Here is a more general proof for every possible combination of
resolutions between 100% and 400% and for values [0..10000]:
program Project1;
uses Math;
const
Resolutions: array[0..8] of Double = (1.00, 1.25, 1.50, 1.75, 2.00,
2.50, 3.00, 3.50, 4.00);
var
SourceResultion, TargetResolution: Double;
I, F, ErrorCountInMiddleValue, ErrorCountAfterSecondScaling,
MiddleValue: Integer;
begin
ErrorCountInMiddleValue := 0;
ErrorCountAfterSecondScaling := 0;
for SourceResultion in Resolutions do
for TargetResolution in Resolutions do
if not SameValue(SourceResultion, TargetResolution) then
begin
for I := 0 to 10000 do
begin
F := I;
// scale from source to target and back
F := Round(F / SourceResultion * TargetResolution);
F := Round(F * SourceResultion / TargetResolution);
MiddleValue := F;
if not SameValue(F, I) then
begin
Inc(ErrorCountInMiddleValue);
// scale from source to target and back again
F := Round(F / SourceResultion * TargetResolution);
F := Round(F * SourceResultion / TargetResolution);
if not SameValue(F, MiddleValue) then
begin
Writeln('Error after second scaling: ', I, ': ', F, '
SourceResultion:TargetResolution (', SourceResultion, ':',
TargetResolution, ')');
Inc(ErrorCountAfterSecondScaling);
end;
end;
end;
end;
Writeln('ErrorCountInMiddleValue: ', ErrorCountInMiddleValue);
Writeln('ErrorCountAfterSecondScaling: ', ErrorCountAfterSecondScaling);
ReadLn;
end.
Ondrej
--
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