High-Quality Unstructured Volume Rendering on the PC Platform

Transcription

1 High-Quaity Unstructured Voume Rendering on the PC Patorm Stean Guthe, Wogang Strasser WSI/GRIS University o Tuebingen Stean Röttger, Andreas Schieber, Thomas Ert II/VIS University o Stuttgart Hardware Workshop 22

2 Overview Introduction Motivation Ce Projection High Resoution Ray Integra Opacity Reconstruction Chromaticity Reconstruction Hardware Acceerated Pre-Integration Resuts & Concusion 2/32

3 Introduction

4 Motivation Tetrahedra Meshes Common or numerica simuations Adaptive resoution Straight orward mutiresoution agorithms Genera purpose hardware Widey avaiabe Fast poygona rendering Fexibe ragment shading or recent generations Fast deveopment o uture generations Cheap compared to specia purpose hardware 4/32

5 Ce Projection Projected Tetrahedra (PT) Agorithm Shirey and Tuchman 9 Cassiy tetrahedra based on proie o projection Spit tetrahedra into 3 or 4 trianges Cass 21b 1a 5/32

6 Ce Projection Projected Tetrahedra (PT) Agorithm Render projected proies Chromaticity vector κ =κ ( ( x, y, z) ) Scaar optica density ρ = ρ ( ( x, y, z) ) Resuting ray integra C α S ( x) = S + ( S S ) ( S, S, ) ( S, S, ) b b = = e t ρ ( S ( u) ) du 1 e x κ SS b ( S ( t) ) ρ( S ( t) ) ρ b ( S ( t )) dt dt 6/32

7 Ray Integra

8 Opacity Reconstruction Approximation o opacity Corresponding portion o the ray integra S = e α 1 (, S, ) b ( S ( t )) ρ dt Origina approximation Cacuate correct vaues or vertices Interpoate ineary between vertices Improvement by Stein et a. 94 Cacuate average extinction coeicient Use texture map or exponentia ookup α ρ ( ρ) = 1 e Linear opacity or piecewise inear (HIAC 98) ρ 8/32

9 Opacity Reconstruction Approximation o opacity Corresponding portion o the ray integra S = e α 1 (, S, ) b ( S ( t )) ρ dt Further improvements 2D texture map or ookup o average extinction 1D dependent texture ookup ρ ( ) ( S, S ) ρ S ( t) α b 1 = ρ ( ρ) = 1 e No restriction to inear opacity dt 9/32

10 Opacity Reconstruction Approximation o opacity (GeForce 4) Texture setup unit coordinates S, S b RGB chrom. (RGA) 1 A ( ( t) ) ρ S dt 1,, 1 e ρ Pixe shader ps.1.3 de c, 1, 1,, tex t // oad chromaticity and density texdp3 t1, t // dependent ookup rp r.rgb, c, t, t.a // extract chromaticity... +mov r.a, t1.a // and apha or ina coor 1/32

11 Opacity Reconstruction Approximation o opacity (Radeon 85) Texture setup unit coordinates S, S b RGB chromaticity 1 A ( ( t) ) ρ S dt 1,, 1 e ρ Pixe shader ps.1.4 texd r, t // oad chromaticity and density texcrd r1, t1 // pass into register mu r1, r.a, r1.b // mutipy density and phase texpass r, r // transer chromaticity texd r1, r1 // dependent ookup mov r.a, r1.a // correct apha or ina coor 11/32

12 Chromaticity Reconstruction Approximation o chromaticity Corresponding portion o the ray integra C ρ ( S ( u) ) du, = e κ ρ ( S S, ) b Origina approximation t ( S ( t) ) ( S ( t) ) Cacuate correct vaues or vertices Interpoate ineary between vertices Improvement in HIAC 98 Cacuate vaues or sices through tetrahedra Texture ookup instead o inear interpoation Support o piecewise inear transer unctions dt 12/32

13 Chromaticity Reconstruction Approximation o chromaticity Corresponding portion o the ray integra C ρ ( S ( u) ) du, = e κ ρ ( S S, ) b t ( S ( t) ) ( S ( t) ) Improvement by Roettger et a. 3D texture or chromaticity and opacity Sow update o transer unction High memory requirements o 3D textures Accurate ony or sma tetrahedra due to imited resoution o pre-integration tabe dt 13/32

14 Chromaticity Reconstruction Approximation o chromaticity Corresponding portion o the ray integra C ρ ( S ( u) ) du, = e κ ρ ( S S, ) b Dierent approach t ( S ( t) ) ( S ( t) ) Higher order poynomias in Number o trianges equa to PT Ony 4 sices or cubic poynomias C Higher resoution tabe high image quaity Faster update o transer unction, b 1 e ρ ( S S, ) ( S ( t )) dt n i= i C i dt ( S, S ) b 14/32

15 Opacity Reconstruction Approximation o chromaticity (GeForce 4) Texture setup (B and A swapped or unit ) unit coordinates S, S b S, C S, S b - S b S, S b,, RGB ( S ) 2 S b ( ) 1 ( ) C, C S, S b - 1 A ( ( t) ) ρ S - 1 e ρ dt Additionay store in primary coor apha Distribution o dupicate vaues via vertex shader 15/32

