1. A method for forming a lens, comprising:
defining a surface of the lens as a combination of inter-connected cross-sections;
wherein (i) one of the cross-sections has a minimum thickness at a first angle along an optical axis and (ii) another one of the cross-sections has a maximum thickness with respect to the minimum thickness, at a second angle along the axis;
wherein the thickness ratios of each of the other cross-sections is a function of the minimum thickness, each of the other thickness ratios corresponding to a different angle; and
molding the cross-sections together to form a single lens having a smooth surface.
2. The method of claim 1, wherein the first angle is about 90\xb0 and the second angle is about 30\xb0.
3. The method of claim 2, wherein the maximum ratio is about 3;
wherein additional cross-sections have thickness ratios of about 1.2, 1.6, 2.1, and 2.5 with respect to the minimum thickness, respectively;
wherein a first of the additional cross-sections is adjacent to the one cross-section, each of the additional cross-sections being adjacent to another of the additional cross-sections; and
wherein the corresponding different angles are separated by about 10\xb0 .
4. The method of claim 3, wherein the thicknesses are responsive to an inverted cosine cube law.
5. The method of claim 4, wherein the inverted cosine cube law is a function of 1cos3 \u03b8, where \u03b8 is an angle measured from a vertical direction of the lighting apparatus.
6. A method for forming a lens in lighting apparatus having a substantially uniform illumination distribution, comprising:
defining a lens for area lighting having an inner surface and an outer surface;
wherein a profile of the inner surface is composed of a first plurality of piecewise circular arcs;
wherein a profile of the outer surface is composed of a second plurality of piecewise circular arcs;
wherein a cross-sectional profile of the lens is a function of the first and second plurality of piecewise circular arcs, each of the first and second plurality of circular arcs (i) being representative of a center point and a radius and (ii) defining a geometry of the lens; and
molding the first and second plurality of arcs together to form a single lens having a smooth surface.
7. The method of claim 6, wherein the second plurality of arcs is a larger quantity than the first plurality of arcs.
8. The method of claim 7, wherein radii associated with each of the first plurality of arcs ranges from about 2.5 to 400; and
wherein radii associated with each of the second plurality of arcs ranges from about 7 to 27.
9. The method apparatus of claim 7, wherein radii associated with each of the first plurality of arcs ranges from about 3 to 41; and
wherein radii associated with each of the second plurality of arcs ranges from about 2.6 to 15.
10. The method of claim 6, wherein the first plurality of arcs is a larger quantity then the second plurality of arcs;
wherein radii associated with each of the first plurality of arcs ranges from about 5 to 30; and
wherein radii associated with each of the second plurality of arcs ranges from about 2.5 to 12.6.
11. The method of claim 6, wherein each center point and radius is different from all of the other center points and radii.
12. The method of claim 11, wherein the profiles are responsive to an inverted cosine cube law.
13. The method of claim 12, wherein the inverted cosine cube law is a function of 1cos 3\u03b8 , where \u03b8 is an angle measured from a vertical direction of the lighting apparatus.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A floor wipe for use with a foot to provide for easy clean up of small areas of a floor during a cleaning procedure, the floor wipe comprising:
a) a foot contact side to provide for contact with the foot during the cleaning procedure;
b) a floor contact side to provide for contact with the floor during the cleaning procedure, the floor contact side opposing the foot contact side;
c) a toe end cleaning area positioned on the floor contact side of the floor wipe and having a first cleaning characteristic during the cleaning procedure, the first cleaning characteristic generally associated with a wiping and absorbent portion of the cleaning procedure;
d) a heel end cleaning area positioned on the floor contact side of the floor wipe and having a second cleaning characteristic during the cleaning procedure, the second cleaning characteristic generally associated with a scouring portion of the cleaning procedure;
e) a circular sewing pattern on the floor contact side and generally centered on the toe end cleaning area.
2. The floor wipe defined in claim 1 further comprising a semi-rigid insert positioned between the foot contact side and the floor contact side and generally aligned with the toe end cleaning area, the semi-rigid insert having a perimeter wall extending at least partially around a containment area, the containment area of the semi-rigid insert to assist in retention of the foot in proper orientation on the floor wipe during the cleaning procedure.
3. The floor wipe defined in claim 1 further comprising an embroidered border and an embroidered toe pattern, the embroidered border extending around the floor wipe and extending onto a perimeter of the foot contact side and onto a perimeter of the floor contact side, the embroidered toe pattern having a shape generally associated with toes and nails of the foot and positioned on the foot contact side opposing the toe end cleaning area of the floor contact side.
