Pattern in perspective (see the depth effect with the chosen regression) -from the mandalas series link-

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Perspective and 3D effect

This post is a note about perspective tools or features that drawing softwares propose to computer aided users.

The idea popped up when doing a pattern intentionally having a depth illusion, in fact part of a wider

project about mandalas and patterns. The design that has been made combines the mandala and the

pattern, and finally, a 3D illusion by using a nonuniform grid decreasing along lines intersecting at a

I show the design made manually, in blue, below. In red, I made the same design assisted by image

editing tools. The center checkerboard with regular square tiles is copied/pasted to make surrounding

walls.

I needed to use an editor able to distort the original selection (the background tiles). However, the front

view square has the same size on the blue and on the red, this to achieve the same cell increase ratio.

I show below examples of bottom gridded sides of the 3D box. This is to explain that the coordinate

grids have to show non uniform grids as well, and so on, depending on desired accuracy to reproduce

construction points of the basis drawing (the flower). Of course, the grid of the initial drawing on the

back side is uniform.

A manual transformation of a curve drawn in a center cell of a uniform grid onto a distorted non-

uniform grid shown on the next illustration.

This is really an art amateur approach similar to the viewfinder methodology (so, the points are not

mathematically identified with coordinates, that would need to build a referential, axis, units, and so

on).

Just to notice that the transformation is a plane transformation (so 2D, bidimensional), focusing on the

illusion, not the rigidity of the mathematical framework.

At this point, the drawing maker has the freedom to choose how much non-uniform the grid (increase

or decrease factor) can be, to give the desired effect of depth.

This is an effect that is used in 3D drawing editors (as explained in the paragraph Designing in 3D), but

the choice of the setting is given to the programmer of the 3D drawing program, not the drawing maker

(the user of the program).

Outline of this post

An introduction about an illustrative example: Le café de nuit by Van Gogh
Practice: Le café de nuit is a paragraph about the objective, the start an the finish, what has be done
Explanatory GIF animated image is about additional explanatory information, and how a vector

graphics perspective box has been set-up to the artwork Le café de nuit

Original and pool improved is a section showing a comparison, finally, of the original artwork

image and a suggested “correction” (in fact, to conform to a perspective framework that can be

used on a layer background and used as a guideline)

Room with perspective lines gives more insight on the previous item (the perspective

framework tool)

Room “1pt” perspective, pool “2pts” perspective is a paragraph showing the perspective boxes

with the construction lines and vanishing points

Other “3D” effects shows briefly effects of some deformation tools
Finally, other 3D effects are talked and how a 3D drawing software automates illusions to make

drawing in 3D easier

Introduction

Zoom on the pool, left the original added to a “2pts” perspective” box; right, suggested deformation to

align the pool back to a standard “2pts” perspective.

Sequence:

Le café de nuit, Van Gogh (image from wikipedia, or, alternative)
Perspective lines of the room
Perspective lines of the pool board
Suggested lean improvements (in fact the VanGogh’s original pool is not drawn according to some

academics perspective standard) pointed by red/yellow arrows