RConics (version 1.1.2)

intersectConicLine: 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)

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.

Arguments

C

\((3 \times 3)\) matrix representation of conics.

l

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

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")