# R/singleIntersection.R In Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

#### Defines functions singleIntersection

```# Script comments and history
# 2011
# 5:35:25 PM

# Author: Federico Comoglio @ D-BSSE, ETH Zurich
###############################################################################

singleIntersection <-
function (pointsij, kind = "binary")
{
sint <- 0
pointsij2D <- pointsij[, c(1, 2)]
vectors3D <- matrix(c(pointsij[2, ] - pointsij[1, ], pointsij[4,
] - pointsij[3, ]), nrow = 2, byrow = TRUE)
vectors2D <- vectors3D[, c(1, 2)]
if (nrow(unique(pointsij)) <= 3)
return(0)

detv <- vectors2D[1, 1] * vectors2D[2, 2] -
vectors2D[1,2] * vectors2D[2,1]
if (identical(detv, 0)) {
if (pointsij[1, ] == pointsij[2, ] || pointsij[3, ] == pointsij[4, ]) {
warning("collapsed edge")
return(0)
}
else {
E <- t(rbind(vectors2D, pointsij2D[3, ] - pointsij2D[1, ]))
E[2, ] <- E[2, ] - (E[2, 1] / E[1, 1]) * E[1, ]
if(identical(E[2, ], c(0, 0, 0)))
{
ksi <- c(0, 0)
segment <- pointsij2D[2, ] - pointsij2D[1, ]
for (i in 1 : 2)
ksi[i] <- segment %*% (pointsij2D[i + 2, ] - pointsij2D[1, ]) / (segment %*% segment)
if ((0 < ksi[1] && ksi[1] < 1) || (0 < ksi[2] && ksi[2] < 1)) {
warning("superimposed edges")
return(0)
}
}
}
}
else {
inverse <- (1 / detv) * matrix(c(vectors2D[2, 2], vectors2D[1, 2], -vectors2D[2, 1],
-vectors2D[1, 1]), nrow = 2)
temp <- pointsij2D[3, ] - pointsij2D[1, ]
ks <- inverse %*% temp
conditionI <- ((0 < ks[1] && ks[1] < 1) && (0 < ks[2] && ks[2] < 1))
if (!conditionI)
return(0)
binary <- (kind == "binary")
if (conditionI && binary)
return(1)
else {
zs <- c(pointsij[1, 3] + ks[1] * vectors3D[1, 3],
pointsij[3, 3] + ks[2] * vectors3D[2, 3])
sign <- sign(zs[1] - zs[2])
Qs <- vectors3D
ifelse (sign == 1, {i <- 1; j <- 2}, {i <- 2; j <- 1})
Qs[i, ] <- pointsij[2 * i - 1, ] + ks[i] * vectors3D[i, ]
Qs[j, ] <- Qs[i, ]
Qs[j, 3] <- zs[j]
sint <- switch(kind,
sign = sign,
q = list(sign = sign, Qs = Qs),
k = list(sign = sign, ks = ks[1]),
ks = list(sign = sign, ks = ks, Qs = Qs),
lk = list(sign = sign, ks = ks[1], Q2D = Qs[1, 1:2], Qs = Qs),
warning("unmatched call option"))
}
}
return(sint)
}
```

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Rknots documentation built on May 29, 2017, 1:38 p.m.