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Unformatted text preview: UMass Lowell Computer Science 91.504 Advanced Algorithms Computational Geometry
Prof. Karen Daniels
Spring, 2010 Spring Project Project Deliverables
Deliverable D li bl Due Date D D t Grade G d %
10% 6% 19% Proposal & Lead Class Discussion 4/15 on Related Paper Status Report 4/29 Final Project Report & Class Presentation* 5/13 Presentation* * in OS 311 35% of course grade Project Guidelines: Proposal
Objective: Objective: State the goal of the project
State topic/research question Provide motivation: why do you find this topic interesting? Scope it to be doable in approximately one month Plan: Plan: List the tasks you need to accomplish Resources: What d Resources: Wh t do you need? R d?
Specialized equipment, language, OS? Specialized software/libraries? Additional research papers, books? More background in some area? Assessment Checklist: Characterize your project (see next 2 Checklist:
slides) Guidelines: Proposal (continued)
Assessment Checklist: Checklist:
Characterize your project's theoretical aspects:
Clarity Creativity Impact Algorithmic Paradigm Design Difficulty Analysis Technique Design Algorithm D i Al ith Design Scope Data Structure Design Algorithm d/ D S Al i h and/or Data Structure Analysis A l i correctness Organization running time and/or space Correctness Observations/Conjectures Guidelines: Proposal (continued)
Assessment Checklist: Checklist:
Clarity Characterize your project's implementation aspects: Difficulty
Reuse of existing Code/Libraries New Code Experimental Design Test Suites Degenerate/boundary cases g y Numerical robustness
Scope Creativity Impact Organization Correctness Guidelines: Class Discussion
20 minutes per student Briefly state your project's topic/research question Present (with slides) some interesting aspect of what you've learned so far from background/related work investigation Prepare several questions or observations to use as discussion points Lead a class discussion Provide handouts: copies of relevant paper from the literature
Send to me prior to class (preferably several days in advance) and I will have copies made Guidelines: Final Report
Abstract Introduction Theoretical Results Algorithm Implementation Results R lt Summary & Conclusion Future Work References
WellWell written final submissions with research content may be eligible for publishing as UMass Lowell CS technical reports. With some additional work (beyond class) some projects could be polished into CCCG conference submissions Guidelines: Final Report (continued)
Abstract: Abstract: Concise overview (at most 1 page) Introduction: Introduction:
Motivation: Why did you choose this project? State Topic / research question Background people need in order to understand project Related Work: Context with respect to literature
Conference, journal papers, web sites Summary of R lt S f Results Overview of paper's organization Guidelines: Final Report (continued)
Theoretical Results:
Clear, concise statements of definitions, lemmas, theorems and proofs Notation guidelines Algorithm: Algorithm: g
HighHighlevel algorithm description (& example) Algorithmic paradigm Data structures Pseudocode Analysis:
Correctness Solutions generated by algorithm are correct account for degenerate/boundary/special cases If a correct solution exists algorithm finds it exists, Control structures (loops, recursions,...) terminate correctly Asymptotic Running Time and Space Usage Guidelines: Final Report (continued)
Experimental Design & Implementation: Implementation:
Enough of the right kind of information to allow other researchers to duplicate your work
Resources & environment:
What language did you code in? Wh l d i ? What existing code did you use? (software libraries, etc.) What equipment did you use? (machine (& processor speed), OS, compiler) Assumptions A ti Parameter values Treatment of special issues, such as numerical robustness How Ho did you decide what kinds of meas rements would be meaningful? o hat measurements o ld meaningf l? Randomness: statistical significance Test cases
Representative examples Controlled tests to establish correctness Boundary/extreme cases Benchmarks, if available Guidelines: Final Report (continued)
Results: Results:
Experimental analysis
Randomness: statistical analysis Test cases
Tables Figures Graphs and Charts Comparison with benchmarks Meaningful measurements:
CPU time? Combinatorial size of output? Effect of decisions on issues, such as numerical robustness Drawing appropriate conclusions
Subjective? Objective? Were the results what you expected? Guidelines: Final Report (continued)
Summary: Summary: Summarize what you did Conclusion: Conclusion: Summarize results & impact Future Work: Work: What would you do if you had more time? References: References: Bibliography Papers, b k web sites that you used P books, b i h d Consistent format All work not your own must be cited! Others' exact words must be quoted! Guidelines: Final Presentation
