Coordinate Systems

1
Coordinate Systems
Coordinate Systems (conventional
Cartesianreference system)
Y
Z
Y
X
Z
X
2
Transformations

• Transformation occurs about the origin of the
  coordinate systems axis

Scale
Translate
Rotate
3
Order of Transformations Make a Difference
Rotate about Z 45 Translate along X 1
Box centered at origin
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
The Camera
Parallel Projection
Perspective Projection
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Rendering Pipeline

• Hardware

Modelling
Transform
Visibility
Illumination Shading
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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
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Approximating Curved Surfaces with Flat Polygons
Flat Shading each polygon face has a normal
that is used to perform lighting calculations.
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Gouraud Shading

• Compute vertex normals by averaging face normals.
• Compute intensity at each vertex.

I1
Raster Scan line
I1,2
I1,3
I1,2,3,4
I3
I2
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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)
• well review the important models

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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
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 offto zero
here)
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Light Effects

• Usually only considering reflected part

Light
reflected
specular
Light
absorbed
ambient
diffuse
transmitted
Lightrefl.absorbedtrans.
Lightambientdiffusespecular
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Ambient Light

• is the light in the environment evenly reaching
  all surfaces from all directions
• light location doesnt matter
• eye position doesnt matter

• IA ambient light
• ka materials ambient reflection coefficient

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Ambient Light

• IA ambient light
• ka materials ambient reflection coefficient
• Models general level of brightness in the scene
• Accounts for light effects that are difficult to
  compute (secondary diffuse reflections, etc)

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Ambient Light Example
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Diffuse Light

• Light absorbed by the surface and then reflected
  equally to all directions
• Models dullness, roughness of a surface

Light
Lamberts Law(perfectly diffusesurface)
N
L
f

• Id intensity of light source
• kd materials diffuse reflection coefficient
• N normal vector (normalized)
• L light source vector (normalized)

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Diffuse Light
22
Diffuse Lighting Example
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Specular Light

• Light that is reflected from the surface
  unequally to all directions
• Models reflections on shiny surfaces

Phongs Law
Light
N
Eye
R
L
f
f
a
R
R
R
nsmall
nlarge
ninf.
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Specular light example
25
Specular light calculation

• The effect of n in the phong model

n 10
n 90
n 30
n 270
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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

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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.

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Flat and Smooth Shading

• Getting smooth Curvature interpolation

Gouraud Shading
Flat Shading
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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.

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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

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Gouraud shading
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Phong shading
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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

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Phong Shading

• Gouraud Shading

Phong Shading
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Specular
Large n
Small n
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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
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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?

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Option Varieties of projections
41
Texture Mapping

• Steps
• Define texture
• Specify mapping from texture to surface
• Lookup texture values during scan conversion

(0,1)
y
(1,0)
t
v
u
x
s
(0,0)
Modeling Coordinate System
Image Coordinate System
Texture Coordinate System
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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)
y
(1,0)
t
v
u
x
s
(0,0)
Modeling Coordinate System
Image Coordinate System
Texture Coordinate System
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Texture Mapping

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

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Texture Filtering

• Aliasing is a problem

Area filtering
Point sampling
Angel Figure 9.5
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Texture Filtering

• Size of filter depends on projective warp
• Can prefiltering images

Magnification
Minification
Angel Figure 9.14
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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

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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
• ...

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Bump Mapping

• Modifies the direction of the surface normal.

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Texture and Bump Mapping

• Diffuse and normal remapping

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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.

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Programmable Shaders

• Vertex Shader - Small Vertex program that can
  modify the vertex between submission to the
  pipeline and rendering

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Programmable Shaders

• Vertex Shader - Small program that can
• modify every vertex before rendering
• 3 examples
• Renderman (software-based, non real-time),
• Microsofts DirectX (GPU real time)
• Nvidias Cg (GPU real time)
• http//www.nzone.com/object/nzone_luna_videos.html