scheme - How transform-painter works in the picture language in SICP -

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I'm having trouble understanding how change-painter process works: 

 (define - painter painter original corner 1 corner 2) (lambda (frame) (let's (frame-conform-map frame) (Give ((new-origin (M original))) () The composer (make-frame New-Oral (sub-works (m-corner 1) new-root (sub-vector (m-corner 2) new-root)))))))   
 Specifically why the logic frame by the new root Vector subtraction of slogan mapping is necessary I have thought that the mapping of the new corners, i.e  (m corner 1)  and  (m corner 2) , forms of new edges of the transformed frame Can work in  
 I have done some calculations and I want to know where I am mixed. For example  flip-vert  is taking,  
  (define - flip-bizarre painter) (conversion-painter painter (make-wacker 0.0.0); new Original (Make) -act 1.0 1.0); New end of edge 1 (Make-Vect 0.0 0.0));   
 Let  flip-veer  form a frame with the following dimensions as the argument,  
 
 origin = (0, 0 ), Edge 1 = (4, 0), edge 2 = (0, 4)   
 Thus the mapping formula will become  (0,0) + x (4,0) ) In the case of  original ,  corner1  . . . Code> as argument for  (0,1) ,  (1,1) , and  corner 2  arguments The form has been passed as  and  (0,0)  respectively.  
 Then after placing them in the mapping form, one after the other, we get the result  
 
 new root = (0,0) + 0 * (4, 0) + 1 * (0,4) = (0,4)  
 map-corner1 = (0,0) + 1 * (4,0) + 1 * (0,4) = (4,4)  
 map-corner2 = (0,0)   
 Now the  change-painter  takes the last two results and Reduces them from  new original  for the construction of new frames, resulting in a frame with the following dimension.  
 
 Genesis = (0,4), new-corner1 = (4,0), new-corner2 = (0, -4)   
  
 
 
 Please refer to the attached picture (sorry for my drawing skills :)). I have marked the vector marked as  m corner 1  which you say that it will be sufficient as a new corner for the new frame on which the painter is going to work ( M corner1  is  Convert the mapped conversion to <1  point  
 but keep in mind that it is a vector that just "ends" at the right point You must also translate the original to get the right frame. See that the new original is at the  new original  point and the new corner you search for (red one) is actually the difference between the vector difference of the last two.  
  The blue frame in the unit square is mapped to red frame   
 (pic

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