EUROGRAPHICS 2012 / P. Cignoni, T. Ertl Volume 31 (2012), Number 2 (Guest Editors)

Rasterized Hierarchies

Jan Novák and Carsten Dachsbacher

Computer Graphics Group / Karlsruhe Institute of Technology

Supplementary Material

In this supplementary material we provide the complete evaluation of the performance and quality of our Rasterized Bounding Volume Hierarchy (RBVH). Figure1 shows seven models represented with different levels of approximation: from the finest (Q0) to the coarsest (Q4) (columns 2 - 6), and the reference rendering (column 1), which was obtained by the triangle based BVH from [AL09]. All results were measured on an NVIDIA GTX 470. Figure2 shows the quality and performance for secondary rays. Note that higher error due to the higher approximation is clearly visible in the reconstruction with primary rays (Figure1), but it is hardly noticeable when tracing for secondary rays (Figure2).

References

[AL09]A ILA T., LAINE S.: Understanding the efficiency of ray traversal on GPUs. In Proc. of High Performance Graphics (2009), pp. 145–149.1,2,3

c 2012 The Author(s) Forum c 2012 The Eurographics Association and Blackwell Publish- ing Ltd. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. Jan Novák & Carsten Dachsbacher / Rasterized Bounding Volume Hierarchies

ρs = 2M ρs =1M ρs = 512 k ρs = 128 k ρs = 32 k Reference Q0 ( α = 0.85) Q1 ( α = 0.80) Q2 ( α = 0.75 ) Q3 ( α = 0.70 ) Q4 ( α = 0.65) 137.2 111.6 139.8 169.4 229.4 287.2 Dragon

144.6 147.5 183.9 226.2 307.2 386.4 Happy Buddha

123.2 121.2 148.8 177.6 232.2 282.8 Children Beast

120.4 131.9 163.1 195.4 256.0 298.3 85.9 158.5 190.2 216.1 263.7 304.4 Asian Dragon

122.9 197.4 250.5 302.7 375.4 454.6 Thai Statue

ρs = 2M ρs =1M ρs = 512 k ρs = 128 k ρs = 32 k Reference Q0 ( ϕ = 45°) Q1 ( ϕ = 50°) Q2 ( ϕ = 55° ) Q3 ( ϕ = 60° ) Q4 ( ϕ = 65° ) Hand

178.7 145.3 176.6 209.9 266.0 300.0

Figure 1: Quality and performance of individual RBVH configurations for tracing primary rays. All scenes, except for the Hand, have been constructed using the less restrictive projected surface area. ρs is the pixel-to-scene sampling density, from which we compute the pixel-to-area by simply dividing ρs by the area of the scene. α is the ratio of projected surface area to the total area, and ϕ is the opening angle of the cone of normals. The sampling density and the refinement criterion is shown in brackets next to the level of quality. The left most column consists of references ray traced using the BVH from [AL09]. Numbers in the corners report ray tracing performance in million rays per second.

c 2012 The Author(s) c 2012 The Eurographics Association and Blackwell Publishing Ltd. Jan Novák & Carsten Dachsbacher / Rasterized Bounding Volume Hierarchies

ρs = 2M ρs =1M ρs = 512 k ρs = 128 k ρs = 32 k Reference Q0 ( α = 0.85) Q1 ( α = 0.80) Q2 ( α = 0.75 ) Q3 ( α = 0.70 ) Q4 ( α = 0.65) 38.2 20.7 21.7 27.6 38.7 53.3 Dragon

37.2 21.7 24.9 30.5 41.4 54.6 Happy Buddha

36.1 21.2 23.6 28.1 39.1 51.0 Children Beast

37.8 20.7 23.3 27.8 37.9 47.4 36.7 23.0 25.6 30.1 40.1 51.3 Asian Dragon

32.9 30.7 35.5 41.9 51.7 59.9 Thai Statue

ρs = 2M ρs =1M ρs = 512 k ρs = 128 k ρs = 32 k Reference Q0 ( ϕ = 45°) Q1 ( ϕ = 50°) Q2 ( ϕ = 55° ) Q3 ( ϕ = 60° ) Q4 ( ϕ = 65° ) Hand

55.9 32.5 37.1 44.3 56.6 69.1

Figure 2: Quality and performance of individual RBVH configurations for tracing secondary (diffuse) rays. All scenes, except for the Hand, have been constructed using the less restrictive projected surface area. ρs is the pixel-to-scene sampling density, from which we compute the pixel-to-area by simply dividing ρs by the area of the scene. α is the ratio of projected surface area to the total area, and ϕ is the opening angle of the cone of normals. The sampling density and the refinement criterion is shown in brackets next to the level of quality. The left most column contains references ray traced using the BVH from [AL09]. Numbers in the corners report ray tracing performance in million rays per second. c 2012 The Author(s) c 2012 The Eurographics Association and Blackwell Publishing Ltd.