Last Update June 14, 2003  日本語はこちら


NUMERICAL SPACE / CASSINI



    The equation of Cassinian Ovals is ;
        (x2 + y2)2 - 2a2(x2 - y2) + a4 - c4 = 0
    I replaced "a" with "z" to get this 3D image.

    Scene file : lpcscasn.txt

Cassinian Ovals / 28k / May 2003 / by Tsutomu Higo


      The equation of Lemniscate of Bernoulli is ;
        (x2 + y2)2 - a2(x2 - y2) = 0
      I got this 3D image by replacing "y2" with "y2 + z2 - 16".

      Scene file : lpcslmns.txt



    Lemniscate of Bernoulli / 27k / May 2003 / by Tsutomu Higo


      For the equation of Lemniscate of Bernoulli ;
        (x2 + y2)2 - a2(x2 - y2) = 0
      I replaced only former member's "y2" with "y2 + z2 - 16".

      Scene file : lpcslmnd.txt



    Slightly modified Lemniscate / 30k / May 2003 / by Tsutomu Higo


    For getting eggs I replaced "y2" with "y2 + z2".
    The function makes not only eggs but also silkworm cocoons.

    Scene file : lpcsegg.txt

Cassinian eggs / 26k / June 2003 / by Tsutomu Higo


    For the equation of 3D Cassinian Ovals I mage
      (x2 + y2 + z2)2 - 4z2x2 - c4 = 0
    I slightly reduced the middle member gradually.
    You can see that the shape may become to the sphere.

    Scene file : lpcscart.txt

Modifying the equation / 31k / June 2003 / by Tsutomu Higo


    For the above mentioned equation, which has four arms, I compressed the angle of coordinates around the axis.
    This technique may be applied generally for modifying the 3D images?!

    Scene file : lpcsaxis.txt



Exchanging coordinates - Compressing rotation / 24k / May 2003 / by Tsutomu Higo


    For the same equation I rotated the cordinates around the axis in proportion to the length from the axis.

    Scene file : lpcsswrl.txt



Exchanging coordinates - Swirling rotation / 16k / May 2003 / by Tsutomu Higo


    For the same equation I translated the cordinates along the axis in proportion to the squared length from the axis.

    Scene file : lpcsplbl.txt



Exchanging coordinates - Parabolic translation / 18k / May 2003 / by Tsutomu Higo



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