HighQuality Unstructured Volume Rendering on the PC Platform

High-Quality Unstructured Volume Rendering on the PC Platform Stefan Guthe WSI/GRIS University of Tuebigen Stefan Röttger, Andreas Schieber If. I/VIS University of Stuttgart Hardware Workshop 2002

Overview Introduction • Motivation • Cell Projection High Resolution Ray Integral • Opacity Reconstruction • Chromaticity Reconstruction Hardware Accelerated Pre-Integration Results & Conclusion 2/32

Introduction

Motivation Tetrahedral Meshes • Common for numerical simulations • Adaptive resolution • Straight forward multiresolution algorithms General purpose hardware • Widely available • Fast polygonal rendering • Flexible fragment shading for recent generations • Fast development of future generations • Cheap compared to special purpose hardware 4/32

Cell Projection Projected Tetrahedra (PT) Algorithm • Shirley and Tuchman ’ 90 • Classify tetrahedra based on profile of projection • Split tetrahedra into 3 or 4 triangles 5/32

Cell Projection Projected Tetrahedra (PT) Algorithm • Render projected profiles • Chromaticity vector • Scalar optical density • Resulting ray integral 6/32

Ray Integral

Opacity Reconstruction Approximation of opacity • Corresponding portion of the ray integral • Original approximation • Calculate correct values for vertices • Interpolate linearly between vertices • Improvement by Stein et al. ’ 94 • Calculate average extinction coefficient • Use texture map for exponential lookup • Linear opacity or piecewise linear (HIAC ‘ 98) 8/32

Opacity Reconstruction Approximation of opacity • Corresponding portion of the ray integral • Further improvements • 2 D texture map for lookup of average extinction • 1 D dependent texture lookup • No restriction to linear opacity 9/32

Opacity Reconstruction Approximation of opacity (Ge. Force 4) • Texture setup unit coordinates 0 1 RGB A chrom. (RGA) 0, 0, l • Pixel shader ps. 1. 3 def texdp 3 lrp +mov c 0, 1, 1, 0, 0 t 0 // t 1, t 0 // r 0. rgb, c 0, t 0. a // r 0. a, t 1. a // load chromaticity and density dependent lookup extract chromaticity. . . and alpha for final color 10/32

Opacity Reconstruction Approximation of opacity (Radeon 8500) • Texture setup unit coordinates 0 1 RGB A chromaticity 0, 0, l • Pixel shader ps. 1. 4 texld texcrd mul phase texpass texld mov r 0, t 0 r 1, t 1 r 1, r 0. a, r 1. b // load chromaticity and density // pass l into register // multiply density and l r 0, r 0 r 1, r 1 r 0. a, r 1. a // transfer chromaticity // dependent lookup // correct alpha for final color 11/32

Chromaticity Reconstruction Approximation of chromaticity • Corresponding portion of the ray integral • Original approximation • Calculate correct values for vertices • Interpolate linearly between vertices • Improvement in HIAC ‘ 98 • Calculate values for slices through tetrahedra • Texture lookup instead of linear interpolation • Support of piecewise linear transfer functions 12/32

Chromaticity Reconstruction Approximation of chromaticity • Corresponding portion of the ray integral • Improvement by Roettger et al. ‘ 00 • 3 D texture for chromaticity and opacity • Slow update of transfer function • High memory requirements of 3 D textures • Accurate only for small tetrahedra due to limited resolution of pre-integration table 13/32

Chromaticity Reconstruction Approximation of chromaticity • Corresponding portion of the ray integral • Different approach • Higher order polynomials in l • Number of triangles equal to PT • Only 4 slices for cubic polynomials –Higher resolution table high image quality –Faster update of transfer function 14/32

Opacity Reconstruction Approximation of chromaticity (Ge. Force 4) • Texture setup (B and A swapped for unit 0) unit coordinates RGB A 0 1 - 2 - 3 0, 0, l - • Additionally store l in primary color alpha • Distribution of duplicate values via vertex shader 15/32

Chromaticity Reconstruction Approximation of chromaticity (Ge. Force 4) • Pixel shader ps. 1. 3 def tex texdp 3 lrp mad +mov c 0, 1, 1, 0, 0 t 1 t 2 t 3, t 0 r 0. rgb, c 0, t 0. a r 0. rgb, v 0. a, r 0, t 1 r 0. rgb, v 0. a, r 0, t 2 r 0. a, t 1. a // load chromaticity and density // dependent lookup // extract chromaticity // calculate polynomial. . . // and get alpha for final color 16/32

