Making the Transition to 3D Modeling

• right-handed xyz coordinate system
• how our TUGL library should handle 3D points

• camera set on the orgin looking down the negative z axis
• using glFrustum(left, right, bottom, top, near, far) for perspective projection
• using the keyboard to control
• elevation
• azimuth
• twist
• distance to near plane
  

Review of Vectors Hill: Chapter 4 through 4.5

• vector vs point
• vector operations
  • difference between two points and how it relates to parametric representation of a line (and to tweening)
  • sum
  • scalar product
  • dot product
  • length (magnitude)
  • unit vectors
• linear combination of vectors
  • affine linear combination
  • convex affine linear combination

2D and 3D Transformations

Transformations of Objects       Hill: Chapter 5;   

• Affine Transformations

  Task: Develop general procedures for applying translation, rotation, and scaling parameters to reposition and resize 2D objects. Then extend to 3D.

  • Matrix Multiplication
    • the Identity Matrix
  • Translation
    • with respect to the origin
    • with respect to an arbitrary fixed point
  • Scaling
    • with respect to the origin
    • with respect to an arbitrary fixed point
  • Rotation
    • with respect to the origin
    • with respect to an arbitrary fixed line
      
      
  • Homogeneous Coordinates
    
    
  • Composition of Transformations
    
    
• OpenGL and Affine Transformations
  • the pipeline
  • the Current Transformation
  • the stack

REFERENCE(S):

Computer Graphics Using OpenGL (Hill):
     Section 4.1, 4.2, 4.3, 4.4 (p. 132 - 154)
    Appendix A2.3 (pages 707-708)
   
Computer Graphics Using OpenGL (Hill): Chapter 5; 

GLUT Programming Interface: Chapters 11 (Object Rendering);   
  
OpenGL Manual/v.1.2: p. 129-130
OpenGL Manual/v.1.2:  Modeling Transformations, pages 104 - 112;

GLUT Programming Interface:

part of the spinning square

/classes/cs3014/files/Viewing/sphericalview.cpp

/classes/cs3014/files/Transformations (everything in this directory)