20 minute class presentation Explain to the class what you did. did Structure it any way you like. Some ideas:
slides (electronic or transparency) demos handouts Project Topics P T Sample Prior Project Topics
Multiple robotic arm reachability implementation Coreset algorithm implementation for approximate clustering Geometric modeling implementation: Marching Cubes 2D polygonal covering implementation: Constrained triangulation for improved subdivision g p Recursive algorithm for 2contact group generation 2Orthotopes in 2D and higher dimensions Algorithms for approximate 3D convex hull construction Parallel coordinates for highdimensional visualization highThrackle reduction theoretical results Splines: convex hull of planar splines Creating skeletons for complex Chinese characters using stable medial C i k l f l Chi h i bl di l axis method New "glow clustering" heuristic inspired by physics of light and g p galaxies images of spiral g RealRealtime map labelling for mobile applications Motion planning through a set of static obstacles Implementation of a convex polygon intersection algorithm Project Topics (some possibilities)
Extend a Part I assignment (or a deBerg et al. exercise) al. Work on a problem from an "open problems" list p p p
Open Problem Project (O'Rourke, Demaine, Mitchell)
http://maven.smith.edu/~orourke/TOPP/ Many conference, journal papers pose open problems
Symposium on Computational Geometry Computational Geometry: Theory and Applications p y y pp Journal of Experimental Algorithmics Algorithm Engineering and Experiments Some conferences h ld open problem sessions S f hold bl i
Canadian Conference on Computational Geometry Project Topics (some possibilities)
Investigate a topic not covered in class g p
"Parallel" Computational Geometry (or multiple threads)
Reference: Parallel Computational Geometry by Akl, Lyons, 1993 Parallel 3D meshing Randomized C R d i d Computational Geometry algorithms i lG l ih
Reference: Computational Geometry: An Introduction Through Randomized Algorithms by Mulmuley, 1994 Dynamic Computational Geometry y p y
Reference: Kinetic Data Structures: A StateoftheArt Report by Guibas, Proc. Stateoftherd Workshop on Algorithmic Foundations of Robotics, 1998 3 Specialized Computational Geometry Application Areas:
Nanomanufacturing: Lattice packings Video Games: Graphics CGAL library: Add a new feature or experiment with a complex existing feature. Covering: 2D BSpline Covering
[CORS/INFORMS2004, UMass Lowell Student Research Symposium 2004, Computers Graphics Forum, 2006] Supported under NSF/DARPA CARGO p g pp program Out T1 I S In E T2 With graduate student C. Neacsu Covering: Box Covering
[12th WSEAS Int. Conf. on Computers, 2008] Int Conf Computers
Supported under NSF/DARPA CARGO p g pp program Goal: Goal: Translate boxes to cover another box Orthotope ( ) covering in 2D, 3D, ... p (box) g , , 2D views of 3D covering Partial cover (red part uncovered) Full cover With Masters student B. England Geometric Modeling: Mesh Generation for Finite Element Modeling [Research Note for 17th Int.
Meshing Roundtable, 2008; also presented at 2009 Fall CG Workshop] Needed for signal integrity in printed circuit board interconnect routing 2D constrained Delaunay triangulation is extruded into 3D to form triangular prism mesh Courtesy of Cadence Design Systems Doctoral student S. Ye Computational Geometry: Thrackle Extensibility [CCCG 2006]
Thrackle:
Drawing of a simple graph on the plane:
each edge drawn as a smooth arc with distinct endpoints, endevery two edges have exactly one common point, endpoints of each edge are two vertices; no edge crosses itself. Conway's thrackle conjecture:
Number of edges for n vertices is at most n.
With graduate student W. Li and Math Prof. Rybnikov Sample Future Packing and Covering Topics
Packing/Layout:
3D translational lattice packings for groups of shapes 3D containment using extensions to CGAL 3D constrained layout/packing of rectilinear objects Covering:
Explore "phase transitions" for 2D translational covering Rotational 2D covering Union formulation:
Target shape does not intersect complement of union of covering shapes Combinatorial union equivalence for pairwise Minkowski "difference" Regions of Minkowski "difference" that maintain coverage
Useful for dynamic covering? Convex relaxation & linear programming?
Necessary but not sufficient condition for coverage: Target inside complement of convex hull of union ...
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This note was uploaded on 02/13/2012 for the course CS 91.504 taught by Professor Daniels during the Spring '10 term at UMass Lowell.
 Spring '10
 DANIELS
 Algorithms

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