Exercises

 

 

Final Project

 

Scenario

 

A billiards competition takes place on a flat tabletop, without side rails, approximately

    1.2 m (4 ft) x 1.2 m (4 ft) square. Pockets into which the balls are placed are on

    the corners of the area as shown.

A 30 cm by 30 cm square is marked on the tabletop with one side centered on

   and adjacent to the table's edges.

Dimples in the tabletop, approximately 1/2 in in diameter and 1/8 inch deep, retain

   the balls in positions.

When placed on the table, the cue ball will be adjacent to the center of the square's

    in the center of the table. The remaining balls form an equilateral triangle with one

    side parallel to the table's edge opposite the square.

The diameter of each ball is 2.25 inches.

Each corner of the table is cut out to facilitate placing the balls in the pockets.

The scenario is depicted below.

 

 

  The cue ball is a wild card and earns points as if it were one of the other 15 balls. It will

    be designated as the ball which earns the maximum points for the pocket it is in.

  The eight ball will be counted as a solid ball.

  A maximum of 8 points per pocket may be awarded as follows.

 

      One point for each ball placed in a pocket (max 4 points per pocket)

      One point if the pocket contains a solid colored ball and its matching color striped

      ball.

      One point if the pocket contains two or more striped balls.

      One point if the pocket contains two or more solid colored balls.

 

  Example: If the cue ball is in a pocket with the yellow striped ball (9), solid orange

   ball (5), and orange striped ball (13), it would be designated as the solid yellow ball (1)

   and the score for the pocket would be 8 points (4 balls in pocket-4 points, 2 solids-1 point,

   2 stripes-1 point, yellow solid and yellow striped balls-1 point, orange solid and orange

   striped balls - 1 point.

 

Rules

 

The robot must stay on the table as described above.

  Robot configuration and size.

 

       Assume a 6 inch by 6 inch square. If you believe the vertical dimension is relevant,

       state the assumption as described below.

       The robot has a grabber capable of securing one ball at a time for transport and

       subsequent release.

 

  Robot restrictions-The robot

 

       Can grab and deposit only one ball at a time.

       Cannot reach over a ball; it can grab only balls located on the current outer perimeter.

       Is not allowed to clear a path by bumping balls.

 

  Required assumptions:

 

       The holes are labeled A through D going counter clockwise beginning with the hole to

       the right of the 30 cm by 30 cm square as described above.

       Make some reasonable assumptions concerning the robot's navigations around the balls;

       state the assumptions used.

       Make a reasonable assumption concerning the distance from the side of the triangle

       opposite the 1 ball (side containing balls 11 through 15) from the edge of the table;

       state the assumption used.

 

  Additional assumptions:

 

       You can make any other reasonable assumptions.

       Additional assumptions cannot violate any of the items stated.

       Clearly describe any additional assumptions that you make.

 

Requirements

 

  Determine the hole (A, B, C, or D) each ball (16 total) is placed in and the sequence of

   placement so that the maximum number of points is achieved in minimum time (distance)

  Total distance traveled

  Required average speed.

 

Turn In

 

  One-page summary of your solution approach

  Code with appropriate comments

  The hole each ball is placed in and the sequence of placement (Ball 1 placed in pocket A,

    ball 3 in pocket A, ball 10 in pocket D, etc.

  Total distance traveled.

  Average speed the robot would have to maintain in order to complete the task in 5 minutes.

  A 1/2 page summary (no code, no output) of another major solution technique that could

   have been used to solve the problem. Summarize the setup only.