The Far Side of the Shadow Screen
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Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Some men are born into a destiny. Others have their destinies thrust upon them. Peter Grant was born a rich man's son, destined to inherit the family business. Fate had another plan. An anthropological assignment as a grad student takes Grant to Indonesia where he passes beyond the magical shadow screen barrier between man's domain and the regions of the gods.
There he bat Some men are born into a destiny. There he battles Batara Kala for the woman he loves and the souls of all mankind. Get A Copy. Kindle Edition , pages. Credit: Getty Images. What if your car not only had technology that warned you not only about objects in clear view of your vehicle—the way that cameras, radar, and laser can do now in many standard and autonomous vehicles—but also warned you about objects hidden by obstructions?
But the new system could change that. In a paper in Nature , Goyal and a team of researchers say they can compute and reconstruct a scene from around a corner by capturing information from a digital photograph of a penumbra, which is the partially shaded outer region of a shadow cast by an opaque object.
Against a matte wall, Goyal explains, light scatters equally rather than concentrating or reflecting back in one direction like a mirror.
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To the human eye, such a penumbra may not look like much. By inputting the dimensions and placement of the object, the team can use their computer program to organize the light scatter and determine what the original scene looks like—all from a digital photograph of a seemingly blurry shadow on a wall. For their research purposes, they created different scenes by displaying different images on an LCD monitor. Could their approach reconstruct the image of a human being standing around the corner, for example? Then we build this inverse projection as the usual projection matrix, as shown here, where matrices are written in a row-major style:.
So the formula for the resulting transformed z coordinates, which go into a shadow map, is:. This is why the ray hits all points in the correct order and why there's no need to use "virtual slides" for creating post-projective space. But for another projection transformation caused by a light camera, these points are located behind the camera, so the w coordinate is inverted again and becomes positive.
By using this inverse projection matrix, we don't have to use virtual cameras. As a result, we get much better shadow quality without any CPU scene analysis and the associated artifacts. The only drawback to the inverse projection matrix is that we need a better shadow map depth-value precision, because we use big z -value ranges.
However, bit fixed-point depth values are enough for reasonable cases. Virtual cameras still could be useful, though, because the shadow quality depends on the location of the camera's near plane. The formula for post-projective z is:.
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As we can see, Q is very close to 1 and doesn't change significantly as long as Z n is much smaller than Z f , which is typical. That's why the near and far planes have to be changed significantly to affect the Q value, which usually is not possible. At the same time, near-plane values highly influence the post-projective space. In this respect, if we change Z n to 2 m, we will effectively double the z -value resolution and increase the shadow quality. That means that we should maximize the Z n value by any means. The perfect method, proposed in the original PSM article, is to read back the depth buffer, scan through each pixel, and find the maximum possible Z n for each frame.
So we should use another perhaps less accurate method to find a suitable near-plane value for PSM rendering. Such other methods for finding a suitable near-plane value for PSM rendering could include various methods of CPU scene analysis:.
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These methods try to increase the actual near-plane value, but we could also increase the value "virtually. When sliding the camera back, we increase the near-plane value so that the near-plane quads of the original and virtual cameras remain on the same plane. When we slide the virtual camera back, we improve the z -values resolution. However, this makes the value distribution for x and y values worse for near objects, thus balancing shadow quality near and far from the camera.
Because of the very irregular z -value distribution in post-projective space and the large influence of the near-plane value, this balance could not be achieved without this "virtual" slideback. The usual problem of shadows looking great near the camera but having poor quality on distant objects is the typical result of unbalanced shadow map texel area distribution. Another problem with PSMs is that the shadow quality relies on the relationship between the light and camera positions.
With a vertical directional light, aliasing problems are completely removed, but when light is directed toward the camera and is close to head-on, there is significant shadow map aliasing. We're trying to hold the entire unit cube in a single shadow map texture, so we have to make the light's field of view as large as necessary to fit the entire cube. This in turn means that the objects close to the near plane won't receive enough texture samples.
