ENDS 375 - HW 10

Homework 10 Problems

1. What has been the primary motivation behind the development of the various "mapping" techniques?
The primary motivation is to enhance and image visually, create more visual details, and make an image become as realistic looking as possible.

2. What is a "mipmap"? Why is it used? How is a mipmap created?
Mipmapping is a prefiltering technique. Prefiltering techniques are approaches where cost does not grow in proportion to mapped texture area. To create a mipmap Williams uses many images all derived by averaging down the original image to successively lower resolutions. Each image in the sequence is at exactly half the resolution of the previous.

3. Compare "displacement" maps and "bump" maps? How are they similar? How are they different?
Displacement maps are when the actual surface is displaced, instead of only the surface normals This process must be carried out before visible surface determination. Bump maps are a way to provide the appearance of modified surface geometry that avoids explicit geometrical modeling. His approach involves perturbing the surface normal before it is used in the illumination model, just as slight roughness in a surface would perturb the surface normal. They both take a 2d image and place it on a 3d object, the displacement map is not really smooth though.

4. If a polygon with reflected color [.2, .4, .5] and uniform transmission coefficient .5 is positioned in front of an opaque polygon with reflected color [.3, .6, .4], what color will be seen by the virtual camera in the area where these polygons overlap?

Ir = (1 - kt) I1 + kt I2
(The transmission coefficient kt is the transparency of polygon 1, and ranges between 0 and 1)
I1 =[.2,.4,.5], I2 = [.3,.6,.4], kt = .5

Ir = (1 - 0.5) * 0.2 + (0.5 * 0.3) = 0.25
Ig = (1 - 0.5) * 0.4 + (0.5 * 0.6) = 0.5
Ib = (1 - 0.5) * 0.5 + (0.5 * 0.4) = 0.45

RGB = [0.25, 0.5, 0.45]

5. What is a "transparency" map? How is it different from a "texture" map? How are they similar?
The transparency map tends to resemble the texture map closely, except that it consists of differing shades of gray (including black and white). The transparency map determines where the texture map will be applied. Areas in the map that are black will cause the corresponding region of the model to become invisible (i.e. transparent); areas that are white will be opaque, and areas that are gray will have varying degrees of transparency dependent on the shade of gray.

6. What is a "dark-side" shadow? Give an example?
There are 2 kinds of shadows, dark-side and cast. Dark-side shadows are shadows that are created because the light is coming from the opposite side of the image and never reaches it. An example would be any building in the morning. The west side of the building will have a dark-side shadow since the sun rises in the east.

7. What is the general concept used in determining cast shadows?
To determine cast shadows, any point that cannot be seen by its specific light source will be in shadow from this light.

8. Describe the depth or shadow-buffer based approach to cast shadows?
The algorithm is a two-step process. A scene is 'rendered' and depth information stored into the shadow Z-buffer using the light source as a viewpoint. No intensities are calculated, rather it computes a 'depth image' from the light source of these polygons that are visible to the light source. The second step is to render the scene using a Z-buffer algorithm.

9. Describe environment maps. How are they used?
An environment maps is a reflection of an surrounding environment into an object to make it appear to be in a certain environment. ie, a window environment map reflected on a glass.

10. Why do cast shadows have "penumbras"? What factors determine the extent of the penumbra?
The penumbra is an area that receives some light from the source. A penumbra surrounds an umbra and there is always a gradual change in intensity from a penumbra to an umbra. The light sources’ size, shape, and distance from the object determine the size of a penumbra.