5D Warped Perspective

"Day & Night" 44.9K GIF < [Escher-like image]

How does one generate mesh objects with complicated perspectives in today's 3D, X-Y-Z coordinate-based rendering programs? The example shown here, titled "Day & Night," was created in 3D Studio r3, but you should be able to build it in most any 3D program.
___ I've always been a fan of M.C. Escher. His work is extraordinary. The 1947 litho "Up and Down" is a study of his ideas about curved lines of perspective in which the viewer sees an object, such as a tall building, in three perspectives simultaneously. Middle (straight on), up, and down. The effect is not unlike a wide-angle or fish-eye lens. The study "Up and Down" doubles this effect by continuing a copy of the first building upside down in the lower half of the image. He connects the two scenes by making the ground and ceiling a common element and by using the simple buildings on the sides as a seam between the two worlds. I couldn't help feeling that this and many of his other perspective images were possible only because they were done in 2D <footnote>.
___ For us, 3D artisans not yet walking upright, life is not so kind. We actually have to build the thing to give us that look. An X-Y-Z based program doesn't have enough perspective points for us to build this type of image accurately. Morph software won't do it. Stretching the camera lens beyond fish-eye won't do it. But bending the objects in a specific way just might fake it. The following should help you create scenes of this type with most any object.
___ The first thing I notice about Escher's "Up and Down" is that the viewer (or camera) is looking straight down (or up) and that the ground, which is also the ceiling for the lower half of the picture, is the key point from which to work. That is to say, the ground at the center of the image is the most normal location in the image, perspective wise, and that everything else distorts away from that point. As we must first build our objects in X-Y-Z coordinates, it is important that the base of the objects be placed in the right location in relation to the camera and its field of vision. There is no one formula for calculating this placement.
___ I started with the placement of the top view only, making sure my four main buildings were placed in real-world positions, that the four corners were equidistant from the camera center, and that all objects which were constructed to connect from one building to another actually did (see Figure 1). I used low-quality sample meshes for placement and distortion tests. I then checked my front and side views to see that all building bases (or building tops for the bottom part of the image) were placed on the same "ground level." The green line with the "U" at one end represents our main working view, a User view rotated on the Z axis 45 degrees. The white arrows show the direction you will bend your objects.
___ The camera is then placed looking straight down at the center of our group, rolled at -45 degrees so the closest corners of our four buildings are occupying the north, south, east, and west positions in the camera view.
___ The aspect of the finished image is 2:1, so I set up a screen rendering of 240x480. The safe-frame guide now accurately represents the shape of the finished image. You will need to dolly your camera for the correct distance from the objects (this is the trial-and-error part). It will help to work from the 45-degree side view (see Figure 2). From there you can see the camera cone and the first building you will Modify/Object/Bend from the proper angle.

Fig. 1 (29.7K GIF) [Fig. 1]

Fig. 2 (19.5K GIF)

Fig. 3 (20.5K GIF) [Fig. 3]

Fig. 4 (21.8K GIF)

___ Unfortunately, 3DSr3's camera cone does not adjust its size based on the rendered image size, so you might have to make a guide. I made a cube for my guide, placed it in my side user view where I thought the camera cone should be, and switched to camera view to see where it was located. I continued going back and forth till the object was placed just at the edge of the green safe-frame line at the top of my camera's view. From the side, this object now gave an accurate location of the camera's cone, and I could perform the next step. For the sake of this instruction, the blue camera cone in Figure 2 has been exaggerated to more accurately represent where the cone should be.
___ As it turns out, the most important consideration is the location of the bent object's center or pivot point (Figure 3). The black X marks the estimated pivot point. This point must fall inside the camera's view in order for it to see the building from both above and below. From the side user view, Modify/Object/Bend the object(s) with your icon arrow up, away from the camera. You'll be looking for two things to happen: 1) that the object's center of bend (there is no visual indicator of this point) falls inside the camera view, and 2) the top part of the object is angled beyond the camera so that we can see the underside of the ceiling.
___ I bent my object several times, each time paying close attention to the pivot location, the angle of the top of my building, and the location of my camera. I moved my camera several times and eventually wound up with an object bent at 60 degrees with the camera at a distance from ground level roughly equal to 1.5 times the height of the building (Figure 4).
___ The duplicate upside-down building (for the lower half of the image) was bent in the opposite direction. The side buildings were only grid cubes with a window attached to the one on the right. Less attention was needed for these objects. The center of their bend occurs outside the camera and the degree of their bend is not that important. Trial and error. Do it till it looks good.
___ All other additions such as lights and background stuff are less important. I also recommend that you give your meshes plenty of extra vertices and faces for smoother bending of objects, and that you map your objects before you bend them.
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Footnote: Escher did many 3D sculptures but most of his images, such as this one, don't lend themselves easily to 3D interpretation. Try to imagine how this image would work if you pointed the camera in any other direction.

Robert Stein III's recent credits include work on the 7th Guest and XIth Hour CD games for Trilobyte and promotional imagery for Autodesk. You may also remember his distinctive work on Banana Republic catalogs before the advent of desktop computer graphics.
___ Note that there is no 2D post-processing to create the "Day & Night" image. The truth is in the viewing of the stereo pair. (To view that image, let your eyes relax, focussing behind the monitor, until the four dots become three, and above the middle dot you see a fully stereo image.)--Ed.

issue supplement [3DA#16]

Revised: 21 Aug 00
http://www.3dartist.com/3dao/s/16/srescher.htm
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