Volume of revolution

I'm struggling to try and find a way to generate a volume of revolution from a graph of a function f=y(x). I'm wishing to generate a surface from rotating my function about the line X=500 (from graph attached) - then display on a Gizmo plot Any help appreciated THanks

Igor

Assuming that you want to revolve this around the Y-axis I'd create a parametric surface in Gizmo. Here is an example. Suppose your function has the form:


Function fr(inr,rmax)
	Variable inr,rmax
	
	Variable x2=inr/rmax
	return sqrt(1-x2*x2)
End

I'd create a parametric surface of the desired resolution, e.g.,


•make/n=(101,101,3) ddd
•ddd[][][0]=p-50
•ddd[][][1]=q-50
•ddd[][][2]=fr(sqrt((p-50)^2+(q-50)^2),50)

Now create a new Gizmo and append a parametric surface. You can do so manually or simply execute the following recreation macro:


Window Gizmo0() : GizmoPlot
	PauseUpdate; Silent 1	// Building Gizmo 6 window...
	NewGizmo/N=Gizmo0/T="Gizmo0" /W=(536,44,1167,675)
	ModifyGizmo startRecMacro
	AppendToGizmo Surface=root:ddd,name=surface0
	ModifyGizmo ModifyObject=surface0 property={ srcMode,4}
	ModifyGizmo ModifyObject=surface0 property={ surfaceCTab,Rainbow}
	ModifyGizmo setDisplayList=0, object=surface0
	ModifyGizmo SETQUATERNION={0.571268,0.028073,0.091655,0.815146}
	ModifyGizmo autoscaling=1
	ModifyGizmo currentGroupObject=""
	ModifyGizmo compile
	ModifyGizmo endRecMacro
End

I hope this helps,

A.G.
WaveMetrics, Inc.

August 15, 2013 at 09:47 am - Permalink

s.r.chinn

With all due respect to the Gizmo-meister, A.G., my preference (with more tutorial transparency) for the parametric Gizmo surface would be expressed in terms of the rotation angle as one parameter, and the function argument axis as the other, as in:


function foo( rin, rmax)
	variable rin, rmax
	
	variable rho = rin/rmax
	return (cos(2*pi*rho))^2
end

function show()
	variable rmax =10
	make/O/N=(90, 100, 3) wsurf
	setscale/I x, 0, 2*pi,"" wsurf
	setscale y, 0, rmax, "" wsurf
	wsurf[][][0] = cos(x)* y
	wsurf[][][1] = sin(x) * y
	wsurf[][][2] = foo(y, rmax) // use this as
// a parametric surface for Gizmo
end

August 15, 2013 at 11:35 am - Permalink