question: Can an object's shadow be smaller then an object?
comment: Yes. At noontime, the sun is straight above you so you cast a very small puddle of shadow by your feet that is much smaller than you.
passages: BULLET::::- 2011 "Silhouettes Are Shadows", "Acta Analytica" 26 2:187-197. Here a solution is proposed to Sorensen’s problem about the eclipse of Near and Far. Since a silhouette is a shadow, what is seen is the silhouette or shadow of Far, into which Near has disappeared, as a smaller object might. Shadows are seen because the surface in shadow fails to reflect light.
   Around the year 2000, several people discovered that Heidmann's method can be made to work for all camera positions by reversing the depth. Instead of counting the shadow surfaces in front of the object's surface, the surfaces behind it can be counted just as easily, with the same end result. This solves the problem of the eye being in shadow, since shadow volumes between the eye and the object are not counted, but introduces the condition that the rear end of the shadow volume must be capped, or shadows will end up missing where the volume points backward to infinity.
   The farther the distance from the object blocking the light to the surface of projection, the larger the silhouette (they are considered proportional). Also, if the object is moving, the shadow cast by the object will project an image with dimensions (length) expanding proportionally faster than the object's own rate of movement. The increase of size and movement is also true if the distance between the object of interference and the light source are closer. This, however, does not mean the shadow may move faster than light, even when projected at vast distances, such as light years. The loss of light, which projects the shadow, will move towards the surface of projection at light speed.
   There is also a problem with the shadow where the faces along the silhouette edge are relatively shallow. In this case, the shadow an object casts on itself will be sharp, revealing its polygonal facets, whereas the usual lighting model will have a gradual change in the lighting along the facet. This leaves a rough shadow artifact near the silhouette edge which is difficult to correct. Increasing the polygonal density will minimize the problem, but not eliminate it. If the front of the shadow volume is capped, the entire shadow volume may be offset slightly away from the light to remove any shadow self-intersections within the offset distance of the silhouette edge (this solution is more commonly used in shadow mapping).
   A shadow occupies a three-dimensional volume of space, but this is usually not visible until it projects onto a reflective surface. A light fog, mist, or dust cloud can reveal the 3D presence of volumetric patterns in light and shadow.
   One thing that needs to be specified is whether the shadow being cast is dynamic or static. A wall with a shadow on it is a static shadow. The wall is not moving and so its geometric shape is not going to move or change in the scene. A dynamic shadow is something that has its geometry changes within a scene.
   Heidmann proposed that if the front surfaces and back surfaces of the shadows were rendered in separate passes, the number of front faces and back faces in front of an object can be counted using the stencil buffer. If an object's surface is in shadow, there will be more front facing shadow surfaces between it and the eye than back facing shadow surfaces. If their numbers are equal, however, the surface of the object is not in shadow. The generation of the stencil mask works as follows:
  
  BULLET::::1. Disable writes to the depth and color buffers.
  
  BULLET::::2. Use back-face culling.
   The names umbra, penumbra and antumbra are often used for the shadows cast by astronomical objects, though they are sometimes used to describe levels of darkness, such as in sunspots. An astronomical object casts human-visible shadows when its apparent magnitude is equal or lower than -4. Currently the only astronomical objects able to produce visible shadows on Earth are the sun, the moon and, in the right conditions, Venus or Jupiter.
  
  A shadow cast by the Earth on the Moon is a lunar eclipse. Conversely, a shadow cast by the Moon on the Earth is a solar eclipse.
  
  Section::::Daytime variation.
   Section::::Construction.
  
  In order to construct a shadow volume, project a ray from the light source through each vertex in the shadow casting object to some point (generally at infinity). These projections will together form a volume; any point inside that volume is in shadow, everything outside is lit by the light.
   A simple way of drawing a drop shadow of a rectangular object is to draw a gray or black area underneath and offset from the object. In general, a drop shadow is a copy in black or gray of the object, drawn in a slightly different position. Realism may be increased by:
  
  BULLET::::1. Darkening the colors of the pixels where the shadow casts instead of making them gray. This can be done with alpha blending the shadow with the area it is cast on.
   Stencil buffer implementation of spatial drawing shadows is any shadow of a geometric body that its volume includes part of the scene that is in it. If any part of the scene belongs to this volume, light is not illuminated given, otherwise it is. This problem is compounded by the increase in the number of lights, but does not address the number of areas on which the shadows fall. There are several solutions to the problem, but we followed the following algorithm: 
  
  1. Draw a scene without light 
   BULLET::::- When conversing with Elric, Sheridan says, "If we went back in time a thousand years and tried to explain this place to people, they could only accept it in terms of magic," foreshadowing Babylon 4 being transported a millennium back in time and becoming a part of Minbari mythology.
  
  Section::::Production details.
   BULLET::::- Shadow Stereopsis : Antonio Medina Puerta demonstrated that retinal images with no parallax disparity but with different shadows are fused stereoscopically, imparting depth perception to the imaged scene. He named the phenomenon "shadow stereopsis". Shadows are therefore an important, stereoscopic cue for depth perception.
   The absence of diffusing atmospheric effects in the vacuum of outer space produces shadows that are stark and sharply delineated by high-contrast boundaries between light and dark.
  
