Sinusoidal Projection

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Introduction

Sinusoidal projection is a pseudo-cylindrical equal-area projection created by French cartographer Samson in 1650. It is also called the Samson projection or the Samson-Flamsteed projection. Its core features are that the latitudes are equidistant parallel straight lines, the meridians are sinusoidal curves symmetrical to the central meridian, the central meridian is a straight line with a length ratio of 1, and the equator is a non-deformed line, which can effectively maintain the accurate area ratio. After projection, the length of the equator is twice that of the central meridian, the poles are projected as points and form protruding edges, and the graticule is symmetrically distributed along the equator and the central meridian.

Projection Method

The sinusoidal projection achieves the accuracy of area ratio by projecting the meridians as sinusoidal curves and the latitudes as parallel straight lines. The projection method is simple and intuitive, suitable for mapping areas near the equator, but there is significant deformation in high-latitude areas. This projection method has unique advantages in thematic maps that need to maintain area ratio (such as climate distribution maps and population density maps), but its deformation distribution characteristics should be noted.

Pros

Equal-area characteristics: As an equal-area projection, the sinusoidal projection can accurately maintain the area ratio and is suitable for scenes that require accurate comparison of regional areas.
Small deformation near the equator: Within the range of ±40 degrees of the equator, this projection can better maintain the shape and direction, and is suitable for mapping areas near the equator.
Simple structure: Its mathematical formula and projection method are relatively intuitive, easy to understand and implement.

Cons

**Large deformation at high latitudes: **As the latitude increases, the length and angle deformation gradually increase. The length deformation rate in the 45-degree latitude area can reach more than 50%, and the shape distortion of the projection edge area is obvious, which is not suitable for mapping in high-latitude areas.
**Significant edge distortion: **The boundary meridian protrudes outward excessively, resulting in significant distortion near the map outline, affecting the visual effect and measurement accuracy.
**Direction distortion: **Except for the central meridian and the equator, the local angles of other locations are deformed, which may affect applications that are sensitive to direction.

Application Scenario

The sinusoidal projection is suitable for mapping areas that need to maintain accurate area ratios and focus on areas near the equator, such as the full picture of continents such as Africa and South America, as well as thematic mapping areas such as climate distribution maps and population density maps. Its equal-area characteristics give it a unique advantage in scenes that need to accurately reflect regional area relationships, but it should be avoided in high-latitude areas or scenes that require high directional accuracy.

Example

Sinusoidal projection of the world.

The sinusoidal projection with Tissot’s indicatrix of deformation

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