We'll always have problems fitting the entire unit cube into a single shadow map texture. Two solutions each tackle one part of the problem: Unit cube clipping targets the light camera only on the necessary part of the unit cube, and the cube map approach uses multiple textures to store depth information. This optimization relies on the fact that we need shadow map information only on actual objects, and the volume occupied by these objects is usually much smaller than the whole view frustum volume especially close to the far plane.
That's why if we tune the light camera to hold real objects only not the entire unit cube , we'll receive better quality. Of course, we should tune the camera using a simplified scene structure, such as bounding volumes. Cube clipping was mentioned in the original PSM article, but it took into account all objects in a scene, including shadow casters in the view frustum and potential shadow casters outside the frustum for constructing the virtual camera.
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Because we don't need virtual cameras anymore, we can focus the light camera on shadow receivers only , which is more efficient. Still, we should choose near and far clip-plane values for the light camera in post-projective space to hold all shadow casters in the shadow map. But it doesn't influence shadow quality because it doesn't change the texel area distribution. Because faraway parts of these bounding volumes contract greatly in post-projective space, the light camera's field of view doesn't become very large, even with light sources that are close to the rest of the scene. In practice, we can use rough bounding volumes to retain sufficient quality—we just need to indicate generally which part of the scene we are interested in.
In outdoor scenes, it's the approximate height of objects on the landscape; in indoor scenes, it's a bounding volume of the current room, and so on. We'd like to formalize the algorithm of computing the light camera focused on shadow receivers in the scene after we build a set of bounding volumes roughly describing the scene.
In fact, the light camera is given by position, direction, up vector, and projection parameters, most of which are predefined:. So the most interesting thing is choosing the light camera direction based on bounding volumes. The proposed algorithm is this:. In this way, we could find an optimal light camera in linear time depending on the bounding volume number, which isn't very large because we need only rough information about the scene structure.
This algorithm is efficient for direct lights in large outdoor scenes. The shadow quality is almost independent of the light angle and slightly decreases if light is directed toward the camera. Figure shows the difference between using unit cube clipping and not using it. Though cube clipping is efficient in some cases, other times it's difficult to use. For example, we might have a densely filled unit cube which is common , or we may not want to use bounding volumes at all.
Plus, cube clipping does not work with point lights. A more general method is to use a cube map texture for shadow mapping. Most light sources become point lights in post-projective space, and it's natural to use cube maps for shadow mapping with point light sources.
But in post-projective space, things change slightly and we should use cube maps differently because we need to store information about the unit cube only. The proposed solution is to use unit cube faces that are back facing, with respect to the light, as platforms for cube-map-face textures. The number of used cube map faces ranging from three to five depends on the position of the light. We use the maximum number of faces when the light is close to the rest of the scene and directed toward the camera, so additional texture resources are necessary.
For other types of light sources located outside the unit cube, the pictures will be similar. For a point light located inside the unit cube, we should use all six cube map faces, but they're still focused on unit cube faces. We could say we form a "cube map with displaced center," which is similar to a normal cube map, but with a constant vector added to its texture coordinates.
In other words, texture coordinates for cube maps are vertex positions in post-projective space shifted by the light source position:. By choosing unit cube faces as the cube map platform, we distribute the texture area proportionally to the screen size and ensure that shadow quality doesn't depend on the light and camera positions. In fact, texel size in post-projective space is in a guaranteed range, so its projection on the screen depends only on the plane it's projected onto.
This projection doesn't stretch texels much, so the texel size on the screen is within guaranteed bounds also. Because the vertex and pixel shaders are relatively short when rendering the shadow map, what matters is the pure fill rate for the back buffer and the depth shadow map buffer. So there's almost no difference between drawing a single shadow map and drawing a cube map with the same total texture size with good occlusion culling, though.
The cube map approach has better quality with the same total texture size as a single texture. The difference is the cost of the render target switch and the additional instructions to compute cube map texture coordinates in the vertex and pixel shaders. Let's see how to compute these texture coordinates. First, consider the picture shown in Figure The blue square is our unit cube, P is the light source point, and V is the point for which we're generating texture coordinates.
We render all six cube map faces in separate passes for the shadow map; the near plane for each pass is shown in green.