Physics of Realistic Modelling and Animation

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Credits
6
Types
Elective
Requirements
This subject has not requirements, but it has got previous capacities
Department
FIS
Web
www-fen.upc.es/~fmar
The aim of this course is to provide students with an understanding of physics-and in particular mechanics-in order to enable them to build physically realistic mathematical models of articulated systems (robots, vehicles, animated bodies with skeletons, etc.). The models they study will enable them to describe the kinematics and dynamics of the physical systems they study, and they will also be introduced to the numerical integration methods used for obtaining the resulting movement, which thus yields a physically realistic form of animation.

Teachers

Person in charge

  • Joaquim Casulleras Ambros ( )

Weekly hours

Theory
2
Problems
1
Laboratory
1
Guided learning
0
Autonomous learning
6

Competences

Technical Competences

Common technical competencies

  • CT1 - To demonstrate knowledge and comprehension of essential facts, concepts, principles and theories related to informatics and their disciplines of reference.
    • CT1.2A - To interpret, select and value concepts, theories, uses and technological developments related to computer science and its application derived from the needed fundamentals of mathematics, statistics and physics. Capacity to solve the mathematical problems presented in engineering. Talent to apply the knowledge about: algebra, differential and integral calculus and numeric methods; statistics and optimization.
    • CT1.2B - To interpret, select and value concepts, theories, uses and technological developments related to computer science and its application derived from the needed fundamentals of mathematics, statistics and physics. Capacity to understand and dominate the physical and technological fundamentals of computer science: electromagnetism, waves, circuit theory, electronics and photonics and its application to solve engineering problems.
  • CT5 - To analyse, design, build and maintain applications in a robust, secure and efficient way, choosing the most adequate paradigm and programming languages.
    • CT5.1 - To choose, combine and exploit different programming paradigms, at the moment of building software, taking into account criteria like ease of development, efficiency, portability and maintainability.
    • CT5.2 - To know, design and use efficiently the most adequate data types and data structures to solve a problem.
    • CT5.5 - To use the tools of a software development environment to create and develop applications.

Transversal Competences

Reasoning

  • G9 [Avaluable] - Capacity of critical, logical and mathematical reasoning. Capacity to solve problems in her study area. Abstraction capacity: capacity to create and use models that reflect real situations. Capacity to design and perform simple experiments and analyse and interpret its results. Analysis, synthesis and evaluation capacity.
    • G9.1 - Critical, logical and mathematical reasoning capacity. Capacity to understand abstraction and use it properly.

Technical Competences of each Specialization

Computer science specialization

  • CCO2 - To develop effectively and efficiently the adequate algorithms and software to solve complex computation problems.
    • CCO2.2 - Capacity to acquire, obtain, formalize and represent human knowledge in a computable way to solve problems through a computer system in any applicable field, in particular in the fields related to computation, perception and operation in intelligent environments.

Objectives

  1. To know, understand and use correctly the relationships between reference frame transformations.
    Related competences: G9.1,
  2. To be able to develop mathematical models of articulated rigid bodies systems.
    Related competences: G9.1, CT5.2,
  3. Mastering the Denavit-Hartenberg formalism.
    Related competences: CT5.2, CCO2.2,
  4. To be able to identify the appropriate set of variables for the physical system studied. To be able to determine the
    joint variable values in order to achieve a given configuration in static conditions.
    Related competences: CT5.2,
  5. To build a mathematical model of the physical properties of large bodies (a rock, a rigid element of arbitrary shape), articulated rigid systems (robots, industrial manipulators). To understand the concept of inertia tensor to describe the mass distribution of an object.
    Related competences: G9.1,
  6. To understand and to be able to use the laws of kinematics and dynamics in systems of many particles.
    Related competences: G9.1, CCO2.2,
  7. Understand and properly use conservations theorems for some quantities of motion.
    Related competences: G9.1, CT1.2B,
  8. to know how to describe and determine the effects of various forces: gravity, aerodynamic drag, elastic forces.
    Related competences:
  9. To use the Lagrangian formalism in order to determine statics and dynamics equations.
    Related competences: G9.1,
  10. To identify the relevant variables in systems acting under restricted dynamic conditions.
    Related competences: G9.1,
  11. To be able to incorporate the effects of constraint conditions on the dynamic equations.
    Related competences: G9.1,
  12. To know and be able to use computer mathematical methods for the integration of dynamic equations.
    Related competences: CT1.2A, CT5.2, CT5.5, CT1.2B,
  13. Being able to build an animation on the basis of the computer numerical solution of the dynamic equations of the system.
    Related competences: CT1.2A, CT5.2, CT5.5, CT5.1, CT1.2B,

