R：将2D坐标与3D绘图中的线连接，并根据坐标添加正态分布pdf

Question

Similar to 3D Plot of normal distribution in R around a (x,y) point using code like

library(rgl)
open3d()

x <- seq(0, 10, length=100)
y <- seq(0, 10, length=100)


z = outer(x,y, function(x,y) dnorm(x,2.5,1)*dnorm(y,2.5,1))

persp3d(x, y, z,col = rainbow(100))

I want to draw a normal distribution onto a (x,y) diagram. However, differently to the first question, I want to draw this normal distribution along some specific coordinates (they have all z=0 and "lie on the ground" of (x,y)). They mimic the walk of a person and have coordinates

g=matrix(c(0,0,3,1,4,2,5,3,6,4,5,5,4,6,6,6,8,5,9,6)
  ,nrow=10,ncol=2,byrow= TRUE)

So my questions are: (1)How can I add this 2D data to the 3D plot and connect all points through a line such that it depicts the walk? It should lie on the ground. (2) How can I draw a normal distribution around the "walk"? This should be 3D.

Thanks a lot

Update: The idea is to assign probabilities in a next exercise to the walk of a second person, too, and then compute the probability they met somewhere.

Update2: I was maybe not very clear what I want, so I try my best to be more precise. The walk, as depicted by the coordinates in g, is just a rough line. It should be displayed on the ground. The real task I am interested in is as follows: it is possible that the person is not exactly walking on the line. The probability, however, at any point is given by a Normal function (the PDF) of its shortest distance to the line. So I want to draw a normal PDF multiple (probably infinite times) around the line. The final 3D plot will probably look like some mountains. This is related to my earlier question where I asked how to draw a normal PDF multiple times such that its 3D plot looks like a vulcano.

Update3: The answer below does not show the result to Update2 but it clearly provides guidance for a part of the original question. Thus, I mark it as solved.

Answer 1

How about this. (Note that I made the rainbow surface transparent).

library(rgl)
open3d()

x <- seq(0, 10, length=100)
y <- seq(0, 10, length=100)

z = outer(x,y, function(x,y) dnorm(x,2.5,1)*dnorm(y,2.5,1))

persp3d(x, y, z,col = rainbow(100),alpha=0.5)

# now draw the line 
#    note:
#    -  the "add=T" parameter that appends it to the previous 3d-plot

g=matrix(c(0,0,3,1,4,2,5,3,6,4,5,5,4,6,6,6,8,5,9,6)
         ,nrow=10,ncol=2,byrow= TRUE)

lines3d(g[,1],g[,2],0,color="purple",add=T)

Yielding: