#descriptive geometry

New geometric watercolor art:

Spinning Projection

Me: oh no

Geometry lecturer: *shows pic of hands drawn from different perspectives*

Circles to Lines - still work in prgress

"Rolling, Not Slipping!

A geometrical construction - an analog calculation - of the positions of a symmetrical ellipsoid rolling (not slipping) on an invariable plane (from ist yellow stage to red to blue).

The curves traced out by the points of contact on the ellipsoid are both circles and also constructed.

You could see this as the motion of a physical ellipsoid. But this concept is used to visualized the motion of a spinning top, to which an abstract "inertia ellipsoid" or "energy ellipsoid" is "attached". Related physics equations included as sort of "technical calligraphy".

I've using the principles of traditional descriptive geometry to construct the three straight-on views step-by-step, and the orthographic projection based on them. The ellipsoid is built up from the three ellipses obtained but intersecting it with three planes containing the principle axes and by finally finding its outline from these ellipses and various tangent lines.

This has been my most involved construction so far. Espcially the red ellipsoid is already pretty "3D" in the three based projections, all these main ellipses are one some general plane tilted in two directions, and I needed quite a lot of helper constructions and clues to "calculate" all the points.

Reality and Imagination for real

Real and imaginary part of complex function 1/z - "Reality and Imagination" - for the first time drawn traditionally on paper, therefore I call it: "Reality and Imagination for real".

I picked the colors intuitively, but now I see: Red pill versus blue pill :-)

Geometric drawing - axonometry, creating the "3D view" from the view from above - "cloverleaf-like", placed in the center of the drawing - and from the side - where circles become just lines. Graphite pencil, watercolor pencils, ballpoint pens.

"Circles to Lines (2026)"

... is done! It is finally also a canvas print!! Originally also created on canvas ... which has been a challenge as I gessoed and sanded this canvas, and watercolors do not stick to this surface at all!

As usual: Traditional descriptive geometry - "how we did 3D before software" :) This is about stereographic projection (circles through the North Pole onto lines), displayed using orthographic projection.

I took the photo for the print after varnishing the original canvas. Varnishing has been necessary to make the watercolor pigments adhere to the canvas. The upside of using this difficult drawing surface: Colors stay way more vibrant!

Available in three sizes; the smallest one is the same size as the original drawing / painting: