橫圓筒相似投影函數의 歪曲特性을 考慮한 地籍測量 分野 平面直交座標 體系 設定과 適用 = Derivation of a new map grid system with consideration of projection distortion and its application to cadastral surveying

다국어 초록 (Multilingual Abstract)

The thesis focuses on deriving a new rectangular coordinate system in
Korea, which can be effectively applied for a board range of cadastral
surveying. To this end, comparative studies of functions used in the
transverse cylindrical projection have been theoretically and numerically
carried out to understand their distortion characteristics. The functions
can be classified according to a way of the mathematical derivation as
well as a selection of coefficients and terms, for example
Gauss-Schreiber(GS) and Gauss-Kr?ger(GK) types. Although the transverse
cylindrical projection itself is assigned to a system, projected coordinates
would be diverse with respect to the function used in the actual
calculation. In order to investigate the impact of functions used in the
computation, five different equations (i.e., 2 GS and 3 GK) were
implemented in this study by using MATLAB. A series of numerical
simulation tests has been carried out to compare and characterize them
in terms of projection accuracy, difference of projected coordinates and
distortion. Furthermore, a comparison between GS and GK function was
made under the Korean grid system, consisting of four zones. Results
from the numerical computations were qualitatively analyzed and
summarized.
Based on the series of the analysis, a single-zone grid system has been
firstly derived through reflecting effectiveness of database construction
and management. This is followed by analyzing characteristics of its
distortion by using scale factor, area distortion and Arc-To-Chord
correction. In addition, the four different multiple grid systems comprising
more than 3 zones have been numerically analyzed from the standpoint
of minimizing the distortion in the East-West direction as well as their
relevance to real world applications. Finally, this research has proposed
the single-zone and the three zones system for the most applicable
schemes to the cadastral surveying in Korea. Note that the latter system
is bounded along the West and East coast lines.

목차 (Table of Contents)

• 제1장 서 론 ·············································································· 1
• 1.1 연구배경 및 목적 ···············································································1
• 1.2 연구동향 ·······························································································3
• 1.3 연구내용 및 방법 ···············································································8
• 제2장 측지계와 평면직교좌표체계 ········································ 9
• 2.1 측지계 ···································································································9
• 2.1.1 개요 ···········································································································9
• 2.1.2 동경측지계 ·····························································································10
• 2.1.3 세계측지계(대한민국 측지계 2002) ···················································12
• 2.2 투영이론 ·····························································································14
• 2.2.1 개요 ·········································································································14
• 2.2.2 가우스 기본량 ·······················································································16
• 2.2.3 축척계수 ·································································································20
• 2.2.4. 등척위도(Isometric Latitude) ······························································22
• 2.3 횡원통상사투영 함수 ·······································································23
• 2.3.1 Gauss-Schreiber(GS) 함수 ···································································23
• 1) 가우스-램버트(GL) 투영 ·······································································24
• 2) 타원체를 구체로 상사투영 ··································································25
• 2.3.2 Gauss-Kr?ger(GK) 투영 ·······································································29
• 1) GK 투영함수 ···························································································31
• 2.4 우리나라 평면직교좌표체계 ···························································33
• 제3장 투영함수 특성분석을 위한 수치실험 ························35
• 3.1 투영함수 구현과 수치실험 ·····························································35
• 3.2 GS 투영함수의 정확도와 좌표 비교 ············································38
• 3.3 GK 투영함수의 정확도와 좌표 비교 ············································41
• 3.4 GS-GK 함수의 투영좌표 및 축척계수 비교 ·······························48
• 3.5 수치분석 결과 요약 ·········································································51
• 3.5.1 GS 투영함수 ···························································································51
• 3.5.2 GK 투영함수 ··························································································51
• 3.5.3 GS-GK 투영함수 비교 ·········································································52
• 제4장 단일 평면직교좌표체계 도출 ···································· 54
• 4.1 해외 사례조사 ···················································································54
• 4.1.1 미국 ·········································································································54
• 4.1.2 영국 ·········································································································55
• 4.1.3 일본 ·········································································································56
• 4.1.4 호주 ·········································································································57
• 4.1.5 뉴질랜드 ·································································································58
• 4.2 현행 평면직교좌표체계에 대한 수치적 특성분석 ·····················59
• 4.2.1 분석범위와 방법 ···················································································59
• 4.2.2 투영함수에 따른 평면직교좌표 차이 ···············································62
• 4.2.3 투영면적 왜곡 ·······················································································66
• 4.2.4 분석결과 요약 ·······················································································72
• 4.3 면적왜곡을 고려한 단일 평면직교좌표체계 도출 ·····················74
• 4.3.1 개요 ·········································································································74
• 4.3.2 투영법 및 함수 ·····················································································75
• 4.3.3 투영원점의 위도 ···················································································76
• 4.3.4 투영구역과 중앙자오선 ·······································································77
• 4.3.5 중앙자오선의 축척계수 ·······································································78
• 4.3.6 단일 평면직교좌표체계의 제원 ·························································82
• 제5장 다중 평면직교좌표체계와 적용방안 ··························84
• 5.1 단일 평면직교좌표체계의 왜곡특성 분석 ···································84
• 5.1.1 축척계수 ·································································································84
• 5.1.2 면적왜곡 ·································································································85
• 5.1.3 Arc-To-CHORD 보정량(t-T) ·······························································91
• 5.1.4 자오선수차 ·····························································································93
• 5.2 다중 평면직교좌표체계 연구 ·························································94
• 5.2.1 개요 ·········································································································94
• 5.2.2 축척계수 ·································································································96
• 5.2.3 면적왜곡 ·································································································98
• 5.2.4 다중 평면직교좌표체계 설정 방안 비교 ·······································100
• 5.3 지적측량 분야에 대한 적용방안 ·················································102
• 5.3.1 연속지적도 ···························································································102
• 5.3.2 지적재조사사업 ···················································································105
• 5.3.3 지적도 면적왜곡 해결방안 ·······························································108
• 제6장 결 론 ············································································110
• <부 록> ······························································································113
• <참고문헌> ······························································································132
• <Abstract> ······························································································137