colinear {RConics}

Test for colinearity

Description

Tests if three points are colinear. The coordinates of the points have to be in homogeneous coordinates.

Usage

colinear(p1, p2, p3)

Arguments

p1

(3 \times 1) vector of the homogeneous coordinates of point 1.

p2

(3 \times 1) vector of the homogeneous coordinates of point 2.

p3

(3 \times 1) vector of the homogeneous coordinates of point 3.

Value

TRUE if the three points are colinear, else FALSE.

Source

Richter-Gebert, Jürgen (2011). Perspectives on Projective Geometry - A Guided Tour Through Real and Complex Geometry, Springer, Berlin, ISBN: 978-3-642-17285-4

Examples

# points: homogeneous coordinates
p1 <- c(3,1,1)
p2 <- c(0,2,1)
p3 <- c(1.5,-2,1)
p4 <- c(1,3,1)

# homogeneous line passing through p1 and p2
l1 <- join(p1,p2)

# homogeneous line passing through p3 and p3
l2 <- join(p3,p4)

# homogeneous points formed by the intersection of the lines
p5 <- meet(l1,l2)

# test for colinearity
colinear(p1, p2, p3)
colinear(p1, p2, p5)
colinear(p3, p4, p5)

# plot
plot(rbind(p1,p2,p3,p4),xlim=c(-5,5),ylim=c(-5,5),asp=1)
abline(h=0,v=0,col="grey",lty=3)
addLine(l1,col="red")
addLine(l2,col="blue")
points(t(p5),cex=1.5,pch=20,col="blue")