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CSE546 Introduction Slide 1
CSE 546:Computational Geometry
CSE 546:Computational Geometry
Spring 2014
CSE546 Introduction Slide 2
OutlineOutline
• What is Computational Geometry?
• Course Mechanics
CSE546 Introduction Slide 3
OutlineOutline
• What is Computational Geometry?
• Course Mechanics
CSE546 Introduction Slide 4
Computational GeometryComputational Geometry
• Algorithms for reasoning with geometry– Design and analysis of efficient algorithms for problems involving
geometric input and output
CSE546 Introduction Slide 5
Computational GeometryComputational Geometry
• Concerned with geometry that– Has low dimensions (usually 2 or 3)
– Is discrete and flat (as opposed to continuous curves or surfaces)
Point
Line Line segment
Triangle Polygon
CSE546 Introduction Slide 6
A typical CG problemA typical CG problem
• How to fill the inside of an n-vertex 2D polygon with(non-overlapping) triangles?
• How to fill it with triangles that minimize the sum ofedge lengths?
CSE546 Introduction Slide 7
ComplexityComplexity
• The quality of an algorithm is measured by time complexity– We usually consider asymptotic worst-case running time
• E.g., O(n) better than O(n Log n) better than O(n^2)
– Sometimes use average case running time
CSE546 Introduction Slide 8
A typical CG problemA typical CG problem
• How to fill the inside of an n-vertex 2D polygon with(non-overlapping) triangles?
• How to fill it with triangles that minimize the sum ofedge lengths?
O(n)
O(n^3)
CSE546 Introduction Slide 9
ApplicationsApplications
• Computer graphics
– Surface construction
CSE546 Introduction Slide 10
ApplicationsApplications
• Computer graphics
– Surface construction
– Collision detection
CSE546 Introduction Slide 11
ApplicationsApplications
• Computer graphics
– Surface construction
– Collision detection
• Computer vision
– Pattern recognition
CSE546 Introduction Slide 12
ApplicationsApplications
• Computer graphics
– Surface construction
– Collision detection
• Computer vision
– Pattern recognition
• Geographical Information System
– Range queries
“Pizza near me”
CSE546 Introduction Slide 13
ApplicationsApplications
• Computer graphics
– Surface construction
– Collision detection
• Computer vision
– Pattern recognition
• Geographical Information System
– Range queries
• Robotics
– Motion planning
CSE546 Introduction Slide 14
Overview of semesterOverview of semester
• Convex hulls
• Triangulations
• Voronoi diagram andDelaunay triangulations
• Line arrangements
• Spatial query structures
• Visibility graphs
CSE546 Introduction Slide 15
OutlineOutline
• What is Computational Geometry?
• Course Mechanics
CSE546 Introduction Slide 16
MaterialsMaterials
• Textbook: “Computational Geometry:Algorithms and Applications” (or 4M)
• Notes by David Mount from U Maryland
– Linked from our course website
• Many online resources
CSE546 Introduction Slide 17
HomeworkHomework
• 4 written homework (due in class)
– Typesetting (e.g., in Word or LaTex) will be appreciated by TAs
• The answer to each problem should include:
– A pseudo code of the algorithm
– Analysis of runtime
– Argument that the algorithm gives the correct output
• They are to be completed individually
– See collaboration policies on the course webpage
CSE546 Introduction Slide 18
ExamsExams
• 2 in-class exams
– Feb 25 and Apr 22
– Each covering half of the materials (no Final exam)
• Close-book, except one letter-size cheat sheet
CSE546 Introduction Slide 19
Final ProjectFinal Project
• Three categories:
– Graphical applets illustrating concepts/algorithms learned in class
– Research on open problems
– Solution to a practical application
• 1-3 person group, due at the end of semester
CSE546 Introduction Slide 20
Other stuffOther stuff
• Course webpage (all materials, plus calendar)– http://www.cse.wustl.edu/~taoju/cse546/
• Piazza page (discussion board)– https://piazza.com/wustl/spring2014/cse546/