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.

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

Abstract: A method for producing a multiple surface system that may be a two-mirror surface. The method involves first finding from a given primary curve an appropriate secondary curve. The method then uses ideas from exterior differential systems to grow from the primary curve and the secondary curve, primary and secondary mirror surfaces. The Cartan-Kähler theorem gives a strong indication of the existence of such solution surfaces.

Abstract: A method for producing a multiple surface system that may be a two-mirror surface. The method involves first finding from a given primary curve an appropriate secondary curve. The method then uses ideas from exterior differential systems to grow from the primary curve and the secondary curve, primary and secondary mirror surfaces. The Cartan-Kähler theorem gives a strong indication of the existence of such solution surfaces.

Abstract: The invention relates to a reflective surface substantially perpendicular to a vector field described by the equation: W ? ( x , y , z ) = target ? ( x , y , z ) - [ x , y , z ] ? target ? ( x , y , z ) - [ x , y , z ] ? + source ? ( x , y , z ) - [ x , y , z ] ? source ? ( x , y , z ) - [ x , y , z ] ? and a computer program for forming the reflective surface. The reflective surface is capable of providing a substantially undistorted wide-angle field of view. It is particularly useful as a driver's side mirror of a vehicle to provide an enlarged, substantially undistorted field of view which may be used to reduce or eliminate blind spots.

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

Abstract: The invention relates to a reflective surface substantially perpendicular to a vector field described by the equation: and a computer program for forming the reflective surface. The reflective surface is capable of providing a substantially undistorted wide-angle field of view. It is particularly useful as a diver's side mirror of a vehicle to provide an enlarged, substantially undistorted field of view which may be used to reduce or eliminate blind spots.

Abstract: A mirror for use in a catadioptric system, is provided which is a substantially circular mirror having a rotationally symmetric cross section by a set of points substantially close to a curve satisfied by a differential equation as follows: 2 ⁢ F ′ ⁡ ( x ) 1 - F ′ ⁡ ( x ) 2 = d ⁡ ( x ) - x F ⁡ ( x ) where x is the radius of the mirror and F(x) is the cross-sectional shape.