1. (conventional Cartesian reference system)
Coordinate Systems
Coordinate Systems
(conventional Cartesian reference system) Y Z Y X Z X

2. Transformations
Transformation occurs about the origin of the coordinate system’s axis
Scale
Translate
Rotate

3. Order of Transformations Make a Difference
Box centered at
origin
Rotate about Z 45; Translate along X 1
Translate along X 1;
Rotate about Z 45

4. Hierarchy of Coordinate Systems
Local coordinate system
Also called:
Scene graphs
Tree structures

5. The Camera Near Clipping Plane Far Clipping Plane Projection Plane
View Volume

6. Perspective Projection
The Camera
Parallel Projection
Perspective Projection

7. Rendering Pipeline Hardware Modelling Transform Visibility
Illumination + Shading
Color
Perception, Interaction
Texture/ Realism

8. Polygons, Meshes & Scan Conversion - In scan line rendering (the most common): Each polygon is calculated along each scan line. From the top scan line to the bottom of a frame in the 2D projection plane. V1
Raster
Scan line V3 V2

9. Approximating Curved Surfaces with Flat Polygons
Flat Shading – each polygon face has a normal that is used to perform lighting calculations.

10. Gouraud Shading Compute vertex normals by averaging face normals.
Compute intensity at each vertex. I1
Raster
Scan line
I1,2
I1,2,3,4
I1,3 I3 I2

11. Illumination / Shading
Distinction between illumination and shading models
illumination - calculate intensity at a point on surface
shading - uses calculated intensities to shade polygons (uses illumination models)
we’ll review the important models

12. Illumination / Shading
global illumination:
ray tracing + radiosity
mapping and other techniques
texture maps, bump maps, reflection maps, transparency, anti-aliasing, shadows
ray tracing radiosity

13. Local Illumination Local vs. global illumination models
local (typically) - how is one point of the scene illuminated directly by the light source
is light source only source of illumination?
Simple models lump the rest into a single ambient term
do not account for reflections within the environment

14. Local Illumination Local vs. global illumination models
global - illuminates the whole scene
typically makes use of local illumination model
incorporates inter-reflectance of objects

15. (light starts to drop off to zero here)
Lighting Types
Ambient – basic, even illumination of all objects in a scene
Directional – all light rays are in parallel in 1 direction - like the sun
Point – all light rays emanate from a central point in all directions – like a light bulb
Spot – point light with a limited cone and a fall-off in intensity – like a flashlight
Cone angle
Penumbra angle
(light starts to drop off to zero here)

16. Light Effects Usually only considering reflected part Light Light
specular
Light
absorbed
ambient
diffuse
transmitted
Light=refl.+absorbed+trans.
Light=ambient+diffuse+specular

17. Ambient Light
is the light in the environment evenly reaching all surfaces from all directions
light location doesn’t matter
eye position doesn’t matter
IA: ambient light
ka: material’s ambient reflection coefficient

18. Ambient Light IA: ambient light
ka: material’s ambient reflection coefficient
Models general level of brightness in the scene
Accounts for light effects that are difficult to compute (secondary diffuse reflections, etc)

19. Ambient Light Example

20. Lambert’s Law: (perfectly diffuse surface)
Diffuse Light
Light absorbed by the surface and then reflected equally to all directions
Models dullness, roughness of a surface
Light
Lambert’s Law: (perfectly diffuse surface) N f L
Id: intensity of light source
kd: material’s diffuse reflection coefficient
N: normal vector (normalized)
L: light source vector (normalized)

21. Diffuse Light

22. Diffuse Lighting Example

23. Specular Light
Light that is reflected from the surface unequally to all directions
Models reflections on shiny surfaces
Phong’s Law:
Light N
Eye R f f L a R R R
n=small
n=inf.
n=large

