An Effective Hardware Architecture for Bump Mapping Using Angular Operation

Transcription

1 An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee, Woo-Chan Park, Won-Jong Lee, Tack-Don Han, and Sung-Bong Yang Media System Lab. (National Research Lab.) Dept. of Computer Science Yonsei University

2 Contents Introduction Background and related work Bump mapping algorithm Vector rotation Illumination calculation Hardware architecture Experimental results Conclusions

3 Contents Introduction Background and related work Bump mapping algorithm Vector rotation Illumination calculation Hardware architecture Experimental results Conclusions

4 Background: bump mapping Represent the bumpy parts of the object surface in detail using geometry mapping without complex modeling Three steps Fetch the height values from a 2D bump map Perturb the normal vector N Calculate the illumination with three vectors, the perturbed vector N, the light vector L, and the halfway vector H A large amount of per pixel computations is required.

5 Background: reference space The normal vector perturbation can be preprocessed by defining the surfaceindependent space (reference space). [Peercy et al., Ernst et al.] Instead, transformations from the object space into the reference space should be provided for each pixel (or for each small polygon). Definition of a 3 3 matrix & a 3 3 matrix multiplication The normalization of the vectors for the illumination calculation is also required.

6 Background: polar coordinates Representation of a vector P P = (ϕ P, θ P ) ϕ P is an angle between the x-axis and a vector Q θ P is an angle between P and the z-axis An effective approach from the viewpoint of hardware requirements [Kim et al., Ikedo et al., Kugler] Only two angles No normalization of vectors However, the matrix multiplication for the transformation or a large map for the normal vector perturbation are still required.

7 Previous work related with PCS Support bump, reflection, refraction, and texture mapping in a single LSI chip [Ikedo et al.] Classical straightforward method require a large amount of logic for matrix operations May produce the incorrect reflection angle to calculate the intensity of specular light IMEM: integrate the arithmetic units and the reference tables into one dedicated memory chip [Kugler] Support the simple normal vector perturbation method Reduce the amount of computations by using the precomputed LUTs and maps However, a map of large size over 3 Mbytes is required

8 Previous work related with PCS Hardware architecture supporting the bumpmapped illumination by using the Phong illumination hardware [Kim et al.] Give a small reduction to the hardware requirements for the illumination calculation

9 Overview of this paper We propose a new transformation method and present its hardware architecture. Direct transformation of the vectors into the reference space No hardware for matrix transformation, but only a few hardware logics for the vector rotations Also, we present an effective illumination calculation hardware. Use of the law of cosine

10 Contents Introduction Background and related work Bump mapping algorithm Vector rotation Illumination calculation Hardware architecture Experimental results Conclusions

11 Processing flow Vector rotation stage 3D object space 3D reference space Use of the angular operation Use of the projection onto the plane and the proportion onto the sphere Bump vector fetch stage The perturbed normal vectors are fetched from the bump vector map. Illumination calculation stage The inner products are computed. The illumination is calculated by referring to the diffuse and specular tables.

12 Vector rotation

13 Geometric information Geometric information required to find the polar coordinate (ϕ Α, θ Α ) of the transformed vector A

14 Calculation of ϕ A

15 Geometric relationship for θ A The geometric relationship of the vectors on a sphere A mnxz 1 r m C m z A mn C n C 0 C myz O y0 A 0 A mnyz r m 1 We assume two arbitrary vectors that begin with the origin and end with points at which the plane in parallel with the xz-plane intersects the circles, C m and. When these vectors move on C m and C myz under the above assumption, the ratio of the angular variation to the variation range of each vector for C m is equal to that of. y x 1

16 Calculation of θ prop

17 - 17 -

18 Illumination calculation Phong illumination model In order to calculate the inner products of the vectors, the vectors should be transformed into the vectors in the Cartesian coordinates. The inner products of the transformed vectors are calculated as follows.

19 Illumination calculation However, applying the law of cosine to these equations makes it possible to reduce the amount of computations for the inner products. The number of multiplications 6 2 The number of cosines 10 6

20 Contents Introduction Background and related work Bump mapping algorithm Vector rotation Illumination calculation Hardware architecture Experimental results Conclusions

21 Proposed bump mapping hardware The Bump Vector Map N N The Vector Rotation Unit + The Vector Rotation Unit cos cos cos cos cos cos + - L L H H L L H H + - The illumination calculation unit consists of two parts that calculate the intensities of the diffuse and the specular light. The intensities of lights are obtained from the light tables referred to by the values of the inner products. This unit can be implemented with 6 cosine tables, 1 diffuse table, 1 specular table, 2 multipliers, and 13 adders. Shift Right 1 Shift Right 1 X Shift Right 1 Shift Right 1 X Light table method + + Diffuse Table Specular Table + I Bump mapped

22 Vector rotation unit Shift Right 1 X sin & cos sin + Shift Right 1 SIN -1 - Z 1/sin & 1/cos 1/sin X TAN Shift Right 1 Y sin & cos sin cos - Shift Right /cos X X + cos This unit can be implemented with 6 tables, 3 multipliers, and 8 adders. For arbitrary values of y k s, θ prop s are precomputed by the following equation., where θ prop s are fetched from T prop with the indices of y k s.

23 Hardware complexity Architecture Peercy Kugler Kim Ernst Ours Coordinate System Cartesian Polar Polar Cartesian Polar Processing Steps Illumination Environment Setup 27 Multipliers 9 Division Units 3 SQRTs 18 Adders 1 Map 5 Multipliers 3 LUTs 2 Adders 31 Multipliers 6 LUTs 18 Adders 27 Multipliers 9 Division Units 3 SQRTs 18 Adders 6 Multipliers 12 LUTs 16 Adders Illumination calculation N/A 8 Multipliers 2 Maps 5 LUTs 4 Adders 6 Multipliers 12 LUTs 5 Adders 7 Multipliers 1 LUT 5 Adders 2 Multipliers 8 LUTs 11 Adders

24 Contents Introduction Background and related work Bump mapping algorithm Vector rotation Illumination calculation Hardware architecture Experimental results Conclusions

25 Experimental results We modified Mesa 3.0 to implement the conventional method and the proposed method. To differentiate the image qualities, we have performed texture- and bump-mapping using various objects with various maps. Wooden wall : mapping onto a plane In case of wooden wall, there is little difference in the quality between these two images, to the extent of not being differentiated by the naked eyes. (a) The conventional method (b) The proposed method Brick wall : mapping onto a cube Map of the world : mapping onto a sphere

26 Experimental results There is also little difference in the image quality as in the case of the previous simulation. Wooden wall : mapping onto a plane Brick wall : mapping onto a cube (a) The conventional method (b) The proposed method Map of the world : mapping onto a sphere

27 Experimental results The images don t look vivid because these mapping methods wear the maps converted from resolution into resolution on the surface of the object. Wooden wall : mapping onto a plane However, we can hardly differentiate the image quality between these two images. (a) The conventional method (b) The proposed method Brick wall : mapping onto a cube Map of the world : mapping onto a sphere

28 Contents Introduction Background and related work Bump mapping algorithm Vector rotation Illumination calculation Hardware architecture Experimental results Conclusions

29 Conclusions Bump mapping method with the effective vector rotation and illumination calculation algorithm. Reduce a large amount of computations and hardwares Generate nearly the same quality of images as the conventional method

30 Thank you!!! We appreciate NRL project supported from the Ministry of Science & Technology of Korea. NRL Project homepage address sklee@kurene.yonsei.ac.kr