Calculating an area of a map in square kilometers/miles using expressions?

I just had an idea that I'm going to try tomorrow. Here is the idea.

Select the path around one of the vector shapes and choose Create Nulls From Paths.jsx/Null follows Path from the Window Menu. This will give you a null that moves around the entire vector path in just a few frames. If you set the keyframes apart 50 keyframes and recorded the X and Y position value for each frame, you could generate a 50-sided shape around the shape. If you use the shape's center point (sourceRectAtTime() height and width of a single shape layer) as the first vertex of a triangle and the x/y position of the first two frames, you could calculate the area of that triangle. Do that for every pair of position values, and you should have a reasonably accurate calculation of the area of the convoluted shape. 

Run the script again to create a second instance of a null tracing the path. Set the keyframes down the timeline, ending on the last frame of the path animation, and you should be able to calculate the ending area of the shape. Then, you should be able to set up an expression that converts the number of total pixels to square kilometers or miles if you know the number of pixels per mile of your map. 

If the expressions don't turn out to be incredibly recursive, so they slow down the render time, this approach might work. All I should have to do is figure out a way for the x,y position of the null between two frames to be remembered, so the area of the first, then second, then third, and on to the rest of the triangles can be added, I've got it licked. 

I think I have a solution that will get you a decent estimate--not perfect, but very close.

To use this method, you will have to blur the shape, so you will need to create a linked copy of your shape layer (or at least its alpha channel), whether that is by linking shapes with expressions or using an effect like Set Matte on a solid. I tested this on a shape layer but either method should work.

Set your project to 32-bit color, make sure your shape is 100 opacity and everything else on the layer is 0% opacity, then apply two fast box blurs to the layer with Iterations set to 1 and Repeat Edge Pixels set to ON. One of these blurs must be set to Vertical with a Radius equal to the pixel height of the layer, and the other blur must be Horizontal with Radius equal to the layer width. The result will be a transparent solid color across the layer with an opacity roughly equal to the average opacity of all the layer's pixels. Now you can then use a sampleImage expression to find the opacity in the center of the layer, and multiply this value by the number of pixels in the comp to get the number of pixels that were 100% opacity before you applied the blurs. The result will be (pretty close to) the area of the solid shape.

The expression would look something like this:

var layerToMeasure = thisComp.layer("Shape Layer 1");	//sub in your layer name/reference here
var totalLayerArea = layerToMeasure.width*layerToMeasure.height;
var samplePoint = [layerToMeasure.width/2, layerToMeasure.height/2];
var sampleRadius = [1,1];
var shapeArea = layerToMeasure.sampleImage(samplePoint, sampleRadius)[3]*totalLayerArea;
shapeArea

If you want this in units other than onscreen pixels, you'll have to do that math. Also, in case it's not obvious, since this is done through image processing it can only measure the part of the shape that is inside the bounds of the layer, so the shape can't be cropped. In the case of an actual shape layer, the bounds of the layer are the same as the bounds of the comp.

The math required to calculate the area of an irregular shape can be very complicated. I don't know of of way to calculate the number of pixels that are a certain color or use an alpha channel. 

The only possible option that I can think of would be to calculate the length of the vector path. I'm not even sure that is possible.

I think you are out of luck, looking for a simple expression solution to the problem. 

Nope. Not a gun for hire, at least not for that kind of work. In my hayday I might have tackled this as a challenge to explore the math and algorithms and even done it for free, but these days I just don't have the time and energy.

Mylenium

Yes, it's possible, but not easy. Anything from working with a grid-based approach to recursive triangular decomposition. Since you need to hold a lot of temporary data any expression is probably going to be slow as molasses in winter and a script would be more suitable.

Mylenium