Perspective Reconstruction
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Key-words: Framing Shape of Light (FSL), Light Plane (LP), Orthogonal Picture, Plane Diagonal, Principal Light Beam (PLB), Recipient Surface (RS), Shadow Casting Edge (E), Shadow Casting Point (P), Source of Light, Spatial Diagonal.

     According to my personal method described below, let's envisage the direction of the Principal Light Beam (PLB) as if it were a spatial diagonal of a simple cube modeling the Framing Shape of Light (FSL)!

1. Basic situation - The Principal Light Beam represented by a cube's spatial diagonal.

2. Adding orthogonal pictures to the basic situation - the principal light beam appears on lateral squares as plane diagonals.

     Answering plane diagonals of the FSL-box correspond to the selected light beam's orthogonal pictures. It is more convenient to find intersections between the Light Plane (LP) and the Recipient Surface (RS) in their orthogonal pictures first. These very intersections represent cast shadows' borders we are looking for.
     We derive the Light Plane (LP) from having set a series of light beams parallel to the Principal Light Beam (PLB) along the Shadow Casting Edge (SCE) in question.

3. Origin of Light Plane.

     As to start with we may presume that the Principal Light Beam's position would exactly coincide with the corresponding spatial diagonal of the cube (called Framing Shape of Light). In order to get the cast shadow on the floor of the upper corner (P) we place the principal light beam (now: the spatial diagonal) on it. This will point exactly to the opposite bottom corner (PS). The cast shadow of the upper corner is at the opposite bottom corner.

4. Source of Light, Principal Light Beam and the Framing Shape of Light in perspective and in orthogonal pictures.

     As for the cast shadow of the first chosen point (P) we may freely determine its piercing through the recipient surface. This will be the Desired Point of Cast Shadow (DPS). Here we generally make our choice guessing the best possible final outcome of the whole picture to be completed with constructed cast shadows.

5. The Desired Point of Shadow. Moving PS to PDS means a construction step backwards.

     By connecting the Desired Point of Shadow (DPS) with the initial Shadow Casting Point (P) we settle in perspective the true direction of light we are from now on working with. This will finally shape the new spatial diagonal of our modified Framing Shape of Light.
     After this starting procedure we may ascertain in three orthogonal pictures (top- front- and side views) the definitive proportion between adjoining sides of the Modified Framing Shape of Light.
     While constructing cast shadows in perspective, we should carefully follow the answering projected pictures of the light beam in its orthogonal pictures (L', L", L"') as well. In the following let's sum up the most frequent basic situations modeled within the structural basic grid! We should study these simplified cases first in order to solve more complicated situations later.

6 - 9: Most frequent cast shadow situations within the Structural Basic Grid (in parentheses: cause and result).

6. A Vertical's Cast Shadow on a Horizontal Plane (V/H)

8. A Horizontal's Cast Shadow on a Horizontal Plane (H/H)

7. A Vertical's
Cast Shadow on a Vertical Plane

9. A Horizontal's
Cast Shadow on a Vertical Plane (H/V)


10. Cast shadow of an empty "floating cube" (Flying height = one unit). Structural bars represent two cubes.

     The selection procedure of Shadow Casting Edges (SCE) means to settle a reasonable boundary between light and dark surfaces. Shadow Casting Edges of solid objects formulate a continuous line resulting finally in a closed cast shadow area. Check interim convergence of parallels even during shadow construction!

11. Cast shadow of a "floating cube" with complete planes.

12. Cast shadow of a "floating square" (Flying height = one unit).

13. Cast shadow of a cylinder incorporated into its framing cube.

Construction steps:

•     Cast Shadow of the Top Plane
•     Circle construction (supported by octogonal tangents)
•     Circle / Square / Tangents / Vertical borders

14. Cylinder's upper rim with its cast shadow on inward mantle.

15. Cast shadows of curves on horizontal, vertical and tilted surfaces - The "Sausage Slicing" Method.

16. Light-Cylinder's zigzag-sections cause ellipsoids belonging firmly to the original volume.


1 - Cast shadow of a mast on a flight of stairs modeled by cubes

17. Perspective and orthogonal pictures to assignment No. 1

2 - Cast shadow of a ladder on a terraced heap of cubes

18. Perspective and orthogonal pictures to assignment No. 2

3 - Light Stripe of an upper row window

19. Situation - Short and long wall views and plan of the hall in question with accurate quadratic net (prefixed proportions: L = 2, D = 3, H = 1 1/3 units)

20. Perspective sketch of the hall.

21. Steps toward solution lead us by gradually transforming the Framing Shape of Light. After having fixed the Desired Point of Shadow within the perspective and on adjacent orthogonal pictures as well, by adequately condensing or extending the original cube (FSL) we finally arrive at connecting P with DPS through the principal light beam figuring as spatial diagonal.

•     Original Cube
•     First step: condensing
•     Second Step: extending
•     Final Result: the Modified Cube (transformed        finally into a prism)

DPS = Desired Point of Shadow

22. Supposed light stripe in perspective

VPD = Vanishing Point of Diagonals


     Initially we may presume that the Principal Light Beam's position exactly coincides with a cube's spatial diagonal. We name this virtual cube as the "Framing Shape of Light".
     By connecting the Desired Point of Shadow (DPS) with its corresponding Shadow Casting Point (P) we settle in perspective the true direction of light beam. After this starting procedure we may easily ascertain in orthogonal pictures the definitive proportion of the Modified Framing Shape of Light.

 © All rights reserved Associated Professor Balazs Mehes PhD
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