4. The floor wipe defined in claim 1 further comprising hanging means to provide for a hanging storage retention of the floor wipe in a generally vertical orientation while not being used for the cleaning procedure.
5. The floor wipe defined in claim 4 wherein the hanging means further comprises an aperture penetrating the floor wipe from the foot contact side to the floor contact side and at a rearward extent of the floor wipe behind the heel end cleaning area of the floor contact side.
6. The floor wipe defined in claim 1 further comprising an extra layer of absorbent material between the floor contact side and the foot contact side and generally aligned with the toe end cleaning area of the floor contact side, the extra layer of absorbent material extending along the floor wipe between the floor contact side and the foot contact side less then the distance to the heel end cleaning area of the floor contact side.
7. A floor wipe for use with a foot to provide for easy clean up of small areas of a floor during a cleaning procedure, the floor wipe comprising:
a) a foot contact side to provide for contact with the foot during the cleaning procedure;
b) a floor contact side to provide for contact with the floor during the cleaning procedure, the floor contact side opposing the foot contact side;
c) a toe end cleaning area positioned on the floor contact side of the floor wipe and having a first cleaning characteristic during the cleaning procedure;
d) a heel end cleaning area positioned on the floor contact side of the floor wipe and having a second cleaning characteristic;
e) a semi-rigid insert positioned between the foot contact side and the floor contact side and generally aligned with the toe end cleaning area, the semi-rigid insert having a perimeter wall extending at least partially around a containment area, the containment area of the semi-rigid insert to assist in retention of the foot in proper orientation on the floor wipe during the cleaning procedure.
8. The floor wipe defined in claim 7 further comprising an extra layer of absorbent material between the floor contact side and the foot contact side and generally aligned with the toe end cleaning area of the floor contact side, the extra layer of absorbent material extending along the floor wipe between the floor contact side and the foot contact side less then the distance to the heel end cleaning area of the floor contact side.
9. The floor wipe defined in claim 7 further comprising a circular sewing pattern on the floor contact side and generally centered on the toe end cleaning area.
10. The floor wipe defined in claim 7 further comprising attachment of the semi-rigid insert to the floor wipe utilizing a sewing which penetrates semi-rigid insert.
11. The floor wipe defined in claim 7 wherein the floor contact side of the floor wipe at the toe end cleaning area is formed of a Terri cloth material.
12. The floor wipe defined in claim 7 further comprising an extra layer of absorbent material between the floor contact side and the foot contact side and generally aligned with the toe end cleaning area of the floor contact side, the extra layer of absorbent material extending along the floor wipe between the floor contact side and the foot contact side less then the distance to the heel end cleaning area of the floor contact side and further comprising attachment of the semi-rigid insert to the floor wipe utilizing a sewing which penetrates semi-rigid insert.
13. A floor wipe for use with a foot to provide for easy clean up of small areas of a floor during a cleaning procedure, the floor wipe comprising:
a) a foot contact side to provide for contact with the foot during the cleaning procedure;
b) a floor contact side to provide for contact with the floor during the cleaning procedure, the floor contact side opposing the foot contact side;
c) a toe end cleaning area positioned on the floor contact side of the floor wipe and having a first cleaning characteristic during the cleaning procedure;
d) a heel end cleaning area positioned on the floor contact side of the floor wipe and having a second cleaning characteristic;
e) an embroidered border extending around the floor wipe and extending onto a perimeter of the foot contact side and onto a perimeter of the floor contact side;
f) an embroidered pattern positioned on the foot contact side opposing the toe end cleaning area of the floor contact side and wherein the embroidered pattern further has a shape generally associated with toes and nails of the foot.
14. The floor wipe defined in claim 13 further comprises an aperture penetrating the floor wipe from the foot contact side to the floor contact side and at a rearward extent of the floor wipe behind the heel end cleaning area of the floor contact side, the aperture to provide for a hanging storage retention of the floor wipe in a generally vertical orientation while not being used for the cleaning procedure.
15. The floor wipe defined in claim 14 further comprising an embroidered border around the aperture.
16. The floor wipe defined in claim 13 wherein the floor wipe has a symmetrical shape generally corresponding to the shape of a human foot print wherein the floor wipe can be used with either foot.