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Presentation
Presentation
The objectives of this curricular unit are to give students a basic understanding of mathematics and physics, mainly as a tool for developing games. studies' cycle) In this curricular unit, the students will learn concepts of trigonometry, vector and matrix calculus, coordinate systems, probabilities and statistics, numerical computation, parametric functions and geometric primitives. They will also be introduced to more practical applications of mathematics for games (for example: Python with the libraries NumPy and Pygame for developing a rudimentary 3d graphics engine, or other programming languages).
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 4
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULHT1075-17337
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
Cartesian coordinate systems and basic trigonometry Vectors: definition, properties and operations Coordinate spaces: practical application, examples and transformations Matrices: definition and geometric interpretation, determinantes, inverse Linear transforms: rotation, scaling, translation, projection Transform hierarchy and composition Different representation of 3d rotation: matrices, Euler angles and quaternions Probability and mathematical distribution Parametric functions Geometric primitives Math for 3d graphics Examples: NumPy e Pygame (or another programming language)
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Objectives
Objectives
At the end of this curricular unit, the student should: Master trigonometry and coordinate systems Have basic knowledge of vector and matrix math, as well as linear transforms Know the common geometric primitives used in game development, and how to compute distance, intersection, etc Have basic knowledge of probability and statistics Master parametric functions and know how to use them in real-world problems. Have a good grasp of the render pipeline and 3d rendering. Ability to solve problems involving visualization, interpretation, and implementation of virtual worlds in 2D and 3D, on paper, and with Python (for example).
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Teaching methodologies and assessment
Teaching methodologies and assessment
Peer review and PBL
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References
References
Dunn, F., & Parberry, I. (2011). 3D Math Primer for Graphics and Game Development (2nd ed.). CRC Press. Craven, P. (2016). Program Arcade Games: With Python and Pygame. Apress. Brownlee, J. (2018). Basics of Linear Algebra for Machine Learning: Discover the Mathematical Language of Data in Python. Self-published. Inva¿lido para
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Office Hours
Office Hours
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Mobility
Mobility
No
