imbalSubdiv_mu {treeDbalance}

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)

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).

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.

Author(s)

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)