2. An Advanced Evenly-Spaced Streamline Placement Algorithm Zhanping Liu Robert J. Moorhead II Joe Groner Visualization Analysis and Imaging Lab High Performance Computing Collaboratory Mississippi State University

3. Outline Results Conclusions Introduction ADVESS Accelerating Placement Generation Enhancing Placement Quality Detecting Streamline Loops IEEE VISUALIZATION 2006

4. Introduction Texture-based (e.g., LIC) Evenly-Spaced Streamlines (ESS) There has been significant research on flow visualization Geometry-based (e.g., arrow plots) IEEE VISUALIZATION 2006

5. Introduction Evenly-Spaced Streamlines (ESS) a global but cluttered image or Streamlines remain one of the simplest and fastest techniques Without effective streamline placement, the result tends to be an incomplete coarse view IEEE VISUALIZATION 2006

6. Introduction Evenly-Spaced Streamlines (ESS) A global ESS placement provides an aesthetic and intuitive pattern to facilitate mental reconstruction of the flow IEEE VISUALIZATION 2006

7. Introduction Evenly-Spaced Streamlines (ESS) Four problems with ESS placement generation Non-uniformity Flow convergence and divergence cause three closely-related issues IEEE VISUALIZATION 2006

8. Introduction Evenly-Spaced Streamlines (ESS) Four problems with ESS placement generation Non-uniformity Flow convergence and divergence cause three closely-related issues Discontinuity IEEE VISUALIZATION 2006

9. Introduction Evenly-Spaced Streamlines (ESS) Cavity Discontinuity Non-uniformity Flow convergence and divergence cause three closely-related issues Four problems with ESS placement generation IEEE VISUALIZATION 2006

10. Introduction Evenly-Spaced Streamlines (ESS) Loop-cluttering Cavity Discontinuity Non-uniformity Flow convergence and divergence cause three closely-related issues Four problems with ESS placement generation IEEE VISUALIZATION 2006

11. Introduction Existing ESS Algorithms Image-guided methods Sample-controlled methods Turk-Banks [96] and Mao et al [98] Take a streamline placement as a binary-valued image Compare each intermediate placement against a reference gray-scale image to drive an iterative refinement process Jobard-Lefer [97], Verma et al [00], Mebarki et al[05], and et al Use inter-sample distance control to approximate inter-line distance control Distance checking is performed on each newly generated sample against other existing samples to determine if the distance is less than a threshold IEEE VISUALIZATION 2006

12. Introduction incoming sample to the controller locate the containing cell and the eight nearest neighbor cells any sample registered in the cells is at a distance less than the threshold to the incoming sample? pop queue head to get a seed use FSSI to get the next sample register samples save the sample to the line buffer outside field? critical point? N delete samples in the line buffer sample is a seed? the number of samples in the line buffer > M ? queue is empty? N streamline placement ENDs a simplistic FIFO queue of candidate seeds push to queue tail two orthog- onal neighbors for each sample BEGIN: push a seed to the queue N Y Y Y N Y Y Y N inter-sample distance controller seeding strategy A Sample-Controlled ESS Pipeline Jobard-Lefer pipeline FSSI: fixed step size integrator RK4-ASSEC + CHPI + fewer samples Improved for ADVESS RK4-ASSEC: fourth-order Runge-Kutta integrator with adaptive step size & error control CHPI : cubic Hermite polynomial interpolation double queues (primary & secondary) of candidate seeds candidates by seeds to weighted prim., others goto FIFO second. begin: push topology seeds to prim. queue seeding strategy any sample registered in the cells is at a distance less than the threshold to the incoming sample? adaptive threshold distance based on local flow characteristics a loop formed? YN IEEE VISUALIZATION 2006

13. ADVESS Accelerating Placement Generation RK4-ASSEC (Runge-Kutta 4th-order integrator with Adaptive Step Size and Error Control) is used for fast and accurate streamline advection The distance between two successive raw samples obtained from RK4-ASSEC may be very large Inter-sample distance control mandates the distance between any two successive samples along a streamline be less than the threshold distance to well approximate inter-line distance control ADVESS uses CHPI (Cubic Hermite Polynomial Interpolation) for fast and flexible curve sampling to create evenly-spaced samples along a streamline A large sampling size may be chosen to reduce the number of samples and accordingly the amount of distance checking IEEE VISUALIZATION 2006

14. ADVESS Accelerating Placement Generation PTD (Proximity Tolerance Degree) of an ESS placement the extent to which the inter-line distance may be actually less than the advetion threshold d_test (a percentage of the seeding threshold d_sep) S A1A1 B1B1 B2B2 A2A2 S d_test 1 2 L1L1 L2L2 L1L1 L2L2 longer line segment shorter line segment larger distance control error 1 larger PTD smaller distance control error 2 smaller PTD Suppress PTD by using a larger d_test to maintain uniformity IEEE VISUALIZATION 2006 Raw samples and CHPI samples are used for distance checking against each new sample while only raw samples are rendered S A B C D E F G H I J black dots: raw ( RK4-ASSEC) samples red dots: interpolated CHPI samples blue dot: newly generated sample d_test

