TecnoCampus Foundation
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General information

Subject type: Mandatory

Coordinator: Juan José Pons López

Trimester: Third term

Credits: 4

Teaching staff: 

Albert Carrillo Sorolla

Teaching languages

  • Catalan

The classes of the subject will be done in Catalan. Bibliography and supporting material may also be in Spanish and English.

Skills

Specific skills

  • E6. Develop video games in high-level programming languages ​​in graphics engines based on specifications.

General competencies

  • G1. Demonstrate having and understanding advanced knowledge of their area of ​​study that includes the theoretical, practical and methodological aspects, with a level of depth that reaches the forefront of knowledge.

  • G2. Solve complex problems in their field of work, by applying their knowledge, developing arguments and procedures, and using creative and innovative ideas.

  • G3. Gather and interpret relevant data (usually within their area of ​​study) to make judgments that include reflection on relevant social, scientific, or ethical issues.

  • G5. Develop the learning skills needed to undertake further studies with a high degree of autonomy.

Description

The subject of Mathematical Fundamentals of Video Games is within the framework of the subject of Development, largely includes the simulation of real physical phenomena such as the movement of characters and objects, shocks, translations, rotations, camera movements, scaling d image and other phenomena that require the use of fundamental mathematical tools and concepts, such as geometry, algebra or trigonometry. The subject consists of theoretical sessions. In order to achieve the knowledge of the subject, individual exercises are evaluated on the one hand and exercises to be carried out in groups on the other.

Contents

Topic 0. Basic mathematical tools

0.1. Solving first degree equations.

0.2. Solving quadratic equations.

0.3. Systems of equations.

Topic 1. Algebra and Geometry in plane I (2D)

1.1. Coordinate systems.

1.2. Games: Applied coordinate systems (world, screen, camera, objects).

1.3. Vectors. Concepts. Coordinates and module. Free vectors and fixed vectors. Unit vectors.

1.4. Basic operations with vectors: addition, subtraction, product for a scalar.

1.5. Games: Positions, distances and routes.

1.6. Scalar product and vector product. Angles and relative position between vectors. Parallelism and perpendicularity.  

1.7. Games: Vector properties of game objects.

1.8. Games: Images and coordinate systems, vector images.

1.9. Vectors in space

Topic 2. Trigonometry

2.1. Measurement of angles. Units.

2.2. Trigonometric ratios.

2.3. Equivalent triangles. Symmetry. Complementary angles. 

2.4. Vectors and trigonometry: Cartesian coordinates and polar coordinates. 

2.5. Unit vectors and trigonometric ratios. 

2.6. Games: Projection of shadows, angles between objects, decomposition of vector quantities.

Topic 3. Rectilinear trajectories in the plane (2D)

3.1. Equation of the line. Sloping and ordered at the origin.

3.2. Rectilinear routes.

3.3. Linear interpolation.

3.4. Relative position of two straight lines. Angle, intersection, parallelism, perpendicularity.

3.5. Specular reflection.  

3.6. Games: rectilinear trajectories, projectile simulation, surface reflection.

3.7. Games: Intersection of trajectories, interpolation of motion.

Item 4. Physics of motion

4.1. Uniform rectilinear motion.

4.2. Uniformly accelerated rectilinear motion.

4.3. Circular movement.

4.4 Particular cases: free fall and parabolic shooting.

4.5. Games: gravity creation, free fall, parabolic jump, friction, wind, projectile launch.

4.6. Elastic and inelastic shocks. Refund coefficient.

4.7. Physics of motion in space

Item 5. Algebra and Geometry in Plan II (2D)

5.1. Matrix. Concept, representation and basic operations.

5.2. Identity matrix. Diagonal matrix. Inverse matrix.

5.3. Vector spaces and bases. Matrix representation. 

5.4. Reference system. Base change matrices.

5.5. Games: changes in reference systems. 

5.6. Transformation matrices: translation, rotation, scaling, deformation.

5.7. Games: translation of objects and characters, rotation, scaling. Camera movements. 

 

Evaluation system

The grade of each student will be calculated following the following percentages:

A1. Exercises at home 10%

A2. Exercises in class: Mathaton 10%

A3. Individual work: Exercises and problems 30%

A4. Final exam 50%

Final grade = A1 0,1 + A2 0,1 + A3 0,3 + A4 0,5

Considerations:

  • It is necessary to obtain a mark higher than 4 in the final exam to pass the subject.
  • An activity not delivered or delivered late and without justification (court summons or medical matter) counts as a 0.
  • It is the responsibility of the student to prevent plagiarism in all its forms. In the case of detecting a plagiarism, regardless of its scope, in some activity it will correspond to have a note of 0. In addition, the professor will communicate to the Head of Studies the situation so that measures applicable in matter of sanctioning regime are taken. .
  • Students who have failed the subject, may take a resit exam on the dates pre-established by the same university in the official academic calendar. 

Recovery:

  • You must obtain a grade higher than 5 in the resit exam to pass the course.
  • In case of passing the recovery, the maximum final mark of the subject will be 5.

REFERENCES

Basic

LENGYEL, E. (2012). "Mathematics for 3D Game Programming and Computer Graphics" (Third edition). Boston, MA (USA): Course Technology PTR (Cengage Learning)

"Discover Math with GeoGebra." GeoGebra - Dynamic Mathematics, www.geogebra.org

DUNN, F .; PARBERRY, I. (2002). "3D Math Primer for Graphics and Game Development". Plano, Texas (USA): Wordware Publishing, Inc.