## Title: plot-3d-various-1 ## Author: Paul Johnson ## Date posted: 2011-> ## Description. A little file of test cases myx <- seq(-10, 10, by = 1) myy <- seq(-10, 10, by = 1) myNorm <- function(x,y) sqrt(x^2 + y^2) z <- outer(X = myx,Y = myy, function(X,Y) myNorm(X,Y)) persp(myx, myy, z) myx <- seq(-.2, .2, by = 0.01) myy <- seq(-.2, .2, by = 0.01) mycircle <- function(x,y) sqrt(x^2 + y^2) z <- outer(X = myx,Y = myy, function(X,Y) myNorm(X,Y)) persp(myx, myy, z) persp(myx, myy, z, phi = -20, theta = 20) library("rgl") mycirc <- function(adf){ theta1 <- adf$theta1 theta2 <- adf$theta2 r <- adf$r x0 <- adf$x0 y0 <- adf$y0 z0 <- adf$z0 x <- x0 + r*sin(theta1)*cos(theta2) y <- y0 + r*sin(theta1)*sin(theta2) z <- z0 + r*cos(theta1) cbind(x,y,z) } theta1 <- seq(0, pi, length.out=15) theta2 <- seq(0, 2*pi, length.out=15) mygrid <- expand.grid(theta1=theta1,theta2=theta2,r=1,x0=0,y0=0,z0=0) mycoords <- mycirc(mygrid) mymat <- matrix(mycoords, ncol=3) plot3d(mymat, col="pink", cex=0.3) ### add a line plot3d(matrix(c(0,0,0,mymat[20,]),byrow=T,ncol=3), type="l", add = TRUE) library(scatterplot3d) s3d <- scatterplot3d(mymat, pch = 18, cex.s = 0.4, angle = 20, box = FALSE) newline <- matrix(c(0,0,0,mymat[20,]),ncol=3,byrow=T) s3d\$points3d (newline,type="b") ## Want to see more? try this ## example(scatterplot3d) ## curve3d is in emdbook ## install.packages("emdbook") library(emdbook) ## Please RUN. there are some nice plots they have there ## example(curve3d) ## At one time, I could make this draw in 3d, but fail now ## curve3d( sqrt(x^2 + y^2), from = c(0,0), to = c(0.5,0.5), type = "rgl", add=T) ## http://en.wikipedia.org/wiki/Cone_%28geometry%29 ## A right circular cone with height h and aperture 2θ, whose axis is the z coordinate axis and whose apex is the origin, is described parametrically as ## S(s,t,u) = \left(u \tan s \cos t, u \tan s \sin t, u \right) ## where s,t,u range over [0,θ), [0,2π), and [0,h], respectively. ## In implicit form, the same solid is defined by the inequalities ## \{ S(x,y,z) \leq 0, z\geq 0, z\leq h\}, ## where ## S(x,y,z) = (x^2 + y^2)(\cos\theta)^2 - z^2 (\sin \theta)^2.\, ## More generally, a right circular cone with vertex at the origin, axis parallel to the vector d, and aperture 2θ, is given by the implicit vector equation S(u) = 0 where ## S(u) = (u \cdot d)^2 - (d \cdot d) (u \cdot u) (\cos \theta)^2 ## or ## S(u) = u \cdot d - |d| |u| \cos \theta ## where u = (x,y,z), and u \cdot d denotes the dot product. ## d vector ## aperture 2*theta ## S(u) = 0 = (u * d)^2 - (d * d ) (u * u) (cos(theta))^2 ## S(u) = 0 = u * d - |d| |u| cos(theta) ## x*d1 + y*d2 + z*d3 - |d| sqrt(x^2 + y^2 + z^2) cos(theta)