function TMainForm.NumberLineDistReal(valOne, valTwo: Real): Real;
//UTILITY FUNCTION
//simple arithmetic operations of the kind that you do all the time
//in graphics can produce erroneous outputs if one is not extremely
//careful about 'abs-ing' values where appropriate: this function
//bundles up the algorithm to find the 'absolute distance along the
//number line' between two Real values so that we can just call it
//up as appropriate...
begin
Result := InitialValue;
if ((valOne >= 0) and (valTwo >= 0)) then
begin
if (valOne >= valTwo) then Result := (valOne - valTwo)
else Result := (valTwo - valOne);
end;
if ((valOne < 0) and (valTwo >= 0)) then
begin
if (valOne >= valTwo) then Result := (abs(valOne) + valTwo)
else Result := (abs(valOne) + valTwo);
end;
if ((valOne >= 0) and (valTwo < 0)) then
begin
if (valOne >= valTwo) then Result := (valOne + abs(valTwo))
else Result := (abs(valTwo) + valOne);
end;
if ((valOne < 0) and (valTwo < 0)) then
begin
if (valOne >= valTwo) then Result := (abs(valTwo) - abs(valOne))
else Result := (abs(valOne) - abs(valTwo));
end;
end;
//////////////////////////////////////////////////////////////////////////
function TMainForm.NumberLineDistInteger(valOne, valTwo: Integer): Integer;
//UTILITY FUNCTION
//see notes in NumberLineDistReal() above...
begin
Result := InitialValue;
if ((valOne >= 0) and (valTwo >= 0)) then
begin
if (valOne >= valTwo) then Result := (valOne - valTwo)
else Result := (valTwo - valOne);
end;
if ((valOne < 0) and (valTwo >= 0)) then
begin
if (valOne >= valTwo) then Result := (abs(valOne) + valTwo)
else Result := (abs(valOne) + valTwo);
end;
if ((valOne >= 0) and (valTwo < 0)) then
begin
if (valOne >= valTwo) then Result := (valOne + abs(valTwo))
else Result := (abs(valTwo) + valOne);
end;
if ((valOne < 0) and (valTwo < 0)) then
begin
if (valOne >= valTwo) then Result := (abs(valTwo) - abs(valOne))
else Result := (abs(valOne) - abs(valTwo));
end;
end;