Determination of the volume of space enclosed by an SVG element

I have an SVG with a fish bowl shape, and I am attempting to calculate the volume of the pink area as a percentage of the space between the "fill level" and "empty level".

It's not straightforward to calculate this percentage due to the irregular shape of the fish bowl. A simple top-to-bottom approach won't give accurate results, so I need an algorithm to accurately determine the volume for various fish bowls of different shapes.

Is there a way to achieve this using JavaScript on an SVG element? If it is possible, how can I go about calculating these volumes within specific element areas as percentages?

Update: A sample SVG has been uploaded to jsfiddle

javascriptcssmathsvganalytics

Answer №1

To begin, start by breaking down the SVG path into individual lines. Since none of these lines intersect the Y axis, our focus shifts to finding the area under the curve created by the fishbowl shape, also referred to as the integral.

Let's denote the absolute values of the X coordinates of the line segments as {x_0, x_1, ..., x_n}.

The fishbowl graph can be defined by a piecewise function:

f(x) = 
 { (x - x_0)/(x_1 - x_0) if x_0 ≤ x < x_1
 { (x - x_1)/(x_2 - x_1) if x_1 ≤ x < x_2
 {  ... 
 { (x - x_(n-1))/(x_n - x_(n-1)) if x_(n-1) ≤ x < x_n

The volume of the fishbowl is then given by the integral of πf(x)2 (the three-dimensional figure formed by revolving that function).

Assuming an empty level e, fill level v, and water level w, the ratio of the filled part of the fishbowl is:

(∫ew πf(x)2 dx) / (∫ev πf(x)2 dx)

If your fishbowl shape is determined by a specific function graph, substitute that function as f(x) and proceed with the aforementioned integral calculation.

Numerical techniques like Simpson's rule or Newton-Cotes methods can provide approximations for integrals.

Answer №2

When faced with the need for a solution that is not computationally expensive and lacking the motivation to write optimized code, I decided to render it against a transparent background, convert it to raster, and then count pixels. While I acknowledge that those experienced in graphics and geometry may have cleaner solutions, my expertise lies more in high-level programming languages rather than low-level assembly coding.

It's important to note that the complexity of the fishbowl's geometry may require adjusting the rendering resolution accordingly.

[Update for 2021]

This response on Stack Overflow outlines how to calculate the area of one <path> using the brute-force method mentioned above: Scaling the filling portion of an SVG path

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