conicThrough5Points {RConics}

Compute the conic that passes through 5 points

Description

Return the matrix representation of the conic that passes through exactly 5 points.

Usage

conicThrough5Points(p1, p2, p3, p4, p5)

Arguments

p1

(3 \times 1) vectors of the homogeneous coordinates of one of the five points.

p2

(3 \times 1) vectors of the homogeneous coordinates of one of the five points.

p3

(3 \times 1) vectors of the homogeneous coordinates of one of the five points.

p4

(3 \times 1) vectors of the homogeneous coordinates of one of the five points.

p5

(3 \times 1) vectors of the homogeneous coordinates of one of the five points.

Value

A (3 \times 3) matrix representation of the conic passing through the 5 points.

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

# five points
p1 <- c(-4.13, 6.24, 1)
p2 <- c(-8.36, 1.17, 1)
p3 <- c(-2.03, -4.61, 1)
p4 <- c(9.70, -3.49, 1)
p5 <- c(8.02, 3.34, 1)

# matrix representation of the conic passing
# through the five points
C5 <- conicThrough5Points(p1,p2,p3,p4,p5)

# plot
plot(rbind(p1,p2,p3,p4,p5),xlim=c(-10,10), ylim=c(-10,10), asp=1) 
# from matrix to ellipse parameters
E5 <- conicMatrixToEllipse(C5)
lines(ellipse(E5$saxes, E5$loc, E5$theta, n=500))