Geometry of new lava parcels - demichie/MrLavaLoba GitHub Wiki

Lava parcels are represented by elliptical lobes having a constant area and a prescribed thickness (i.e. the volume is fixed).

The geometry of the a new elliptical parcel l_i (the lobe) is defined by the eccentricity e_i and by the azimuthal orientation of the major axis of the ellipse az_i''. Lobe position, instead, is defined by the geographic coordinates (x_i,y_i) of the center of the ellipse (c_i) representing the parcel.

The first parcel is set on the vent, then each parcel buds from the edge of a parcel (denoted as parent parcel), which has been already set. The point where the new parcel will bud (budding point, bp) is determined according to the following steps:

1. A preliminary direction az_i is given by the direction from the center of the parent lobe (c_p) to the point of minimum elevation on the boundary of the elliptical parcel;
2. A random perturbation ε_az, with a probability distribution defined as a function of the local slope, is added to az_i resulting in a new preliminary orientation az_i'.
3. An inertial factor accounting for the orientation of the parent lobe (az_p) is considered, resulting in the final orientation az_i''=f(az_i',az_p). This final direction from the center of the parent lobe determines on its boundary the budding point b_p.

Finally, the eccentricity e_i of the budding lobe is defined as a function of the slope from the center of the parent lobe to the budding point bp, defined as the intersection between the boundary of the parent lobe and the ray from the center of the lobe with direction az_i''. The steeper the slope the larger the eccentricity, with circular lobes forming over a flat topography. We remark here that while the eccentricity of the lobes changes as a function of the slope, the area and the thickness are fixed (unless otherwise stated in the input settings).