24. Specular light example

25. Specular light calculation
The effect of ‘n’ in the phong model
n = 10
n = 90
n = 30
n = 270

26. Shading a Polygon
Illumination Model: determine the color of a surface (data) point by simulating some light attributes.
Local IM: deals only with isolated surface (data) point and direct light sources.
Global IM: takes into account the relationships between all surfaces (points) in the environment.
Shading Model: applies the illumination models at a set of points and colors the whole scene.
Texture Mapping: remappes and avgs. any value above (diffuse) from a 2d picture or map

27. Shading a Polyhedra Flat (facet) shading:
Works well for objects
really made of flat faces.
Appearance depends on
number of polygons for
curved surface objects.
If polyhedral model is an approximation then need to smooth.

28. Flat and Smooth Shading
Getting smooth Curvature : interpolation
Flat Shading
Gouraud Shading

29. Flat Shading
Polygon meshes approximate smooth curved surfaces with planar facets. Using the previous methods does not generate an illusion of smooth curved surface. N1 N2
Reason: discontinuity of the normal vectors.

30. Gouraud Shading Assign vertex the normal of the smooth surface. Or
Average the normal of all neighboring polygons N N1 N2
Interpolate colors along edges and scan-lines

31. Gouraud shading

32. Phong shading

33. Phong Shading
Gouraud Shading does not properly handle specular highlights.
Reason: Colors are interpolated
Solution:
Compute averaged normal at vertices (Gouraud)
Interpolate normals along edges and scan lines!
Apply illumination model at every pixel

34. Phong Shading
Gouraud Shading
Phong Shading

35. Specular
Small n
Large n

36. Textures
Images (textures) applied to polygons (models) to enhance the visual effect of a scene
Texture
Surface
Image
Angel Figure 9.3

37. Surface Textures Add visual detail to surfaces of 3D objects
With surface texture
Polygonal model

38. Surface Textures
Add visual detail to surfaces of 3D objects

39. + = Parameterization geometry image texture map
Q: How do we decide where on the geometry each color from the image should go?

40. Option: Varieties of projections

41. Texture Mapping Steps: Define texture
Specify mapping from texture to surface
Lookup texture values during scan conversion
(0,1) t
(1,0) y v u x s
(0,0)
Texture
Coordinate
System
Modeling
Coordinate
System
Image
Coordinate
System

42. Texture Mapping When scan convert, map from …
image coordinate system (x,y) to
modeling coordinate system (u,v) to
texture image (t,s)
(1,1)
(0,1) t
(1,0) y v u x s
(0,0)
Texture
Coordinate
System
Modeling
Coordinate
System
Image
Coordinate
System

43. Texture Mapping Interpolate texture coordinates down/across scan lines
U,V mapping can be arbitrary and manipulated
Distortion due to interpolation approximation

44. Texture Filtering Aliasing is a problem Area filtering Point sampling
Angel Figure 9.5

45. Texture Filtering Size of filter depends on projective warp
Can prefiltering images
Magnification
Minification
Angel Figure 9.14

46. Mip Maps Keep textures prefiltered at multiple resolutions
For each pixel, linearly interpolate between two closest levels (e.g., trilinear filtering)
Fast, easy for hardware

47. What is a Texture?
MAP surface detail from a predefined (easy table (“texture”) to a simple polygon
Color
Specular ‘color’ (environment map)
Normal vector deviation (bumpmap)
displacement mapping
transparency
...

48. Bump Mapping
Modifies the direction of the surface normal.

49. Texture and Bump Mapping
Diffuse and normal remapping

50. Displacement Mapping
Modifies the surface position in the direction of the surface normal.
the actual geometric position of points over the textured surface are displaced along the surface normal according to the values stored into the texture.

51. Programmable Shaders
Vertex Shader - Small Vertex program that can modify the vertex between submission to the pipeline and rendering

52. Programmable Shaders Vertex Shader - Small program that can
modify every vertex before rendering
3 examples:
Renderman (software-based, non real-time),
Microsoft’s DirectX (GPU real time)
Nvidia’s Cg (GPU real time)