15. ADVESS Enhancing Placement Quality Adaptive step sizing requires line-clipping against boundaries without line-clipping artifacts line-clipping without normal distance checking on the extended part remain IEEE VISUALIZATION 2006 streamlets shown in red encroach inward near the field boundaries

16. ADVESS boundary artifacts are removed with line-clipping + normal distance checking on the extended part Enhancing Placement Quality Adaptive step sizing requires line-clipping against boundaries there are still cavities and discontinuities IEEE VISUALIZATION 2006

17. ADVESS Enhancing Placement Quality Double-queue seeding strategy primary queue head secondary queue head Two queues: primary queue has priority over secondary queue in seeding Only when primary queue is temporarily empty is secondary queue used as backup to enable primary queue to be fed with new candidate seeds Primary queue is a sorting queue and is initialized with some topological seeds of a highest weight (through the use of simply topological templates) sort and insert Candidate seeds introduced by the seed of a streamline are stored in primary queue (to help spread the schematic topological seeding pattern) and sorted by the weight the streamline length (to favor long streamlines) append to tail Secondary queue is simply an FIFO queue Candidate seeds introduced by each regular sample (non-seed) of a streamline are appended to the tail of secondary queue IEEE VISUALIZATION 2006

18. ADVESS Enhancing Placement Quality Topological structures are well shown in the ESS placement Discontinuities are reduced long streamlines are favored Uniformity is not degraded Cavities are reduced to some extent, but some remain IEEE VISUALIZATION 2006

19. ADVESS Enhancing Placement Quality Adaptive distance control is used to reduce cavities by exploiting flow characteristics Inspired by the use of 2 distance parameters in sample-controlled algorithms d_sep for distance control over seeding d_test = d_sep a; a < 1.0 for relaxed distance control over advection to alleviate discontinuity fine-granularity / context-sensitive / flow-driven distance control Obtain the local flow variance magnitude about convergence & divergence Map the magnitude to [0, 1] & use it to locally adjust threshold distance(s) The adjusted threshold distance is larger for laminar areas and smaller for turbulent areas to reduce cavities without noticeable uniformity degradation IEEE VISUALIZATION 2006

20. ADVESS Detecting Streamline Loops rarely mentioned in ESS algorithms A naïve intra-line inter-sample distance checking does not work since the distance between any two successive samples of a streamline is less than the threshold distance and a simplistic intra-line inter-sample distance checking always terminates advection from the beginning A loop is a closed streamline or an open but tightly spiraling streamline A streamline is ill-looping when the distance between two successive cycles is less than the advection threshold distance d_test A closed streamline is always ill-looping A spiraling streamline is ill-looping when it spirals tightly enough and then it may be ill-looping as a whole or only in part The ill-looping part of a streamline (closed or spiraling) is what a loop detector should be really focused on and the ill-looping part does not necessarily begin with the seed ill-looping as a whole seed the ill-looping part of each streamline is shown in red ill-looping only in part seed d_test IEEE VISUALIZATION 2006

21. ADVESS Detecting Streamline Loops so far without a robust solution for ESS A strategy using seed-based inter-sample distance checking does not work regardless of the use of a seed-based curve length or accumulated angle as a threshold to begin such kind of distance checking Our principle is to allow the ill-looping part of a streamline to advect as long as within a one-cycle limit and this encourages a closed streamline to form the first cycle and a spiraling streamline to show the structure in more detail without cluttering the placement Our universal, effective, and robust strategy is to perform both distance checking and ill-looping angle checking on each existing sample against the current sample (NOT the seed) to see whether or not the ill-looping part approaches the one-cycle limit and is going to cause loop problems The use of dot-product for ill-looping angle representation, cell-based inter-sample distance checking for saving the approach-the-one-cycle- limit judgment, and sample-stamp checking for skipping unnecessary inter-sample distance checking makes our strategy a fast solution closed streamlines are shown as distracting broken ones and spiraling streamlines cause an ambiguity by tightly merging the negative part ( blue ) and the positive part ( green ) the approach-the-one-cycle-limit judgment distinguishes sample p n (which approaches the one-cycle limit relative to the current sample p 0 ) from sample p m (which is still far from the one-cycle limit relative to the current sample p 0 ) due to the use of dot-product for indirect but efficient ill-looping angle representation

