3D Computer Game Design

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????????3D Computer Game Design

• Chapter 4
• Transformations and Matrices (Part I)
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In this chapter, you will learn

• Coordinate transformations
• The camera and viewing transformations
• OpenGL matrices and matrix stacks
• Projections
• Using your own matrices with OpenGL

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Understanding Coordinate Transformations

• Local coordinate system
• Unique for every object
• Centered on the object
• Doesnt depend on any other objects

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Understanding Coordinate Transformations

• When rendering 3D scenes, vertices pass through
  four types of transformations
• Modeling transformation
• Move objects from local coordinates into world
  coordinates
• Viewing transformation
• Move objects form world coordinates into eye or
  camera coordinates

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Understanding Coordinate Transformations

• Projection transformation
• Map objects from eye coordinates to clip
  coordinate
• Viewport transformation
• Map the clip coordinates into the 2D viewport, or
  window, on your screen

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Understanding Coordinate Transformations

• OpenGL includes and combines the modeling and
  viewing transformation
• Modelview transformation
• These transformations execute in a specific order

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Eye Coordinates

• Define the cameras position and orientation
• In OpenGL
• The default camera is always oriented to look
  down the negative z axis

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Viewing Transformations

• Used to position and aim the cameras
• Specify before any other modeling transformations
• Create the viewing transformation

void glLoadIdentity()
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Viewing Transformations

• After initializing the current matrix, you can
  create the viewing matrix in several ways
• Using the gluLookAt()
• Using the translation and rotation modeling
  commands
• Create your own routines

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Modeling Transformations

• Allow you to position and orient a model
• Translation
• Moving an object along a specified vector
• Rotation
• Rotate about a vector
• Scaling
• Increase or decrease the size of an object

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Projection Transformations

• Define the viewing volume and clipping planes
• OpenGL offers two types of projections
• Perspective projection
• Show 3D worlds exactly as you see things in real
  life
• Orthographic projection
• Show objects on the screen in their true size,
  regardless of their distance from the camera

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Viewport Transformations

• Map the clip coordinates onto your windows
  rendering surface
• The final images should be enlarged or shrunk

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OpenGL and Matrices

• Transformations in OpenGL rely on the matrix for
  all math computations
• Matrix stack
• Construct complicated models

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The Modelview Matrix

• Define the coordinate system
• To place and orient objects
• 4 x 4 matrix
• Modify matrix
• To modify the modelview matrix
• Use the argument GL_MODELVIEW

void glMatrixMode(Glenum mode)
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The Modelview Matrix

• Other arguments for glMatrixMode
• GL_PROJECTION, GL_COLOR, or GL_TEXTURE
• Reset the modelview matrix to the default
  position (0, 0, 0) and orientation
• Call the glLoadIdentity() function

glMatrixMode(GL_MODELVIEW) glLoadIdentity() //
do other transformations
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Translation

• Move an object from one position to another
  position
• The OpenGL function
• For example

void glTranslatefd(TYPE x, TYPE y, TYPE z)
glMatrixMode(GL_MODELVIEW) glLoadIdentity() glTr
anslatef(5.0f, 5.0f, 5.0f) DrawCube()
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Rotation

• Rotation
• Angle
• Measure in degrees in the counterclockwise
  direction
• For example
• Rotate clockwise around the y axis 135 degrees

void glRotatefd(TYPE angle, TYPE x, TYPE y,
TYPE z)
glRotatef(-135.0f, 0.0f, 1.0f, 0.0f)
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Scaling

• Increase or decrease the size of an object or
  coordinates system

void glScalefd(GLfloat x, GLfloat y, GLfloat
z) For example glScalef(2.0f, 2.0f, 2.0f)
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Matrix Stacks

• There are four types of matrix stacks in OpenGL
• The modelview matrix stack
• The projection matrix stack
• The color matrix stack
• The texture matrix stack

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Matrix Stacks

• The modelview matrix stack allows you to save the
  current state of transformation matrix
• The functions to push and pop the matrix stacks
• glPushMatrix() and glPopMatrix()

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The Robot Example

• RobotExample
• Show an animated walking robot around which the
  camera rotate

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Reference

• Dave Astle and Kevin Hawkins, Beginning OpenGL
  Game Programming, 1st Edition, Course Technology
  PTR, 2004.
• http//glbook.gamedev.net