Figure 1: The pelican-antelope figure is a prototypical ambiguous picture indicating a pelican when seen as the head of an animal with a large bill looking upward to the left and an antelope when seen as a horned animal looking downward to the right. Though utterly simple, people enjoy mastering the reversal forth and back between the two interpretations, thus keeping the ambiguity intact and controlling it rather than settling for either one or the other version.
Figure 2: Kepler investigated the trajectory of the rays point by point. He realized that each point of the source of light (ABC) produces a patch of light that has the shape of the aperture (square). However, taken together, all the points of the source will produce a combination of patches that constitutes an inverted image A'B'C'of the light source (triangle).
Footnote 2: One of Durer's Perspective Machines and Dürer's perspective drawing of a reclining nude
image source: http://www.dartmouth.edu/~matc/math5.geometry/unit11/unit11.html and http://www.physics.hku.hk/~tboyce/ss/assignments/ascent/perspective.html
image source: http://www.dartmouth.edu/~matc/math5.geometry/unit11/unit11.html and http://www.physics.hku.hk/~tboyce/ss/assignments/ascent/perspective.html
Footnote 3: In Giotto's representation of the Cana Wedding, the top of the curtain surrounding the scene lies on a straight line. However, only the back of the depicted room is parallel to the picture plane. The left and right extremities of the line, following the side walls, represent orientations that are at an angle with respect to the back wall.
image source: http://www.wga.hu
image source: http://www.wga.hu
Footnote 4: Donatello's Raising of Drusiana illustrates the same principle: an ambiguous straight line with a unitary compositional function in 2D but containing segments with different orientations in 3D.
image source: http://www.wga.hu
image source: http://www.wga.hu
Footnote 5a: The stovepipe at the ceiling in Van Gogh's Hospital Room appears to lie on a vanishing line, suggesting a simple symmetrical perspective. In fact, falling at an angle with respect to the back wall, the perspective is complicated even though the slanted pipe segment, which could even be parallel to the picture plane, misleadingly makes it look simple.
Footnote 5b: The original Van Gogh's Ward in the Hospital in Arles.
image source: http://www.paletaworld.org - see also http://www.vangoghgallery.com
image source: http://www.paletaworld.org - see also http://www.vangoghgallery.com
Footnote 5c: some animations showing Van Gogh's Bedroom in Arles.
Figure 3: The pilasters in Masaccio's Trinity fresco have ornamental capitals in Corinthean style; the columns supporting the vault have ornamental capitals in Ionic style. All of these ornamental capitals line up along straight lines that happen to be vanishing lines. The Ionic capitals atop the front columns lie with the Corinthean capitals in a plane that is parallel to the picture plane. But those same Ionic capitals atop the front columns lie with the Ionic capitals atop the back columns in a plane that is orthogonal to the picture plane. So what look like simple straight lines in two dimensions represent segments that have very different orientations in three dimensions.
Figure 4: The reconstruction of Masaccio's Trinity inspired by Polzer (1971) proceeds from a vertical organization of three squares. The circular arch that covers the front of the vault coincides with the top half of a circle inscribed in the top square. The top of the nimbus behind the head of God the Father coincides with the center of the circle. Christ's head is exactly in the middle of the lower half of the square. When a vanishing point is chosen at the location of the head of the viewer shown in the bottom square, the whole construction of this convincing perspective, including the semi-circular vault, can be done according to traditional pre -perspective two-dimensional rules.
Footnote 6: some animations showing Masaccio's Trinity Fresco.
Footnote 7: Arcimboldo's Librarian and the Four seasons
image source: http://www.wga.hu
image source: http://www.wga.hu
Figure 5: The chandelier of Jan Van Eyck's Arnolfini double portrait is shown here partly in a computer reconstruction developed at Ghent University by the author and architect Wim De Boever. It is an image from an animation that also partly appeared in David Hockney's Secret Knowledge on BBC television. The 3D computer model was developed to check on the lighting and the perspective of the chandelier and the vantage point of the viewer.
A similar reconstruction has recently been developed by Stork (2005) whom we sent our chandelier material on his request but he preferred to have it redone in order to be able to draw the vanishing lines for the small decorative hanging quatrefoils of the chandelier carefully checking the preciseness of the linear perspective. Apparently Stork does not consider our reconstruction and animated representation of it in any way convincing or relevant as he leaves out in his paper any reference to the materials we sent him on his request. We agree however that his test confirms the exultant but hackneyed claim that Jan van Eyck did not use linear perspective in the strict sense of that specific criterion. So what? Is it falsifying Hockney’s claim for the use of the concave mirror, apparently Stork’s major concern? Or again, vanishing lines as deadly arrows in what some prefer to consider Jan Van Eyck’s Achilles tendon?
original image can be found at the site of the National Gallery in London.
