treeDbalance (version 1.0.1)

imbalSubdiv_mu: Calculation of the centroid distances

Description

imbalSubdiv_mu - Calculates the node imbalance value "relative centroid distance" of a vertex which subdivides the edge \((p,v)\) at \(v+x \cdot (p-v)\) with \(x \in [0,1]\). For example, we can obtain the node imbalance value of \(v\) if \(x=0\), and \(x=0.5\) would indicate a subdividing node exactly in the middle of \(v\) and \(p\).
Attention: If \(x=1\), this function will not calculate the node imbalance value of \(p\) with respect to its own incoming edge but with respect to the edge \((p,v)\) itself. This enables us to estimate the node imbalance integrals over the entire edge length.

imbalSubdiv_M - Calculates the node imbalance value "expanded relative centroid distance" of a vertex which subdivides the edge \((p,v)\) at \(v+x \cdot (p-v)\) with \(x \in [0,1]\). For example, we can obtain the node imbalance value of \(v\) if \(x=0\), and \(x=0.5\) would indicate a subdividing node exactly in the middle of \(v\) and \(p\).
Attention: If \(x=1\), this function will not calculate the node imbalance value of \(p\) with respect to its own incoming edge but with respect to the edge \((p,v)\) itself. This enables us to estimate the node imbalance integrals over the entire edge length.

dist3dToLine - Calculates the distance of a \(point\) to the infinite line between two points \(a\) and \(b\) in 3D space.

cross3d_prod - Calculates the cross-product of two 3D vectors.

Usage

imbalSubdiv_mu(x, p, v, centr_v, centr_v_weight, edge_weight)
imbalSubdiv_M(x, p, v, centr_v, centr_v_weight, edge_weight)
dist3dToLine(point, a, b)
cross3d_prod(a, b)

Value

imbalSubdiv_mu Numeric value \(\in [0,1]\) (higher values indicate a higher degree of asymmetry).

imbalSubdiv_M Numeric value \(\in [0,2]\) (higher values indicate a higher degree of asymmetry).

dist3dToLine Numeric value.

cross3d_prod Numeric vector of size 3.

Arguments

x

Numeric value \(\in [0,1]\) which indicates where on the edge \((p,v)\) the subdivision takes place: \(v+x \cdot (p-v)\).

p

Numeric vector of size 3 (3D coordinates of parent node \(p\)).

v

Numeric vector of size 3 (3D coordinates of node \(v\)).

centr_v

Numeric vector of size 3 (3D coordinates of the centroid of the pending subtree of node \(v\)).

centr_v_weight

Numeric value >=0 (weight of the pending subtree of node \(v\)).

edge_weight

Numeric value >=0 (weight of the edge \((p,v)\)).

point

Numeric vector of size 3 (e.g. 3D coordinates).

a

Numeric vector of size 3 (e.g. 3D coordinates).

b

Numeric vector of size 3 (e.g. 3D coordinates).

Author

Sophie Kersting, Luise Kühn

Examples

imbalSubdiv_mu(x=0.5,p=c(1,0,1),v=c(0,0,0),centr_v=c(0.5,0,0),
centr_v_weight=1,edge_weight=1)
imbalSubdiv_M(x=0.5,p=c(1,0,1),v=c(0,0,0),centr_v=c(0.5,0,0),
centr_v_weight=1,edge_weight=1)
dist3dToLine(point=c(1,1,1),a=c(0,0,0),b=c(1,2,2)) # 0.47140...
cross3d_prod(a=c(1,-1,1),b=c(1,2,2)) # c(-4, -1, 3)