[NFB-Science] Graphiti and Desmos report
John
johnmillerphd at hotmail.com
Fri Jun 28 00:01:46 UTC 2024
> Hello,
>
his
> write-up is mostly about using Graphiti to look at the output in real-time of an on-line graphical calculator.
>
> I experimented using Desmos which is an on-line graphical calculator.
>
> I used the JAWS screen reader, a 40-cell refreshable braille display, and Graphiti.
>
> I am using Graphiti in HDMI mode.
>
> Recall that with Graphiti the new tactile image appears within 5 seconds of an update on the HDMI monitor.
>
> For simple line plots the Graphiti plotting is rather quiet.
>
> At this time I cannot add braille labels at specified locations in my plot.
>
> To get around this I would find it helpful to toggle on and off a horizontal or a vertical line with a specified offset.
>
> I did this in Desmos and it was helpful for reference.
>
>
>
> I plotted curves such as:
>
> 1. y = sin x
>
> I found the expected tactile curve.
>
> It is something like a horizontal snake.
>
> 2. y = 2 * sin x
>
> This has noticeably taller humps than the first equation.
>
> By default I have grid lines appearing at x = -6, -4, -2, 0, 2, 4, 6, ...
>
> 3. y = 2 * cos x
>
> In Desmos the equation plots as you type it.
>
> Just press enter to start forming a second equation to plot on top of the first.
>
> I wanted to see on Graphiti where is the y-axis.
>
> So I intentionally drew a vertical line that is near y = 0 but not precisely 0.
>
> Remember I have a grid line already at y = 0.
>
> I made the second line y = 0.5.
>
> Now there are vertical lines every 2 units but 2 very close together vertical lines where the y-axis should be.
>
> I went through the exercise of deleting the second equation and adding it back.
>
> The image did not flicker or blank or anything.
>
> Rather the single line y = 0.5 would appear or disappear.
>
> As I recall it erased vertically starting at the top or bottom and moving up or down the screen.
>
>
>
> How long is the period of the function?
>
> Starting from the 2 vertical lines which is the peak of a hump I move to the right to the grid line 2, see the valley, to the grid line 4, and come to the peak at grid line 6.
>
> From peak to peak the period is approximately 6.
>
> The true peak-to-peak is 2 times pi or 6.28 but this appears as 6 graphically with this scale.
>
> It remains an exercise to examine how the period changes for equations such as
>
> y = cos (0.5 * x) and y = cos (2 * x)
>
>
>
> The Graphiti has a braille keypad and a set of up-down left-right arrows.
>
> It is possible to zoom in by pressing dot 5 and zoom out by pressing dot 2.
>
> It is possible to pan upward by pressing the up arrow and pan downward by pressing the down arrow.
>
> At times I plotted circles centered at the origin, shifted to the right or left of the origin, and shifted above or below the origin.
>
> Panning and zooming helped find my grid lines into focus or instead zoom in on the circle center.
>
>
>
> 4. 4 = x^2 + y^2
>
> The Graphiti has 60 horizontal pins by 40 vertical pins.
>
> Because my monitor has a different aspect ratio than this, what results is an ellipse.
>
> The ellipse is tall in the vertical direction and has an aspect ratio of 3 to 2.
>
> 5. 1 = (x^2) / 3^2 + (y^2) / 2^2
>
> This forms a perfect circle on the Graphiti.
>
> This means that with some care the aspect ratio can be corrected in a graphing calculator such as Desmos to correspond to 1 unit horizontal maps to 1 unit vertical on the Graphiti in HDMI mode.
>
> 6. 4 = (x-2)^2 + y^2
>
> This is a circle shifted in the horizontal direction from being centered at the origin.
>
>
>
> Very best,
>
> John
>
>
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