Jing Ming

Jing Ming

M. Eng. at the School of Information and Communication, University of Electronic Science and Technology of China (UESTC)

Single-Objective Programming based Sun’s Shadow Location Optimization Model

September, 2015 - September, 2015. At UESTC

Mathematical Contest in Modeling of China. Supervised by Prof. Guanghui Cheng

Background

It was a mathematical modelling problem issued by the committee of the Mathematical Contest in Modeling of China. Our team, which consisted of three junior undergraduate students, chose the task named the Sun’s Shadow Positioning Problem. Once we take a picture of something, the shadow will be recorded if there exists sunshine. Since the shadow of substance changes with certain rules, we can determine the shooting location or date under examinations of the sun’s shadow in the picture.

Main Task

Our work was to find the pattern to build the mathematical relationship between the shadow’s length and the several parameters, including longitude, latitude, substance’s height and the shooting date. To achieve it, a dozen of shadow related data was provided to figure out this shadow length to position, height and date model. As a model made up by five variables, it was critical to discover a optimazation model when the input elements were limited to three or less. In the end, we were required to determine the shooting location of a video which recorded the shooting date and changing length of a pole’s shadow with the use of the proposed Location Optimization Model.

pole's shadow one frame of the video

My Duty

In this teamwork, my work was to establish the relationship formula and the difficulty lay in the model assumption made and the parameters chosen which abandoned trivial factors and remained the vital importance. Meanwhile, the knowledge of geography took a significant role in this task, peculiarly the various solar angles determination. Also, the single-objective programming model with regard to the minimum sum of differences between the measured shadow length and the calculated one was presented as a solution to the limited input cases. What’s more, the fourth question which was about determining the shooting location of the video demanded us to recognize the changing length of the pole’s shadow in the picture. Considering the transformation of the pole in a 2-dimensional video, the software SketchUp was applied to conduct the 3-dimensional modelling of the pole to extract the precise length.

3-dimensional modeling of the pole the SketchUp 3D modelling