30
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

An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

  • Upload
    others

  • View
    4

  • Download
    0

Embed Size (px)

Citation preview

Page 1: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

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

Page 2: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 2 -

Contents

IntroductionBackground and related work

Bump mapping algorithmVector rotationIllumination calculation

Hardware architectureExperimental resultsConclusions

Page 3: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 3 -

Contents

IntroductionBackground and related work

Bump mapping algorithmVector rotationIllumination calculation

Hardware architectureExperimental resultsConclusions

Page 4: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 4 -

Background: bump mapping

Represent the bumpy parts of the object surface in detail using geometry mapping without complex modelingThree stepsFetch the height values from a 2D bump mapPerturb the normal vector NCalculate 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.

Page 5: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 5 -

Background: reference space

The normal vector perturbation can be preprocessed by defining the surface-independent 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.

Page 6: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 6 -

Background: polar coordinates

Representation of a vector P

P = (ϕP, θP) ϕP is an angle between the x-axis

and a vector Q θP 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.

Page 7: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 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 pre-

computed LUTs and mapsHowever, a map of large size over 3 Mbytes is required

Page 8: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 8 -

Previous work related with PCS

Hardware architecture supporting the bump-mapped illumination by using the Phong illumination hardware [Kim et al.]

Give a small reduction to the hardware requirements for the illumination calculation

Page 9: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 9 -

Overview of this paper

We propose a new transformation method and present its hardware architecture.Direct transformation of the vectors into the

reference spaceNo 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”

Page 10: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 10 -

Contents

IntroductionBackground and related work

Bump mapping algorithmVector rotationIllumination calculation

Hardware architectureExperimental resultsConclusions

Page 11: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 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.

Page 12: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 12 -

Vector rotation

Page 13: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 13 -

Geometric information

Geometric information required to find the polar coordinate (ϕΑ’, θΑ’) of the transformed vector A’

Page 14: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 14 -

Calculation of ϕA’

Page 15: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 15 -

Geometric relationship for θA’

The geometric relationship of the vectors on a sphere

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, Cm and .

When these vectors move on Cm and Cmyz under the above assumption, the ratio of the angular variation to the variation range of each vector for Cm is equal to that of .

x

y

z

1

1

1

0A

mnA

0C

mC

O 0y

mr

xzmnAnC

yzmnA

yzmC

mr

Page 16: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 16 -

Calculation of θprop

Page 17: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 17 -

Page 18: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 18 -

Illumination calculation

In order to calculate the inner products of the vectors, the vectors should be transformed into the vectors in the Cartesian coordinates.

Phong illumination model

The inner products of the transformed vectors are calculated as follows.

Page 19: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 19 -

Illumination calculationHowever, 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

The number of cosines

6 2

10 6

Page 20: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 20 -

Contents

IntroductionBackground and related work

Bump mapping algorithmVector rotationIllumination calculation

Hardware architectureExperimental resultsConclusions

Page 21: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 21 -

Proposed bump mapping hardwareThe 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.

Light table method

The VectorRotation Unit

The VectorRotation Unit

+

The BumpVector Map

DiffuseTable

-- + --

cos cos cos cos cos cos

+ -

ShiftRight 1

ShiftRight 1

X

+

+

SpecularTable

+ -

ShiftRight 1

ShiftRight 1

X

+

N

NL L H H

mappedBumpIuvLL H H

Page 22: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 22 -

Vector rotation unit

-

+

-

Shift

Rig

ht 1

Shift

Rig

ht 1

sin

&

cos

sin

&

cos

+

-

cos

cos

sin

sin

Shift

Rig

ht 1

Shift

Rig

ht 1

SIN

-1 -

1/s

in &

1/c

os X

X

TAN

-1

X

1/c

os

1/s

in

X

Y

Z

-90

+

This unit can be implemented with 6 tables, 3 multipliers, and 8 adders.

, where

For arbitrary values of yk’s, θprop’s are precomputed by the following equation.

θprop’s are fetched from Tprop with the indices of yk’s.

Page 23: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 23 -

Hardware complexity

Architecture Peercy Kugler Kim Ernst Ours

Coordinate System Cartesian Polar Polar Cartesian Polar

ProcessingSteps

IlluminationEnvironment

Setup

27 Multipliers9 Division

Units3 SQRTs

18 Adders

1 Map5 Multipliers

3 LUTs2 Adders

31 Multipliers

6 LUTs18 Adders

27 Multipliers9 Division

Units3 SQRTs

18 Adders

6 Multipliers12 LUTs

16 Adders

Illuminationcalculation

N/A

8 Multipliers2 Maps5 LUTs

4 Adders

6 Multipliers12 LUTs5 Adders

7 Multipliers1 LUT

5 Adders

2 Multipliers8 LUTs

11 Adders

Page 24: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 24 -

Contents

IntroductionBackground and related work

Bump mapping algorithmVector rotationIllumination calculation

Hardware architectureExperimental resultsConclusions

Page 25: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 25 -

Experimental results

Wooden wall : mapping onto a plane

Brick wall : mapping onto a cube Map of the world : mapping onto a sphere

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.

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

Page 26: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 26 -

Experimental results

Wooden wall : mapping onto a plane

Brick wall : mapping onto a cube Map of the world : mapping onto a sphere

There is also little difference in the image quality as in the case of the previous simulation.

(a) The conventional method(b) The proposed method

Page 27: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 27 -

Experimental results

Wooden wall : mapping onto a plane

Brick wall : mapping onto a cube Map of the world : mapping onto a sphere

The images don’t look vivid because these mapping methods wear the maps converted from 512×256 resolution into 512×512 resolution on the surface of the object.

However, we can hardly differentiate the image quality between these two images.

(a) The conventional method(b) The proposed method

Page 28: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 28 -

Contents

IntroductionBackground and related work

Bump mapping algorithmVector rotationIllumination calculation

Hardware architectureExperimental resultsConclusions

Page 29: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 29 -

Conclusions

Bump mapping method with the effective vector rotation and illumination calculation algorithm.Reduce a large amount of computations

and hardwaresGenerate nearly the same quality of

images as the conventional method

Page 30: An Effective Hardware Architecture for Bump Mapping Using ... · An Effective Hardware Architecture for Bump Mapping Using Angular Operation Seung-Gi Lee†, Woo-Chan Park, Won-Jong

Graphics Hardware 2003Media System Lab., Yonsei Univ.

- 30 -

Thank you!!!

We appreciate NRL project supported from the Ministry of Science & Technology of Korea.NRL Project homepagehttp://msl.yonsei.ac.kr/3d/

E-mail [email protected]