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Math Help - How to find an equal to plot a 3D arc of 2 intersecting curved surfaces?

  1. #1
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    How to find a formula to plot a 3D arc of 2 intersecting curved surfaces flattened?

    Hello all,
    I am working on a problem right now where I have 2 surfaces that connect at n degrees. Both surfaces are curved. Let's say that they are both 28in radius and they are intersecting at 90 degrees. How would I go about making a formula where I can plot the points of the resulting intersecting 3D curve flattened? I am not really sure if this is the forum to post this in. If it is not please point me to the correct topic to post in. Any help would be great. Here is a visual of what I am talking about.
    How to find an equal to plot a 3D arc of 2 intersecting curved surfaces?-curvedsurfacevisual.jpg
    Thanks in advance,

    JJ
    Last edited by Jjonesiii; May 17th 2012 at 01:55 PM. Reason: Adding Image and adjusting title.
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  2. #2
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    Re: How to find an equal to plot a 3D arc of 2 intersecting curved surfaces?

    That depends strongly upon the precise surfaces- and to have a formula, you have to have a coordinate system. You appear to have pieces of two cylinders. Setting up a coordinate system so the axes are along the x and y axes, with radii r, they would be given by y^2+ z^2= r^2 and x^2+ z^2= r^2 then we would have z^2= r^2- x^2= r^2- y^2 which reduces to x^2= y^2. That is, the projection of that curve of intersection in the xy-plane (Was that what you meant by "if it was flat and not 3D"?) would be y= x or y= -x, depending upon exactly how you set up the axes. To write the curve in 3D, you would need parametric equations- take x= t, y= t and then z= \sqrt{r^2- t^2}. Or if you mean as it would be written in the plane the curve lies in, which is the plane y= x, then it would be just z= \sqrt{r^2- x^2} or, equivalently z= \sqrt{r^2- y^2}.

    All of those are, of course, part of a circle.
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  3. #3
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    Re: How to find an equal to plot a 3D arc of 2 intersecting curved surfaces?

    I do have 2 pieces of cylinders. They might meet at a 90 degree angle and they might not. My side radius and my front radius may be different. My height from the bottom of the radius to the top will most often be bigger than the depth of the curved piece. I need to know what all information I need. The completed project will be a hood vent for a kitchen that will look something like this:

    http://www.wood-hood.com/IMAGES/HOOD...0-%20whole.jpg

    Right now I have variables for the front and side radii, the height of the curved section, the height of the apron at the bottom, the height of the apron at the top, the angle of the curved section (these again may be different from front and side), the depth of the hood at the bottom, the depth of the hood at the top, 20 variables for the X position, and 20 variables for the Y position. I need to "UNROLL" this curve to be flat and be able to plot the points of the resulting spline. Also I need to be able to do this spline curve with tangental arcs so it looks continuous. I am working in a solid modeling program where I can only shape things flat. Then I can put in a radius on an axis. This is how I have to make the graphic representation of this part. Does this clear things up some? The above equations are not working for what I need. Anything you can do to help would be great!

    JJ
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  4. #4
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    Re: How to find an equal to plot a 3D arc of 2 intersecting curved surfaces?

    Have I posted this in the wrong area? Can no one help me with this? Man! I thought I had finally found a place that could help me get these things answered. Now I have another problem and I haven't even finished this this one. Any help appreciated.

    JJ
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