Mapping between screen and world
mapping world and screen by R.Tschaggelar
Mapping from screen ( integer) coordinates to world ( real) coordinates
- linear
In the status bar panels you can see the coordinates of mouse position in world and screen values.
That is linear mapping : iX:=Ax*eX+Bx
eX:=(iX-Bx)*StepX where StepX:=1/Ax
iX = screen coordinate ( integer type X )
eX = world coordinate ( extended type X)
You can see that in Delphi origin ( 0,0) is in the left upper corner of the image.
If you want you should change it.
-
Mirror symmetry around x axis:
Special case: y:=0 is in the middle of image. Then color of pixel (x, y) is the same as color of pixel (x,-y). :
Programs using this symmetry for drawing Mandelbrot set in special case:
Programs using this symmetry for drawing Mandelbrot set in general case:
General case: the program checks if y:= 0 is in the drawing region and then
- uses the symmetry or not.
- computes symmetric and non symmetric regions, and symmetry axis
- is using integer not real numbers ( its better to use integer numbers)
Source code in delphi
- black line= axis of symmetry
- blue = part made without symmetric procedure
- yellow = non-symmetric part made with symmetric procedure
- red and green = symmetric parts made with symmetric procedure
- axis of symmetry is out of range of drawing area (iYaxisOfSymmetry < iYmin )
Ornaments - program by Martin von Gagern
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Author: Adam Majewski adammaj1-at-o2-dot-pl
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