Contents

  1. Geometric transformations in space. Denavit-Hartenberg formalism.
    Transformation relationships between reference systems. Denavit-Hartenberg formalism. Mathematical modelling of rigid, articulated systems.
  2. Rigid body physics.
    Mathematical modelling of the physical properties of large bodies (a rock, a rigid element), articulated rigid systems (robots, industrial handling devices). Mass distribution, inertia tensor.
  3. Interacting N-body systems.
    Kinematics and dynamics in many particles systems. Conservation theorems. Types of relevant forces: gravity, aerodynamic drag, elastic forces. Collisions.
  4. Dynamics of N degrees of freedom systems. Dynamics in restricted conditions.
    Identification of relevant generalized variables. Systems under constrained dynamic conditions. Restricted dynamic equations.
  5. Physically realistic animations.
    integration of dynamic equations. Trajectory. Visualization of objects and systems in motion subject to kinematic constraints.

Activities

Activity Evaluation act


partial exam

written examination.
Objectives: 1 5 2 3 4
Week: 9
Theory
1.5h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
8h

Final exam

Course final exam.
Objectives: 1 5 2 3 4 6 7 8 9 11 10
Week: 14
Theory
2.5h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h

Execution and delivery of the final practice

Preparation of the final practice with its report.
Objectives: 5 2 3 4 6 7 8 9 11 10 12 13 1
Week: 14
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h

Development of Theory classes

Combining blackboard expositions and projection of multimedia content.
Objectives: 1 5 2 3 4 6 7 8 9 11 10 12 13
Contents:
Theory
26h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

problems classes

Discussing and solving problems.
Objectives: 1 5 2 3 4 6 7 8 9 11 10
Contents:
Theory
0h
Problems
15h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h


Study and preparatory work for lab sessions.

Students will study the material provided, and on the basis of the theoretical tools explained in class, prepare work to be held in the laboratory.
Objectives: 1 5 2 3 4 6 7 8 9 11 10 12 13
Contents:
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
36h

Solving problems and exercises

Personal work, solving problems and exercises
Objectives: 1 5 2 3 4 6 7 8 9 11 10
Contents:
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
22h

Teaching methodology

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Evaluation methodology

The evaluation will be done by means of two exams (partial and final), which will provide an exam mark (Ex_grade), together with the realization of a series of computation lab practices and assignments which will provide the laboratory grade (Lab_grade).
The relative weights of the partial and final exam will be 25% and 75% respectively (0% and 100% in case the final exam grade is higher than the partial ones). The degree of achievement of the objectives set in the different phases will be taken into account in the assessment of the computation lab practices (Lab_grade)..

The course grade will be calculated based on the average of the two grades:

Course_grade = (Ex_grade + Lab_grade) / 2


The assessment of the transversal competence G9.1 will be done by means of the weighted average of the marks assigned to this competence in the partial and final exams, with the same weights of 25% and 75% respectively, (0% and 100% in case that of the end it is a note superior to the partial one).

The assessment of transversal competence G9.1 will be made through a weighted average of the grades assigned to this competence in the partial and final exams, with the same weights of 25% and 75% respectively (0% and 100% should the final exam result be better than the partial one).

Bibliography

Basic:

Previous capacities

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