22. Results Three Algorithms in Comparison Our ADVESS algorithm RK4-ASSEC + CHPI, streamline clipping, double-queuing, adaptive distance control, and our loop detector Jobard-Lefers algorithm Developed using C++ on WinTel with exactly the same code as that of ADVESS on vector interpolation, inter-sample distance controller, and data structures for storing streamlines Fixed step size RK4 integrator, FIFO neighborhood seeding strategy Mebarki et als algorithm (online executable program from Mebarki) Test platform WindowsXP / P4 / 1.70GHz / 512MB RAM Comparison through 2.0%, 1.5%, and 1.0% density ESS placements ESS placement quality regarding uniformity, continuity, & coverage using a 300 300 flow without centers or tight foci for ESS placement generation speed a loop-free comparison IEEE VISUALIZATION 2006

23. ESS placements generated using our ADVESS algorithm ESS placements generated using Jobard-Lefers algorithm

24. ESS placements generated using our ADVESS algorithm ESS placements generated using Mebarki et als algorithm

25. Results Three Algorithms in Comparison Jobard-Lefer algorithmour ADVESS algorithmMebarki et als algorithmplacement density (% width) 1.0% 1.882s 1.262s 0.241s 1.5% 1.382s 0.811s 0.140s 2.0% 1.142s 0.621s 0.080s Timings measured on Pentium IV (1.70GHz, 512MB RAM) Our ADVESS algorithm is an order-of-magnitude faster than Jobard & Lefers algorithm with better placement quality Our ADVESS algorithm is over 5 times faster than Mebarki et al.s algorithm with comparable placement quality (without considering that Mebarki et als algorithm is not robust in loop detection and hence streamline loops may affect placement quality when a flow field with centers or tightly spiraling foci is handled) When considering loop-related issues, our ADVESS is better in overall placement quality than Mebarki et als algorithm as we will demonstrate IEEE VISUALIZATION 2006

26. Results ADVESS adopts an effective, robust, and fast loop detector generated with our loop detector (time: 0.280 seconds) two 1% density ESS placements generated for a 400 400 flow field generated without loop detection (time: 0.671 seconds) without loop detection excessive samples are generated due to ill-looping streamlines more distance checking is needed for them more time consumed IEEE VISUALIZATION 2006

27. ESS placement generated without our loop detection (0.307 seconds) threshold distance = 4.82 in cell size flow field size = 525 241 ESS placement generated with our loop detector (0.253 seconds) IEEE VISUALIZATION 2006

28. Results our loop detector adds a negligible cost to ADVESS the same 1% density ESS placement produced using ADVESS with (0.262s) and without (0.224s) our loop detector for a 400 400 flow field without centers or tightly spiraling foci it takes ADVESS 0.038s to run the loop detector for this placement IEEE VISUALIZATION 2006

29. generated using ADVESS (threshold distance: 2.34 in cell size) Northeast Pacific Ocean (180 W ~ 78 W, 20 N ~ 62 N) Flow field size: 468 337 Hawaii islands IEEE VISUALIZATION 2006

30. Results generated using Mebarki et als algorithm (time: 1.684 seconds) two 1% density ESS placements produced for a 201 201 ROI of the Pacific Ocean generated using our ADVESS algorithm (time: 0.362 seconds) IEEE VISUALIZATION 2006

31. ESS placement (1% of height) generated using our ADVESS algorithm for a 661 481 ocean flow IEEE VISUALIZATION 2006

32. ESS placement (1% of height) generated using Mebarki et als algorithm for a 661 481 ocean flow IEEE VISUALIZATION 2006

33. Conclusions ADVESS is capable of interactive placement of evenly-spaced streamlines RK4-ASSEC allows rapid but accurate streamline advection, which is critical to the fast and robust loop detection strategy CHPI provides a fast and flexible curve-sampling scheme to generate evenly- spaced samples along a streamline for inter-sample distance control The use of a large sampling size for CHPI considerably reduces the amount of distance checking while maintaining acceptable uniformity A double-queue seeding strategy helps preserve important flow structures and favors long streamlines in an ESS placement Adaptive distance control exploits flow characteristics to reduce cavities and discontinuities by context-sensitively adjusting inter-line threshold distance An effective, robust, and fast loop detector is capable of handling complex flow fields without cluttering an ESS placement ADVESS is an order-of-magnitude faster than Jobard-Lefers algorithm with better placement quality ADVESS is over five times faster than Mebarki et als algorithm with comparable placement quality but with more robust loop detection IEEE VISUALIZATION 2006

34. Conclusions Future Work to extend ADVESS to view-dependent placement of evenly-spaced streamlines for 2D planar flows, 3D curved surface flows, and volume flows Acknowledgments DoD HPCVI Program NSF grant EPS-0132618 NGI URI Program Abdelkrim Mebarki for his online executable program Anonymous reviewers for their valuable suggestions Welcome to Our ADVESS Open to Your Advice Any Questions? Thank you!