  For a person or object touching the surface where the shadow is projected (e.g. a person standing on the ground, or a pole in the ground) the shadows converge at the point of contact.
  
  A shadow shows, apart from distortion, the same image as the silhouette when looking at the object from the sun-side, hence the mirror image of the silhouette seen from the other side.
  
  Section::::Astronomy.
   Although the edge of a shadow appears to "move" along a wall, in actuality the increase of a shadow's length is part of a new projection which propagates at the speed of light from the object of interference. Since there is no actual communication between points in a shadow (except for reflection or interference of light, at the speed of light), a shadow that projects over a surface of large distances (light years) cannot convey information between those distances with the shadow's edge.
  
  Section::::Color.
   Shadow volume is one way that self-shadowing can be used in a 3D image or scene. The method basically makes a 3D object occupy an enclosed volume in a scene where a shadow is being cast. This allows the renderer, or shader, to perform an analysis on whether or not the point or pixel is inside a shadowed area. This eventually allows the program to determine how the object will be lit.
  
  Section::::Techniques.:Shadow Maps.
  
  3D shadow mapping is another method which creates approximate shadows from a set position to create very diffuse shadows that may not be entirely accurate.
   However, if the object has a diameter greater than the acoustic wavelength, a 'sound shadow' is cast behind the object where the sound is inaudible. (Note: some sound may be propagated through the object depending on material).
  
  Section::::Optical atmospheric diffraction.
   BULLET::::- Proposition 17a in al-Tusi's medieval Arabic version of the book "On Sizes" states that the ratio of the distance of the vertex of the shadow cone from the center of the Moon (when the Moon is on the axis [that is, at the middle of an eclipse] of the cone containing the Earth and the Sun) to the distance of the center of the Moon from the center of the Earth is greater than the ratio 71 to 37 and less than the ratio 3 to one (Berggren & Sidoli 2007:218). In other words, that the tip of the Earth's shadow cone is between 108/37 and 4 times farther away than the Moon.
   After Crow, in 1991 Tim Heidmann showed how to use the stencil buffer to render shadows with shadow volumes quickly enough for use in real time applications. There are three common variations to this technique, depth pass, depth fail, and exclusive-or, but all of them use the same process:
  
  BULLET::::1. Render the scene as if it were completely in shadow.
  
  BULLET::::2. For each light source:
  
  BULLET::::1. Using the depth information from that scene, construct a mask in the stencil buffer that has holes only where the visible surface is not in shadow.
   By contrast, the penumbra is illuminated by some parts of the light source, giving it an intermediate level of light intensity. A viewer located in the penumbra region will see the light source, but it is partially blocked by the object casting the shadow.
  
  If there is more than one light source, there will be several shadows, with the overlapping parts darker, and various combinations of brightnesses or even colors. The more diffuse the lighting is, the softer and more indistinct the shadow outlines become, until they disappear. The lighting of an overcast sky produces few visible shadows.
   On Earth, the shadow cast during an eclipse moves very approximately at 1 km per sec. This depends on the location of the shadow on the Earth and the angle in which it is moving.
  
  Section::::Eclipse cycles.
   In 1989 Antonio Medina Puerta demonstrated with photographs that retinal images with no parallax disparity but with different shadows are fused stereoscopically, imparting depth perception to the imaged scene. He named the phenomenon "shadow stereopsis". Shadows are therefore an important, stereoscopic cue for depth perception. He showed how effective the phenomenon is by taking two photographs of the Moon at different times, and therefore with different shadows, making the Moon to appear in 3D stereoscopically, despite the absence of any other stereoscopic cue.
  
  Section::::Human stereopsis in popular culture.
   Self-Shadowing methods have trade-offs between quality and speed depending on the desired result. To keep speed up, some techniques rely on fast and low resolution solutions which could result in wrong looking shadows which may be out of place in a scene. Others require the CPU and GPU to calculate with algorithms the exact location and shape of a shadow with a high level of accuracy. This requires a lot of computational overhead, which older machines could not handle.
  
  Section::::Techniques.
  
  Section::::Techniques.:Height Field Self-Shadowing.
   In Roger L'Estrange’s relation of "The Dog and a Shadow", "He Chops at the Shadow and Loses the Substance"; Brooke Boothby, in his translation of the fables of Phaedrus, closes the poem of "The Dog and his Shadow" with the line "And shade and substance both were flown". The allusive proverb is glossed as "Catch not at shadows and lose the substance" in a recent dictionary.
   When calculating the brightness of a surface during rendering, our illumination model requires that we know the surface normal. However, a 3D model is usually described by a polygon mesh , which may only store the surface normal at a limited number of points, usually either in the vertices, in the polygon faces, or in both. To get around this problem, one of a number of interpolation techniques can be used.
  
  Section::::Computer graphics.:Interpolation techniques.:Flat shading.
  