumination environment setup and the illumination alulation. The frontend is the part that prepares the environment for the illumination alulation and inludes the transformation into the referene spae the normal vetor perturbation and the normaliation. First we will observe the hardware ompleit of the il ; Right Diffuse Table The Eurographis ssoiation 2003.

7 Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration rhiteture Peer 8 Kugler Kim 9 Ernst 0 urs Coordinate Sstem Cartesian Polar Polar Cartesian Polar 27 Multipliers Map 3 Multipliers 27 Multipliers 6 Multipliers Illumination 9 Division Units 5 Multipliers 6 LUTs 9 Division Units 2 LUTs Environment 3 SQRTs 3 LUTs 8 dders 3 SQRTs 6 dders Setup 8 dders 2 dders 8 dders Proessing Steps Illumination Calulation ot vailable 8 Multipliers 6 Multipliers 7 Multipliers 2 Multipliers 2 Maps 2 LUTs LUT 8 LUTs 5 LUTs 5 dders 5 dders dders 4 dders Table : The omparison of the arhitetures based on the hardware ompleit. lumination environment setup. Twent multipliations and eight additions are required to perform the normal vetor perturbation b the Blinn s method. To simplif this omputation Kugler uses LUTs and a map. His arhiteture is implemented b five multipliers two adders three LUTs and one map; but the sie of the map reahes 32 Kbtes. For Peer 8 and Ernst 0 that use the referene spae the transformation of L and H into the referene spae whih requires two 3 3 matri operations is implemented b eighteen multipliers and twelve adders and the normaliation of the transformed vetors is organied into nine multipliers three SQRTs nine division units and si adders. In Kim et al. 9 the transformation omputations in the polar oordinate sstem is performed b thirt one multipliers si LUTs and eighteen adders. However the abovementioned methods have to reonstrut a matri for the transformation of eah piel or polgon hene these methods require larger amount of omputations than those shown in Table. The proposed arhiteture redues the hardware requirements for the transformation into the referene spae to si multipliers twelve LUTs and siteen adders b using onl rotations and table referenes without an matri operations. In the Illumination Calulation Stage Kugler s approah alulates the illumination through the address generation of the light map the aess to the light map and the olor blending without the inner produt operation. His method uses eight multipliers four adders and five LUTs to generate the address of the light map and eploits two MB light maps to alulate the intensit of the light. Ernst uses a straightforward method for the Phong illumination model whih requires seven multipliers five adders and one power table. Kim s arhiteture performs the illumination alulation b omputing the inner produt of the vetors with angles and b referring to the diffusespeular light table with the omputed innerprodut value. Their illumination alulation unit is omposed of si multipliers twelve LUTs and five adders. We use the same method as the one used in Kim et al. but two multipliers eight LUTs and eleven adders are onl needed for our arhiteture. The Eurographis ssoiation In omparisons with other approahes using the Cartesian oordinate sstem the amount of hardware for the illumination alulation is inreased a little but the amount of hardware for the illumination environment setup is dereased relativel a lot. bserve that our hardware arhiteture redues the hardware requirement onsiderabl ompared with other polaroordinate approahes. 5. Eperimental results The algorithm and hardware arhiteture proposed in this paper have been simulated in C. For the simulation we modified Mesa to implement the onventional bump mapping method and the proposed bump mapping method. To investigate the qualit differenes between ours and the onventional approah we performed teture and bumpmapping using various objets with various teture and bumpmaps. Figure 9 shows the results generated b mapping a wooden wall teture and bumpmap onto a plane. Figures 9(a) and 9(b) are made b the onventional method using the objet spae with the Cartesian oordinate sstem and b the proposed method using the referene spae with the polar oordinate sstem respetivel. When Comparing these images there is little differene in the qualit between these two images to the etent of not being differentiated b the naked ees. Figures 0(a) and 0(b) show the results of mapping a brik wall teture and bumpmap onto a ube b the onventional method and b the proposed method respetivel. There is also little differene in the image qualit as in the ase of a plane in Figure 9. Figure has been generated b mapping a map of the world onto a sphere. The images of this figure are obtained b mapping a teture and bumpmap with resolution onto a sphere objet with resolution. In Figure the overall images don t look vivid beause these mapping methods wear the maps onverted from resolution into resolution on the surfae of the objet. However we an hardl differentiate the image qualit between these two images generated b both methods.

8 Lee et al. n Effetive Hardware rhiteture for Bump Mapping Using ngular peration Figure 9: Images generated b mapping a wooden wall onto a plane. (a) the onventional method (b) the proposed method Figure 0: Images generated b mapping a brik wall onto a ube. (a) the onventional method (b) the proposed method Figure : Images generated b mapping a map of the world onto a sphere. (a) the onventional method (b) the proposed method 6. Conlusions In this paper we have proposed a bump mapping method with the effetive vetor rotation and illumination alulation algorithm. The proposed arhiteture redues a large amount of omputations and hardwares required for the transformation and the illumination alulation in bump mapping. Furthermore it ould also generate nearl the same qualit of images as the onventional method. knowledgements This work is supported b the RL Fund from the Ministr of Siene & Tehnolog of Korea. 75 Referenes. J. F. Blinn Simulation of Wrinkled Surfaes CM Computer Graphis (Pro. of SIGGRPH 78) pp Watt 3D Computer Graphis 3rd Ed. ddison Wesle T. Moller and E. Haines RealTime Rendering K Peters Ltd VIDI Corp. =produts. 5. T. MRenolds D. Blthe B. Grantham and S. elson dvaned Graphis Programming Tehniques Using pengl In Course otes of SIGGRPH M. Kilgard Pratial and Robust Bumpmapping Tehnique for Toda s GPUs VIDI Corporation G. Miller M. Halstead and M. Clifton nthefl Teture Computation for RealTime Surfae Shading IEEE Computer Graphis and ppliations 8(2) pp M. Peer J. ire and B. Cabral Effiient Bump Mapping Hardware Computer Graphis 3(4) pp J. S. Kim J. H. Lee and K. H. Park fast and effiient bump mapping algorithm b angular perturbation Computers and Graphis 25(5) pp I. Ernst H. Russeler H. Shul and. Wittig Gouraud Bump Mapping In Pro. of EurographisSIGGRPH Workshop on Graphis Hardware pp Kugler IMEM: an intelligent memor for bumpand refletionmapping In Pro. of EurographisSIGGRPH Workshop on Graphis Hardware pp T. Ikedo and J. Ma n dvaned Graphis Chip with Bumpmapped Phong Shading In Pro. of IEEE Computer Graphis International 97 pp T. Ikedo and J. Ma The Truga 00: Salable Rendering Proessor IEEE Computer Graphis and ppliations 8(2) pp T. Ikedo and E. buhi Realtime Rough Surfae Renderer In Pro. of IEEE Computer Graphis International 200 pp The Mesa 3D Graphis Librar org. The Eurographis ssoiation 2003.