Degree  Type  Year  Semester 

2503873 Interactive Communication  OB  2  2 
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.
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.
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
 Selfcorrected 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 followup 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 
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.
Title  Weighting  Hours  ECTS  Learning Outcomes 

1st Midterm exam  30%  2  0.08  2, 3, 6, 13 
2nd Midterm 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://ebookcentralproquestcom.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.
