Mega Code Archive
Calculations with points
<![CDATA[
Title: Calculations with points
Question: 1) Calculating a point using angles and distance
2) Calculating an angle from two points
3) Finding distance between two points
Answer:
1)
How do I calculate the x and y coordinates of a point that is
at some distance and angle away?
The following example shows how to convert a polar coordinate to a
rectangular coordinate:
procedure TForm1.Button1Click(Sender: TObject);
var
Angle : Double;
x : Double;
y : Double;
Distance : Double;
Radians : Double;
begin
Distance := 100;
Angle := 270;
Radians := Angle * DegToRad;
x := Round(Distance * Cos(Radians));
y := Round(Distance * Sin(Radians));
ShowMessage(FloatToStr(x) + ' ' + FloatToStr(y));
end;
2)
How can I tell the given angle expressed by two points?
The following example shows how to tell the angle of a
given point from the coordinate 0, 0. In this example, the
caption of the form shows the current point and angle from
the center of the form. The y coordinates are inverted to
show a more natural north orientation where north is
directly up.
Example:
const RADTODEG = 180 / Pi;
function AngleOfPt(pt : TPoint) : double;
begin
Result := 0;
if ((Pt.x = 0) and (Pt.y Result := 270 else
if ((Pt.x = 0) and (Pt.y 0)) then
Result := 90 else
if ((Pt.x 0) and (Pt.y = 0)) then
Result := ArcTan(Pt.y / Pt.x) * RADTODEG else
if ((Pt.x 0)) then
Result := 180 - (ArcTan(Pt.y / Abs(Pt.x))* RADTODEG) else
if ((Pt.x Result := 180 + (ArcTan(Pt.y / Pt.x) * RADTODEG) else
if ((Pt.x 0) and (Pt.y Result := 360 - (ArcTan(Abs(Pt.y) / Pt.x) * RADTODEG) else
Result:=0;
end;
procedure TForm1.FormMouseMove(Sender: TObject; Shift:
TShiftState; X, Y: Integer);
var
XYMove : TPoint;
RotateAngle : Double;
begin
XYMove := (Point(x - (Form1.Width div 2),
(Form1.Height div 2) - y));
RotateAngle :=
AngleOfPt(XYMove);
Form1.Caption := IntToStr(XYMove.x) + #32 +
IntToStr(XYMove.y) + ' = ' +
FloatToStr(RotateAngle);
end;
procedure TForm1.FormPaint(Sender: TObject);
begin
Form1.Canvas.MoveTo(Form1.Width div 2,
0);
Form1.Canvas.LineTo(Form1.Width div 2,
Form1.Height);
Form1.Canvas.MoveTo(0,
Form1.Height div 2);
Form1.Canvas.LineTo(Form1.Width,
Form1.Height div 2);
end;
procedure TForm1.FormResize(Sender: TObject);
begin
Invalidate;
end;
3)
How can I find the distance between two points?
The following example shows how to tell the distance between two
points. In this example, the caption of the form shows the current
point and distance from the center of the form. The y coordinates are
inverted to show a more natural north orientation where north is
directly up.
Example:
funcTion Distance(Pt1 : TPoint;
Pt2 : TPoint) : Double;
var
dx : LongInt;
dy : LongInt;
begin
dx:= pt1.x - pt2.x;
dy:= pt1.y - pt2.y;
Result := Sqrt((Dx * Dx) + (Dy * Dy));
end;
procedure TForm1.FormMouseMove(Sender: TObject; Shift:
TShiftState; X, Y: Integer);
var
Pt1 : TPoint;
Pt2 : TPoint;
Dist : Double;
begin
Pt1.x := Form1.Width div 2;
Pt1.y := Form1.Height div 2;
Pt2.x := x;
Pt2.y := y;
Dist := Distance(Pt1, Pt2);
Form1.Caption := IntToStr(Pt2.x - Pt1.x) + #32 +
IntToStr(Pt1.y - Pt2.y) + ' = ' +
FloatToStr(Dist);
end;
procedure TForm1.FormPaint(Sender: TObject);
begin
Form1.Canvas.MoveTo(Form1.Width div 2,
0);
Form1.Canvas.LineTo(Form1.Width div 2,
Form1.Height);
Form1.Canvas.MoveTo(0,
Form1.Height div 2);
Form1.Canvas.LineTo(Form1.Width,
Form1.Height div 2);
end;
procedure TForm1.FormResize(Sender: TObject);
begin
Invalidate;
end;
]]>