• Download Glut for Windows. The glut.dll file must be installed to \Windows\System directory.
• Download a bouncing ball example.

ASSIGNMENT (2 parts)

1. Exercise 2.4, implement a turtle graphics API using OpenGL. A typical turtle graphics API includes:

   init(x, y, theta)	Initialize (x,y) turtle position and orientation angle.
   forward( distance )	Move turtle forward distance in turtle world. Draw line if pen is down.
   right( angle )	Turn turtle right by angle degrees.
   left( angle )	Turn turtle left by angle degrees.
   pen( position )	Position down for line drawing as turtle moves forward or up for no line drawing.

    

   For example, a turtle (OK, a cat):

   • initially at the center of turtle world pointing toward the positive x axis - init(0,0,0)
   • positions the pen down - pen(down)
   • moves forward 2 - forward( 2 )
   • turns left 90 degrees - left( 90 )
   • and moves forward 1 - forward( 1 )

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   Test by:

1. rotating a square about one corner,
2. generating the Sierpinski gasket of Figure 2.36 on page 80.

Hints:

1. the turtle is in degrees but C math functions use radians (the conversion of angle q from degrees to radians is: q*3.14159/180.0)
2. forward(distance) must compute the change in X and Y position when moving distance at orientation q degrees.

   X += distance * cos(q*3.14159/180.0)
   Y += distance * sin(q*3.14159/180.0)

2. Exercise 2.16, yet another bouncing ball.

   Hints: The simulation can be relatively simple but should account for gravity and the elasticity of the ball.  You should consult an elementary physics text for a detailed discussion of gravity and elasticity.

   • The basic simulation starts with the ball dropped from some arbitrary height.
   • There are at least two approaches to modeling:

      

     1. Determining the current vertical position from an initial velocity (which is 0 when dropped or at the peak height and negative when bounced). With the ball dropped from some arbitrary height, y₀, at a velocity of 0 or after bouncing, when downward velocity is negative, the vertical position is:

        y = y₀ + velocity * time - gravity * time² / 2

        When the balls bounces the velocity is:

        velocity = (velocity - gravity * time)*e

        where e (coefficient of restitution which we can arbitrarily choose 0..1). This is intuitively appealing time is always incremented and downward velocity is positive or negative.

   2. Determining the distance traveled by the ball and upward travel time following the rebound. The vertical distance traveled is:

   distance traveled = gravity * time² / 2

   One way to model the ball bouncing is to increment time on the way down and decrement time on the way up after a bounce.

   The height of the bounce is determined by e (coefficient of restitution which we can arbitrarily choose 0..1) where:

   height' = e²*distance traveled

   A ball with elasticity of 0.4 dropped from 10 meters would rebound to 1.6 meters.

   The height of the rebound allows the calculation of the time of upward travel by:

   time = sqrt( 2*height'/gravity)

   • To smooth the display of the ball to a more natural effect examine Sections 3.11.1 Idle function, 3.11.2 Double Buffering and 3.11.3 Using a Timer. Each will be discussed in class.

TEST

1. Using your turtle graphics API, draw a square with the upper-right corner centered in the window; redraw the square in small, uniform angle increments, 360 degrees about the original square's upper-right corner. To verify the accuracy of your algorithm, repeat, rotating 3600 degrees about the original upper-right corner. The visual effect will be interesting.
2. Using your turtle graphics API, generate the Sierpinski gasket of FIGURE 2.38 on page 80.
3. The bouncing ball; the visual effect should be based on the physical model of a bouncing ball.

EMAIL

1. To  with subject: YOUR NAME: B481 and Homework 2.
2. Send a Web accessible link to a zip file named with your last name as Lastname.zip containing:
   • Three directories named 1, 2 and 3:
     • 1 contains all files (include exe) for TEST 1
     • 2 contains all files (include exe) for TEST 2
     • 3 contains all files (include exe) for TEST 3

   Files stored on your W: drive are Web accessible by: http://homepages.ius.edu/username/filename

   To setup your IUS account to publish Web pages: Login to the IUS LAN. Click http://www.ius.edu/SpinWeb to run a setup utility and follow instructions.

   Ftp files by:

   1. ftp webftp.ius.edu
   2. ads/username
   3. password
3. Instructions on executing each.

COMPILING AND EXECUTING IN VISUAL STUDIO

The following assignment serves as an introduction to OpenGL and Glut on a Microsoft system. OpenGL is part of Visual Studio while Glut for Windows must be downloaded (see above link).

To create an empty console project:

1. In Visual Studio, select: File | New | Project
2. In Other Languages select: C++ | Console Application
3. Name: gasket
4. On next screen, select: Application Settings | Empty Project

To add the code for the Sierpinski gasket:

1. Select: View | Solution Explorer
2. Right click: Source Files | Add | New Item
3. Download gasket.c
4. Copy and paste the code.

To define the location of glut.h and glut libraries

1. Select: Project | Properties | Configuration Properties | C/C++
2. Enter: Additional Include Directories, the location of the glut installation, probably C:\glut
3. Select: Linker
4. Enter: Additional Library Directories, the location of the glut installation, probably C:\glut

To execute and produce Figure 2.2 on page 45 of the text:

1. Select: Build | Build Solution (ignore the warning).
2. Select: Debug | Start without Debugging