Extending a straight line

[kapibara]

There is a sloping LineSeries with two points showing a straight line.
How can I calculate the Y value so the line continues in the same direction?

This line is like a guide-line that should follow along when values are added to another Series in the same chart. But must never change angle.

[taazz]

the formula to calculate the slope of a line is m=(y1-y2)/(x1-x2) having two points (x1,y1) and (x2,y2) of the line you can calculate the slope after that you use the same formula but now you use (x2,y2) as the first point and (x3,y3) as the second point which is the new point you are searching for. I'm assuming you already know the x3 value and you are searching for the y3 value and that is calculated by taking the slope formula and solving for y3 something along the lines of m=(y2-y3)/(x2-x3)=>m*(x2-x3)=(y2-y3)=>(m*(x2-x3)) /y2 = -y3=>y3=-((m(x2-x3)) /y2) and that is the final formula you have to use to find your new Y point.

[engkin]

y3=-((m(x2-x3)) /y2) and that is the final formula you have to use to find your new Y point.

Building on Taazz's work:
y3=-((m(x2-x3)) /y2)

you can calculate m and c once:

Code: [Select]

m := (y2-y1)/(x2-x1);
c := -m*x2/y2;
then you can find y for any x using:

Code: [Select]

y := m*x+c;

[wp]

Or you can use the built-in TFitSeries (add a "Least-squares fit series") and assign the first two points to it. It will automatically calculate the line through both points and paint it beyond the two points with these settings:
- FitEquation = fePolynomial
- ParamCount = 2
- DrawFitRangeOnly = false

[kapibara]

Thanks for helping, but the angle of the GuideLine changes when it is extended. I cant find out why:

Code: [Select]

procedure TForm1.FormCreate(Sender: TObject);
begin
  { Some values for the GuideLine }
  Pt1.X:=3;
  Pt1.Y:=1.3;
  Pt2.X:=6;
  Pt2.Y:=1.65;

  { Populate GuideLine Series }
  GuideLine.AddXY(Pt1.X, Pt1.Y);
  GuideLine.AddXY(Pt2.X, Pt2.Y);

  { Populate Line Series, for comparison }
  LineSeries.AddXY(1, 1);
  LineSeries.AddXY(10, 2);
end;

procedure TForm1.btnExtendClick(Sender: TObject);
const
  LAST_REC = 1;
begin
  m := (Pt2.Y - Pt1.Y) / (Pt2.X - Pt1.X);
  c := -m * (Pt2.X / Pt2.Y);
  Pt2.X:= LineSeries.GetXMax;
  Pt2.Y := m * Pt2.X + c;

  GuideLine.SetXValue(LAST_REC, Pt2.X);
  GuideLine.SetYValue(LAST_REC, Pt2.Y);
end;
@wp: The FitSeries extends as you said. So far I have used a TLineSeries that the user can resize and move around. Maybe it can be substituted with the FitSeries. But I'm anyway interested in how to do this with a TLineSeries.

[taazz]

the angle of a line can't change when you extend it unless it stops being a line and breaks in to two or more lines.

[kapibara]

@Taazz: You know, then you still have straight lines, just more of them. 

The demo shows the problem clearly.

[kapibara]

This function seems to work very well:

function PointAtX(a, b: TDoublePoint; x: Double): TDoublePoint;
var
  aSlope: Double;
  y: Double;
begin
    aSlope:= (b.Y - a.Y) / (b.X - a.X);
    y:= a.Y + (x - a.X) * aSlope;
    Result.X:= x;
    Result.Y:= y;
end;