imbalSubdiv_A {treeDbalance}R Documentation

Calculation of the centroid angles

Description

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

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

angle3dVec - Calculates the angle in the interval [0,π][0,\pi] between two 3D vectors aa and bb. Note that the function returns 0 if one entry vector is (0,0,0)(0,0,0).

Usage

imbalSubdiv_A(x, p, v, centr_v, centr_v_weight, edge_weight)

imbalSubdiv_alpha(x, p, v, centr_v, centr_v_weight, edge_weight)

angle3dVec(a, b)

Arguments

x

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

p

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

v

Numeric vector of size 3 (3D coordinates of node vv).

centr_v

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

centr_v_weight

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

edge_weight

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

a

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

b

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

Value

imbalSubdiv_A Numeric value [0,π]\in [0,\pi] (higher values indicate a higher degree of asymmetry).

imbalSubdiv_alpha Numeric value [0,π/2]\in [0,\pi/2] (higher values indicate a higher degree of asymmetry).

angle3dVec Numeric value in [0,π][0,\pi].

Author(s)

Sophie Kersting, Luise Kühn

Examples

imbalSubdiv_A(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_alpha(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)
angle3dVec(a=c(1,0,0),b=c(0,1,0)) # right angle = pi/2 = 1.5707...

[Package treeDbalance version 1.0.1 Index]