Log-Aesthetic Magnetic Curves and Their Application for CAD Systems

Algorithm 1

Three control points start and end curvatures, and user tolerance are given. Using Principal Axis

minimization method, shape parameter is searched. Using the new parameter, a new curve

is transformed back into the original orientation and position, and be plotted.

Input:

Output:

Begin

Step  0. set and

Step  1. if

    ;

   else

    ;

Step  2. Translate to ()

Step  3. if

    Reflect triangle over -axis;

Step  4. Rotate triangle such that tangent vector at () coincides with -axis;

Step  5. ;

Step  6. if

     Set ; ; ;

     if

   else

     if

       ; go to Step  8

     else if

       ; go to Step  8

     else

      if

       ;

       ;

      else

       ;

       ;

      Find from such that

     end if

Step  7. if

    Output: “Solution does not exist or method failed to converge”;

   else

    Transform LMC back to

    Plot LMC

End