Hello!
I have spent the last 2 hours, working on tracing a curve from a jpeg image that looks like logarithmic spiral or some similar curver.
Tracing with styling feature cannot give me the accuracy that I need, as the final model will go to cnc for prototyping. (PLS see attached prt)
I would like, to show you this jpeg image and kindly give me your feedback; how to trace or design the curve of the housing with an equation!
a) I have tried with fibonacci spiral and involute curve but doesnt fit to this shape.
b)If is a logaritmic spiral (http://mathdl.maa.org/images/upload_library/23/picado/seashells/espiraleng.html) , I cannot figure out how to insert the equation to Pro E, even to try if it fits. I m stuck here for hours, Please help!
c) I attach the part that came from tracing. As you can see, the spline is not smooth. How can I be sure that if I keep this one part, CNC will not see the joins of the nodes and make sinks on the surface?
Best Regards,
Amanda
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oops, forgot. I am on Creo 2.0.
Play with the center some more. If you place the shaft of the drawing at the datum intersection, you will be able to scale the image to fit the curve.
The image I included shows as 20.47 high and 17.71 wide in the image dialog. I had to rotate the image 90 degrees CW. I just duplicated the effort and the values came out the same. The center is located on the default datum plane intersection. Here is a more detailed overlay:
I don't think that any equation can fit the original sketch any better. I will again refer to the use of french curves to document to original patent application. It is hard to tell how accurate the original prototype was cast as well. Regardless, the functionality could have been sufficient albeit not optimized.
There may well be a much better profile based on pressures in particular zones. It may not follow this curve at all. Today, most turbo pumps use a common profile that expands in all directions proportionally.
This is a poor man's version of the turbo curve. 8 points at 45 degrees on equally spaced concentric circles and tangent ends on the spline.
Antonius Dirriwachter,first of all thanks so much for your prompt and helpfull reply ! 
1. I didnt knew about jpeg and png matter. I will convert the image as well. This silly image is the only thing they gave me and they insist on designing the basic casing of this turbo based on this specific image. I will use it as a reference only for comparing my results.
2. I like your suggestion with concentric centers and 8 points. How much bigger gets the diameter of each circle ?
3. The flute of this turbo I think is the easiest part, as it seems to be tangent to the very outer circle. Right?
4. If we assume that this turbine shape is based on a mathematical spiral curve, is this the Logarithmic one? AND if yes, I want to try inserting the equation, but since I am a newbie in insering equations, I cannot find the way I should write the equation for Pro E. Does anyone knows how to ? ( here in this community, I can find too many other equations except this one 
)
Thanks again for your feedback.
Looking forward to more suggestions!
2. All the little "guide" circles are 10.7 based on a 1:1 image import. I could go to 11.0 and it still follows the image fairly well.
And I guess it is actually 9 points
I suspect the equation and my geometry based version will come out identical if the sketch is properly defined.
Answer to 3. is that you can make the flute tangent to the spline.
You might have to ask the mathmatica guys how to read in a curve equation. Certainly not a strong point for me. I like letting my geometry do the work. But it is clear your assignment wants you to find this information.
I can never find how to import data in Creo when I need to. Not even sure you can import the curve directly from an equation, of if you have to create the points and then create the curve. If you fit the curve to points, be sure to set the spline end conditions.
I take it back, they make -datum- curves from equations:
try this for an equation:
r = IR + t * (OR - IR)
theta = t * 360 * #T
z = 0
Where:
IR = Inner Radius
OR = Outer Radius
#T = Number of Rotations
remember to use a cylindrical coordinate type.
Just saw your newest replies. You have helped me a lot. I have already tried the "create datum curve" for inserting equations, but probably I couldnt insert the correct one. I will try your suggestion later tonight and i will revert with results. Its first time for me to deal with a draft jpeg and not with full technical dwg. I guess now enginners need to be more open minded Thanks again, I will check again tonight and I ll let you know the results.
ps. for the flute, geometry will lead me and God help us!
I'd say the supplied image from your assignment is not very accurate to the original.
Here is the image overlay from the patent site on a curve from the equation:
Trying to align the photo (playing with scale) with the datum curve - from equation- I cannot get your result.
The curve made from
r = 6 + t * (8 - 2)
theta = t * 360 * 2
z = 0
give as concentic circles while in Tesla's dwg it is kind of involute or sth....
Pls see below attached .... The datum curve in blue does not match with scaled image . I know that is not a perfect aligment but I can see that no matter moving I do, there is a slight difference in the geometry.
Where I am mistaken?
cannot open! Gives me:
\prt0009.prt.1 was created in a newer release of Pro/ENGINEER.
I have wildfire 5.0. What are u running?
oops, forgot. I am on Creo 2.0.
Play with the center some more. If you place the shaft of the drawing at the datum intersection, you will be able to scale the image to fit the curve.
The image I included shows as 20.47 high and 17.71 wide in the image dialog. I had to rotate the image 90 degrees CW. I just duplicated the effort and the values came out the same. The center is located on the default datum plane intersection. Here is a more detailed overlay:
I don't think that any equation can fit the original sketch any better. I will again refer to the use of french curves to document to original patent application. It is hard to tell how accurate the original prototype was cast as well. Regardless, the functionality could have been sufficient albeit not optimized.
There may well be a much better profile based on pressures in particular zones. It may not follow this curve at all. Today, most turbo pumps use a common profile that expands in all directions proportionally.
You were right!
Now I need to get the details for the flute....As you said , it is just a tangent line ....Reverting with that as well.
