Where's my Shadow?

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Problem Description

Here's a program which displays the shadow cast when sun is at a given azimuth and altitude.

Background & Techniques

Based on a user's request, here's an attempt to draw a 3D image of the shadow of a vertical rod produced by the sun at a given  azimuth and altitude. 

A second set of edit controls allow you to change your viewpoint by adjusting the bearing, altitude, and distance from the base of the rod.

A late addition was the ability to plot an "analemma", a figure representing the path of the sun af observed from a fixed location and time of day for an entire year. Because the earth is tilted relative to is path around the sun and because it's path is slightly elliptical, the analemma, or its shadow version, traces a lopsided figure 8. Azimuth and altitude points may be entered individually and the "Plot shadow point" button clicked. A better method is to build a text file of azimuth and altitude values, one pair per line, and use he "Load Analemma" button to load and plot the data. File "Sample Analemma.txt", included with the downloads,  has 24 values for noon on the 1st and 15th of each month for my home town.

Non-programmers are welcome to read on, but may want to skip to the bottom of this page to download executable version of the program.

Notes for programmers

I wish I could give you a concise analysis of the math behind drawing a 3D shadow view, but the fact is, there was a lot of trial and error to draw the images.  There are six parameters altogether: Azimuth and altitude define the direction of the sun from a particular location on the earth's surface  the "Horizontal Coordinate System".  Azimuth is the angle clockwise from North and Altitude is the angle above the horizon.   The third parameter affecting the true position of the tip of a vertical rod's (or person's) shadow is the height of the rod.  For a give altitude and rod height (R),  the length of the shadow (L) can be derived from considering the right triangle formed by the rod, its shadow and the sun ray.  Tangent(altitude) = R/L,  from which we can define the circle with radius L upon which the shadow tip will lie.  The azimuth angle determines exactly where on the circle the point lies.  Procedure RecalcBaseCircle does this every time one of the three position parameters changes.  

The base circle represents the shadow tip points as we would see them when standing directly over the rod  looking straight down.  When we move away from the rod in a given direction for a given distance with our eye at a given height, the apparent position of the shadow changes.  These three "Eye" parameters determine the apparent location of the shadow tip on an ellipse.  This set of points is calculated by the RecalcVisualCircle procedure.  It is called whenever the eye position is changed or when the base circle changes. 

The third set of trigonometric calculations came from my, perhaps foolish,  decision to display directional letters N, E, W, S representing our eye position bearing (direction) from the rod.  Since we cannot actually rotate the monitor screen as we walk around the rod, we must rotate the view circle and those letters on the screen.  In order to make the letters appear as if they were painted on the ground, I decided to rotate them as they moved in a circle concentric with the view circle so that the base of the letter was always facing the rod.  This is performed by the SetFontAngle procedure.  The code to draw  the letters is contained in the PaintFigure procedure which redraws the entire image.   It looks like this sample for the letter N (North):

angle:= (eyeaz-halfpi);
setfontangle(font, -angle+halfpi);

And finally, I decided to allow shadow points to be saved and plotted each time the image is redrawn  This introduced its own set of problems since the points have no relation to the current base circle .  

Whew!  For the first forty hours working on a program, it's great fun.  After the 2nd forty hours, one is ready for the darn thing to just work!  That's about where this program lies now and I'm movin' on.   But I'm already looking forward to doing it all over again  with a new project next week!

Running/Exploring the Program 

bullet Download source
bullet Download  executable

Suggestions for Further Explorations

I spent a day, without success,  trying to distort the angled direction letters as the eyepoint height changes so that the height decrease as the eye approaches ground level.   I suppose I'll revisit it one day.



Original Date: March 1, 2009

Modified: May 15, 2018


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