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The Linear Perspective

 (Rudolf Stalder in collaboration with Darrel Madis)

 (All rights reserved 2004, Legal notice)

    Introduction Central projection
      Cone of view, angle of view
    Definitions and terms  
    How to draw The square-grid
    Basic concepts and rules The square-size concept d/h
         Lines and planes  
         Shadows Inscription of an ellipse into a four-cornered
         Reflections Missing repair-points



  A02 Definitions and terms :
  Axis of Vision   (AV)   Horizontal Line  (HL)   Picture Plane  (PP)
  Center Line of Vision  (CLV)   Plane of Vision  (PV)   Stand Point  (SP)
  Eye Level Line  (EL)       Vanishing Line (VL)
  Ground Plane  (GP)       Vanishing Point (VP)
  A20 How to draw
  A21 Studio arrangement suitable for learning
    Basic concepts and rules
    Lines and planes
  A17 Parallel lines
  A18 Parallel planes
  A19 One-point-, two-point-, three-point-perspective and beyond


  A23 Walls and posts 
    Equal intercept
    Proportional intercepts,
    Translation of a "frontal" view into a "perspective" view
  A25 The basic building
    Parallel buildings
    Non-parallel buildings
top   Buildings on different levels
  A33 Stairs 


  S09 Shadows of posts
  S11 Shadow of walls
  S13 Shadows onto walls
  S22 Post in the water,
  S24 Reflection of the sky in the water
  S25 post near the border
  S35 Landing place, ship,
  C01 Central projection
  A12 Cone of view, angle of view
  C05 The square-grid
  C07 The square-size concept h/d
  C09 Application of h/d
  C11 More about h/d, presentation of angles
  G11 Inscription of a circle in a four-cornered (suitable for high accuracy)
  G13 Method I
  G16 Method II
  S05 Missing points of repair


  The emphasis of this presentation is to provide an overview on the linear perspective and some related procedures covering practical as theoretical aspects as well.

The linear perspective is best understood on a pure mathematical base. Its principles apply only within limits to the image creation of the human eye, suggesting their use in a rather appropriate than in an absolute manner.

Some of the difficulties arising while using the linear perspective are due to its mathematical nature, others relate to the fact, that its terms are frequently used without proper reference, and that some of these terms lack a clear underlying rational or a well conceived definition.

Before applying the linear perspective, it should be clarified, that it presents really the most suitable method to use. If high accuracy in regard of proportions of lines and angles is a request, such as for architectural purposes, support by photography and/or technical means such as computers should be envisaged from the begin. If the goal is purely artistic these remedies are better avoided, as entirely “true“ lines frequently interfere negatively with the artistic intention.

The strengths and weaknesses of the linear perspective in comparisons with other methods of graphical presentation - including aspects of historical interest - will be addressed in a part actually in preparation.




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