# The line crossing 3D point `p` in the direction of `vector` `v` (or if `v` is a point, in direction of $v-r_0$) An object of class `"Lines3D"`. Returns the equation, $x$-, $y$-, and $z$-coordinates of the line crossing 3D point $r_0$ in the direction of `vector` `v` (of if `v` is a point, in the direction of $v-r_0$) with the parameter `t` being provided in `vector` `t`. ```r Line3D(p, v, t, dir.vec = TRUE) ``` ## Arguments - `p`: A 3D point through which the straight line passes. - `v`: A 3D `vector` which determines the direction of the straight line (i.e., the straight line would be parallel to this vector) if the `dir.vec=TRUE`, otherwise it is 3D point and $v-r_0$ determines the direction of the the straight line. - `t`: A scalar or a `vector` of scalars representing the parameter of the coordinates of the line (for the form: $x=p_0 + a t$, $y=y_0 + b t$, and $z=z_0 + c t$ where $r_0=(p_0,y_0,z_0)$ and $v=(a,b,c)$ if `dir.vec=TRUE`, else $v-r_0=(a,b,c)$). - `dir.vec`: A logical argument about `v`, if `TRUE` `v` is treated as a vector, else `v` is treated as a point and so the direction `vector` is taken to be $v-r_0$. ## Returns A `list` with the elements - **desc**: A description of the line - **mtitle**: The `"main"` title for the plot of the line - **pts**: The input points that determine a line and/or a plane, `NULL` for this function. - **pnames**: The names of the input points that determine a line and/or a plane, `NULL` for this function. - **vecs**: The point `p` and the `vector` `v` (if `dir.vec=TRUE`) or the point `v` (if `dir.vec=FALSE`). The first row is `p` and the second row is `v`. - **vec.names**: The names of the point `p` and the `vector` `v` (if `dir.vec=TRUE`) or the point `v` (if `dir.vec=FALSE`). - **x,y,z**: The $x$-, $y$-, and $z$-coordinates of the point(s) of interest on the line. - **tsq**: The scalar or the `vector` of the parameter in defining each coordinate of the line for the form: $x=p_0 + a t$, $y=y_0 + b t$, and $z=z_0 + c t$ where $r_0=(p_0,y_0,z_0)$ and $v=(a,b,c)$ if `dir.vec=TRUE`, else $v-r_0=(a,b,c)$. - **equation**: Equation of the line passing through point `p` in the direction of the `vector` `v` (if `dir.vec=TRUE`) else in the direction of $v-r_0$. The line equation is in the form: $x=p_0 + a t$, $y=y_0 + b t$, and $z=z_0 + c t$ where $r_0=(p_0,y_0,z_0)$ and $v=(a,b,c)$ if `dir.vec=TRUE`, else $v-r_0=(a,b,c)$. ## Examples ```r A<-c(1,10,3); B<-c(1,1,3); vecs<-rbind(A,B) Line3D(A,B,.1) Line3D(A,B,.1,dir.vec=FALSE) tr<-range(vecs); tf<-(tr[2]-tr[1])*.1 #how far to go at the lower and upper ends in the x-coordinate tsq<-seq(-tf*10-tf,tf*10+tf,l=5) #try also l=10, 20, or 100 lnAB3D<-Line3D(A,B,tsq) #try also lnAB3D<-Line3D(A,B,tsq,dir.vec=FALSE) lnAB3D summary(lnAB3D) plot(lnAB3D) x<-lnAB3D$x y<-lnAB3D$y z<-lnAB3D$z zr<-range(z) zf<-(zr[2]-zr[1])*.2 Bv<-B*tf*5 Xlim<-range(x) Ylim<-range(y) Zlim<-range(z) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] zd<-Zlim[2]-Zlim[1] Dr<-A+min(tsq)*B plot3D::lines3D(x, y, z, phi = 0, bty = "g", main="Line Crossing A \n in the Direction of OB", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05), zlim=Zlim+zd*c(-.1,.1), pch = 20, cex = 2, ticktype = "detailed") plot3D::arrows3D(Dr[1],Dr[2],Dr[3]+zf,Dr[1]+Bv[1], Dr[2]+Bv[2],Dr[3]+zf+Bv[3], add=TRUE) plot3D::points3D(A[1],A[2],A[3],add=TRUE) plot3D::arrows3D(A[1],A[2],A[3]-2*zf,A[1],A[2],A[3],lty=2, add=TRUE) plot3D::text3D(A[1],A[2],A[3]-2*zf,labels="initial point",add=TRUE) plot3D::text3D(A[1],A[2],A[3]+zf/2,labels=expression(r[0]),add=TRUE) plot3D::arrows3D(Dr[1]+Bv[1]/2,Dr[2]+Bv[2]/2,Dr[3]+3*zf+Bv[3]/2, Dr[1]+Bv[1]/2,Dr[2]+Bv[2]/2,Dr[3]+zf+Bv[3]/2,lty=2, add=TRUE) plot3D::text3D(Dr[1]+Bv[1]/2,Dr[2]+Bv[2]/2,Dr[3]+3*zf+Bv[3]/2, labels="direction vector",add=TRUE) plot3D::text3D(Dr[1]+Bv[1]/2,Dr[2]+Bv[2]/2, Dr[3]+zf+Bv[3]/2,labels="v",add=TRUE) plot3D::text3D(0,0,0,labels="O",add=TRUE) ``` ## See Also `line`, `paraline3D`, and `Plane` ## Author(s) Elvan Ceyhan

Line3D function