Hello my students, I would like to introduce you today to one of the most amazig aspects of the curved Spaces: Custom spaces. If you have followed my previous lessons, the thing to retain is that in a curved spaces we do not have straight lines, instead we have a short o curved lines called geodesics. And this geodesics curves can be as crazy as we want.In this tutorial I will show you how to freehand a custom curve space an make a drawing on it.
The very first step is to build a curved space which will host our drawing features. To make it simple and clear, I have choosen a space with two vanishing points. Then, from those vanishing points, I drew some nice curves trying to maintain a certain consistency in it:
I try to match the vanishing perspective lines with the curves in my space:
Then I complete the oultines of the features I want to represent :
A girl from the group did not hesitated and talked to me in an awful english.
“Excuse me, your drawing is very interesting, but, why do you bent the space?”
I replied in a perfect French.
“Since 1853, young Lady, Bernard Riemann established the basis of a geometry in curved spaces, sending your compatriote Mr Descartes to the science retreat.”
She could not believe what she was hearing. It was the first time in her life that someone downgraded Mr Descartes.
I kept on going with my speech:
“The planar perspective considers the space as a flat plane. Today, thanks to Mr Riemann and Mr Einstein, we now that the space is not flat, but has a curvature. This curvature can be represented through the Metric Tensor and the Christofell Symbols.”
It was the first time in her life she was talking to an Alien. Her eyes where egging.
“Do you like mathematics, young Lady?”
“Now, I am a Philosophy student”, she replied.
“Okay, sketchers and graphic designers are completely obsolete. They still consider the line horizon as a straight line and the space as a plane. If they where sailors, they would still believe that the earth is plane. It is time to update those things”
She was more and more interested:
“Who are you?” She asked
“I am an Alien.” I replied.
As I want this drawing to be the first custom watercolor curved freehand drawing in the history , I open my color box:
Curved drawing lessons published so far:
curved drawing lessons 1 # geometry beyond planar perspective
curved drawing lessons 2 # The spherical geometry
curved drawing lessons 3·# Deep inside the equirectangular grid
curved drawing lessons 4·# Deep inside the equirectangular grid (and II)
Other curved drawings related with the subject