22C151 Homework 3

Homework 3

22C:151 Introduction to Computer Graphics

PART I due Thursday, September 25, 2008
PART II (the full program) due Thursday, October 2, 2008

35 points

PART I REQUIREMENTS: (1) do questions 1, 2, and 3 and (2) get the camera movement/viewing control part of the programming assignment working properly. You don't have to draw any objects (but you can if you want). I only require that you draw the global coordinate frame and have your viewing control commands working. I.e. I should be able to swing, elevate, and zoom the camera to look at the global coordinate frame from different places.

1. An object is to be translated 9 units in direction (0,0,1) and then rotated by 60 degrees about the (global/world) X axis. Show the 4-by-4 transformation matrix that can be used to accomplish this.

2. Assume an object is defined with a local coordinate frame that initially coincides with the global coordinate frame. The object is to be rotated -30 degrees about Y axis, and then translated (-8, 0, 0) in the direction of the object's local X axis.

Show the 4-by-4 transformation matrix that can be used to accomplish this.
Show a two-line OpenGL sequence that produces the matrix using a glRotate followed by a glTranslate.
Show a two-line OpenGL sequence that produces the matrix using a glTranslate followed by a glRotate.

3. In terms of matrices and coordinate frames (not OpenGL code), show how the viewing matrix is formed in terms swing, elevate, and zoom.
NOTE: This problem is certainly best done before implementing the the code! The code is easy once you get the equations right.

PROGRAMMING ASSIGNMENT

Write an OpenGL program that allows interactive creation and movement of lighted shaded objects, camera movement, and both orthographic and perspective viewing projections.

Your program must:

allow creation of cubes, spheres, cones, and one additional shape of your own choice. When created, the objects should initially be placed at the world origin, with their local frames coinciding with the world frame.
draw a representation of a global/world frame (which is located at the position the camera "looks at"). It should also be able to draw a representation of the local frame associated with each object. You should make it possible to toggle frame drawing on and off so that you can view the scene without the frames. It is easy to draw representations for frames using lines or long thin boxes. (Note: the frame axes should not be affected by lighting).
allow users to translate, rotate, and scale objects. You do not have to implement mouse-based "picking" or object selection (which was required in Homework 2). You may simply use menus to select the object you wish to move (or allow cycling through the objects via a keyboard key). For translation, it should be possible to select between translation relative to the directions of the global axes and also relative to the current local axes. (Note that for local translation, the local frame should remain fixed to the object. Translation with respect to the local frame simply means that the translation direction is defined with respect to the local frame axes.) For rotation, you only need to provide rotation with respect to the objects' local frames. Additional notes: 1) you only need to provide the major axis (x, y, and z) rotations. That is, you don't need to provide means for rotating about a user-defined axis.
enable movement of the camera to obtain different views. At any instant, imagine that the camera is attached to the surface of a sphere and is aimed at the world origin. Your program must allow users to (1) "swing" the camera horizontally along latitudinal lines of the current sphere (you could, e.g., use left and right arrow keys for this), (2) "elevate" the camera vertically along longitudinal lines, and (3) "zoom" the camera toward and away from the world origin (thereby changing the radius of the sphere we imagine the camera to be on). To implement viewpoint changes you simply need to determine how to create the appropriate viewing transformation. There are several possible ways, including: 1) store, at all times, a world-to-camera transformation, update it as appropriate based on movement operations, and load the resulting matrix onto the GL modelview stack, or 2) use gluLookAt, if you can figure out the appropriate parameters, or 3) store current values for swing, elevate, and zoom, and use an appropriate combination of glRotates and glTranslates to create the correct view. (HINT: 1 is perhaps the most interesting, 2 is perhaps the most difficult, 3 is probably the easiest.)
support switching between parallel and perspective projections.
provide lighting and smooth shading, and depth buffering must be enabled so that hidden surface elimination is done and a nice looking image will be rendered.