Lect 3 Textures

Question 1

1. Why is Surface Texturing important.

Answer 1

• Even the best synthesised images lack the richness of a real surface.
• Irregularities and imperfections are difficult to represent with polygons – such detail would require a huge number of facets and vertices.
• Techniques are possible that allow for realistic detail to be added without increasing the polygon count, these are all surface texturing of some kind.

Important for gaming.

Question 2

2. What is texture mapping?

Answer 2

• Also known as image mapping.
• Any image may be used as the source for the image map.
• An image is a 2D array of intensities.
• We can “paint” these images onto polygons – it’s like taking some giffwrap and sticking it onto the polygons.

Question 3

3 How useful is texture/ image mapping?

Answer 3

• It’s not limited to actual pictures; surface textures like skin and cloth can also be added using this method.
• Helps in situations where we want to limit the polygon count.
• Allows greater control over the appearance of a texture.

Question 4

4. How is an image mapped?

Answer 4

• Have to map from coordinates in the object’s space to points in the image.
• Textures repeat themselves, like giftwrap with a repeating motif.
• In general, mapping a 2D image to a polygon is just a 2D transformation. However, some surfaces are more difficult – like the problems encountered when giftwrapping a spherical object.

Question 5

5. What are the coordinate systems used in texture mapping?

Answer 5

• Texture coordinates
‐ Used to identify points in the image to be mapped

• Object or World Coordinates
‐ Conceptually, where the mapping takes place

• Window/Device Coordinates
‐ Where the final image is really produced

• Parametric coordinates
‐ May be used to model curves and surfaces

Question 6

6. Why is knowing the difference between world and local coordinates important in **texture mapping? **

Answer 6

In object coordinates the origin and coordinate axes remain fixed relative to an object no matter how the object’s position and orientation change.

Most mapping techniques use object coordinates.

Normally, if a teapot’s spout is painted white, the spout should remain white as the teapot flies and tumbles through space.

When using world coordinates, the pattern shifts on the object as the object moves through space.

Question 7

7. Describe the 3 shapes used to bound an object.

Answer 7

Depending on the mapping situation, we may need to bound an object with a box, a cylinder, or a sphere. It’s often useful to transform the bounding geometry so its coordinates range between zero and one.

Question 8

8. Name two things to consider when **mapping a 2D image to a 3D mesh. **

Answer 8

We consider two things: map shape and map entity.

In 2D texture mapping, we have to decide how to paste the image on to an object.

In other words, for each pixel in an object, we encounter the question, “Where do I have to look in the texture map to find the colour?”

Question 9

9. Describe Map Shapes.

Answer 9

For a map shape that’s planar, we take an (x,y,z) value from the object and throw away (project) one of the components

• which leaves us with a 2D (planar) coordinate We use the planar coordinate to look up the color in the texture map.

Question 10

10. How can you tell which componant has been projected when texture mapping?

Answer 10

You can determine which component was projected by looking for color changes in coordinate directions - movement along the z-axis does not produce a change in color.

This is how you can tell that the z- component was eliminated.

This slide shows several textured-mapped objects that have a planar map shape.

None of the objects have been rotated. In this case, the component that was thrown away was the z- coordinate.

Question 11

11. Describe the process of texturing using a cylinder shape.

Answer 11

An (x,y,z) value is converted to cylindrical coordinates of (r, theta, height).

For texture mapping, we are only interested in theta and the height.

To find the color in 2D texture map, theta is converted into an x-coordinate and height is converted into a y- coordinate. This wraps the 2D texture map around the object.

The texture-mapped objects in this image have a cylindrical map shape, and the cylinder’s axis is parallel to the z-axis.

Question 12

12. How is a sphere shape used to map a texture to an object?

Answer 12

• When using a sphere as the map shape, the (x,y,z) value of a point is converted into spherical coordinates.
• For purposes of texture mapping, we keep just the latitude and the longitude information.
• To find the color in the texture map, the latitude is converted into an x-coordinate and the longitude is converted into a y- coordinate.

Question 13

13. Describe the process of spherical mapping.

Answer 13

• The objects have a map shape of a sphere
• The poles of the sphere are parallel to the y- axis. At the object’s “North Pole” and “South Pole”, the squares of the texture map become squeezed into pie-wedge shapes.
• The spherical mapping stretches the squares in the texture map near the equator, and squeezes the squares as the longitude reaches a pole.

Question 14

14. Descibe the use of box shapes for texture mapping an object.

Answer 14

Using a box as the map shape is similar to planar mapping.

Instead of using one texture map, box mapping uses six – one each for the left, right, front, back, top and bottom sides of the object.

To texture map the front and back sides, we eliminate the z-component of an object’s point.

Use the remaining x- and y-components to locate the color in the corresponding texture maps.

Question 15

15. Describe the use of Map shape and Map identity.

Answer 15

Map shape takes an (x,y,z) value from the object and converts this in various ways.

• but what is that value?

The map entity determines what we use as the (x,y,z) value.

Commonly-used map entities are:

1) a point on the object relative to the object’s bounding box,
2) the surface normal at the point being rendered,
3) a vector running from the object’s centroid through the point,
4) the reflection vector at the current point. (Remember that the reflection vector depends not only on the position of the point and its normal, but on the position of the viewer.)

Question 16

16. How are textures layered?

Answer 16

Technique is similar to a weather map on TV. Green Screen..

An example:

We want to place the word “hello” on top of a map of the world. The black background of the “hello” image will be treated as transparent.

To create a pixel in the final image, we find the colors in the corresponding pixel locations in the two input images and combine the two.

