3 Replies Latest reply on Sep 14, 2009 10:21 AM by Robert Stupplebeen

    Looking for equation driven curve examples

    Matt Lombard

      Does anyone have a cool example of a parametric equation that can be used in 2010s new equation driven curve function? I have some basic parametric equations, but I'm looking for something that shows what it is capable of.

       

      Also, does anyone have any examples of 3D equations? The new functionality looks cool as far as I can test it. I'm not that familiar with 3D cartesian curve equations. Someone want to point me to a source?

       

      Thanks,

       

      Matt

        • Re: Looking for equation driven curve examples
          Harold Brunt
          Hey Matt,
          This is a link to an older thread that references a couple formulas that you might try. I am curious to know how 2010 handles the creation of the surfaces. The curves were accurate enough but the surfaces were not. I cannot play with the 2010 beta since my Add-in won't work with it until after official release.
          It's the conic thing again. I'll keep beating that issue long after most think it's dead (if they don't think so already). It is something I use everyday.
          Conics? Cool? I can think of a few who would say "not".
          • Re: Looking for equation driven curve examples

            There are several examples here:

            http://www.math.uri.edu/~bkaskosz/flashmo/parcur/

            Does 2010 support parametric equations in cylindrical and spherical Coordinates too?

             

            the concept is easy to understand. Basically if you think of t as the variable for time, x=x(t)  y=y(t) , Fully describes time dependent motion of a particle in 2D plane. ( one can extract velocity, acceleration of the particle from the equations.) now if we eliminate time (t) from the equations, it leaves us with geometry only. (path of the particle, which is what solidwork draws for us.)

            x=sin(t) , y=cos(t) describes a circle in 2d xy plane. why? eliminating t from those equations using the familiar form of: sin(t)^2+cos(t)^2=1 by substituting sin(t) with x, cos(t) with y,leaves us with: x^2+y^2=1 which is the equation of a circle.

             

            similarly in 3d for example: a particle that traces a circle when viewed normal to xy plane and simutaniously moves in z direction(with constant velocity.), forms a helix.

            x=sin(t),y=cos(t),z=t

             

            in above equation:

            z=t is describing a constant velocity motion in z direction (why? because the first derivative with respect to t which is the velocity, is 1 meters per second)

            and x=sin(t),y=cos(t) is describing a particle that traces a circle with constant velocity of 1 in xy plane.

            superimposing the two motions, you can actually imagine that it is tracing a helix.

            • Re: Looking for equation driven curve examples
              Robert Stupplebeen

              Mathematica's web page has a bunch of cool equation driven surfaces.  Below are 2 links.  Can 2010 do equation driven surfaces or just 3D curves?  Conics are definitely needed and the parameters need to be in design tables.  If the equation curves could have their equations in a design table then there would be no need for the connics.

              http://mathworld.wolfram.com/RomanSurface.html

              http://mathworld.wolfram.com/HeartSurface.html