This document discusses curvilinear perspective with 5 vanishing points and provides examples. It includes diagrams showing: 1) The projection of lines on a hemispherical field of view, with horizontal and vertical lines curving. 2) Methods for drawing a 45 degree grid on the hemisphere. 3) Examples of projecting cubes and cars onto the hemisphere from different angles. 4) Perspective charts for drawing objects at 0, 45, and 30/60 degree angles.

1. Prospettiva ZeroSei
Massimo Marrazzo
Curvilinear perspective: 5 vanishing points with examples
March 2017
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5 vanishing points

2. 1
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5
5 vanishing points
Front Side
Top
Projection of a cube on the hemispherical field of view
Front view of the lines
projected on the hemisphere
horizontal lines
verticallines
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21
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21
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2
1
4
4 1
Projection of parallel lines on the hemispherical surface
In spherical perspective the horizontal
lines and the vertical are curved. The
view is wide up to 180° vertically and
horizontally.

3. 2Prospettiva ZeroSei
45° 45°45°
Top view
Front view
0°
15°
30°
45°
60°
75°
0°15°
30°
45°
60°
75°
Angles
The divisions for horizontal angles
correspond to the vertical ones,
Drawing 45° grid

4. 3
Side Front
A horizontal line projected on
the hemispherical field of view
1/2 1/21/21/21/2 1/21/21/2
1/2 1/21/21/2
2 3 4 5
6 7 8
1
2 K
K
1
K
As an alternative to graphical construction, it is also possible to use plastic ellipse templates.

5. 4Prospettiva ZeroSei
30°
45°
60°
Objects Lateral to the hemispherical
field of viewFront Side
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°

6. 5
Objects Lateral to the hemispherical field of view
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°

7. 6Prospettiva ZeroSei
Cube rotated 45°
60°
Objects Lateral to the hemispherical
field of viewFront Side
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°
45°
15°
30°
45°
60°
75°
15°
30°
45°
60°
75°

8. 7
Objects Lateral to the hemispherical field of view
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°
0°
15°
30°
45°
60°
75°
15°
30°
45°
60°
75°
15°
30°
45°
60°
75°

9. 8Prospettiva ZeroSei
30°
41°
139°
41°
139°
30°
Objects Frontal to the hemispherical
field of viewFront Front
Car rotated 60°
0°15°30°45°
60°
75°

10. 9
Objects Frontal to the hemispherical field of view

11. 10Prospettiva ZeroSei
0°
15°
30°
45°
60°
75°
0°15°
30°
45°
60°
75°
Perspective chart 0°

12. 11
45° 45°
Perspective chart 45°

13. 12Prospettiva ZeroSei
30°45°60°30°
0°15°
30°
45°
60°
75°
Perspective chart 30°/60°

14. 13
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 2.0 Generic License.
To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/2.0/
Massimo Marrazzo - 2017
http://www.biodomotica.com/
http://prospettivazerosei.blogspot.it
https://logicalcells.blogspot.it