CPSC 4050 / 6050

Spring 2014

Quiz 9 - Making a Scene

Due: In Class, Monday April 14

The following two questions assume that you have a model of a 1m x 1m x 1m cube, centered at the origin. You would like to use this as a primitive to construct a model of a flag on a pole according to the design shown below. Ground coordinates are x (horizontal) and z (depth). Height is the y coordinate. The groundplane is horizontal, at height 0. Each of the components of the model is a rectangular solid. The base is 1m x 0.125 m x 1 m. The pole is 0.125 m x 2.5 m x 0.125 m. The flag is 0.75 m x 0.5 m x 0.0625 m. The flag is hanging down so its far side is 0.125 m down from its side attached to the pole.

1. Draw a scene graph for a scene including the flag model to make a row of flags, like at the UN Headquarters. The scene graph should show the complete construction of the scene, starting from the cube. If you want to get accurate, use Google Maps to check out the UN Headquarters. It is fine to approximate the buildings with rectangular solids, even though the lower building has curved walls.
   
   
   





2. Now, construct two of the matrices that would be needed to implement the scene graph. For each matrix, show your work, so I know how you constructed it, and draw a picture of how the object will look, located in its modeling coordinate system after applying the matrix transform.
   
   

   • Give a single 4x4 matrix that can be used to transform the 1m cube into the base.
     
     
   • Assume that you already have the flag and pole, each in its own modeling coordinate system. Draw a picture of each in its modeling coordinate frame, so I know your starting configuration. Now give the 4x4 matrix that would be required to attach the flag to the pole.