05-第3章--圓錐投影-展示頁(yè)
2024-08-09 13:44本頁(yè)面
【正文】 are straight equidistant lines, converging at a point which may or not be a pole. Compared with the sphere, angular distance between meridians is always reduced by a fixed factor, the cone constant. （ 2） parallels are arcs of circle, concentric in the point of convergence of meridians. As a consequence, parallels cross all meridians at right angles. Distortion is constant along each parallel. Due to simple construction and inherent distortion pattern, conic projections have been widely employed in regional or national maps of temperate zones (while azimuthal and cylindrical maps were favored for polar and tropical zones, respectively), especially for areas bounded by two not toodistant meridians, like Russia or the conterminous United States. On the other hand, conic projections are seldom appropriate for world maps. 8 ?正軸圓錐投影的極坐標(biāo)公式： ????? ?? )(f?正軸圓錐投影的直角坐標(biāo)公式： ????? s i nc o s ??? yx s?：緯線投影半徑； f ：取決于投影性質(zhì)； ?：投影常數(shù)； ?： 經(jīng)差。 ?s y ? A? x ? ? y x ?s 圖 正軸圓錐投影示意 9 ?圓錐投影經(jīng)、緯線長(zhǎng)度比、面積比和角度變形公式： ????????????????????))( c o s ( ))s i n (()s i n ()c o s (???????????????yxddyddx????? s i nc o s ??? yx s對(duì)上式求偏導(dǎo)數(shù)： 一般公式： ????? ?? )(f10 batgbabanmPrrGnMddMEm?????????????)445(2s i n??????或沿經(jīng)緯線長(zhǎng)度比、面積比和最大角度變形公式： m之所以取負(fù)號(hào)在于 ?和 ?的起算方向相反。 ?正軸圓錐投影經(jīng)、緯線長(zhǎng)度比、面積比和角度變形公式推導(dǎo) (第二種方法 )： 12 batgbabaMrddnmPrrddABBAnMddADDAm????????????????????)445(2s i n?????????????或經(jīng)緯線長(zhǎng)度比、面積比和角度變形公式： ? ?? d???? d?A B C D A? B?’ C? D? ?d?dS ??d?d?13 ???????????????si nc o s2si n )(?????????????yxbabamnPrnMddmfs?正軸圓錐投影的一般公式為： 對(duì)于橢球體： 對(duì)于球體： ????????????????si nc o s2si nc o s )(?????????????yxbabamnPRnRddmfs14 167。 e1為第一偏心率 16 ))si n1si n1)(245(( lnlnln)si n1si n1)(245(ln ln)si n1l n (2)si n1l n (2)245(ln ln)si n()si n11si n11(21)245(ln lnsi n1c o sc o sln211211111111112211111eeeetgUUKKUKeetgKeeeetgKedeeetgKdeeed???????????????????????????????????????????????????????????????????? ?其中或按照以下方法進(jìn)行積分 17 正軸等角圓錐投影的長(zhǎng)度比、面積比和角度變形公式： 0)( 222??????????????rUKnmPrUKrnm18 0)(si n ,c o s ,)si n1si n1)(245( ,22222212111????????????????????????????????????????rUKnmPrUKrnmyxabaeeetgUUKse正軸等角圓錐投影的一般公式為： 在上式中，尚有常數(shù) ? 和 K 還需要進(jìn)一步確定。 為此先求 n 對(duì) ? 的一階導(dǎo)數(shù)： rn???2rddrddrddn ????????因?yàn)? rMdd ???? ??rMdd ???? ??所以 20 ?????????????????????????
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