An Advanced Evenly-Spaced Streamline Placement Algorithm

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

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

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

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

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

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

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

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

11. Existing ESS Algorithms • Image-guided 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 • Sample-controlled methods • 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 ADVESS Introduction

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

13. 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 samplesobtained 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 ADVESS ADVESS

14. PTD(Proximity Tolerance Degree) of an ESS placement the extent to which the inter-line distance may be actually less than the advetion thresholdd_test (a percentage of the seeding threshold d_sep) • Suppress PTD by using a larger d_test to maintain uniformity • Raw samples and CHPI samples are used for distance checking against each new sample while only raw samples are rendered longer line segment shorter line segment A2 C B1 B2 A1 A B D S E H F L1 L2 L1 L2 I J d_test G d_test S black dots: raw(RK4-ASSEC) samples red dots: interpolated CHPIsamples blue dot: newly generated sample 1 2 S larger distance control error 1 larger PTD smaller distance control error 2 smaller PTD IEEE VISUALIZATION 2006 ADVESS ADVESS • Accelerating Placement Generation

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

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

17. 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) • Candidate seeds introduced by the seed of a streamline are stored in primary queue (to helpspread the schematic topological seeding pattern) and sorted by the weight — the streamline length (to favor long streamlines) • Secondary queue is simply an FIFO queue • Candidate seeds introduced by each regularsample (non-seed) of a streamline are appended to the tail of secondary queue sort and insert primary queue head append to tail secondary queue head IEEE VISUALIZATION 2006 ADVESS ADVESS • Enhancing Placement Quality • Double-queue seeding strategy

18. 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 ADVESS ADVESS • Enhancing Placement Quality

19. 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 IEEE VISUALIZATION 2006 ADVESS ADVESS • Enhancing Placement Quality • 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

20. ill-looping only in part ill-looping as a whole d_test seed seed the ill-looping part of each streamline is shown in red IEEE VISUALIZATION 2006 ADVESS 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

21. the approach-the-one-cycle-limit judgment distinguishes sample pn (which approaches the one-cycle limit relative to the current sample p0) from sample pm (which is still far from the one-cycle limit relative to the current sample p0) due to the use of dot-product for indirect but efficient ill-looping angle representation 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) IEEE VISUALIZATION 2006 ADVESS ADVESS • Detecting Streamline Loops — so farwithout 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

22. Three Algorithms in Comparison • Our ADVESS algorithm RK4-ASSEC + CHPI, streamline clipping, double-queuing,adaptive distance control, and our loop detector • Jobard-Lefer’s 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 al’s 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 IEEE VISUALIZATION 2006 ADVESS Results a loop-free comparison

23. ESS placements generated using our ADVESS algorithm ESS placements generated using Jobard-Lefer’s algorithm

24. ESS placements generated using our ADVESS algorithm ESS placements generated using Mebarki et al’s algorithm

25. Timings measured on Pentium IV (1.70GHz, 512MB RAM) placement density (% width) Jobard-Lefer algorithm Mebarki et al’s algorithm our ADVESS algorithm 1.0% 1.882s 1.262s0.241s 1.5% 1.382s 0.811s0.140s 2.0% 1.142s 0.621s0.080s • Our ADVESS algorithm is an order-of-magnitude faster than Jobard & Lefer’s 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 al’s 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) IEEE VISUALIZATION 2006 ADVESS Results Three Algorithms in Comparison Three Algorithms in Comparison When considering loop-related issues, our ADVESS is better in overall placement quality than Mebarki et al’s algorithm as we will demonstrate

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

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 ADVESS

28. Results our loop detector adds a negligible cost to ADVESS the same 1% density ESS placement produced using ADVESSwith (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 ADVESS

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 IEEE VISUALIZATION 2006 ADVESS Hawaii islands

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

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

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

33. IEEE VISUALIZATION 2006 ADVESS 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-Lefer’s algorithm with better placement quality • ADVESS is over five times faster than Mebarki et al’s algorithm with comparable placement quality but with more robust loop detection

34. 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 IEEE VISUALIZATION 2006 ADVESS Conclusions ADVESS Welcome to Our ADVESS Open to Your Advice Any Questions? Thank you!