een218 autumn 2001, assignment 4

Changed Monday 12th November

This is not a major change; you will not need to modify your work in any way. I accidentally added an extra requirement for the shape class. This HTML page originally said that your shape class must include a method float dispance(point p). That was an editing error, I didn't state that requirement in class, so you don't have to do it. Finding the distance from a shape to a point is not as easy as you might imagine.

If anyone actually implemented that method, I'll give you extra credit for it.

Assignment 4

Due Tuesday 13th November.

This assignment has three parts, plus an optional fourth for extra credit.

Part A
        In programming terminology, a Vector is an object that behaves exactly like a normal array, except that its size can be changed at any time, and accesses to the contents are protected, so that improper accesses (for example trying to use A[-3]) do not crash the program.
        Implement a Vector-of-ints object (almost exactly as we investigated it in class). Use your object definition in a program that thoroughly tests it.
        Part A should be a separate program, there is nothing to gain by trying to combine it with parts B and C.

Part B
        Implement a class representing a geometric point in 2-dimensional space (that is, it has two components, its x co-ordinate and its y co-ordinate). Very much like the second question of the recent mid-term.
        Make sure that your definition includes all appropriate constructors, etc. It must include the following required methods:

void scale(float factor)
void rotate(float angle)
void translate(float xshift, float yshift)
float distance(point p)
void print()

Rotation and translation are of course relative to the origin (0,0), angles are in radians.

Part C
Implement a class representing a geometric shape in 2-dimensional space. A shape (in this case) is just a connected collection of straight lines, and can be completely described by the co-ordinates of its vertices (i.e. corners). You should implement a shape as a vector of points, so part C should be combined with part B into a single program.
Your shape class must include the following required methods:

void scale(float factor)
void rotate(float angle)
void translate(float xshift, float yshift)
float perimeter()
float area()
void print()

Note that the perimeter and area methods are new to part C (they are not part of the requirements for part B). As an example, this snippet of code shows a square (between x=1 and x=2 and y=3 and y=4) being defined. The calculated area should be 1, and the perimeter 4.

{ shape s;
  s.add(new point(1,3));
  s.add(new point(1,4));
  s.add(new point(2,4));
  s.add(new point(2,3));
  float a=s.area();
  float p=s.perimeter();
  printf("shape ");
  s.print();
  printf(" has area %f and perimeter %f\n", a, p); }

Optional Part D for extra credit only
and implement some useful methods
Design that find the intersections between two shape objects. One possibility is to find out whether two shapes intersect at all; another is to find out how many intersection points there are; another would be to find all the points of intersection, and construct a new shape that represents the whole area of intersection (although this is quite tricky).