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Unit outline_

COMP5045: Computational Geometry

Semester 1, 2022 [Normal day] - Camperdown/Darlington, Sydney

In many areas of computer science- robotics, computer graphics, virtual reality, and geographic information systems are some examples- it is necessary to store, analyse, and create or manipulate spatial data. This course deals with the algorithmic aspects of these tasks: we study techniques and concepts needed for the design and analysis of geometric algorithms and data structures. Each technique and concept will be illustrated on the basis of a problem arising in one of the application areas mentioned above.

Unit details and rules

Academic unit Computer Science
Credit points 6
Assumed knowledge

Experience with data structures and algorithms as covered in COMP9103 or COMP9123 or COMP2123 or COMP2823 or INFO1105 or INFO1905 (or equivalent UoS from different institutions)

Available to study abroad and exchange students


Teaching staff

Coordinator Joachim Gudmundsson,
Lecturer(s) Joachim Gudmundsson,
Type Description Weight Due Length
Oral exam
Final exam
Oral exam using Zoom
32% Please select a valid week from the list below 20 minutes (oral)
Outcomes assessed: LO1 LO3 LO5 LO6
Assignment Assignment 1
Problem solving assignment
17% Week 04 n/a
Outcomes assessed: LO1 LO2 LO7
Assignment Assignment2
Problem solving assignment
17% Week 07 n/a
Outcomes assessed: LO1 LO2 LO3 LO7
Assignment Assignment 3
Problem solving assignment
17% Week 10 n/a
Outcomes assessed: LO2 LO4 LO5 LO7
Assignment Assignment 4
Problem solving assignment
17% Week 13 n/a
Outcomes assessed: LO2 LO5 LO7

Assessment summary

Detailed information for each assessment can be found on Canvas.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range


High distinction

85 - 100



75 - 84



65 - 74



50 - 64



0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

Late submission is not accepted. Special consideration up to 7 days are accepted without any changes to the assignment. Special consideration for longer than 7 days are handled by alternative assignments.

Academic integrity

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.  

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

WK Topic Learning activity Learning outcomes
Week 01 Art gallery theorems and polygon triangulation Lecture (2 hr)  
Week 02 Sweepline algorithms, convex hulls, lower bounds Lecture (2 hr)  
Week 03 Line segment intersection and polygon partitioning Lecture (2 hr)  
Week 04 Linear programming and probabilistic analysis Lecture (2 hr)  
Week 05 Orthogonal range searching 1: kd-tress and range trees Lecture (2 hr)  
Week 06 Orthogonal range searching 2: fractional cascading and interval trees Lecture (2 hr)  
Week 07 Planar point location Lecture (2 hr)  
Week 08 Arrangements and duality Lecture (2 hr)  
Week 09 Voronoi diagrams and Delaunay triangulation Lecture (2 hr)  
Week 10 Approximation algorithms Lecture (2 hr)  
Week 11 The Frechet distance Lecture (2 hr)  
Week 12 Binary space partition Lecture (2 hr)  
Week 13 Recap Lecture (2 hr)  

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

All readings for this unit can be accessed through the Library eReserve, available on Canvas.

M. de Berg, O. Cheong, M. van Kreveld and M. Overmars., Computational Geometry: Algorithms and Application (3rd edition). SpringerVerlag, Heidelberg, 2008. 978-3-540-77973-5.

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. argue the correctness and efficiency of a proposed solution. Mainly in writing but also orally
  • LO2. demonstrate knowledge of fundamental algorithms for several problems, for example algorithms to compute convex hulls, triangulate polygons, low-dimensional linear programming and Voronoi diagrams, knowledge of fundamental general algorithmic design techniques, such as greedy, dynamic programming and divide-and-conquer
  • LO3. read, understand, analyze and modify a given algorithm. Ability to design algorithmic solutions for given geometric problems
  • LO4. attack theoretical and practical problems in various application domains
  • LO5. understand and apply important techniques and results in computational geometry
  • LO6. analyze the complexity of a given algorithm
  • LO7. demonstrate knowledge of fundamental geometric data structures such as, data structures for range searching, point location, segment intersection and ray shooting. Demonstrate knowledge of fundamental general design techniques for data structures, such as multi-level trees, duality and divide-and-conquer.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities

This section outlines changes made to this unit following staff and student reviews.

No major changes have been made since this unit was last offered


The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

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