Robinson projection

Introduction

Pseudocylindrical compromise map projection The Robinson projection is a map projection of a world map that shows the entire world at once.Pseudocylindrical compromise map projection The Robinson projection is a map projection of a world map that shows the entire world at once.

It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.

The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general purpose world maps since that time.The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general purpose world maps since that time.

Robinson published details of the projection's construction in 1974.Robinson published details of the projection's construction in 1974.

The National Geographic Society (NGS) began using the Robinson projection for general purpose world maps in 1988, replacing the Van der Grinten projection.The National Geographic Society (NGS) began using the Robinson projection for general purpose world maps in 1988, replacing the Van der Grinten projection.

In 1998, NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles".In 1998, NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles".

Strengths and weaknesses

The Robinson projection is neither equal area nor conformal, abandoning both for a compromise.The Robinson projection is neither equal area nor conformal, abandoning both for a compromise.

The creator felt that this produced a better overall view than could be achieved by adhering to either.The creator felt that this produced a better overall view than could be achieved by adhering to either.

The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.

quote| I decided to go about it backwards.quote| I decided to go about it backwards.

I started with a kind of artistic approach.I started with a kind of artistic approach.

I visualized the best looking shapes and sizes.I visualized the best looking shapes and sizes.

I worked with the variables until it got to the point where, if I changed one of them, it didn't get any better.I worked with the variables until it got to the point where, if I changed one of them, it didn't get any better.

Then I figured out the mathematical formula to produce that effect.Then I figured out the mathematical formula to produce that effect.

Most mapmakers start with the mathematics.|1988 New York Times article Latitude X Y 0° 1.0000 0.0000 5° 0.9986 0.0620 10° 0.9954 0.1240 15° 0.9900 0.1860 20° 0.9822 0.2480 25° 0.9730 0.3100 30° 0.9600 0.3720 35° 0.9427 0.4340 40° 0.9216 0.4958 45° 0.8962 0.5571 50° 0.8679 0.6176 55° 0.8350 0.6769 60° 0.7986 0.7346 65° 0.7597 0.7903 70° 0.7186 0.8435 75° 0.6732 0.8936 80° 0.6213 0.9394 85° 0.5722 0.9761 90° 0.5322 1.0000 The table is indexed by latitude at 5 degree intervals; intermediate values are calculated using interpolation.Most mapmakers start with the mathematics.|1988 New York Times article Latitude X Y 0° 1.0000 0.0000 5° 0.9986 0.0620 10° 0.9954 0.1240 15° 0.9900 0.1860 20° 0.9822 0.2480 25° 0.9730 0.3100 30° 0.9600 0.3720 35° 0.9427 0.4340 40° 0.9216 0.4958 45° 0.8962 0.5571 50° 0.8679 0.6176 55° 0.8350 0.6769 60° 0.7986 0.7346 65° 0.7597 0.7903 70° 0.7186 0.8435 75° 0.6732 0.8936 80° 0.6213 0.9394 85° 0.5722 0.9761 90° 0.5322 1.0000 The table is indexed by latitude at 5 degree intervals; intermediate values are calculated using interpolation.

Robinson did not specify any particular interpolation method, but it is reported that others used either Aitken interpolation (with polynomials of unknown degrees) or cubic splines while analyzing area deformation on the Robinson projection.Robinson did not specify any particular interpolation method, but it is reported that others used either Aitken interpolation (with polynomials of unknown degrees) or cubic splines while analyzing area deformation on the Robinson projection.

The X column is the ratio of the length of the parallel to the length of the equator; the Y column can be multiplied by 0.2536 to obtain the ratio of the distance of that parallel from the equator to the length of the equator.The X column is the ratio of the length of the parallel to the length of the equator; the Y column can be multiplied by 0.2536 to obtain the ratio of the distance of that parallel from the equator to the length of the equator.