# Linear Mapping issue

Hello forum,

I am not sure if the title is proper or not. I better explain the issue. I have to generate a fractal curve inside an arbitrary window of size pXq where the lower left corner of the window is (0,0). After the generating the fractal within the window, I have to map the coordinates of the fractal to another domain where the lower left corner of the window may not be at (0,0). It could be (-560,789)/(-23,-45).

I hope that the issue is explained. Some hint/references is appreciated.

Thanks

[QUOTE=sajis997;1280415]Hello forum,

I am not sure if the title is proper or not. I better explain the issue. I have to generate a fractal curve inside an arbitrary window of size pXq where the lower left corner of the window is (0,0). After the generating the fractal within the window, I have to map the coordinates of the fractal to another domain where the lower left corner of the window may not be at (0,0). It could be (-560,789)/(-23,-45).

I hope that the issue is explained. Some hint/references is appreciated.

Thanks[/QUOTE]

Lets say we have window1 and window2. Lets say the window is defined by x,y,w,h where x,y is the a corner and w,h is the width and height. The formula to go from window1.xy to window2.xy is:

P = point on window1;

xfactor = window2.width / window1.width;
yfactor = window2.height / window1.height;

xoffset = window2.x - window1.x;
yoffset = window2.y - window1.y;

P2 = new Point;

P2.x = xfactor ( p.x ) + xoffset;
p2.y = yfactor ( p.y ) + yoffset;

P2 is the point on window2;

Note the xy must be the same corner for both windows. So if the upper-left on window1 is 0,0. And the bottom-left on window2 is 0,0. Then we just invert the y.
Note if both windows have the same size then the y and x factors become 1. Then you can simplify the formula to P2.x = p.x + xoffset, P2.y = p.y + yoffset;

So lets work through a hypothetical example. w1( 0, 0, 1600, 900) upper-left, w2(10, 10, 90, 90) lower-left.
Lets pick a point on w1 to convert to w2. Lets use the middle of the screen. it would be (800, 450) on w1 and (55, 55) on w2.

P = (800,450);

xfactor = 90 / 1600 = 9 / 160;
yfactor = 90 / 900 = 9 / 90 = 1 / 10;

xoffset = 10 - 0 = 10;
yoffset = 10 - 0 = 10;

P2.x = 9 / 160 * ( 800) + 10 = 45 + 10 = 55;
P2.y = 1 / 10 * (450) + 10 = 45 + 10 = 55;

since w1 corner is uppler-left and w2 corner is lower-left, we need to invert y of the solution. P2.y = w2.h + w2.y - w2.y; so we get P2.y = 100 + 10 - 55 = 110 - 55 = 55;

What is the point of mapping if the lower left corner coordinates of both windows (x,y) are same. Is not what you meant ?

They might still have different widths and heights. And some windows use 0,0 as top left, while others use 0,0 as bottom left.