# How to do a parametric study of arbitrary 2D surface?

I need to do a parametric study of the performance of a room heater on different rooms by simulating the temperature distribution in there. The problem here is that the rooms are not simple rectangles like shown in a) (in blue are the walls of the room and in red the heater), where I could just simply sweep over length and wide, but they may have more complex shapes like shown in b) to d). I thought about making a raster and parametrize with 1 or 0 if the given rectangle in the raster is inside the walls, but the number of input variables would be too high and I would to make sure that the parametrization is consistent somehow.

Is there a systematic way to parametrize an arbitrary (limiting the number of nodes could be a possibility to limit complexity) 2D surface?

• What do you mean by the performance of the heater? Do you need to know the largest and smallest temperature in the domain? Or something else? Aug 27, 2022 at 13:05
• Yes something like that. The maximum temp is given by the heater but I'd like to know the lowest temperature and the average temperature in the room Aug 27, 2022 at 13:31
• I would try using statistical moments to classify the shapes of the room. Say you have a vector $R_i$ and $Z_i$ tabulating the nodes. Then from calculating the mean, width, skewness, kurtosis etc. of those you should be able to classify the shape of the room in terms of its characteristic diameter, aspect ratio, asymmetry etc. A separate issue is describing the location of the heater in the room, that would also matter. Aug 27, 2022 at 15:28
• Thank you Maxim!, I will try using those parameters to classify the shapes Aug 29, 2022 at 11:06