Question 17

17. Name an issue with image-based textures and name an alternative way of mapping textures.

Answer 17

• Problem with image‐based textures: they are limited in resolution. When you do a close‐up, you can see the pixels.
• We need another way that we can describe a surface texture.
• What’s important of a texture is that for a given coordinate, we return a value. For image‐based textures, this is implemented as a lookup table. But what if we actually substitute a function?

Procedural Textures!

Question 18

18. What are **procedural textures? **

Answer 18

• Procedural textures are textures that are defined mathematically.

• There are two general types of procedural texture:
– Those that use regular geometric patterns. – Those that use random patterns. (Random Noise)

• Combining these two types can give enhanced realism (e.g. irregular paving slabs, or weathered brickwork).

Question 19

19. Describe 3D texture mapping.

Answer 19

In 3D texture mapping, each point determines its color without the use of an intermediate map shape (Peachey, 1985; Perlin, 1985).

We use the (x,y,z) coordinate to compute the color directly. It’s equivalent to carving an object out of a solid substance.

Most 3D texture functions do not explicitly store a value for each (x, y, z)-coordinate, but use a procedure to compute a value based on the coordinate and thus are called procedural textures. (Algorithm)

Question 20

20. How could a procedural texture create realistic wood?

Answer 20

Making a wood-grained object begins with a three-dimensional texture of concentric rings (Peachey, 1985).

• By using noise to vary the ring shape and the inter-ring distance, we can create reasonably realistic wood.

Question 21

21. What is a random **procedural texture? **

Answer 21

• Usually, the natural look of the rendered result is achieved by the use of:

• fractal noise and
• turbulence functions.
• These functions are used as a numerical representation of the “randomness” found in nature.

Question 22

22. What is **bump mapping? **

Answer 22

• Bump mapping is a lot like texture Mapping. However, where texture mapping added colour to a polygon, bump mapping adds, what appears to be surface roughness.
• Note – the polygon is still flat but it appears to have surface variations.

Question 23

23. How is bump mapping implemented?

Answer 23

• The surface of a 2D texture is flat and therefore the surface normals go straight up.
• Bump mapping evaluates the current light intensity at any given pixel on the texture (texel). It adds “fake” depth by modifying the surface normals rather than the geometry.

Question 24

24. Describe how heightmaps are used for **bump mapping. **

Answer 24

• The most common way to represent bumps is by the height field method. A greyscale texture map is used, where the brightness of each pixel represents how much it sticks out from the surface (black is minimum height, white is maximum height).
• Bump mapping changes the brightness of the pixels on the surface in response to the heightmap that is specified for each surface.

Question 25

25. When **bump mapping,** after texturing, what calulations are performed?

Answer 25

After texturing, a calculation is performed for each pixel on the object's surface: • Look up the position on the **heightmap** that corresponds to the position on the surface. • Calculate the **surface normal** of the **heightmap**. • Add the **surface normal** from step 2 to the **geometric surface norma**l so that the normal points in a new direction. • Calculate the interaction of the new 'bumpy' surface with lights in the scene using, for example, **Phong shading.** • The result is a surface that appears to have real depth. The algorithm also ensures that the surface appearance changes as lights in the scene move around.

Question 26

26. Does **bump mapping** alter an objects geometry?

Answer 26

NO! ## Footnote Bump mapping does not alter an object’s geometry. (This is in contrast to a method known as **displacement mapping** which has a similar effect but does actually alter an object’s geometry (Cook, 1984). Compare the profiles and the shadows cast by these two objects Bump and Displacement.. Displacement alters the gemoetry.

Question 27

27. What is **refelection/environment mapping? **

Answer 27

* The process of reflecting the surrounding environment in a shiny object – it’s a cheap way to create reflections. * Also known as **environment mapping.** * An environment can be viewed as an infinity of light sources and a map can represent any arbitrary geometry of light sources, e.g. striplights are just rectangles of high‐intensity white values in the environment map.

Question 28

28. Describe **Enivronment mapping**.

Answer 28

• When you look at a highly reflective object such as a chrome sphere, what you see is not the object itself but how the object **reflects its environment.** When you gaze at some point on a highly reflective surface, the surface at that point reflects the **view ray**—that is, the ray that travels from your eye to the point on the surface—into the environment. The characteristics of the reflected ray depend on the original view ray and on the **surface normal** at the point where the **view ray** reaches the surface. What you see is not the surface itself but what the environment looks like in the direction of the reflected ray.

Question 29

29. Describe pros and cons of **Environment mapping.**

Answer 29

**Environment mapping** is computationaly cheaper than **raytracing.** It works well when the reflective surface is **planar** or convex. There are no obvious sets of parallel lines in the reflection. In the top example the results from **environment mapping** compare favorably with raytracing, but in the lower example, the reflected lines of the ceiling tiles do not align with the actual ceiling. Its a hack for parallel lines..

Question 30

30. Describe the process of **Environment Mapping.**

Answer 30

* The **"environment"** or synthetic world in which our reflective model is to be placed must first be rendered (or captured and digitized) as viewed from the desired position of our reflective model. This is done by rendering six images in the directions of Sky, Floor, North, South, East, and West. * The object is surrounded by a closed three dimensional surface onto which the environment is projected. Reflected rays are traced from the object, hit the surface and then index onto the **map.**

Question 31

31. Show a **cube mapped reflection. **

Answer 31

• A diagram depicting an apparent reflection being provided by cube mapped reflection. The map is actually projected onto the surface from the point of view of the **observer**. Highlights which in **raytracing** would be provided by tracing the ray and determining the angle made with the normal, can be 'fudged’.

Question 32

32. Describe **Displacement** mapping.

Answer 32

* In **displacement mapping**, the surface is actually modified, in contrast to bump mapping where only the surface normal is modified. * **displacement mapped** surfaces will show the effect even at the silhouette.