Plotting Euler Integration using Polyline(), C++

问题:

So I'm trying to plot the output of this Euler integration function:

typedef double F(double,double);
using std::vector;

void euler(F f, double y0, double a, double b, double h,vector<POINT> Points)
{

POINT Pt;
double y_n = y0;
double t = a;
for (double t = a; t != b; t += h )

{
    y_n += h * f(t, y_n); 

    Pt.x = t; // assign the x value of the point to t.
    Pt.y = y_n; // assign the y value of the point to y_n.
    Points.push_back(Pt);

}


}


// Example: Newton's cooling law
double newtonCoolingLaw(double, double t) 
{
    return t; // return statement ends the function; here, it gives the time derivative y' = -0.07 * (t - 20)
}

I'm trying to use the Polyline() function in a Win32 application, so I do this under the case WM_PAINT:

case WM_PAINT:
    {

    hdc = BeginPaint(hWnd, &ps);

  //Draw lines to screen.

    hPen = CreatePen(PS_SOLID, 1, RGB(255, 25, 5));
    SelectObject(hdc, hPen);


    using std::vector;
    vector<POINT> Points(0);

    euler(newtonCoolingLaw, 1, 0, 20, 1,Points);

    POINT tmp = Points.at(0);
    const POINT* elementPoints[1] = { &tmp };

    int numberpoints = (int) Points.size() - 1 ;


    Polyline(hdc,elementPoints[1],numberpoints);

When I reroute my I/O to console, here are the outputs for the variables:

I'm able to draw the expected lines to the screen using MovetoEx(hdc,0,0,NULL) and LineTo(hdc,20,20), but for some reason none of these functions will work with my vector<POINT> Points. Any suggestions?

回答1:

There are multiple things that seem erroneous to me:

1) You should pass the vector by reference or as a return value:

void euler(/*...*/,vector<POINT>& Points)

Currently you are only passing a copy into the function, so the original vector will not be modified.

2) Don't compare doubles for (in-)equality in your for-loop header. Doubles have a limited precision, so if b is much bigger than h, your loop might never terminate, as t might never exactly match b. Compare for "smaller" instead:

for (double t = a; t < b; t += h )

3) Why are you declaring elementPoints as an array of pointers of size 1? Wouldn't a simple pointer do:

const POINT* elementPoints =  &tmp ; //EDIT: see point 5)

4) You have an of-by-one error when calling Polyline. If you want to stick with the array at all use.

Polyline(hdc,elementPoints[0],numberpoints);

EDIT: Sorry, I forgot an important one:

5) In your code, elementPoints[0] points to a single double (tmp) and not to the array inside of the vector. This would probably work, if you declared tmpas a reference:

POINT& tmp = Points.at(0); //I'm wondering why this doesn't throw an exception, as the vector should actually be empty here

However, I think what you actually want to do is to get rid of tmp and elementPoints altogether and write in the last line:

Polyline(hdc,&Points[0],(int) Points.size()-1);
//Or probably rather:
Polyline(hdc,&Points[0],(int) Points.size());

Btw.: What is the purpose of the -1?