Question

I have a problem due to my terrible math abilities, that I cannot figure out how to scale a graph based on the maximum and minimum values so that the whole graph will fit onto the graph-area (400×420) without parts of it being off the screen (based on a given equation by user).

Let’s say I have this code, and it automatically draws squares and then the line graph based on these values. What is the formula (what do I multiply) to scale it so that it fits into the small graphing area?

vector<int> m_x;
vector<int> m_y; // gets automatically filled by user equation or values

int HeightInPixels = 420;// Graphing area size!!
int WidthInPixels = 400;
int best_max_y = GetMaxOfVector(m_y);
int best_min_y = GetMinOfVector(m_y);
m_row = 0;
m_col = 0;

y_magnitude = (HeightInPixels/(best_max_y+best_min_y)); // probably won't work
x_magnitude = (WidthInPixels/(int)m_x.size());
m_col = m_row = best_max_y; // number of vertical/horizontal lines to draw

////x_magnitude = (WidthInPixels/(int)m_x.size())/2; Doesn't work well
////y_magnitude = (HeightInPixels/(int)m_y.size())/2; Doesn't work well

ready = true; // we have values, graph it
Invalidate(); // uses WM_PAINT

////////////////////////////////////////////
/// Construction of Graph layout on WM_PAINT, before painting line graph
///////////////////////////////////////////
CPen pSilver(PS_SOLID, 1, RGB(150, 150, 150) ); // silver
    CPen pDarkSilver(PS_SOLID, 2, RGB(120, 120, 120) ); // dark silver
    dc.SelectObject( pSilver ); // silver color
    CPoint pt( 620, 620 ); // origin
    int left_side = 310;
    int top_side = 30;
    int bottom_side = 450;
    int right_side = 710; // create a rectangle border
    dc.Rectangle(left_side,top_side,right_side,bottom_side);
    int origin = 310;
    int xshift = 30;
    int yshift = 30;
    // draw scaled rows and columns
    for(int r = 1; r <= colrow; r++){ // draw rows
        pt.x = left_side;
        pt.y = (ymagnitude)*r+top_side;
        dc.MoveTo( pt );
        pt.x = right_side;
        dc.LineTo( pt );
        for(int c = 1; c <= colrow; c++){
            pt.x = left_side+c*(magnitude);
            pt.y = top_side;
            dc.MoveTo(pt);
            pt.y = bottom_side;
            dc.LineTo(pt);
        } // draw columns
    }
    // grab the center of the graph on x and y dimension
    int top_center = ((right_side-left_side)/2)+left_side;
    int bottom_center = ((bottom_side-top_side)/2)+top_side;

Answer 1

You are using ax^2 + bx + c (quadratic equation). You will get list of (X,Y) values inserted by user.
Let us say 5 points you get are

(1,1)
(2,4)
(4,1)
(5,6)
(6,7)


So, here your best_max_y will be 7 and best_min_y will be 1.
Now you have total graph area is

Dx = right_side - left_side //here, 400 (710 - 310)
Dy = bottom_side - top_side //here, 420 (450 - 30)

So, you can calculate x_magnitude and y_magnitude using following equation :


x_magnitude = WidthInPixels / Dx;
y_magnitude = HeightInPixels / Dy;