Opacity Reconstruction Approximation of chromaticity (Radeon 8500) • Texture setup unit coordinates RGB A 0 1 - 2 - 3 - 4 - 5 0, 0, l - • Additionally store l in primary color alpha 17/32

Chromaticity Reconstruction Approximation of chromaticity (Radeon 8500) • Pixel shader ps. 1. 4 texld texcrd mul phase texld texld mad mad +mov r 0, t 0 r 5, t 5 r 5, r 0. a, r 5. b // load chromaticity and density // pass l into register // multiply density and l r 1, t 1 r 2, t 2 r 3, t 3 r 4, t 4 r 5, r 5 r 0. rgb, v 0. a, r 1. a // load other coefficients r 0, // dependent lookup r 1 // calculate polynomial. . . r 2 r 3 r 4 // and get alpha for final color 18/32

Chromaticity Reconstruction Problems of this approach • Limited precision of pixel shader could be a problem normalize coefficients • Additional vertex shader needed • Optimal approximation requires a least square fit for chromaticity (infeasible) • Part of the three-dimensional pre-integration table needs to be computed • Interactive change of classification no longer possible with software-only calculation of approximation textures 19/32

HW Acceleration

HW Accelerated Pre-Int. Hardware accelerated pre-integration • Use blending capabilities of graphics card • Construct pre-integration table slice by slice (l constant) Problems • High error with few blending operations • Slow, due to large amount of frame buffer writes • High error with lots of blending operations • Accuracy of 8 bits too low • No problem with new floating point hardware 21/32

HW Accelerated Pre-Int. High accuracy pre-integration • Use high internal precision of pixel shader • Create pre-integration table using 12 -bit values • Perform multiple blending operations at once • 4 blending operations in one step speedup of approximately 2 • Store high precision values in two 8 -bit values • Loose some instructions to combining and splitting high precision values • No alpha blending ping-pong rendering • Separate passes for R, G and B 22/32

HW Accelerated Pre-Int. Comparison of software and hardware pre-integration • Speedup of about 700% • Relatively low error hardware software difference 8 23/32

HW Accelerated Pre-Int. HW accelerated pre-integration (Radeon 8500) • Pixel shader combine def mad c 0, 0. 0019608, 0, 0, 0 r 0, r 0. ggaa, c 0. r, r 0. rrbb // 1/256 // combine values • Use R and B for calculations • Multiply result by 8 during last blending operation faster split • Pixel shader split add_x 8 mov_d 8 r 0. ga, r 0_x 2. rrbb r 0. rb, r 0. rrbb // get low bits // get high bits 24/32

HW Accelerated Pre-Int. HW accelerated pre-integration (Radeon 8500) ps. 1. 4 def texld. . . texld mad mad mad phase mad mad_x 8 add_x 8 mov_d 8 c 0, r 1, . . . r 4, r 0, r 1, r 2, r 3, r 4, 0. 0019608, 0, 0, 0 t 1 t 4 r 0. ggaa, r 1. ggaa, r 2. ggaa, r 3. ggaa, r 4. ggaa, r 1. rb, r 2. rb, r 3. rb, r 4. rb, r 0. ga, r 0. rb, c 0. r, r 0, 1 -r 1. b, r 1, 1 -r 2. b, r 2, 1 -r 3. b, r 3, 1 -r 4. b, r 4_x 2. rrbb, r 4. rrbb // 1/256 // previous data // 4 samples r 0. rrbb r 1. rrbb r 2. rrbb r 3. rrbb r 4. rrbb // combine values r 1 r 2 r 3 r 4_x 2. rrbb // perform blending // get low bits // get high bits 25/32

Results

Results Prototype (12, 936 tetras) Buckyball (176, 856 tetras) 1280 960 at 89. 45 fps 1280 960 at 2. 46 fps 27/32

Results Blunt fin (187, 395 tetras) 1280 960 at 3. 18 fps 28/32

Results Bonsai (538, 937 tetras) Trumpet (1, 567, 755 tetras) 1280 960 at 1. 20 fps 1280 960 at 0. 48 fps 29/32

Conclusion Algorithm overview • Dependent texture for opacity • Polynomial approximation of chromaticity • High resolution pre-integration table • High quality rendering • 4 slices for cubic approximation • 6 slices for fifth order approximation • Fast update whenever transfer function changes • Number of triangles equal to original PT algorithm • Fast rendering 30/32

Conclusion Migration to new graphics hardware • HW pre-integration • Floating point accuracy improves • More blending steps at once even more performance gain • Image quality will be improved by floating point frame buffer precision • No dependent texture lookup due to exp-function in pixel shader 31/32

Questions? 32/32