A similar reconstruction has recently been developed by Stork (2005) whom we sent our chandelier material on his request but he preferred to have it redone in order to be able to draw the vanishing lines for the small decorative hanging quatrefoils of the chandelier carefully checking the preciseness of the linear perspective. Apparently Stork does not consider our reconstruction and animated representation of it in any way convincing or relevant as he leaves out in his paper any reference to the materials we sent him on his request. We agree however that his test confirms the exultant but hackneyed claim that Jan van Eyck did not use linear perspective in the strict sense of that specific criterion. So what? Is it falsifying Hockney’s claim for the use of the concave mirror, apparently Stork’s major concern? Or again, vanishing lines as deadly arrows in what some prefer to consider Jan Van Eyck’s Achilles tendon?
original image can be found at the site of the National Gallery in London.
Animation of the luster, used in Hockney's Secret Knowledge
Figure 6: The closed panels of the Ghent Altarpiece with the annunciation scene deployed over four panels.
image source: http://www.wga.hu
Figure 7: The open panels of the Ghent Altarpiece with the Adoration of the Lamb as the central panel of the lower tiers.
image source: http://www.wga.hu
Figure 8: The page of the book next to the Holy Virgin in the annunciation scene on which one can detect the readable phrase de visione dei (highlighted), the seeing of God as the final destination of man according to Christian doctrine, the key phrase for understanding the polyptych.
Figure 9: The shadows of the heads of the three main figures of the upper panels in the open polyptych indicate the orientation of the incoming light.
Figure 10: The shadows of the strings of rope on the cloak of God the Father illustrate subtle optics: as the light source is not a point but the plane of the window, shadows are not sharp and are identifiable only very close to the surface on which they project (in late medieval optical treatises: a large light source combined with a small lighted object implies a very short shadow cone). The painter uses this effect to detail the sculptural qualities of the cloak.
Figure 11: The eyes of the depicted figures function as reflecting spheres which produce a reduced image of the light source. The highlights seen in the eyes of figures looking in the direction of the windows show this effect, here demonstrated with the eyes of Adam. Those that look in the other direction do not show this effect.
Figure 12: Cylindrical surfaces provide an image of the light source, elongated along the axis of the cylinder. On the cylindrical brooch worn by the singing angel, the light source can clearly be identified as a window of the Vijd chapel.
Figure 13: Reflection is different on convex and concave surface. The kettle in the annunciation scene reflects light like a sphere with a single small highlight disclosing the light source. In the interior of the basin, which qualifies as a concave surface, repeated highlights reflect the light source accordingly.
Figure 14: The scepter of God the Father is a transparent cylindrical object. The fine whitish vertical line on the right side shows the light that is reflected at the first optical barrier it encounters: the outside of the cylinder. Light penetrating the cylinder hits a second optical barrier at the concave outer boundary of the left side. It is more diffusely scattered, as optics predicts. The light that overcomes those two barriers and that traverses the crystal staff undergoes refraction and results in focal spots on the hand of God the Father and on the pearls and folds of his cloak along the line of the incoming light.
Figure 15 In principle, the metallic organ pipes should have been made by folding a flat metallic plate into a cylinder, leaving a visible seam where the two edges form a joint. By showing two seams, Van Eyck requires the viewer to sort out for himself what is meant to represent a genuine seam and what is only presented as a mirror image of a seam in his painting.
Figure 16: While, in the annunciation scene, the room with the Holy Virgin is still lighted from the windows of the viewer's space (the Vijd chapel), the light entering the oriel behind her comes from another direction.
Figure 17: The optics of the carafe on the window ledge indicate that the light entering from the back comes from the opposite direction of the light entering at the front.
Figure 18: The annunciation scene on the Ghent Altarpiece with arrows added to indicate the two lights: the natural light from the sun entering from the viewer's space and the divine light entering from the opposite direction in the back, affecting the Holy Virgin.
Footnote 16a: The representation of the Virgin Mary in the Ghent Altarpiece is akin to the common "moon sickle" madonnas, in which the Holy Virgin is shown with her feet resting on a moon sickle while the sun radiates from behind her body and a nimbus of twelve stars (representing the apostles) radiates around her head. The picture expresses the hierarchy of reflectors of God's light (symbolized by the mirror attribute): the Virgin, the sun and the moon.
image source: http://www.getty.edu and http://www.leavesofgold.org
Footnote 16b: A late fifteenth or early sixteenth woodcut depicts the Holy Virgin with her most important attributes. The left upper part of the picture shows the sun and the moon with the indications “electa ut sol” (selected above the sun) and “pulcra ut luna” (more beautiful than the moon). The lower right part of the picture contains the image of a mirror with the banderole indicating “speculum sine macula” (spotless mirror).
image source: http://www.chd.dk
Other works by Jan van Eyck:
Madonna with Canon George Van der Paele - Groeningemuseum, Brugge
website: http://www.brugge.be
The Virgin of Chancellor Rolin - Louvre, Paris
website: http://www.louvre.fr
Figure 19: central panel of The Ghent Altarpiece
image source: http://www.wga.hu
Figure 20: The original plan of the central panel of the Ghent Altarpiece might not have contained the fountain. There is no underdrawing for it as there is for most of the other components. Without the fountain, the Ghent Altarpiece provides ample room for the viewer to step into the picture to join the assembled believers who witness Christ's offer, which reopens the way to (seeing) God.