RConics (version 1.1.2)

conicThrough5Points: 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)

Value

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

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.

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))