Dear list,
I've generated a list of 3D coordinates representing ellipsoids in arbitrary orientations. I'm now trying to obtain a 2D projection of the scene, that is to draw the silhouette of each object on a plane (x,y). The only way I could think of is to compute the convex hull of the (x,y) coordinates of each object and use this as the outline of the object. This is clearly not very efficient or satisfying.
I think I'm on the wrong track from the start. Is there an obvious analytical parametrisation of such projections? Any comments are welcome.
Many thanks, baptiste
rotM3d <- function(theta=0, phi=0, psi=0){ # 3D rotation matrix a11 <- cos(psi)*cos(phi) - cos(theta)*sin(phi)*sin(psi) a12 <- cos(psi)*sin(phi) + cos(theta)*cos(phi)*sin(psi) a13 <- sin(psi)*sin(theta) a21 <- -sin(psi)*cos(phi) - cos(theta)*sin(phi)*cos(psi) a22 <- -sin(psi)*sin(phi) + cos(theta)*cos(phi)*cos(psi) a23 <- cos(psi)*sin(theta) a31 <- sin(theta)*sin(phi) a32 <- -sin(theta)*cos(phi) a33 <- cos(theta) matrix(c(a11, a12, a13, a21, a22, a23, a31, a32, a33), ncol=3) } rotM3d() # Iellipsoid <- # idea borrowed from a post in the R-mailing list (John Fox i think) function(x=0, y=0, z=0, radius=1, shape=diag(c(10, 2, 2)),theta=0, phi=0, psi=0, segments=11) {angles <- (0:segments)*2*pi/segments ecoord2 <- function(p) { c(cos(p[1])*sin(p[2]), sin(p[1])*sin(p[2]), cos(p[2])) } unit.sphere <- t(apply(expand.grid(angles, angles), 1, ecoord2))xyz <- t(c(x, y, z) + radius * rotM3d(theta, phi, psi)%* %t(unit.sphere %*% chol(shape)))chull(x=xyz[, 1], y=xyz[, 2])->points mdf <- data.frame(x=xyz[points, 1], y=xyz[points, 2]) polygon(mdf, col=hcl(h = 0, c = 35, l = 85, 0.5)) invisible(xyz) } xx <- seq(-5, 5, len=10) xy <- expand.grid(xx, xx) xy.jit <- apply(xy, 2, jitter, amount=0.4) par(mar=c(0, 0, 0, 0)) plot(xy.jit, t="n", axes=F, xlab="", ylab="") x <- xy.jit[, 1] y <- xy.jit[, 2] twist <- pi*y/max(abs(y)) * rep(1, length(y)) tilt <- pi*x/max(abs(x)) * rep(1, length(x)) b.quiet <- mapply(ellipsoid, theta=twist, psi=tilt,x=x, y=y, SIMPLIFY=F, radius=0.15)
_____________________________ Baptiste Auguié School of Physics University of Exeter Stocker Road, Exeter, Devon, EX4 4QL, UK Phone: +44 1392 264187 http://newton.ex.ac.uk/research/emag ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
