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基于几何方法对太阳影子定位的研究 预览 被引量:1

Solar Shadow Positioning Based on Geometric Techniques
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摘要 目的针对视频中物体的太阳影子与轨迹变化数据,分析太阳影子变化规律并建立数学模型,确定拍摄的地点和日期。方法 (1)对已知地点、时间与影子坐标情况下的投影问题,利用相似三角形原理建立影子长度变化模型,分析影子长度的变化规律,使用寿星天文历软件采集数据,得到模型结果。(2)对已知时间与影子坐标情况下的投影问题,对经度与纬度进行估计分析,建立模拟Analemmatic日晷模型。利用二次拟合和太阳影子长度变化规律,使用MATLAB求解,给出太阳影子定位。(3)对未知地点、时间情况下的投影问题,使用坐标系转换和空间向量建立地平系几何模型,结合模拟Analemmatic日晷模型和二次拟合方法,利用MATLAB求解,得到时间与太阳影子定位的经纬度值。结果(1)2015年10月22日北京时间9∶00-15∶00时之间天安门广场3m高的直杆的太阳影子长度变化曲线图,曲线端点:9∶00,影子长度为6.59m;15∶00,影子长度为6.70m。曲线最低影子长度为3.58m,此时时间为12∶13。(2)文献[1]中直杆所在的地区为111.04°E与4°N以及111.04°E与29~35°N范围内,直杆可能处在中国南海、常德市、十堰市、商洛市和宜昌市。(3)文献[1]日期为9月26日,直杆位于塔吉克斯坦;日期为1月1日,直杆位于中国南海。结论通过分析视频中太阳阴影轨迹的几何属性来进行地理位置估计计算,利用几何关系建立3种模型,对问题进行由浅入深的分析。在3D角度和测量条件未知的情况下也可以使用上述研究方法,这使得该方法具有广泛的应用和更大的灵活性。 Objective In view of the sun's shadow and track changing of data of the object in the video,the changing rule of the sun's shadow was analyzed and the mathematical model was established to determine the filming location and date.Methods(1)For a projection problem with known location,time and shadow coordinates,by using similar triangle principle to establish a change model of shadow length,the variation of the shadow length was analyzed,and the model results were obtained from data acquired by using the software-the longevity of the astronomy and calendar;(2)For the projection problem with known time and shadow coordinates,by evaluating the longitude and latitude,the sundial model of simulated Analemmatic was establish.By using the quadratic fitting,variation of sun shadow length and the MATLAB,the positioning coordinates of sun shadow were obtained.(3)For the projection problem with unknown location and time,by using coordinate transformation and space vector to establish horizon line geometric model,combining analog of Analemmatic sundials model with quadratic curve fitting method,and using MATLAB,the time and longitude and latitude values of the sun shadow position were obtained.Results(1)Between 9∶00-15∶00of October 22,2015 Beijing time,the sun's shadow length variation curve,and the curve ends of the 3-meter-high straight rod on Tiananmen Square were:on 9∶00,the shadow length was 6.59m;on 15∶00,shadow lengths 6.70m;on 12∶13the curve for the lowest shadow lengths was 3.58 m.(2)In literature[1]the straight rod was located in the area between 111.04°E,4°N and 111.04°E,29°-35°N,and the straight rod might be in the South China Sea,Changde city,Shiyan city,Shangluo city and Yichang city.(3)In literature[1],on September 26,the straight rod was located in Tajikistan;on January 1,the straight rod was located in the South China Sea.Conclusions By analyzing the geometric properties of the sun shadow track in video to estimate location,three models were established by using the geometric relationship,and
作者 沈曙昀 王立 郭三敏 闫旭旭 朱家明 SHEN Shu-yun;WANG Li;GUO San-min;YAN Xu-xu;ZHU Jia-min;School of Statistics and Applied Mathematics,Anhui University of Finance and Economics;School of Foreign Languages,Anhui University of Finance and Economics;School of Accountancy,Anhui University of Finance and Economics;
出处 《河北北方学院学报:自然科学版》 2017年第1期18-24,共7页 Journa of Hebei North University:Natural Science Edition
基金 国家自然科学基金项目(11301001) 安徽财经大学教研项目(acjyzd201429)
关键词 太阳影子定位 模拟Analemmatic日晷模型 二次拟合 MATLAB solar shadow positioning sundial model of simulated Analemmatic quadratic fitting MATLAB
作者简介 沈曙昀(1996-),女,安徽合肥人,安徽财经大学统计与应用数学学院在读学生,研究方向:应用统计学. 通讯作者:朱家明(1973-),安徽泗县人,副教授,硕士,研究方向:应用数学与建模.
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  • 1武琳..基于太阳阴影轨迹的经纬度估计技术研究[D].天津大学,2010:
  • 2赵志升,罗德林,李海英.数据挖掘技术与应用[J].河北北方学院学报:自然科学版,2006(6):63-66. 被引量:10

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