Get to Know a Feature: 3D Arrow Plots

Created on September 6 at 11:54 am - by: admin

In the previous Gizmo Plot blog posts I demonstrated some variations on the generic scatter plot and path plot. In this blog post I’ll use the same data set to illustrate variations on a 3D arrow plot.

All arrow plots depend on the elementary arrow shape. Gizmo draws 3D arrows as special cases of 3D lines.

The simple arrow would initially look like the following graph:

Here I added the axis cue to show that the arrow points in the positive z-direction.
Executing the command:

ModifyGizmo enhance

would give us the following single arrow plot:

The arrow (or the supercharged line) is a regular drawing object that can be used as a marker in a scatter plot. For example, we can draw the arrow object (instead of spheres) at the location of the data points of the Lissajous set that we used in previous blog posts. By default the arrows are all pointing in the z-direction.

To align the arrows with the local direction of the path we need to provide the scatter object with a rotation wave. The rotation wave contains four numbers for each scatter point. The first number is the rotation angle in degrees. The last three numbers represent a normalized vector about which the object is rotated. Here is the code I used to calculate the rotation wave:

Function makeRotationWave(pathw)

    Wave pathw      // triplet path wave

    // for a closed path the rotation wave needs to 

    // have the same rows as pathw and 4 cols.

    Variable rows=DimSize(pathw,0)

    Make/O/N=(rows,4) rotationWave

    Variable i

    Variable x1,x2,y1,y2,z1,z2

    Variable dx,dy,dz,nor,vx,vy

    for(i=0;i<rows;i+=1)

        x1=pathw[i][0]

        y1=pathw[i][1]

        z1=pathw[i][2]

        if(i==(rows-1))

            // closing the path

            x2=pathw[0][0]

            y2=pathw[0][1]

            z2=pathw[0][2]

        else

            x2=pathw[i+1][0]

            y2=pathw[i+1][1]

            z2=pathw[i+1][2]

        endif

        // desired vector direction:

        dx=x2-x1

        dy=y2-y1

        dz=z2-z1

        nor=sqrt(dx*dx+dy*dy+dz*dz)

        // normalize vector:

        dx/=nor

        dy/=nor

        dz/=nor

        // We assume a line object that points in the z-direction

        // i.e., {0,0,1}

        nor=sqrt(dy^2+dx^2)

        vx=dy/nor

        vy=-dx/nor

        rotationWave[i][1]=vx

        rotationWave[i][2]=vy

        rotationWave[i][3]=0        // it is perpendicular to z

        // the angle of rotation is computed from the dot product between the line and z

        // which is simply dz so

        rotationWave[i][0]=-180*acos(dz)/pi

    endfor

End