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

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Computational GeometryComputational Geometry

• Algorithms for reasoning with geometry– Design and analysis of efficient algorithms for problems involving

geometric input and output

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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

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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?

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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

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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)

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ApplicationsApplications

• Computer graphics

– Surface construction

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ApplicationsApplications

• Computer graphics

– Surface construction

– Collision detection

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ApplicationsApplications

• Computer graphics

– Surface construction

– Collision detection

• Computer vision

– Pattern recognition

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ApplicationsApplications

• Computer graphics

– Surface construction

– Collision detection

• Computer vision

– Pattern recognition

• Geographical Information System

– Range queries

“Pizza near me”

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ApplicationsApplications

• Computer graphics

– Surface construction

– Collision detection

• Computer vision

– Pattern recognition

• Geographical Information System

– Range queries

• Robotics

– Motion planning

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Overview of semesterOverview of semester

• Convex hulls

• Triangulations

• Voronoi diagram andDelaunay triangulations

• Line arrangements

• Spatial query structures

• Visibility graphs

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OutlineOutline

• What is Computational Geometry?

• Course Mechanics

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MaterialsMaterials

• Textbook: “Computational Geometry:Algorithms and Applications” (or 4M)

• Notes by David Mount from U Maryland

– Linked from our course website

• Many online resources

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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

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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

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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

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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/