1. Game Programming (Mapping)
2014. Spring

9. Texture Mapping The problem Solution
Colors, normals, etc. are only specified at vertices.
How do we add detail between vertices?
Solution
Specify the details in an image (the texture) and specify how to apply the image to the geometry (the map)
Works for shading parameters other than color, as we shall see
The basic underlying idea is the mapping

10. Basic Mapping The texture lives in a 2D space
Parameterize points in the texture with 2 coordinates: (s,t)
These are just what we would call (x,y) if we were talking about an image, but we wish to avoid confusion with the world (x,y,z)
Define the mapping from (x,y,z) in world space to (s,t) in texture space
With polygons:
Specify (s,t) coordinates at vertices
Interpolate (s,t) for other points based on given vertices

11. Basic Mapping

12. I assume you recall… Texture sampling (aliasing) is a big problem d v
Mipmaps and other filtering techniques are the solution u v d

13. I assume you recall…
GL_NEAREST
GL_LINEAR
Mipmappping

14. I assume you recall…
The texture value for points that map outside the texture image can be generated in various ways
Repeat, Clamp, …
Width and height of texture images is constrained (powers of two, sometimes must be square)
Wrap S : GL_CLAMP Wrap T : GL_CLAMP
Wrap S : GL_CLAMP Wrap T : GL_REPEAT
Wrap S : GL_REPEAT Wrap T : GL_CLAMP
Wrap S : GL_REPEAT
Wrap T : GL_REPEAT

15. Textures in Games
The game engine provides some amount of texture support
Artists are supplied with tools to exploit this support
They design the texture images
They specify how to apply the image to the object
Commonly, textures are supplied at varying resolutions to support different hardware performance
Note that the texture mapping code does not need to be changed - just load different sized maps at run time
Textures are, without doubt, the most important part of a game’s look

16. Example Texture Tool

17. Standard Pipeline

18. Multitexturing Bump skin + Key-frame model WOW! geometry Result
Some effects are easier to implement if multiple textures can be applied
Future lectures: Light maps, bump maps, shadows, …
Key-frame
model
geometry
Decal skin
Bump skin
Gloss skin
WOW!
Result +

19. Packing Textures Problem Solution
The limits on texture width/height make it inefficient to store many textures
For example: long, thin objects
Solution
Artists pack the textures for many objects into one image
The texture coordinates for a given object may only index into a small part of the image
Care must be taken at the boundary between sub-images to achieve correct blending
Mipmapping is restricted

20. Combining Textures

21. Texture Matrix
Normally, the texture coordinates given at vertices are interpolated and directly used to index the texture
The texture matrix applies a homogeneous transform to the texture coordinates before indexing the texture
What use is this?

22. Animating Texture (method 1)
Loading a texture onto the graphics card is very expensive
But once there, the texture matrix can be used to “transform” the texture
For example, changing the translation can select different parts of the texture
If the texture matrix is changed from frame to frame, the texture will appear to move on the object
This is particularly useful for things like flame, or swirling vortices, or pulsing entrances, …

23. Projective Texturing
The texture should appear to be projected onto the scene, as if from a slide projector
Solution:
Equate texture coordinates with world coordinates
Think about it from the projector’s point of view: wherever a world point appears in the projector’s view, it should pick up the texture
Use a texture matrix equivalent to the projection matrix for the projector – maps world points into texture image points
Details available in many places

24. Environment Mapping Environment Map Viewer Reflected ray Object
Environment mapping produces reflections on shiny objects
Texture is transferred in the direction of the reflected ray from the environment map onto the object
Reflected ray: R=2(N·V)N-V
What is in the map?
Environment Map
Viewer
Reflected ray
Object

25. Environment Maps The environment map may take one of several forms:
Cubic mapping
Spherical mapping (two variants)
Parabolic mapping
Describes the shape of the surface on which the map “resides”
Determines how the map is generated and how it is indexed
What are some of the issues in choosing the map?

26. Environment Mapping
Cube mapping is the norm nowadays
eye x y z n

27. Need For Speed Underground
Environment Mapping
Need For Speed Underground
Far Cry

28. Light Maps
Speed up lighting calculations by pre-computing lighting and storing it in maps
Allows complex illumination models to be used in generating the map (eg shadows, radiosity)
Used in complex rendering algorithms (Radiance), not just games
Issues:
How is the mapping determined?
How are the maps generated?
How are they applied at run-time?

