Coordinate Systems
Coordinate Systems
(conventional Cartesian
reference system)
Y
Z
X
Z
Y
X
Transformations
 Transformation occurs
about the origin of the
coordinate system’s axis
Rotate
Translate
Scale
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
Hierarchy of Coordinate Systems
Local coordinate system
 Also called:
– Scene graphs
– Tree structures
The Camera
Near Clipping
Plane
Projection Plane
Far Clipping
Plane
View Volume
The Camera
Parallel Projection
Perspective Projection
Rendering Pipeline
Hardware
Modelling
Transform
Visibility
Illumination +
Shading
Perception,
Interaction
Color
Texture/
Realism
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
Approximating Curved Surfaces
with Flat Polygons
Flat Shading – each
polygon face has a
normal that is used to
perform lighting
calculations.
Gouraud Shading
 Compute vertex normals
by averaging face
normals.
 Compute intensity at each
vertex.
I1
I1,2
I1,2,3,4
I1,3
Raster
Scan line
I3
I2
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
Illumination / Shading
– global illumination:
• ray tracing + radiosity
– mapping and other techniques
• texture maps, bump maps, reflection maps,
transparency, anti-aliasing, shadows
ray tracing
radiosity
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
Local Illumination
 Local vs. global illumination models
– global - illuminates the whole scene
• typically makes use of local illumination
model
• incorporates inter-reflectance of objects
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
Penumbra angle
(light starts to drop off
to zero here)
Light Effects
 Usually only considering
reflected
Light
reflected part
specular
Light
absorbed
ambient
diffuse
transmitted
Light=refl.+absorbed+trans.
Light=ambient+diffuse+specular
I  ka I a  kd I d  k s I s
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
I  ka I a
 ka: material’s ambient reflection coefficient
Ambient Light
 IA: ambient light
I  ka I a
 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)
Ambient Light Example
Diffuse Light
 Light absorbed by the surface and then reflected
equally to all directions
 Models dullness, roughness of a surface
Lambert’s Law:
(perfectly diffuse
surface)
I  k d I d cos 
 kd I d N  L 
 Id: intensity of light source
Light
N
f
 kd: material’s diffuse reflection coefficient
 N: normal vector (normalized)
 L: light source vector (normalized)
L
Diffuse Light
Diffuse Lighting Example
Specular Light
 Light that is reflected from the surface unequally
to all directions
 Models reflections on shiny surfaces
Phong’s Law:
I  k s I s cos 
Eye
n
 k d I d E  R 

n
R
R
R
n=inf.
R
n=large
n=small
N
ff
Light
L
Specular light example
Specular light calculation
 The effect of ‘n’ in the phong model
n = 10
n = 90
n = 30
n = 270
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
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.
Flat and Smooth Shading
Getting smooth Curvature : interpolation
Flat Shading
Gouraud Shading
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.
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
Gouraud shading
Phong shading
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
Phong Shading
Gouraud Shading
Phong Shading
Specular
Small n
Large n
Textures
 Images (textures) applied to polygons (models) to enhance
the visual effect of a scene
Texture
Surface
Image
Angel Figure 9.3
Surface Textures
 Add visual detail to surfaces of 3D objects
With surface texture
Polygonal model
Surface Textures
 Add visual detail to surfaces of 3D objects
Parameterization
+
geometry
=
image
texture map
• Q: How do we decide where on the geometry
each color from the image should go?
Option: Varieties of projections
Texture Mapping
 Steps:
– Define texture
– Specify mapping from texture to surface
– Lookup texture values during scan conversion
(0,1)
t
(1,0)
v
s
Texture
Coordinate
System
(0,0)
u
Modeling
Coordinate
System
y
x
Image
Coordinate
System
Texture Mapping
 When scan convert, map from …
– image coordinate system (x,y) to
– modeling coordinate system
(u,v) to
(1,1)
– texture image (t,s)(0,1)
t
(1,0)
v
s
Texture
Coordinate
System
(0,0)
u
Modeling
Coordinate
System
y
x
Image
Coordinate
System
Texture Mapping
– Interpolate texture coordinates down/across scan lines
– U,V mapping can be arbitrary and manipulated
– Distortion due to interpolation approximation
Texture Filtering
 Aliasing is a problem
Point sampling
Area filtering
Angel Figure 9.5
Texture Filtering
 Size of filter depends on projective warp
– Can prefiltering images
Magnification
Minification
Angel Figure 9.14
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
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
 ...
Bump Mapping
 Modifies the direction of the surface normal.
Texture and Bump Mapping
 Diffuse and normal remapping
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.
Programmable Shaders
 Vertex Shader - Small Vertex program that can modify the
vertex between submission to the pipeline and rendering
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)
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