Plumeria Polar Graph Animation Design Process
2023 April 2nd
Kaize Ooi
This year in Dr. Tong’s Honors Precalculus Class at Concordia International School Shanghai, were given a special opportunity to work on a project as a whole class, with that project being making an animation of a flower blooming using only polar equations.
Flower:
The flower I chose to animate for this project was the Plumeria, a small flower that usually grows in groups. At first I was planning to animate the entire group of flowers, but that would be four times the work that I would have to put into this project so I decided to focus on a single flower instead.
The image above was from a video called “Plumeria Time Lapse”, seen from Figure 1 https://youtu.be/5yMgf3wxJAo.
Animation:
I have decided to use frame-by-frame animation because using a slider animation would be too annoying as I would have to keep track of where every line is going and alter dozens of variables in order to get the right placement of each line. Frame by frame may not be as smooth as slider animation, but I prefer convenience over aesthetics.
Process:
If you do not want to read below or think it is confusing, I made a step by step video here: https://estream.concordiashanghai.cn/View.aspx?id=29154~5i~aerngPkf8n&code=Vm~n0mAgZfMW3dKQCIUgfFJteLKrCC2MMy3EFUDJgeax8awQVJXzNeLVdlNSacl8EMDscfcMWI69yGQTLwua6BHBkhz6YzxG6lZSX&ax=7y~fhRpFoIooDiUGY
Choosing Frame Process:
1. First, I had to select different frames in the video above to base my own flower on, so I screen shot 11 frames in total that focuses on one flower.
2. Next, I take the 11 screen shot frames and put them in a drawing software called GIMP, where I trace important parts in every frame so people can recognize that it is a flower without the background video. These images can be found by expanding a Frame Folder and making the first .png file visible.
General Graphing Process:
1. Insert the traced image of the frame into Desmos.
2. Start tracing the highlighted parts using Polar Graphs (Mainly Rose Curves).
a. Because I’m mainly using Rose Curves for this project, the first thing I look for in a traced area is compare the curve with a new equation I had in my clipboard.
b. I then see which area of the rose curve I need to focus on, as I am mainly using the curve with 4 quadrants (ex: r=2cos2θ).
i. The upper left quadrant is 0π<t<0.5π, bottom right is 0.5π<t<1π, bottom left is 1π<t<1.5π, upper left is 1.5π<t<2π.
c.
I alter the parameters of the equation to fit the curve, which can be seen in Figure 2:
Logbook:
2023 March 24th : Chose the video and selected the frames needed to create the project
2023 March 25th : Traced half of the frames
2023 March 26th: Traced the rest of the frames and finished Prototype Frame 1
2023 March 30th: Finished Frames 1 and 2
2023 March 31st: Finished Frames 3, 4, and 5
2023 April 1st: Finished Frames 6, 7, 8, 9
2023 April 2nd: Finished Frames 10, 11, written this Process Paper, and recorded Process Video
Final frame of the product:
