bang {RFOC}

Angle between two 2D normalized vectors

Description

Calculates the angle between two 2D normalized vectors using dot and cross product

Usage

bang(x1, y1, x2, y2)

Arguments

x1

x coordinate of first normalized vector

y1

y coordinate of first normalized vector

x2

x coordinate of second normalized vector

y2

y coordinate of second normalized vector

Details

The sign of angle is determined by the sign of the cross product of the two vectors.

Value

angle in radians

Note

Vectors must be normalized prior to calling this routine. Used mainly for vectors on the unit sphere.

Author(s)

Jonathan M. Lees <[e-mail]>

Examples

v1 = c(5,3)
v2 = c(6,1)

a1 = c(5,3)/sqrt(v1[1]^2+v1[2]^2)
a2 = c(6,1)/sqrt(v2[1]^2+v2[2]^2)

plot(c(0, v1[1],v2[1] ) , c(0, v1[2],v2[2]), type='n', xlab="x", ylab="y" )
text(c(v1[1],v2[1]) , c(v1[2],v2[2]), labels=c("v1", "v2"), pos=3, xpd=TRUE)

arrows(0, 0, c(v1[1],v2[1] ), c(v1[2],v2[2]))

B  = 180*bang(a1[1], a1[2], a2[1], a2[2])/pi
title(paste(sep=" ", "Angle from V1 to V2=",format(B, digits=2)) )