intersectConicLine {RConics}

Intersections between a conic and a line

Description

Returns the point(s) of intersection between a conic and a line in homogeneous coordinates.

Usage

intersectConicLine(C, l)

Arguments

C

(3 \times 3) matrix representation of conics.

l

a (3 \times 3) vector of the homogeneous representation of a line.

Value

The homogeneous coordinates of the intersection points. If there are two points of intersection, it returns a (3 \times 2) matrix whose columns correspond to the homogeneous coordinates of the intersection points. If there is only one point, a (3 \times 1) vector of the homogeneous coordinates of the intersection point is returned. If there is no intersection, NULL is returned.

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

#' # Ellipse with semi-axes a=8, b=2, centered in (0,0), with orientation angle = -pi/3
C <- ellipseToConicMatrix(c(8,2),c(0,0),-pi/3)

# line
l <- c(0.25,0.85,-3)

# intersection conic C with line l:
p_Cl <- intersectConicLine(C,l)

# plot
plot(ellipse(c(8,2),c(0,0),-pi/3),type="l",asp=1)
addLine(l,col="red")
points(t(p_Cl), pch=20,col="red")