2017 HiMCM A题特等奖学生论文下载7879
2017 HiMCM A题特等奖学生论文下载7879
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论文摘要如下：
20th Annual High School Mathematical Contest in Modeling (HiMCM) Summary Sheet (Please make this the first page of your electronic Solution Paper.)
Team Control Number: 7879 Problem Chosen: A
As technology for drones advances, large-scale drone light shows which are capable of forming animated complex displays emerged and have became a popular choice to provide a large crowd with a unique experience for technological innovation. As it is crucial for the mayor to understand specific details about the show before making the decision of whether to include the aerial light show in this year’s festival, the purpose behind our mathematical and computational model is to simulate the whole process of the light show, with transition time minimised, safety guaranteed, displays aesthetically presented.
Our models consist of four steps: formation of displays, transition between displays, animation during each display and lastly take-off and landing. To construct the frames, we put the original images into Matlab and trace out the contour of every display. A point selection was performed to locate important points using an algorithms constructed by our own, generating a list of positions that need to be occupied by drones. Then, to minimise the transition time between every display for better light show experience, which is equivalent to minimising the maximum distance travelled by any drone, we employed bipartite matching and binary search. Animation for the three displays is in the form of rotation or shearing, both of which make use of transformation matrix. Lastly, to minimise takeoff and landing time as well as the area required for holding the drones, we decided to place the drone at a position on the ground directly below the position it will occupy in the sky for the first frame, while the landing process applies the same concept.
Based on our model, 480 drones will be employed to put up the performance so that the whole show will be big enough for thousands of people to view. A restricted ground area with a length of 430m and a width of 330m will be cordoned off and viewers are not allowed to enter this area for safety concerns. With the restricted area taken into account, the total air space required will be 17737500m3, while the required launch area will be 2400m2.Given each display lasting 60s, the duration of the whole aerial light show will be 329s.
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