Normalizing one range of values to another range of values.

To add another generic answer.
If you want to map the linear range [A..B] to [C..D], you can apply the following steps:
Shift the range so the lower bound is 0. (subract A from both bounds:
[A..B] -> [0..B-A]
Scale the range so it is [0..1]. (divide by the upper bound):
[0..B-A] -> [0..1]
Scale the range so it has the length of the new range which is D-C. (multiply with D-C):
[0..1] ->  [0..D-C]
Shift the range so the lower bound is C. (add C to the bounds):
[0..D-C] -> [C..D]
Combining this to a single formula, we get:
       (D-C)*(X-A)
X' =   -----------  + C
          (B-A)
Eg :

Normalizing a range of 0.5 ----> 1.0   to 0 ------> 1
 A=0.5, B=1, C=0, D=1 you get:
       (X-0.5)
X' =   ------- = 2X-1
        (0.5)
Note, if you have to convert a lot of X to X', you can change the formula to:
       (D-C)         C*B - A*D
X' =   ----- * X  +  ---------  
       (B-A)           (B-A)

Comments

Post a Comment

Popular posts from this blog

Bounding Box in PIL (Python Image Library)

Image
Bounding Box in PIL(Python Image Library) : Bounding Box function of PIL can be very useful for removing unused pixels from an image. Eg. If we want to remove unused pixels based on alpha channel of an image, we can use following code.   im = Image.open(imagePath) r,g,b,a = im.split() left,upper,right,lower = a.getbbox() tempImage = im.crop((left,upper,right,lower)) newPath = imagePath.split(".")[0]+"_Cropped" + "." + imagePath.split(".")[1] tempImage.save(newPath) To understand which values, getbbox() function returns and what do they look like on an image, I created an image showing the values returned by the function. left,upper,right,lower = image.getbbox()   Suppose you have a point in an original image and you want to find out the new position of the same point in the cropped image, lets see how we can do it. Suppose the point is at (300,450) position in an original image, so after cr...
Read more

Dictionary vs KeyValuePair vs Struct - C#

Dictionary :  //   Declare   Dictionary and assign value Dictionary < string ,  object >  parameter  =  new   Dictionary < string ,  object >(); parameter [ " View " ] =  viewComp ; parameter [ " Play " ] =  true ; FunctionName( parameter ); //   Use   Dictionary private   void   FunctionName ( object   parameter ) {      Dictionary < string ,  object >  dict  = ( Dictionary < string ,  object >) parameter ;      GameObject   viewComp  = ( GameObject ) dict  [ " View " ];      bool   play  = ( bool ) dict [ " Play " ];      UseValuesInFunction ( viewComp ,  play ); } KeyValuePair : KeyValuePair < GameObject ,  bool >  parameter  =  new   KeyValuePair < GameObject ,  bool >( viewComp ,...
Read more

Rendering order and Z-sorting

Image
Rendering order and Z-sorting . In Unity, there are a couple of options using which we can control render order of the objects, two of them are 1. Render queue in shaders and 2. Painter's algorithm but eventually, what appears in front and what stays hidden is decided by Z-sorting/depth sorting. Here is the authoritative sequence of order of objects that will appear on the screen. Z-sorting/ Depth sorting is the final step to sort pixels based on the z-distance from the camera, but we can still turn ZWrite-off in the shaders (which in a way breaks Z-sorting). If we turn off ZWrite in all the shaders then render-queue will be in charge of deciding what comes in front and what goes in back If all shaders have ZWrite turned off and as well as they are on the same render-queue then the distance of their transform point from the camera will decide the render order. Eg : - ZWrite Off - Render Queue same - Painter's algorithm - ZWrite Off - Render Qu...
Read more