RConics (version 1.0)

Intersection with conics: Intersections with conics

Description

Point(s) of intersection between a conic and a line, and between two conics in homogeneous coordinates.

Usage

intersectConicLine(C, l)
intersectConicConic(C1,C2)

Arguments

C, C1, C2

\((3 \times 3)\) 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.

References

Richter-Gebert, J<U+00FC>rgen (2011). Perspectives on Projective Geometry - A Guided Tour Through Real and Complex Geometry, Springer, Berlin, ISBN: 978-3-642-17285-4

Examples

# NOT RUN {
  # 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)
  
  # Ellipse with semi-axes a=5, b=2, centered in (1,-2), with orientation angle = pi/5
  C2 <- ellipseToConicMatrix(c(5,2),c(1,-2),pi/5)
  
  
  # line
  l <- c(0.25,0.85,-3)
  
  # intersection conic C with line l:
  p_Cl <- intersectConicLine(C,l)
  
  # intersection conic C with conic C2
  p_CC2 <- intersectConicConic(C,C2)
  
  # plot
  plot(ellipse(c(8,2),c(0,0),-pi/3),type="l",asp=1)
  lines(ellipse(c(5,2),c(1,-2),pi/5), col="blue")
  addLine(l,col="red")
  points(t(p_Cl), pch=20,col="red")
  points(t(p_CC2), pch=20,col="blue")
  
# }