29. Example
Call of duty

30. Example Nearest interpolation Linear interpolation
What type of lighting (diffuse, specular, reflections) can the map store?

31. Example
No light maps
With light maps

32. Applying Light Maps Actually, make points darker with light map
Use multi-texturing hardware
First stage: Apply color texture map
Second stage: Modulate with light map
Actually, make points darker with light map
DirectX allows you to make points brighter with texture

33. Fog Maps Dynamic modification of light-maps
Put fog objects into the scene
Compute where they intersect with geometry and paint the fog density into a dynamic light map
Use same mapping as static light map uses
Apply the fog map as with a light map
Extra texture stage

34. Fog Map Example

35. Stores heights: can derive normals
Bump Mapping
Texture values perturb surface normals
Bump map
Stores heights: can derive normals +
Bump mapped geometry =
geometry

36. Dot Product bump mapping
Store normal vectors in the bump map
Apply the bump map using the dot3 operator
Takes a dot product

37. Normal Mapping
DOOM 3
James Hastings-Trew

38. Environment Bump Mapping
Perturb the environment map lookup directions with the bump map
Nvidia
Far Cry

39. Displacement Mapping Normal Mapping Problem Displacement Mapping
Doesn’t take into account geometric surface depth
Does not exhibit parallax
No self-shadowing of the surface
Coarse silhouettes expose the actual geometry being drawn
Displacement Mapping
Displace actual positions from Heightfield Map

40. Displacement Mapping (Result)
Displacement Offset

41. Billboards
Billboards are texture-mapped polygons, typically used for things like trees
Image-based rendering method where complex geometry (the tree) is replaced with an image placed in the scene (the textured polygon)
The texture has alpha values associated with it: 1 where the tree is, and 0 where it isn’t
So you can see through the polygon in places where the tree isn’t

42. Planar Reflections (Flat Mirrors)
Use the stencil buffer, color buffer and depth buffer
Basic idea:
We need to draw all the stuff around the mirror
We need to draw the stuff in the mirror, reflected, without drawing over the things around the mirror
Key point: You can reflect the viewpoint about the mirror to see what is seen in the mirror, or you can reflect the world about the mirror

43. Reflecting Objects
If the mirror passes through the origin, and is aligned with a coordinate axis, then just negate appropriate coordinate
Otherwise, transform into mirror space, reflect, transform back
Wall
Mirror

44. Reflection Example The stencil buffer after the second pass
The color buffer after the second pass – the reflected scene cleared outside the stencil

45. Reflection Example
The color buffer after the final pass

46. So what game did you play recently ?

47. Why Shadows?
Shadows tell us about the relative locations and motions of objects

48. Facts about Shadows
Shadows can be considered as areas hidden from the light source
Suggests the use of hidden surface algorithms
For scenes with static lights and geometry, the shadows are fixed
Can pre-process such cases
Cost is in moving lights or objects
Point lights have hard edges, and area lights have soft edges

49. Ground Plane Shadows
Shadows cast by point light sources onto planes are an important case that is relatively easy to compute
Shadows cast by objects (cars, players) onto the ground
Accurate if shadows don’t overlap
Can be fixed, but not well
L(directional light)
(xp,yp,zp)
(xsw,ysw,zsw)

50. Shadows in Light Maps
Static shadows can be incorporated into light maps
When creating the map, test for shadows by ray-casting to the light source - quite efficient
Area light sources should cast soft shadows
Interpolating the texture will give soft shadows, but not good ones, and you loose hard shadows
Sampling the light will give better results: Cast multiple rays to different points on the area light, and average the results
Should still filter for best results

51. Soft Shadow Example

52. Shadows in Games
Megaman
Grand Theft Auto
Metal Gear

53. Projective Shadows
Create a texture (dark on white) representing the appearance of the occluder as seen by the light
Game programmers frequently call this a shadow map
Can create it by “render to texture” with the light as viewpoint
Use projective texturing to apply it to receivers
Works if the appearance of the occluder from the light is reasonably constant
Requires work to identify occluders and receivers

54. Shadow Volumes
A shadow volume for an object and light is the volume of space that is shadowed
That is, all points in the volume are in shadow for that light/object pair
Creating the volume:
Find silhouette edges of shadowing object as seen by the light source
Extrude these edges away from the light, forming polygons
Clip the polygons to the view volume

57. Shadow Volumes

58. Shadow Volume