CMPT 370 Spring 2007 Lab4 (30 pts): Quaternions

Objectives

• To learn about quaternions.
• To create an easy-to-use virtual trackball interface for rotating 3D models.

  Background

• A virtual trackball interface maps 2D mouse coordinates onto a 3D upper hemisphere. The 2D mouse coordinates in the x-z-plane are (x, 0, z). This projects up to the point (x, y, z) on a hemisphere centred at the origin. Moving the mouse corresponds to moving from point p1 to p2 on the hemisphere. From p1 and p2 we can derive the axis of rotation n, and the rotation angle.
  
• A quaternion can be represented as an array of 4 floats. From the axis of rotation and the rotation angle, a quaternion describing this rotation can be derived. Every incremental mouse motion corresponds to a new quaternion; individual quaternions can be multiplied to give a larger rotation.
• Lastly, from the quaternion, an OpenGL 4x4 rotation matrix needs to be derived.
• If you'd like to read in more complex models rather than generating your own, a fairly basic library to read Alias Wavefront OBJ files is Nate Robins' GLM. You can get it from many places, e.g., Avimator's SVN (glm.cpp and glm.h). Basic usage (see the header file):

  #include "glm.h"
  GLMmodel* myModel = glmReadOBJ("myfile.obj", 0);
  glmDraw(myModel, GLM_NONE, 0);
  

  Basic requirements

• To your OpenGL viewer from Lab3, add a virtual trackball interface using quaternions, to let the user rotate the model in 3D. You must write your own implementation of quaternions. You should write code that translates from 2D mouse motion to a quaternion, and from a quaternion to a 4x4 rotation matrix suitable for glMultMatrix(). Part of that will involve recoding the functionality of glRotate().
• Make the user interface so that when the user moves the mouse with a certain mouse button (e.g., left) held down, the model is rotated using your virtual trackball.

  Extra credit (up to 5 pts, only if basic requirements are met)

• For extra credit, allow the user to "toss" the rotation of an object: if the user releases the mouse button while still moving the mouse, the object continues to rotate on its own. See FLTK idle callbacks.
• Provide a way to stop the animation (perhaps by single-clicking the mouse).

  Lab write-up

• Follow the template lab write-up to document your program. Name your write-up:
  your_name_lab4_writeup.doc (or .txt, etc.)
  Put it in the same project directory as your code so that it will be included in the tarball.

  Electronic turn-in

• Put everything (C++ code, header files, executable, lab write-up) into a tarball/ZIP and upload it to eCourses under "Lab4":
  your_name_lab4.zip