Last Update Dec. 20, 1998 　日本語はこちら

#### NUMERICAL SPACE / OBJECTS 1 by QUALTIC

When I got 3 dimensional figues by POV-Ray's qualtic, I put random numerals on the parameters of qualtic and searched some interesting figues near the origin of the result image. But it's more amusing that I make new figues from a new idear for making 3 dimensional function.
I received a question for POV-Ray's qualtic by E-mail recently. The opportunity made me start trying this deductive reasoning. It has been a very exciting play for me. In this page I show some objects from simple qualtic functions.

These GIF animations below made by Qualtic functions in this page are created and presented by Mr. Gilles Tran in Paris.
. . . . . . Presented by Mr. Gilles Tran (13 Dec. 1998)

 I got this object from the function below "Family Map of Drop". Qualtic can express such a excellent curved face. This seems to be the CYBERBUST. Scene file : lpqbust.txt

Illusion of CYBERBUST / 20k / Oct. 1998 / by Tsutomu Higo

 I made some metamorphosis to a ball by using squared and fourth powered. This method is a useful technique for getting 3 dimensional figues, controlling the inclination changing. Scene file : lpqball.txt

Family Map of Ball / 77k / Oct. 1998 / by Tsutomu Higo

 If you expand a horizontal figue perpendicularly, you can get a 3 dimensional figue having the same cross section figue with the horizontal figue. For example, if the horizontal figue is a circle, you can expand it perpendicularly by using the center point or the diameter length expressed as the function of perpendicularl parameter. If you use the functions having actual number solutions only in limited area or using POV-Ray's bounded_by for limiting the searching area for the solution, you get the limited area's object figues. Of course bounded_by shortens the time of the rendering I made the all objects in this right image by only one function. You can use this function under your control by setting parameters. Please see the scene file and make fine images by this qualtic. Scene file : lpqdrop.txt

Family Map of Drop / 60k / Oct. 1998 / by Tsutomu Higo

 You can make relativery complex figues from the functions that are composed from several functions. This image is based on the function, y^2 = ( (1 - (x-a)^2 - z^2)^0.5 - (1 - (x+a)^2 - z^2)^0.5 )^2. Of course I modified a little. ( Or I took a mistake which lead me discover a new technique.) Scene file : lpqshere.txt

Family map of Twin Sphere / 44k / Oct. 1998 / by Tsutomu Higo

 We can obtain 3 dimensional functions by many ways. And, finding new way to 3 dimenjonal functions is very interesting and useful. For example, you can get the shape rotating the figue on xy plane around the y axis by exchanging x^2 to x^2 + z^2. Making 3 dimensional functions is really flexible and exiting work. Scene file : lpqbulge.txt

Family Map of Bulge / 48k / Oct. 1998 / by Tsutomu Higo

 Such images like left make me interested deeply in the 3 dimensional functions. How about you? This sort of the pleasrure by POV-Ray is unique and charming me. Scene file : lpqeater.txt

Family Map of Eater / 40k / Oct. 1998 / by Tsutomu Higo