Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Medical Visualization and Clinical ... by zSpace 727 views
- Particle based volume_rendering by Subhashis Hazarika 210 views
- Sparse PDF Volumes for Consistent M... by Subhashis Hazarika 322 views
- Pre-Integrated Volume-Rendering wit... by Frank Oellien 723 views
- 3D Visualization of DICOM datasets ... by kkpandya 6485 views
- Latest technology by cn2113 673 views

615 views

428 views

428 views

Published on

No Downloads

Total views

615

On SlideShare

0

From Embeds

0

Number of Embeds

4

Shares

0

Downloads

0

Comments

0

Likes

1

No embeds

No notes for slide

- 1. VOLUME RENDERING OF UNSTRUCTURED TETRAHEDRAL GRIDS
- 2. Flow • Introduction • Problem Formulation • Tetrahedral Interpolation • Implementation • Results • Demo • Endnotes 04-06-2014 Nitesh Bhatia | CPDM 2
- 3. Introduction: Volume Rendering • Volume rendering is a technique that can be used to visualize sampled 3D scalar data as a continuous medium or extract features. Most algorithms for direct volume rendering have assumed structured data in form of rectilinear grid. • In this project we worked on a method for rendering unstructured volume; volume represented by group of tetrahedrals. 04-06-2014 Nitesh Bhatia | CPDM 3
- 4. Problem Formulation • The idea is to convert unstructured input tetrahedral grid (UG) to output structured regular grid (SG) and render it using existing ray casting system. • The data represented in UG must be interpolated to produce SG. • The UG consists of tetrahedrals bounded by four vertices numbered 1,2,3,4, the coordinates of ith vertex being (xi, yi, zi) and associated data value is denoted fi. • The data values are assumed to be the values of an unknown locally smooth trivariate function interpolate discussed in next heading. 04-06-2014 Nitesh Bhatia | CPDM 4 1/3
- 5. Problem Formulation • Let P = (x,y,z) be the point at which the value of interpolation function is to be estimated. Two different interpolation schemes are followed here: • Scheme 1: Map SG to UG • For a given point P of SG and find the tetrahedral associated with P in UG • Estimate the function values for given cell based on interpolate. 04-06-2014 Nitesh Bhatia | CPDM 5 empty SG UG SG 2/3
- 6. Problem Formulation • Scheme 2: Map UG to SG • Take a tetrahedral from UG and find points Ps lying on SG • Estimate the function value at Ps based on interpolate. 04-06-2014 Nitesh Bhatia | CPDM 6 UG empty SG SG 3/3
- 7. Tetrahedral Interpolation: interpolate • Given a tetrahedron T with vertices v1, v2, v3, v4 and function value associated with these vertices be f1, f2, f3 and f4, the problem is to find interpolated function value f for any given point P. 04-06-2014 Nitesh Bhatia | CPDM 7 .P(f) v1(f1) v2(f2)v4(f4) v3(f3) 1/4
- 8. Tetrahedral Interpolation: interpolate Geometric Solution • Take ratio of perpendicular distance of P to a face with perpendicular distance of opposite vertex to that face. • Find these ratios with all four faces and name them l1, l2, l3 and l4. • If the point P is lying inside tetrahedral these ratios will come between 0 and 1. • Sum of these ratios will always be 1. • These l1,l2, l3 and l4 are known as barycentric coordinates of point P with respect to tetrahedral T. • f = l1*f1 + l2*f2 + l3*f3 + l4*f4 04-06-2014 8 2/4 Nitesh Bhatia | CPDM
- 9. Tetrahedral Interpolation: interpolate • Mathemetical Interpretation 04-06-2014 Nitesh Bhatia | CPDM 9 3/4
- 10. Tetrahedral Interpolation: interpolate 04-06-2014 Nitesh Bhatia | CPDM 10 4/4
- 11. Implementation In implementation we are following 3 step approach 1. Load the vertices and tetrahedron information from given .ts file into CPU memory 2. Based on two schemes presented, perform computations using OpenCL (or OpenMP) to form a regular grid 3. Display the grid by Ray Casting in OpenCL using CL-GL Interoperability. 04-06-2014 Nitesh Bhatia | CPDM 11
