# Basics of perspective

This is the partial English translation of the book ‘perspective’ by Riccardo Migliari and Marco fasolo, published by Ulrico Hoepli Editore and presented on the home page.
To access the text, select the index entries.

(Work in progress)

Contents

1 Fundamental concepts
Illusory or virtual spaces
Perspective and the real world
Restricted sight position
The distance circle
Conventions

2 Planes, straight lines and points
Planes
The picture plane
The ground plane
The vertical planes perpendicular to the picture plane
Planes parallel to the picture plane
Straight lines
Straight lines perpendicular to the picture plane
Straight lines parallel to the picture plane
Incident lines that have noteworthy relationships
Square grid pattern
Points
Brief historical considerations

3 Parallel perspective
Measurement of a straight line perpendicular to the picture plane
Measurement on different planes
Parallel perspective of solids
The perspective of a room
Reduced distance circle
Study for a trompe-l’oeil
Variations
Variations of depth
Scale variations
Variations of form
Inverse perspective problem
The cross ratio
Application

4 Oblique and inclined lines
Orthogonality, perpendicularity
Oblique lines
Measurement of an angle on the ground plane
Construction of an angle on the ground plane
Straight lines orthogonal to each other
Inclined straight lines
Measurement of oblique straight lines
Measurement of inclined straight lines
An application

5 Angular perspective
The conditions that determine a perspective
Direct setting of a perspective
An example of angular perspective
Indirect setting
Inaccessible points
Inaccessible vanishing points
Inaccessible measuring points
Inaccessible traces
The Desargues method
The fundamental theorem of perspective, according to Desargues
Studies for a trompe-l’oeil
The rules of the game

6 Inclined Planes
Perpendicularity
i – Construction of a plane perpendicular to a straight line
ii – Construction of a straight line, perpendicular to a plane
Noteworthy straight lines of an inclined plane
Construction of an inclined plane
Measurement of a gradient
The inclined plane of a given gradient
Inclined planes perpendicular to the picture plane
Line of intersection of two planes
Intersection of a straight line with a plane
Straight line perpendicular to a plane

7 Oblique perspective
Measurement of a straight line in a generic position
The measure circle
The inclined picture plane
Direct setting
The measurement
Metamorphosis

8 Perspective of the circle
The circle as a graphic line
The front facing plane
The circle as a conic
The case of the ellipse
The case of the parabola
The case of the hyperbola
Cui prodest?
The harmonic ratio

9 Perspective of surfaces
The apparent contour
The groin vault
The sphere
Surfaces of revolution
The cone

10 Parallel projections
Orthogonal projection
Trimetric projection
Dimetric orthogonal projection
Isometric orthogonal projection
Oblique projection
Pohlke’s Theorem
Cavalier projection
Military projection
Special axonometry
Conclusions

11 Glossary
Symbol glossary
List of the most common symbol
Glossary of terms