Parabola Plotting Web Pages

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Graphics have become more available on web pages. A web page that can design parabolas can show what is now available.

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Step 1:

Different applications require parabolas having different focal points. A parabola follows the following equation.

Y = X^2/(4*focal)

The old camera flash bulbs appeared to use a short focal length when compared to its radius. When the focal is 0.25, then Y will be unity when X is unity.

The web page to do this is only a text file. Feel free to save it as source on you computer.

Step 2:

Solar application may need a long focal length. If the focal is 1, then Y will be 0.25 when X is one. The radius of the parabola can be thought of as being X. The depth of the parabola can be thought of as being Y.

Step 3:

Some applications may require the focal point to be close to one half the depth. Using a focal which is at sqrt(1/8) will do the job.

Step 4:

The new graphing feature can be extended such that a web page can print out the segments of a parabola. The web page that does this is only a text file. Select a focal and whether to plot segments or the sides. Feel free to save  this page on your computer. Look at the page's text.

Step 5:

The parabola is design to step X from 0 to 1 in 0.1 units. The side view plots both the X steps and the corresponding Y steps as lines. This web page should be printable on a single sheet of page. Or it can be saved as a pdf file to be printed later.

Step 6:

Half of a parabola can be constructed by printing out  six segments and a left and right side.

Step 7:

The lines on the half parabola show how well all the X and Y dimension line up.

The plots are 700x700 bitmaps which avoid the auto scaling features found in most plotting resources. The plot will define a segment shape from a input  a focal length which is relative to the parabola's radius. By importing these plots into a graphic application for scaling, it should be possible to construct any type of parabola desired.

10 Discussions

On Step 5, you say that you only generate 11 X points, and (implicitly) do a linear interpolation between them.  For focal depths far from 1, this is not optimal.  I played with the script, putting in 0.05 and 0.005 respectively.  In both cases, the straight lines and corners in Y are quite apparent (the latter has just two lines!).

To get a smother curve, you may want to consider evaluating the inverse problem to get Xmax (positive) for Ymax at the boundary of the plot, then generate a fixed number of steps from X=0 to X=Xmax.

Otherwise, this is a very clever bit of JavaScript.  Nicely done!

3 replies