Currently I'm using "Douglas Peucker" algorithm.
My problem is that when I'm drawing,the previously drawn lines are also changing which of course not realistic. Is there other alternative algorithm to minimize the saved points but not altering the previous drawn points or other way to alter "Douglas Peucker" to fit my need?
Give your pencil drawing tool 2 optional methods for drawing:
Draw a new point on the path using mousemove (which is your current freeform method). This option will let the user add many points which will allow them to be very detailed in their drawing.
Draw a new point on the path only upon mousedown. This option simply connects the previous point on the path to the newly clicked point. This option will let the user add just a few very straight lines which will allow them to outline figures with long running straight edges.
If you are concerned about the freeform path changing while the user is drawing you can apply the simplifying algorithm just once after they have stopped moving the mouse for 1 second.
If you specify the Douglas-Peucker algorithm use a high bias for accuracy then the simplified path will remain quite true to the unsimplified path.
BTW, if you want to draw splines through your points then check out this nice previous post: how to draw smooth curve through N points using javascript HTML5 canvas?