# The plane passing through three distinct 3D points `a`, `b`, and `c` An object of class `"Planes"`. Returns the equation and $z$-coordinates of the plane passing through three distinct 3D points `a`, `b`, and `c` with $x$- and $y$-coordinates are provided in vectors `x` and `y`, respectively. ```r Plane(a, b, c, x, y) ``` ## Arguments - `a, b, c`: 3D points that determine the plane (i.e., through which the plane is passing). - `x, y`: Scalars or vectors of scalars representing the $x$- and $y$-coordinates of the plane. ## Returns A `list` with the elements - **desc**: A description of the plane - **points**: The input points `a`, `b`, and `c` through which the plane is passing (stacked row-wise, i.e., row 1 is point `a`, row 2 is point `b` and row 3 is point `c`). - **x,y**: The input vectors which constitutes the $x$- and $y$-coordinates of the point(s) of interest on the plane. `x` and `y` can be scalars or vectors of scalars. - **z**: The output `vector` which constitutes the $z$-coordinates of the point(s) of interest on the plane. If `x` and `y` are scalars, `z` will be a scalar and if `x` and `y` are vectors of scalars, then `z` needs to be a `matrix` of scalars, containing the $z$-coordinate for each pair of `x` and `y` values. - **coeff**: Coefficients of the plane (in the $z = A x+B y+C$ form). - **equation**: Equation of the plane in long form - **equation2**: Equation of the plane in short form, to be inserted on the plot ## Examples ```r P1<-c(1,10,3); P2<-c(1,1,3); P3<-c(3,9,12) #also try P2=c(2,2,3) pts<-rbind(P1,P2,P3) Plane(P1,P2,P3,.1,.2) xr<-range(pts[,1]); yr<-range(pts[,2]) xf<-(xr[2]-xr[1])*.1 #how far to go at the lower and upper ends in the x-coordinate yf<-(yr[2]-yr[1])*.1 #how far to go at the lower and upper ends in the y-coordinate x<-seq(xr[1]-xf,xr[2]+xf,l=5) #try also l=10, 20, or 100 y<-seq(yr[1]-yf,yr[2]+yf,l=5) #try also l=10, 20, or 100 plP123<-Plane(P1,P2,P3,x,y) plP123 summary(plP123) plot(plP123,theta = 225, phi = 30, expand = 0.7, facets = FALSE, scale = TRUE) z.grid<-plP123$z persp(x,y,z.grid, xlab="x",ylab="y",zlab="z", theta = -30, phi = 30, expand = 0.5, col = "lightblue", ltheta = 120, shade = 0.05, ticktype = "detailed") zr<-max(z.grid)-min(z.grid) Pts<-rbind(P1,P2,P3)+rbind(c(0,0,zr*.1),c(0,0,zr*.1),c(0,0,zr*.1)) Mn.pts<-apply(Pts,2,mean) plot3D::persp3D(z = z.grid, x = x, y = y,theta = 225, phi = 30, expand = 0.3, main = "Plane Crossing Points P1, P2, and P3", facets = FALSE, scale = TRUE) #plane spanned by points P1, P2, P3 #add the defining points plot3D::points3D(Pts[,1],Pts[,2],Pts[,3], add=TRUE) plot3D::text3D(Pts[,1],Pts[,2],Pts[,3], c("P1","P2","P3"),add=TRUE) plot3D::text3D(Mn.pts[1],Mn.pts[2],Mn.pts[3],plP123$equation,add=TRUE) #plot3D::polygon3D(Pts[,1],Pts[,2],Pts[,3], add=TRUE) ``` ## See Also `paraplane` ## Author(s) Elvan Ceyhan

Plane function