12.4. Curves   

What about curves? We can use many very small line segments, perhaps even points (= line segment of unit length with no orientation) to produce curves. 


Example circle:


 An arbitrary point (x,y) on circle of radius R and centre (0.0,0.0)

may be represented by vector pair:


         (R*cos,R*sin)


where  is angle that radius through

the point makes with x-axes. Hence increment  from 0 to 360 in N-equal

increments produces N-gon = N sided equilateral polygon.


If N is large enough, looks like a circle.


   program CIRCLE


      call      export(stdin,stdout);    {Allow library to use stdio.}

      call      askdev(device);

      input     radius ;

      call      start(2);

      call      plot(9.5,7.375,-3);      {centre circle }

      call      plot(radius,0.0,3);      {move to radius of circle}


      theta  0.0;

      theta_inc  2*PI/100;


      for i  1 to 100 do

           theta  theta + theta_inc;

           call      plot(radius*cos(theta),radius*sin(theta),2);

           {draw to next point on circle radius}

      endfor;


      call      enplot;


   end_program_circle.

This produces the circle of Figure 12.2 a but if we mistakenly assume that sin and cos function take an argument in degrees rather than radians we get the star shaped image of Figure 12.2 b.

We can produce other geometric curves in the same way = PARAMETRIC EQUATIONS 


    
(a). Circle.

   
                  Fig. 12.1 : (a). Circle.



    
(b). Circle?

   
                  Fig. 12.2 : (b). Circle?