For this activity, we started by looking for good handwritten graphs. We ended up going to the College of Science library, and browsing some of the journals in a dusty section of the library that were published more than 50 years ago. After obtaining the graphs we liked, we photocopied them and moved to the NIP Admin Office for scanning. The scanned page is in Fig. 1 below.
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| Fig. 1. The scanned image in JPG of my chosen plot. |
The scanned copies of my chosen graphs (see Fig. 2 below) were a bit hard to look at when zooming in, and this quality was noticeable from the photocopies. I think that in the future, it is much better to choose graphs that do not have fine, thinly spaced guidelines. These lines act as a guide for the plotter who did the graph by hand, but they were prone to losing their quality and blurring over once the image is passed through a photocopier and a scanner.
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| Fig. 2. A larger version of the scanned plot. |
The activity itself was alright. Apart from the eye-straining experience of picking points in the graph as I followed the instructions, the activity was still fairly enjoyable and rewarding at the end. I also managed to place the scanned graph as a background image for my Excel plot area, so that was nice.
I was able to locate the pixel coordinates of the six ticks along the x-axis and the three ticks along the y-axis. Subtracting between pixel coordinates gave me the equivalent number of pixels between ticks, which were 74-75 for the x-axis and 93 for the y-axis. By ratio and proportion, the physical value for the x-axis, u, has an equivalence of 1 u to 37 pixels horizontally, while the physical value for the y-axis, ϕ(u), has an equivalence of 1 ϕ to 186 pixels vertically. Meanwhile, the pixel coordinates of the graph's origin are (x-pixel, y-pixel) = (20, 211). These are all shown in Fig. 3 below.
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| Fig. 3. A screenshot of the calibration steps from my spreadsheet file of the activity. |
Meanwhile, I was able to obtain the corresponding equations to convert pixel coordinates to physical values, which I can then plot using Excel. These equations were u = (x - x0)/37 and ϕ = (y0 - y)/186. The subtrahends are reversed for the y-axis since the origin of an image's pixel coordinates is in the upper-left corner of the image, while the origin for the plot is in the lower-left. As in the previous paragraph, 37 and 186 correspond to how many pixels per unit of physical value.
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| Fig. 4. The data points behind the resulting plot. |
I used these equations for columns D21-D31 and E21-E31 in Excel (see Fig. 4 above) to obtain the physical values corresponding to points on the graph that I chose. Plotting u and ϕ(u) using Excel produces a graph very close to the one I scanned (see Fig. 5 below). The slight deviations of the blue line from the original gray line I can attribute to minor distortions of the image from photocopying and scanning. Obtaining more points should produce a graph closer to the original.
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| Fig. 5. The resulting plot using the pixel to physical value equations. |
Overall, the activity was fun and quite worthwhile. I could actually see myself doing these steps for other plots in the future.
Self-Evaluation: 9/10
Thank you to Peter Debye for his January 1925 publication of "Note on the scattering of x-rays" first published on the journal "Studies in Applied Mathematics; Volume 4, Issue 1-4; Pages 133–147." This publication was the source of the graph (Fig. 2 in the text) I used for this activity.
PS: A late thank you to my groupmates from Activity 1, Mich Cirunay and Micholo Medrana. For this activity, thank you to Mich Cirunay, Micholo Medrana, Louie Rubio, Robbie Esperanza, and Carlo Solibet for being there while we scanned handwritten graphs from old journals in the College of Science library. I probably would have had a hard time looking for graphs alone. Thank you to Mich Cirunay and Robbie Esperanza for helping with and answering questions about the activity itself. Thank you to the College of Science library staff for allowing us to browse, and to Ate Lina for scanning and emailing our photocopied graphs.
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