Outline

Overview

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
Prerequisites ?	COMP9123 or COMP2123 or COMP2823
Corequisites ?	None
Prohibitions ?	COMP4445
Assumed knowledge ?	COMP3027 or equivalent and Discrete mathematics and probability (e.g. MATH1064 or equivalent)
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Joachim Gudmundsson, joachim.gudmundsson@sydney.edu.au

Assessment

The census date for this unit availability is 31 March 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Oral exam	Final exam 50 minutes	60%	Formal exam period	50 minutes	AI prohibited
Outcomes assessed:
Out-of-class quiz	Quiz MCQ testing prerequisites	4%	Week 02 Due date: 11 Mar 2026 at 23:59 Closing date: 18 Mar 2026	20 minutes	AI allowed
Outcomes assessed:
Practical skill	Assignment 1 Problem solving assignment	9%	Week 04 Due date: 18 Mar 2026 at 23:59 Closing date: 01 Apr 2026	n/a	AI allowed
Outcomes assessed:
Practical skill	Assignment 2 Problem solving assignment	9%	Week 07 Due date: 15 Apr 2026 at 23:59 Closing date: 29 Apr 2026	n/a	AI allowed
Outcomes assessed:
Practical skill	Assignment 3 Problem solving assignment	9%	Week 10 Due date: 06 May 2026 at 23:59 Closing date: 20 May 2026	n/a	AI allowed
Outcomes assessed:
Practical skill	Assignment 4 Problem solving assignment	9%	Week 13 Due date: 27 May 2026 at 23:59 Closing date: 10 Jun 2026	n/a	AI allowed
Outcomes assessed:
= hurdle task ? = early feedback task ?

Assessment summary

Assignments can be found on Ed and Gradescope.

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	Description
High distinction	85 - 100
Distinction	75 - 84
Credit	65 - 74
Pass	50 - 64
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard. It is a policy of the School of Computer Science that in order to pass this unit, a student must achieve at least 40% in the written examination. For subjects without a final exam, the 40% minimum requirement applies to the corresponding major assessment component specified by the lecturer. A student must also achieve an overall final mark of 50 or more. Any student not meeting these requirements may be given a maximum final mark of no more than 45 regardless of their average.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

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 University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Learning support

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.

Support for students

The Support for Students Policy reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	Art Gallery Problem	Lecture (2 hr)
Week 01	Art Gallery	Tutorial (2 hr)
Week 02	Sweepline Algorithms 1: Segment Intersection and Polygon Triangulation	Lecture (2 hr)
Week 02	Sweepline Algorithms 1: Segment Intersection and Polygon Triangulation	Tutorial (2 hr)
Week 03	Sweepline Algorithms 2: Convex Hull	Lecture (2 hr)
Week 03	Sweepline Algorithms 2: Convex Hull	Tutorial (2 hr)
Week 04	Linear Programming	Lecture (2 hr)
Week 04	Linear Programming	Tutorial (2 hr)
Week 05	Orthogonal Range Searching 1: kd-Trees and Range Trees	Lecture (2 hr)
Week 05	Orthogonal Range Searching 1: kd-Trees and Range Trees	Tutorial (2 hr)
Week 06	Orthogonal Range Searching 2: Interval Trees and Segment Trees	Lecture (2 hr)
Week 06	Orthogonal Range Searching 2: Interval Trees and Segment Trees	Tutorial (2 hr)
Week 07	Voronoi Diagrams and Delaunay Triangulations	Lecture (2 hr)
Week 07	Voronoi Diagrams and Delaunay Triangulations	Tutorial (2 hr)
Week 08	Duality	Lecture (2 hr)
Week 08	Duality	Tutorial (2 hr)
Week 09	Planar Point Location	Lecture (2 hr)
Week 09	Planar Point Location	Tutorial (2 hr)
Week 10	Approximation Algorithms	Lecture (2 hr)
Week 10	Approximation Algorithms	Tutorial (2 hr)
Week 11	Curve Similarity and the Fréchet Distance	Lecture (2 hr)
Week 11	Curve Similarity and the Fréchet Distance	Tutorial (2 hr)
Week 12	Guest lecture	Lecture (2 hr)
Week 12	Guest lecture	Tutorial (2 hr)
Week 13	Summary and research topic	Lecture (2 hr)
Week 13	Summary and research topic	Tutorial (2 hr)

Attendance and class requirements

Lectures are not compulsory to attend and are recorded for students who have timetable clashes. It is strongly recommended that you do attend lectures if you are able, as there may be (optional but useful) interactive tasks to complete during some lectures.

Tutorials are in-person and you may be completed assessable activities during tutorials. If for some reason you miss your tutorial, you can attend a later session if there is space, and the tutor agrees; you need to ask the tutor before taking a seat, since there are limited seats in every tutorial session.

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

Recommended reading (provided) and the book that this unit is based on:

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

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.

Outcomes
Graduate qualities

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, and segment intersection. 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
Learning outcomes

Responding to student feedback

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

- Changed from written exam to oral exam. The key goal for this unit is to learn problem solving skills. This cannot longer be done in open assignments, nor fairly in written exams. - Added an MCQ to check to make students more aware of the prerequisites.

Disclaimer

Important: the University of Sydney regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

COMP5045: Computational Geometry

Semester 1, 2026 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links