Welcome to the
Rocchini's Curves & Surfaces

Bifurcations: my code attempts to create nice positions for arrows and good stream-line density.

Gears: I write the generating code at a stroke without conscious self-censorship. I generate the animation and lost the generating codes! I am no longer able to write it again. Someone can explain me how I did?

Bolza: this is a rehearsal, as a form of practice, to achieve my true goal: the unseizable Klein quartic. The images is a WRML viewer snapshot, the cracks on surface are due to my discontinuous parametrizations. The projection is the usual stereographic one, applied to complex pair coordinates interpreted as 4D real coordinates.

The Whitehead manifold is not so explicit. Inscribed square: with which algorithm I have calculated the square? I cheated of course: I draw the square first, the the curve.

Sarti Surface: I try this file for PovRay, but the "max_gradient" factor is too high and PovRay hangs. So, I write my c++ software for implicit surfaces. The software also exports into vrml format. Heartfelt thanks to Claudio Montani for his teaching. Togliatti Surface: made with POVRay: source code below. Note: I like dark blue materials (must be one of my childhood disorders).


A Luroth Quartic - SVG File
Barth Decic
Chatelet Surface
Endrass Surface
Focal Surface - Vrml (zipped)
Kummer Surface
Sarti Surface - sarti_surface.pov - sarti surface VRML
Sectrix of Maclaurin
Togliatti Surface - togliatti_surface.pov
Inscribed Square - Inscribed_square.svg
Mountain Climbing Problem
Bogdanov-Takens Bifurcation - Bogdanov_takens_bifurcation.svg
Self Avoiding Walk (on grid) - Self_avoiding_walk.svg
Bolza Surface 3D Projection - Generating bolza source code
Circle Caustic
Clelies Curve
Clelies Curve Global
Involute Wheel (gears)
Kochanek-Bartels Splines - Kochanek_bartels_spline.svg
Rhodonea Curve (Rose)
Weierstrass Fractal Function
Whitehead Manifold

Final Notes

The Pseudosphere picture is very gimcrack. But this is the first picture I made with Blender, after painstakingly learned to use it.

Mountain climbing problem: beautyfull problem! But the image is drawn in haste. The two sides of mountain are: 1-cos(x)+(sin(x*4)*pow(PI-x,2))/16 and 1-cos(x)+(sin(x*4)*pow(x,2))/16. The peak-speed (number of peacks reached per unit of time) is constant! As usual, made with Antigrain Graphics.

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