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Mathematics and Physics for Digital Animated Objects

Code: 104729 ECTS Credits: 6
Degree Type Year Semester
2503873 Interactive Communication OB 2 2


F. Xavier Alvarez Calafell

Use of Languages

Principal working language:
catalan (cat)
Some groups entirely in English:
Some groups entirely in Catalan:
Some groups entirely in Spanish:


Rosa Flaquer Galmés


The subject starts from very basic levels of mathematics and physics, but it would be helpful that the student had taken the subjects of Mathematics and Physics at the secondary grade.

Objectives and Contextualisation

The subject, based on physics and mathematics, presents the scientific logics of movement, design of objects, characters, landscapes and architecture. It begins with an introduction to the model of digital objects, and the physics and mathematics of movements / forces of animated objects.

It will also address the usual models for animated objects, the parameters and the simulation and continuity analysis of animated objects (movements, forces, among others). In the course it will be also studied the parameter adjustment for the simulations and its validation.


  • Act with ethical responsibility and respect for fundamental rights and duties, diversity and democratic values.
  • Apply and integrate knowledge in the fields of social sciences, humanities and engineering to generate complex products and services tailored to citizens' needs.
  • Associate mathematical and physical processes and theories, and their application to the world of databases, with the creation of interfaces and with augmented virtual reality.
  • Introduce changes in the methods and processes of the field of knowledge to provide innovative responses to the needs and demands of society.
  • Manage time efficiently and plan for short-, medium- and long-term tasks.
  • Search for, select and rank any type of source and document that is useful for creating messages, academic papers, presentations, etc.
  • Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
  • Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.

Learning Outcomes

  1. Analyse a situation and identify its points for improvement.
  2. Assimilate the fundamental principles of mathematics and physics and apply them to the creation of communication products.
  3. Construct the usual models for creating the animated objects, the parameters and the simulation.
  4. Cross-check information to establish its veracity, using evaluation criteria.
  5. Distinguish the salient features in all types of documents within the subject.
  6. Explain the key concepts of this subject area, on the basis of the knowledge of physics and mathematics acquired in secondary school.
  7. Interpret and analyse continuity in animated objects.
  8. Interpret and analyse the relationship between mathematical concepts and the creation of databases.
  9. Interpret and discuss documents and theories on physics and mathematics of animated digital objects.
  10. Plan and conduct academic studies in the field of information systems.
  11. Propose new methods or well-founded alternative solutions.
  12. Propose projects and actions that are in accordance with the principles of ethical responsibility and respect for fundamental rights and obligations, diversity and democratic values.
  13. Relate physical and mathematical concepts and apply them to the movement/force of animated objects.
  14. Submit course assignments on time, showing the individual and/or group planning involved.


In the first part of the course will be studied the mathematical concepts needed to draw, position and orient polygonal objects in computer simulations. These tools will allow us to draw simple objects and position them in 2D and 3D spaces. In the second part we will study the essential physical laws that allow moving those objects in the space.

1. Basics of mathematics.

Vector space: Properties of vector spaces. Scalar product. Linear combinations and basis. Vectors in 3D.
Matrices and vectorial product: Introduction to matrices. Identity and inverse matrices. Vectorial product. Solving systems of equations using matrices.
Transformations: Transformations in the plane. 3D transformations. Rotations around a general axis. Homogeneous coordinates.
Equations for a straight line: Lines in the plane. Distances. Relative position between lines. Geometric places. 3D straight lines.
Plane equations: Planes in 3D space. Intersection between straight lines and planes. Intersection between planes. Distance from a point to a plane. Projection in the visualization plane

3. Fundamentals of Physics

Equations of motion: Uniform and uniformly accelerated rectilinear motion. Circular motion.
Newton's laws. Weight, Normal, Frictional Forces.
Collisions between objects.


The classes will alternate different methodologies:

- Theory classes where the general concepts of the different topics will be introduced

- Self-corrected questionnaires using the Moodle platform

- Practices writting short programs applying the concepts introduced in theory classes.

- Reading of didactic material where the physical and mathematical concepts are used to draw and move objects in virtual environments.

The calendar will be available on the first day of class. Students will find all information on the Virtual Campus: the description of the activities, teaching materials, and any necessary information for the proper follow-up of the subject. In case of a change of teaching modality for health reasons, teachers will make readjustments in the schedule and methodologies

Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.


Title Hours ECTS Learning Outcomes
Type: Directed      
Computer practices 15 0.6 3, 4, 5, 7, 10
Theory classes 33 1.32 3, 6, 7, 8, 9, 13
Type: Supervised      
Tutorials 8 0.32 4, 5
Type: Autonomous      
Programming 20 0.8 2, 3, 5, 7, 14, 13
Reading of educational material 12 0.48 2, 4, 9
Resolution of computer assisted questionaries 16 0.64 3, 7, 13
Workhome 26 1.04 4, 9, 10, 14


The final grade is divided into two midterm exams (with a weight of 30% each one) and moodle and geogebra / python practices with the remaining 40% weight.

In order to pass , the grade for each of the four items (2 midterm exams - moodle - geogebra / python) must be higher than 3.5

The proposed teaching methodology and evaluation activities may undergo some modifications depending on the health authorities' attendance restrictions.


Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
1st Mid-term exam 30% 2 0.08 2, 3, 6, 13
2nd Mid-term exam 30% 2 0.08 2, 3, 6, 13
Geogebra/Python practice 20% 8 0.32 1, 2, 7, 8, 14, 11, 12
Moodle questionaries 20% 8 0.32 4, 5, 9, 10, 14, 13


1. Lengyel, Eric, and Flynt, John. Mathematics for 3D Game Programming and Computer Graphics (3rd Edition). Boston: Course Technology, 2011. ProQuest Ebook Central. (Accessible com a recurs electrònic a https://ebookcentral-proquest-com.are.uab.cat/lib/uab/detail.action?docID=3136454#)

2. Bourg, David M. and Bywalec, B. Physics for game developers (2nd edition). , 2013. O'Reilly.