First FreeHand Watercolor Curved Drawing from Observation in the History

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:

the geometry grid.jpg

The Geometrical Grid
Next step is forwarding real visual information to the space curve. In this example, I have choosen a building in the Monasteriki Place in Athens, where I am posting today.

I try to match the vanishing perspective lines with the curves in my space:

transforming the space 1.jpg

Forwarding informatin into the space (I)

Then I complete the oultines of the features I want to represent :

transforming the space 2.jpg

Forwarding informatin into the space (II)
To make the drawing a little bit vivant I add some people and some shadows:

final drawing with shapes.jpg

Final drawing
At this point of the drawing, I realized that I had a group of french tourist behind me. French tourists are everywhere in every part of the world, France is a country with 60 millions of tourists!
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:

watercolor step 1.jpg

coloring and ruining the drawing
I kept on adding colors and strokes of watercolors to have this final result:


First FreeHand Watercolor Curved Drawing from Observation in the History
Thank for reading, study mathematics, draw from observation and have a lot of fun. Curved fun!

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

Sketching in a curved space #1
Sketching in curved spaces #2 Rafael, the “Artisant chansonnier”
drawing in curved spaces #3 360º sketch


9 replies
  1. Trula Cureau
    Trula Cureau says:

    I’m really enjoying the design and layout of your website. It’s a very easy on the eyes which makes it much more enjoyable for me to come here and visit more often. Did you hire out a developer to create your theme? Excellent work!

  2. Tamiflu
    Tamiflu says:

    A path is described using the concept of a current point. In an analogy with drawing on paper, the current point can be thought of as the location of the pen. The position of the pen can be changed, and the outline of a shape (open or closed) can be traced by dragging the pen in either straight lines or curves.

  3. erotik izle
    erotik izle says:

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  4. erotik izle
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