Rgl vector diagrams: show right angles for orthogonal vectors

Question

In the matlib package https://github.com/friendly/matlib/ , I have the vectors3d() function for drawing geometric vector diagrams.

The following code gives an example showing the unit vector "J" and some of its projections on the X, Y, Z axis. When calling segments3d each argument is a 2 x 3 matrix giving the coordinates of the beginning and end.

 if (!require(matlib)) devtools::install_github(friendly/matlib) library(matlib) library(rgl) vec <- rbind(diag(3), c(1,1,1)) rownames(vec) <- c("X", "Y", "Z", "J") open3d() vectors3d(vec, col=c(rep("black",3), "red"), lwd=2) # draw the XZ plane, whose equation is Z=0 planes3d(0, 0, 1, 0, col="gray", alpha=0.2) # show projections of the unit vector J segments3d(v1 <- rbind( c(1,1,1), c(1, 1, 0))) segments3d(v2 <- rbind( c(0,0,0), c(1, 1, 0))) segments3d(v3 <- rbind( c(1,0,0), c(1, 1, 0))) segments3d(v4 <- rbind( c(0,1,0), c(1, 1, 0))) 

I want to add to this the straight angular lines, for example |_ , to show that the pairs of vectors that I draw using segments3d are orthogonal. I drew them by hand in the following figure. But I do not know how to calculate the small line segments needed for a given pair of vectors in this form, say, v1 and v2 . I am ready to assume that each segment length |_ is a small number, such as 0.05.

EDIT: The task boils down to this: Given the three points p1 , p2 , p3 , find the points marked p21 , p23 and p123 in the diagram below. The first two are simple examples of finding a point along a line between two points, but I'm confusing finding the coordinates of a third point, p123 , that is, the position of a point at a distance d along a line parallel to the line p2->p3 starting from p21 .

In r that i still

 #' Find position of a point along a line from x1 to x2 point_on_line <- function(x1, x2, d, absolute=TRUE) { v <- x2 - x1 if (!absolute) v <- v / len(v) x1 + d * v } p1 <- c(0,0,0) p2 <- c(1,1,0) p3 <- c(1,1,1) (p21 <- point_on_line(p2, p1, .10)) (p23 <- point_on_line(p2, p3, .10)) points3d(rbind(p21, p23), size=10, col="red") 

This gives me the following diagram. Can someone help me fill it out?