Reflective surface

Abstract

The invention relates to a reflective surface substantially perpendicular to a vector field described by the equation: and a method for forming the reflective surface. The reflective surface is capable of providing a non-reversed, substantially undistorted direct reflection. W  ( x , y , z ) = T  ( proj  ( x , y , z ) ) - ( x , y , z )  T  ( proj  ( x , y , z ) ) - ( x , y , z )  + proj  ( x , y , z ) - ( x , y , z )  ( proj  ( x , y , z ) ) - ( x , y , z ) 

1 - 20 . (canceled) 
     
     
         21 . A non-reversing minor comprising:
 a reflective surface M, wherein the reflective surface M produces a non-reversed perspective view reflection at an image plane when viewed from a perspective of an observer positioned within the field of view of said reflective surface M;   wherein the reflective surface M has an image error quantity, I e , of less than about 15% when viewed from the perspective of the observer positioned within the field of view of the reflective surface M;   wherein the reflective surface M has a magnification of about one unit magnification or less; and   wherein the reflective surface M is a curvilinear surface.   
     
     
         22 . The non-reversing mirror of  claim 21 , wherein the reflective surface is a saddle-like shape or a convex shape. 
     
     
         23 . The non-reversing mirror of  claim 21 , wherein the reflective surface is concave-shaped. 
     
     
         25 . The non-reversing mirror of  claim 21 , wherein the reflective surface M has an image error quantity I e  of less than about 10%. 
     
     
         26 . The non-reversing mirror of  claim 21 , wherein the reflective surface M has an image error quantity I e  of less than about 5%. 
     
     
         27 . The non-reversing mirror of  claim 21 , wherein the reflective surface M has an image error quantity I e  of less than about 3%. 
     
     
         28 . The non-reversing mirror of  claim 21 , wherein said reflective surface M is capable of reflecting at least a 30° field of view when viewed from the perspective of an observer. 
     
     
         29 . The non-reversing mirror of  claim 21 , wherein said reflective surface M is capable of reflecting at least a 40° field of view when viewed from a perspective of an observer. 
     
     
         30 . The non-reversing mirror of  claim 21 , wherein said reflective surface M is capable of reflecting at least a 45° field of view when viewed from a perspective of an observer. 
     
     
         31 . A method for producing a non-reversing mirror that generates a non-reversed perspective view using a reflective surface M comprising steps of:
 a) inputting data comprising an image plane, a domain of an image plane, an object plane, a non-reversing undistorted direct correspondence T and coordinates of an eye of an observer;   b) computing a vector field using the inputted data;   c) calculating a resulting minimizer ƒ* from the vector field and the inputted data; and   d) producing a non-reversing perspective view minor with the reflective surface M using the calculated minimizer ƒ*.   
     
     
         32 . The method of  claim 31 , further comprising calculating coordinates of the vector field by calculating a source point in the image plane. 
     
     
         33 . The method of  claim 32 , wherein the source point is a projection of a point along a line connecting the point and the coordinates of an eye of an observer. 
     
     
         34 . The method of  claim 33 , further comprising determining a corresponding point on the object plane using the source point. 
     
     
         35 . The method of  claim 31 , wherein the minimizer ƒ* is a minimization of an integral. 
     
     
         36 . The method of  claim 35 , wherein calculating the minimizer ƒ* results in solutions lying in a volume determined by the image plane, the domain of the image plane, and the object plane. 
     
     
         36 . The method of claim  37 , wherein the solutions lying in the volume result in the reflective surface M. 
     
     
         38 . A computer software program implemented on a non-transitory computer readable medium executable on a computational device comprising:
 inputting means for inputting data comprising an image plane, a domain of an image plane, an object plane, a non-reversing undistorted direct correspondence T and coordinates of an eye of an observer;   computing means for computing a vector field using the inputted data; calculating a resulting minimizer ƒ* from the vector field and the inputted data; and producing a non-reversing perspective view mirror with the reflective surface M using the calculated minimizer ƒ*.   
     
     
         39 . The computer software program of  claim 38 , wherein the computing means further calculates coordinates of the vector field by calculating a source point in the image plane. 
     
     
         40 . The computer software program of  claim 39 , wherein the source point is a projection of a point along a line connecting the point and the coordinates of an eye of an observer.