Animacja Komputerowa

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Animacja Komputerowa

• Barbara Strug
• Elektroniczne Przetwarzanie Informacji
• Semestr IV, Lato 2005

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Wstep

• Rózne podejscia do tworzenie modeli obiektów
  geometrycznych na potrzeby animacji.
• Rozszerzenia standardowych transformacji do
  struktur hierarchicznych.
• Metody, które mozna wykorzystac w zastosowanaich
  takich jak budowa robotów i animacja postaci, w
  szczególnosci uwzglednimy systuacje gdzie
  zachowanie calosci obiektu jest mocno
  uzaleznione od relacji pomiedzy jego czesciami

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Symbole i instancje

• Jak reprezentowac i przechowywac obiekt/model,
  który moze skladac sie z wielu zlozonych obiektów
  geometrycznych.
• Dwa problemy
• Co to jest obiekt zlozony?
• Jak reprezentowac zbiór takich obiektów?
• Czy daloby sie zrobic taka reprezentacje bez
  uzycia hierarchii? Symbole i zbiory symboli ?

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• Symbole mozemy reprezentowac w pasujacym nam
  rozmiarze i orientacji.
• Walec
• W OpenGL nalezy ustawic wlasciwa transformacje z
  przestrzeni symbolu (lokalnej) do przestrzeni
  swiata (globalnej) przed wywolaniem kodu symbolu.

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• Przyklad transformacja
• M TRS
• zlozenie translacji, rotacji (obrotu) i
  skalowania
• Kod OpenGL
• glMatrixMode(GL_MODELVIEW)
• glLaodIdentity()
• glTranslatef(...)
• glRotatef(...)
• glScalef(...)
• glutSolidCylinder(...)

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• Mozna taki model potraktowac takze jako tablice
• Tablica nie zawiera informacji o relacjach
  pomiedzy obiektami, ale pozwala je narysowac.
• Taka struktura danych pozwala na wiele
  zastosowan, ale ciagle nie mozemy dotrzec do
  relacji/wspólzaleznosci.

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Modele Hierarchiczne

• Budujemy np.. Samochód na potrzeby animacji.
• Niech sklada sie z nadwozia i 4 kól

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• Klatki animacji
• Mozna obliczyc jak daleko przesunelo sie kolo np.
  tak
• calculate(speed, distance)
• draw_right_front_wheel(speed, dist)
• draw_left_front_wheel(speed, dist)
• draw_right_rear_wheel(speed, dist)
• draw_left_rear_wheel(speed, dist)
• draw_chassis(speed, dist)

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• Ale nie calkiem o to nam chodzi.
• Taki zapis jest liniowy i nie pokazuje relacji
  pomiedzy poszczególnymi elementami kola nie
  jada kazde inaczej !
• There are two types of relationships we wish to
  convey
• First, we cannot separate the movement of the car
  from the movement of the wheels
• If the car moves forward, the wheels must turn.
• Second, we would like to note that all the wheels
  are identical and just located and oriented
  differently.
• We typically do this with a graph.
• Def node, edge, root, leaf, ...

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• Tree Representation
• DAG Representation

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A Robot Arm

• Robotics provides many opportunities for
  developing hierarchical models.
• Consider this arm
• It consists of 3 parts

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• The mechanism has 3 degrees of freedom, each of
  which can be described by a joint angle between
  the components
• In our model, each joint angle determines how to
  position a component with respect to the
  component to which it is attached
• q - rotation of the base
• f - rotation of first arm
• y - rotation of second arm piece.

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• We could write it as follows
• display()
• glRotatef(theta, 0.0, 1.0, 0.0)
• base()
• glTranslatef(0.0, h1, 0.0)
• glRotatef(phi, 0.0, 0.0, 1.0)
• lower_arm()
• glTranslatef(0.0, h2, 0.0)
• glRotatef(0.0, 0.0, 1.0)
• upper_arm()

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• Note that we have described the positioning of
  the arm independently of the details of the
  individual parts.
• We have also put it into a tree structure
• This makes it possible to write separate programs
  to describe the components and animate the robot.
• Drawing an object stored in a tree requires
  performing a tree traversal (you must visit every
  node)

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4. Tree Traversal

• Here we have a box-like representation of a human
  figure.
• We can represent this figure as a tree

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• If we put the matrices with each node we can
  specify exactly how to draw the robot
• The issue is how to traverse the tree...
• Typically you do a pre-order traversal.
• This can be done in two ways
• with code and a stack
• recursively (implicit stack)

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• 4.1 A Stack-Based Traversal
• Consider the code necessary to draw the Robot.
• This function might be called from the display
  callback
• The Model-View matrix, M, in effect when the
  function is invoked determines the position of
  the robot relative to the rest of the scene.

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• The function must manipulate the model-view
  matrix before each part of the robot is drawn.
• In addition to the usual OpenGL functions for
  rotation, translation, and scaling, the functions
  glPushMatrix and glPopMatrix are particularly
  helpful for traversing our tree.
• The first glPushMatrix duplicates the current
  model-view matrix
• assuming that we have done a previous
  glMatrixMode(GL_MODELVIEW)
• When we have finished with changes we can do a
  glPopMatrix to get back the original one saved
• Note we must do another glPushMatrix to leave a
  copy that we can later go back to.

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5. Use of Tree Data Structures

• The second approach is to use a standard tree
  data structure to represent our hierarchy and
  then to render it with a traversal algorithm that
  is independent of the mode of traversal.

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• At each node we must store the information
  necessary to draw the object
• a function that defines the object
• the homogeneous coordinate matrix that positions
  the object relative to the parent.
• Typedef struct treenode
• Glfloat m16
• void (f)()
• struct treenode sibling
• struct treenode child

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• Traversing the tree in a preorder traversal can
  be accomplished
• void traverse (treenode root)
• if(root NULL) return
• glPushMatrix()
• glMultMatrix(root-gtm)
• root-gtf()
• if(root-gtchild! NULL) traverse(root-gtchild)
• glPopMatrix()
• if(root-gtsibling! NULL) traverse(root-gtsibling
  )

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6. Animation

• Our robot example is articulated
• consists of rigid parts connected by joints
• We can make such models change their positions in
  time - animate them - by altering a small set of
  parameters.
• Hierarchical models allow us to reflect correctly
  the compound motions incorporating the physical
  relationships among parts of the model.

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• Of the many approaches to animation, a few basic
  techniques are of particular importance when we
  work with articulated figures.
• Kinematics
• describing the position of the parts of the model
  based on only their joint angles.
• Inverse kinematics and inverse dynamics
• given a desired state of the model, how can we
  adjust the angles so as to achieve this position?
• key-frame animation
• position the objects at a set of times.
• Inbetweening
• then fill in (interpolate).

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Animating Articulated Structures

• The desire to use human beings as synthetic
  actors in three-dimensional computer animation
  environments
• Lachapelle, Bergeron, and Robidoux, Tony de
  Peltrie, a jazz pianist
• Magnenat-Thalmann and Thalmann, Rendezvous a
  Montreal, Marilyn Monroe and Humphrey Bogart

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Terminologies of Articulated Figure Animation

• Definition, textbook, page 370
• Kinematics
• Articulated figure
• Degrees of freedom (DOF)
• End effector
• State vector, q(q1, , qN)
• example any unconstrained rigid body has 6 DOFs,
  3 translational and 3 rotational,
  q(x,y,z,m,f,F).

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