Rogue line being drawn to window

Question

I am making a graphing program in C++ using the SFML library. So far I have been able to draw a function to the screen. I have run into two problems along the way. The first is

Answer 1

The first problem looks like a wrong polyline/curve handling. Don't know what API are you using for rendering but some like GDI need to start the pen position properly. For example if you draw like this:

Canvas->LineTo(x[0],y[0]);
Canvas->LineTo(x[1],y[1]);
Canvas->LineTo(x[2],y[2]);
Canvas->LineTo(x[3],y[3]);
...

Then you should do this instead:

Canvas->MoveTo(x[0],y[0]);
Canvas->LineTo(x[1],y[1]);
Canvas->LineTo(x[2],y[2]);
Canvas->LineTo(x[3],y[3]);
...

In case your API needs MoveTo command and you are not setting it then last position is used (or default (0,0)) which will connect start of your curve with straight line from last draw or default pen position.

Second problem

In continuous data you can threshold the asymptotes or discontinuities by checking the consequent y values. If your curve render looks like this:

Canvas->MoveTo(x[0],y[0]);
for (i=1;iLineTo(x[i],y[i]);

Then you can change it to something like this:

y0=y[0]+2*threshold;
for (i=0;i=threshold) Canvas->MoveTo(x[i],y[i]);
  else                   Canvas->LineTo(x[i],y[i]);
 y0=y[i];
 }

The problem is selection of the threshold because it is dependent on x density of sampled points and on the first derivation of your y data by x (slope angles)

If you are stacking up more functions the curve append will create your unwanted line ... instead handle each data as separate draw or put MoveTo command in between them

[Edit1]

I see it like this (fake split):

double x0,y0,x1,y1,a;
for (e=1,x = -pi; x < pi; x += .0005f)
    {
    // last point
    x0=x1; y0=y1;
    // your actual point
    x1=x; y1=-tan(x);
    // test discontinuity
    if (e) { a=0; e=0; } else a=fabs(atan2(y1-y0,x1-x0));
    if (a>0.499*M_PI) curve.append(Vertex(Vector2f(x1,y1), Color::Black));
     else             curve.append(Vertex(Vector2f(x1,y1), Color::Green));
    }

the 0.499*M_PI is you threshold the more closer is to 0.5*M_PIthe bigger jumps it detects... I faked the curve split by black color (background) it will create gaps on axis intersections (unless transparency is used) ... but no need for list of curves ...