麥卡托投影族變形量之解析研究

麥卡托投影族係指由麥忙托投影經修飾而得的系列投影，其製圖方程式為：X=R(λ-λ0)；Y=nR log(下标 e) tan(π/4+ψ/(2m))：沿經線及緯線的變形量推證得h=(n/m)sec(ψ/m)；k=secψ，即沿緯線方向之變形量均相同，至於沿經線方向之變形量則視n、m值決定。為改良麥卡托投影高緯度地區變形過大的缺點，本文將利用n、m值之測試，決定適合的匹配值，並利用該投影族中著名的miller圓柱投影進行驗證。且對該系列投影做進一步的解析，俾利製圖與用圖之應用參考。

關鍵字

麥卡托投影族；變形分析

並列摘要

Mercator projection family is derived from The Mercator projection. They have equations X=R(λ-λ0)；Y=nR log(subscript e) tan(π/4+ψ(2m)), Along the longitude and the latitude, the distortion errors are given by the equations: h=(n/m)sec(ψ/m); k=secψ, where the distortions at x-axis are all the same but at y-axis they depend upon the values of n and m. To avoid enormous distortion at the high latitude areas, Mercator projection family were designed to be a compromise between Mercator and other cylindrical projections by adjusting the values of n and m in order to determine a matched value. Its results can be validated with those from the famous Miller Cylindrical Projections. Hopefully the further analysis for the series forms of Mercator projection is useful to map makers and application of maps.