- 12. Implementation: Description Step1: • The data set given .ts file is form of list of vertices with 3D coordinates and associated function value and then a list of tetrahedrons with asociated 4 vertices. • We are first loading this information into memory. • While loading the vertices we are computing minimum and maximum values for (x,y,z) coordinates and storing it as minX, minY, minZ, maxX, maxY, maxZ. • We are then finding the difference between these minimum and maximum values and storing it as diffX, diffY, diffZ. • We are then computing diff equal to maximum of diffX, diffY and diffZ. • We are then finding dimensions of our bounding box with side equal to diff. 04-06-2014 Nitesh Bhatia | CPDM 12
- 13. Step 2: • Given • We are computing A-1 for each tetrahedron • We define a constant STEP_SIZE = 128 (or any other value) which gives dimension of our volume as 128*128*128. • We are setting the resolution (step size) of our volume as res = diff / STEP_SIZE 04-06-2014 Nitesh Bhatia | CPDM 13
- 14. Scheme 1: 04-06-2014 Nitesh Bhatia | CPDM 14 1. Finding point lying on SG 2. searching for associated T in UG and finding f value using interpolation
- 15. • This scheme is implemented in both OpenCL and OpenMP • In OpenMP implementation we are adding following two lines as compiler directive in starting of loop: • #paragma omp set_num_threads(8) • #paragma omp parallel for shared(i,j,k) • In OpenCL implementation we are setting our dimensions as 1D with • size_t global_size = {STEP_SIZE * STEP_SIZE * STEP_SIZE} • Here we are Parallelizing in terms of volume element 04-06-2014 Nitesh Bhatia | CPDM 15
- 16. Scheme2: 04-06-2014 Nitesh Bhatia | CPDM 16 1. Finding limits of points lying inside tetrahedral 2. For given limits finding f values of points associated with SG
- 17. • Scheme 2 is implemented in OpenCL. We are setting our dimensions as 1D with size_t global_size = tet_qty • Here we are Parallelizing in terms of tetrahedral quantity Step 3: • We are then giving this 1D grid of function values to existing ray tracer (provided by nVidia in their SDK) as input. 04-06-2014 Nitesh Bhatia | CPDM 17
- 18. Results • Hardware / Software for tests 04-06-2014 Nitesh Bhatia | CPDM 18 GPU Model: nVidia Quadro FX 580 Cores: 32 Core Clock: 450 MHz Memory: 512MB Memory Bandwidth: 25.6 GiB/s CPU Model: Intel Core i7 860 Cores / Threads: 4/8 Clock Speed: 2.8GHz (3.0GHz when running on full load) Memory: 8 GB Memory Bandwidth: 21GB/s OS / SDKs Microsoft Windows 7 Professional 64Bit Visual Studio 2010 32Bit Microsoft OpenMP nVidia CUDA SDK 3.2 nVidia OpenCL 1.1 Intel OpenCL 1.1 alpha Input UG Torus1.ts Torusf1.ts Torus8.ts Engine.ts
- 19. 04-06-2014 Nitesh Bhatia | CPDM 19 Scheme 1 Scheme 2 STEP_SIZE = 512 Time: 8.4 sec STEP_SIZE = 512 Time: 2.5 sec
- 20. 04-06-2014 Nitesh Bhatia | CPDM 20 Scheme 1 Scheme 2 STEP_SIZE = 512 Time: 2.5 sec STEP_SIZE = 512 Time: 3.3 sec
- 21. 04-06-2014 Nitesh Bhatia | CPDM 21
- 22. 04-06-2014 Nitesh Bhatia | CPDM 22
- 23. • Demo Video URL: https://www.youtube.com/watch?v=CaBuZ7 se7-o 04-06-2014 Nitesh Bhatia | CPDM 23
- 24. Impressions • Learning OpenCL was a challenging task but we it was interesting. • Debugging OpenCL is difficult task as stream output (“printf” function) cannot be called in openCL kernel. In Intel’s compiler is based on OpenCL 1.1 in which “printf” is supported. • Double precision computations are not supported on my card. • Graphic Driver Crash Problem 04-06-2014 Nitesh Bhatia | CPDM 24
- 25. “We now know a thousand ways not to build a light bulb” 04-06-2014 Nitesh Bhatia | CPDM 25 THANKS !

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment