Chapter 7 Delaunay triangulation metrics
## Classes 'sf' and 'data.frame': 396 obs. of 18 variables:
## $ V1 : int 172 28 168 117 270 92 175 182 253 14 ...
## $ V2 : int 30 188 186 57 253 144 137 148 169 15 ...
## $ V3 : int 186 162 42 63 121 169 240 111 121 116 ...
## $ ID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ angleA : num 72.5 55.9 63.6 65.9 66.9 ...
## $ angleB : num 56.4 72.7 65.3 75.5 56.6 ...
## $ angleC : num 51.1 51.5 51.2 38.6 56.6 ...
## $ incircle_r : num 0.487 0.407 0.428 0.316 0.306 ...
## $ circumcircle_R: num 1.011 0.845 0.872 0.717 0.618 ...
## $ c_Ox : num 8.17 10.46 6.41 -3.77 -7.86 ...
## $ c_Oy : num -3.13 1.76 -3.7 -8.74 2.25 ...
## $ i_Ox : num 8.25 10.31 6.44 -3.57 -7.92 ...
## $ i_Oy : num -2.96 1.77 -3.58 -8.61 2.23 ...
## $ radius_edge : num 0.643 0.639 0.642 0.801 0.599 ...
## $ radius_ratio : num 0.482 0.482 0.491 0.44 0.495 ...
## $ area : num 1.264 0.883 0.963 0.568 0.488 ...
## $ quality : num 0.969 0.97 0.983 0.884 0.991 ...
## $ geometry :sfc_POLYGON of length 396; first list element: List of 1
## ..$ : num [1:4, 1:2] 8.44 9.06 7.16 8.44 -2.16 ...
## ..- attr(*, "class")= chr [1:3] "XY" "POLYGON" "sfg"
## - attr(*, "sf_column")= chr "geometry"
## - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA NA ...
## ..- attr(*, "names")= chr [1:17] "V1" "V2" "V3" "ID" ...
Returned is an sf
object with the following geometric attributes of the user supplied Delaunay triangulation
V1
,V2
, andV3
corresponding vertices ofmesh
matchesmesh$graph$tv
;ID
, numeric triangle id;angleA
,angleB
, andangleC
, the interior angles;- circumcircle radius, circumradius,
circumcircle_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.