Hello  Václav Šmilauer,

Last time I used this method: the ratio between pixel of a photo.

Pendenza=slope = 86/208=0,41 or 41%. So angle = arctan(0,41), near 22.3°

Sw used is  IrfanView, light, small, very quick,free

The angle is relative to prilled (3-5 mm)  Ammonium Nitrate.

Regards

http://www.irfanview.com/

Thanks, but I have 3d coordinates of particles and need something which does not need human intervention. Just numbers.

Have a look at this paper, it discusses the angle of repose test and a few others:

https://www.researchgate.net/publication/276908617_Improving_the_Precision_of_Discrete_Element_Simulations_through_Calibration_Models

Conference Paper Improving the Precision of Discrete Element Simulations thro...

You can get a reasonable approximation (and very fast and simple to code!) by simply finding the max and min locations of the particles. Lets take y as the vertical direction, so the height of the cone would be h=ymax-yground, then the width of the base of the cone will be b=1/4((xmax-xmin)+(zmax-zmin)). The angle of repose is arctan(h/b). Depending on the cohesive of the material, this approximation will be reasonable.

You could also triangulate the surface and calculate the angle the surface triangles make with the horizon, then take the weighted average of these angles. That would be slightly less complicated than trying to fit a cone to the pile with regression.

You can get a better approximation using the approach you suggested of course, but these approaches may be good starting points.

Thanks, Kirk, but both min/max particles will have strong local effects (if the min/max particles happen to be displaced in some funny way), thus are not reliable for measuring the global property. Triangulation and fittingsounds better, I will go that way. I am suprised thatt here is (as far as we see) not a single article dealing with this.

A purely geometry-based approach could be like this: If you are able to identify the particles located at the free-surface you could use their centroids to build a surface mesh, or a spline surface. Then, the repose angle could be computed from the gradient of this surface.