This disclosure generally relates to convex, three dimensional mirrors and, more particularly, to a mirror, sometimes referred to as a “cross-over” or “cross-view” mirror, which affords a bus driver, for example, a school bus driver, visual access in front of, as well as alongside the bus.  Such cross-over mirrors can however also be used at the rear or front corners of other vehicles such as with trucks, mail vans and the like.  More specifically, the present disclosure relates to non-ellipsoidal, asymmetric cross-view mirrors which are optimized to produce more distinct images of objects located in front of or alongside a school bus or similar vehicle. 
For many decades, cross-over mirrors and mirror assemblies have been deployed on school buses, and are in fact required by federal and local regulations.  A substantial body of prior art has been published describing various mirrors of the type to which the present invention relates.  A sample list of such prior art mirrors include U.S. Pat.  Nos.  4,822,157; 4,730,914; 4,436,372; 5,084,785; D346,357; 5,589,984; 6,282,771; 6,328,450; and 6,227,674.  The above list represents but a fraction of the extensive prior art on the subject of cross-over mirrors and their accessories such as mounting hardware, mirror arms and other implements by which such mirror assemblies are secured to vehicles such as busses, school buses, trucks and the like.  The contents of the aforementioned United States patents are incorporated by reference herein. 
The convex, three-dimensional surface of the mirror lens described, for example, in the aforementioned U.S. Pat.  No.  4,436,372, terminates in a continuous, peripheral edge that lies in a 2-dimensional plane and defines, essentially, a circle.  Other similar mirrors also have generally ellipsoidal or convex, i.e. dome, lens surface shapes, such that trace lines drawn over the mirror surface which pass through its center, i.e., apex, have non-constant radii of curvature. 
In more recent years, the prior art has moved to provide convex, three dimensional mirror lens surfaces that have a more horizontally stretched, elongate general shapes.  The aforementioned U.S. Pat.  Nos.  4,822,157; 4,730,914; 4,436,372; 5,084,785; D346,357; 5,589,984; 6,282,771; 6,328,450; and 6,227,674 illustrate the general style of such mirrors. 
Rosco, Inc., the assignee of the present application, has introduced to the trade a novel, stretched and elongate cross-view mirror which became known in the industry as the Rosco “oval” mirror.  The aforementioned U.S. Pat.  No.  D346,357 and such further Rosco patents as the U.S. Pat.  Nos.  6,227,674; 6,282,771 and 6,328,450 illustrate such oval mirrors.  As with many of these cross-view mirrors, the oval mirrors terminate in a continuous, peripheral edge which defines the two-dimensional, elliptical, or “oval” periphery, i.e., footprint, of the mirror lens. 
Other than in the last mentioned three patents of the instant assignee, the prior art three dimensional, generally ellipsoidal or convex surfaces of the aforementioned elongate cross-over mirror lenses have been characterized by radii of curvature (measured along planar cross-sections on the major and minor axes) which were distinctly non-constant, i.e. tending to increase or decrease on the mirror lens toward or adjacent its peripheral, circumferential edge. 
As an example, the convex, ellipsoid mirror lens shown in U.S. Pat.  No.  4,436,372 has a generally flatter, i.e. less curved, center surface, which surface curves sharper as one proceeds toward the peripheral edge.  Stated differently, the “radius of curvature” of the surface decreases from the center, vertical axis (apex) of the mirror surface toward the peripheral edge of the mirror.  A similar relationship is specifically claimed for the elongate, oval mirror described in the aforementioned U.S. Pat.  No.  5,589,984. 
But in another patent, i.e., the U.S. Pat.  No.  5,084,785 to Albers, an opposite relationship is specified—the sharpest curvature, i.e., smallest radius of curvature, is at the center, and the mirror surface flattens out as one proceeds toward the peripheral edge.  In other words, the mirror lens exhibits an increasing radius of curvature, along the major axis. 
One school of prior art thought actually adheres to the notion that it is desirable to vary the radius of curvature, to obtain larger and less distorted images at the mirror center, and smaller, but more distorted, images, at the peripheral regions on the mirror.  The idea is to increase the field of view that the mirror monitors in and around the school bus. 
Further research and insight gained by the instant inventors relative to cross-view mirrors has revealed drawbacks that are still incorporated in the prior art cross-view mirrors and advantages that can be gained from improved, very careful shaping of the convex structure of the mirror lens reflecting surfaces.  For example, it would be advantageous to reduce the size of the “footprint” of the mirror without reducing the field of view.  A decreased mirror foot print size reduces the size of the forward looking blind spot of the mirror in front of the vehicle, improves the mirror's aerodynamic performance, the aesthetics of the vehicle, and also results in reduced mirror weight and reduced cost of mounting the mirror assembly to a vehicle.  Alternatively, the size may be maintained as in the prior art, while obtaining the benefit of increased image sizes, particularly of students standing several feet in front of and far away adjacent the rear wheels of the school bus. 
Furthermore, in general, a cross-view mirror is intended to provide a field of view both in front and alongside the bus.  However, the size and general shape of the monitored area in front of a school bus, differs from that which needs to be monitored alongside the bus.  That is, school buses and similar vehicles have comparative lengths several times larger than the widths of the vehicles.  The image of a child standing alongside a school bus near the rear wheels needs to be sufficiently large to afford the driver a good view of a child who may stoop low or fallen or slipped under or too close to the school bus.  At the front of the bus, it is more important to assure that the entire width and several feet in front of the bus are clearly visible.  In other words, the field of view characteristics in front of the school bus and alongside differ from one another.  Prior art mirrors have not been optimized to fully accommodate these differences. 
Rather, all prior art mirrors, including those that have horizontally stretched bodies, are widthwise symmetrical with respect to their generally vertical mounting axis.  Thus, the mirror surface size and shape and field of view to the right of the axis is identical to the mirror surface and view to the left of the axis.  Therefore, both sides of the lens provide the same image reflecting characteristics at the left mirror side, which is primarily focused on the area in front of the bus, as at the right mirror side which focuses images from alongside the bus (for a mirror mounted to the right of the driver). 
Another concern of the instant inventors is based on the understanding that prior art mirrors, such as the mirrors described in the aforementioned U.S. Pat.  Nos.  5,589,984 and 4,436,372, have varying radii of curvature resulting in continually changing image sizes, along the surfaces of the mirror.  This makes it more difficult for the driver to follow and carefully monitor the movements of a child alongside or in front of the school bus.