In cmjt/stelfi: Hawkes and Log-Gaussian Cox Point Processes Using Template Model Builder

Delaunay triangulation metrics {#meshmetrics}

data("horse_mesh", package = "stelfi")
metrics <- meshmetrics(horse_mesh)
str(metrics)

Returned is an sf object with the following geometric attributes of the user supplied Delaunay triangulation

• V1, V2, and V3 corresponding vertices of mesh matches mesh$graph$tv;
• ID, numeric triangle id;
• angleA, angleB, and angleC, the interior angles;
• circumcircle radius, circumradius, circumcircle_R (\eqn{R});
• incircle radius incircle_r ($r$);
• centroid locations of the circumcircle, circumcenter, (c\_Ox, c\_Oy);
• centroid locations of the incircle, incenter, (i\_Ox, i\_Oy);
• the radius-edge ratio radius_edge $\frac{R}{l_{min}}$, where $l_{min}$ is the minimum edge length;
• the radius ratio radius_ratio $\frac{r}{R}$;
• area, area ($A$);
• quality a measure of "quality" defined as $\frac{4\sqrt{3}|A|}{\Sigma_{i = 1}^3 L_i^2}$, where $L_i$ is the length of edge $i$.

A triangle's circumcircle (circumscribed circle) is the unique circle that passes through each of its three vertices. A triangle's incircle (inscribed circle) is the largest circle that can be contained within it (i.e., touches it's three edges).

To plot each triangle's metric of choice simply change the fill aesthetic. Simply a tool to identify "bad" triangles in the mesh.

ggplot(metrics, aes(fill = area)) +
    geom_sf() + theme_void()

ggplot(metrics, aes(fill = radius_edge)) +
    geom_sf() + theme_void()

ggplot(metrics, aes(fill = quality)) +
    geom_sf() + theme_void()

cmjt/stelfi documentation built on Oct. 25, 2023, 2:53 p.m.