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17-Peridot
August 13, 2010
Question

How to create a curve from the equation?Does Anybody know?

  • August 13, 2010
  • 4 replies
  • 9627 views

How to create a curve from the equation?Does Anybody know?I need this kind of information.

Thanks

    4 replies

    August 13, 2010

    counter-questions:

    where exactly is your problem?

    Do you not find the menu?

    Do you not know what an equasion should look like?

    1-Visitor
    August 13, 2010

    Hi,

    I know

    Is this correct answer?

    And seriously, here is a simple example:

    Video Link : 1349

    Remember that "t" is changing from 0 to 1;

    BR

    Marek

    August 13, 2010

    Thanks for sharing!

    And interesting since I would have created something like that using the cylindrical coordinate system...

    1-Visitor
    August 18, 2010

    hi i m balwan & i know correct ans which type of curve u want to draw by equation

    1-Visitor
    August 19, 2010

    You mean something like this?

    CURVE-01.JPG

    Note the reversal.

    1-Visitor
    August 19, 2010

    This maybe?

    SPIRA_WAVE_SPRING3.JPG

    1-Visitor
    August 23, 2010

    Blue,

    A little more general answer: The Curve-By-Equation technique involves the use of so-called parametric equations. (You may have had a one-day introduction and assignment dealing with them in a high school trigonometry or analytical geometry class.) The equations all depend on just one parameter which takes on all of a finite range of values to determine the simultaneous results for the dependent equations. In this case, the parameter you use must be t and it will take on the continuous values of 0 to 1. (The same idea is used in Variable Section Sweeps where you use trajpar, as opposed to t. Both of these techniques couldn't be more appropriate for parametric software.)

    As an example, if you write the equation x=y you would create a 45 degree "climbing" straight line going to infinity in both directions. If, on the other hand--using the parametric technique, you write the simultaneous equations x=t and y=t you create a 45 degree line from {0,0} to {1,1} only. These equations never go to infinity because the independent variable stops when it "gets to" 1.

    Obviously, you wouldn't use this method for something that simple. On the other hand, if you want to create some kind of interesting variable spiral or the involute for a gear tooth this technique is great. Choose your type of equations carefully. For example, if you are creating some kind of helical curve you can certainly do it with Cartesian coordinates employing sine and cosine functions for two of the 3 equations (usually x & y), but it's much easier to use Cylindrical coordinates and just type in a straightforward function for theta. As a further clarification, if you wrote theta=4*t*360, you would generate 4 complete turns in your helical geometry. (You need to multiply t--0 to 1 only--by 360 to get one complete turn).

    Hope this helps!

    David

    1-Visitor
    August 23, 2010

    For example:

    CS1--Cartesian:
    x=2*cos(3*t*360)
    y=2*sin(3*t*360)
    z=3*t

    CS2--Cylindrical:
    r=2
    theta=3*t*360
    z=3*t

    CS3--Spherical:
    rho=2
    theta=90-(2*t*45)
    phi=3*t*360


    CS4--Cartesian:
    x=4*t-2
    y=2*sin(2*t*360)
    z=3*t

    CS5--Cylindrical:
    r=2
    theta=3*t*360
    z=2*(t+sin(3*t*360))


    CS6--Spherical:
    rho=2
    theta=90-(t*180)
    phi=t*360

    CURVES.jpg

    1-Visitor
    August 23, 2010

    Thanks David for the detailed demo. I'm sure people will find it very useful!