16 Chromaticity Reconstruction Approximation o chromaticity (GeForce 4) Pixe shader ps.1.3 de c, 1, 1,, tex t // oad chromaticity and density tex t1 tex t2 texdp3 t3, t // dependent ookup rp r.rgb, c, t, t.a // extract chromaticity mad r.rgb, v.a, r, t1 // cacuate poynomia... mad r.rgb, v.a, r, t2 +mov r.a, t1.a // and get apha or ina coor 16/32

17 Opacity Reconstruction Approximation o chromaticity (Radeon 85) Texture setup unit coordinates S, S b S, S b S, S b S, S b S, S b,, RGB ( S ) 4 S b ( ) 3 ( ) 2 ( ) 1 ( ) C, C S, S b C S, S b C S, S b C S, S b Additionay store in primary coor apha - 1 A ( ( t) ) ρ S e ρ dt 17/32

18 Chromaticity Reconstruction Approximation o chromaticity (Radeon 85) Pixe shader ps.1.4 texd r, t // oad chromaticity and density texcrd r5, t5 // pass into register mu r5, r.a, r5.b // mutipy density and phase texd r1, t1 // oad other coeicients texd r2, t2 texd r3, t3 texd r4, t4 texd r5, r5 // dependent ookup mad r.rgb, v.a, r, r1 // cacuate poynomia... mad r.rgb, v.a, r, r2 mad r.rgb, v.a, r, r3 mad r.rgb, v.a, r, r4 +mov r.a, r1.a // and get apha or ina coor 18/32

19 Chromaticity Reconstruction Probems o this approach Limited precision o textures coud be a probem normaize coeicients Additiona vertex shader needed Optima approximation requires a east square it or chromaticity (ineasibe) Part o the three-dimensiona pre-integration tabe needs to be computed Interactive change o cassiication no onger possibe with sotware-ony cacuation o approximation textures 19/32

20 HW Acceeration

21 HW Acceerated Pre-Int. Hardware acceerated pre-integration Use bending capabiities o graphics card Construct pre-integration tabe sice by sice ( constant) Probems High error with ew bending operations High error with ots o bending operations Sow, due to arge amount o rame buer writes Accuracy o 8 bits too ow No probem with new oating point hardware 21/32

22 HW Acceerated Pre-Int. High accuracy pre-integration Use high interna precision o pixe shader Create pre-integration tabe using 12-bit vaues Perorm mutipe bending operations at once 4 bending operations in one step speedup o approximatey 2 Store high precision vaues in two 8-bit vaues Loose some instructions to combining and spitting high precision vaues No apha bending ping-pong rendering Separate passes or R,G and B 22/32

23 HW Acceerated Pre-Int. Comparison o sotware and hardware pre-integration Speedup o about 7% Reativey ow error hardware sotware dierence 8 23/32

24 HW Acceerated Pre-Int. HW acceerated pre-integration (Radeon 85) Pixe shader combine de c,.1968,,, // 1/256 mad r, r.ggaa, c.r, r.rrbb // combine vaues Use R and B or cacuations Mutipy resut by 8 during ast bending operation aster spit Pixe shader spit add_x8 r.ga, r_x2.rrbb, r_x2.rrbb // get ow bits mov_d8 r.rb, r.rrbb // get high bits 24/32

25 HW Acceerated Pre-Int. HW acceerated pre-integration (Radeon 85) ps.1.4 de c,.1968,,, // 1/256 texd r, t // previous data texd r1, t1 // 4 sampes texd r4, t4 mad r, r.ggaa, c.r, r.rrbb // combine vaues mad r1, r1.ggaa, c.r, r1.rrbb mad r2, r2.ggaa, c.r, r2.rrbb mad r3, r3.ggaa, c.r, r3.rrbb mad r4, r4.ggaa, c.r, r4.rrbb phase mad r1.rb, r, 1-r1.b, r1 // perorm bending mad r2.rb, r1, 1-r2.b, r2 mad r3.rb, r2, 1-r3.b, r3 mad_x8 r4.rb, r3, 1-r4.b, r4 add_x8 r.ga, r4_x2.rrbb, r4_x2.rrbb // get ow bits mov_d8 r.rb, r4.rrbb // get high bits 25/32

26 Resuts

27 Resuts Prototype (12,936 tetras) Buckyba (176,856 tetras) at ps at 2.46 ps 27/32

28 Resuts Bunt in (187,395 tetras) at 3.18 ps 28/32

29 Resuts Bonsai (538,937 tetras) Trumpet (1,567,755 tetras) at 1.2 ps at.48 ps 29/32

30 Video 3/32

31 Concusion Agorithm overview Dependent texture or opacity Poynomia approximation o chromaticity High resoution pre-integration tabe High quaity rendering 3 sices or quadratic approximation 5 sices or ourth order approximation Fast update whenever transer unction changes Number o trianges equa to origina PT agorithm Fast rendering 31/32

32 Concusion Migration to new graphics hardware HW pre-integration Foating point improves accuracy More bending steps at once even more perormance gain Image quaity wi be improved by oating point rame buer precision No dependent texture ookup due to exp-unction in pixe shader 32/32

33 Questions? 33/32