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SI23Introduction to Computer
Graphics
SI23Introduction to Computer
Graphics
Lecture 14 – Polygon Shading Techniques
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Reflection ModelsReflection Models
We have seen how the reflected intensity at a point may be calculated
A reminder of the Phong reflection model...
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Phong Reflection ModelPhong Reflection Model
lightsourceN
LR
Veye
surface
I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*() / dist
In practice, we evaluate IRED, IGREEN, IBLUE for red, green, blue intensities:IRED= Ka
REDIaRED + ( Kd
RED( L . N ) + Ks( R . V )n ) I*RED/dist
dist = distance attenuation factor
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Phong Reflection ModelPhong Reflection Model
Remember calculation depends on:– surface normal at a point– light source intensity and position– material properties– viewer position
L.N and R.V constant if L, V taken to be far away
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Viewing PolygonsViewing Polygons
We have also seen how a 3D polygon can be projected to screen space via a sequence of transformations
This lecture looksat how we shade the polygon, usingour reflection model
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Constant (or Flat) ShadingConstant (or Flat) Shading
Calculate normal (how?)
Assume L.N and R.V constant (light & viewer at infinity)
Calculate IRED, IGREEN, IBLUE using Phong reflection model
Project vertices to viewplane
Use scan line conversion to fill polygon
N
lightviewer
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2D Graphics - Filling a Polygon
2D Graphics - Filling a Polygon
Scan line methods used to fill 2D polygons with a constant colour– find ymin, ymax of vertices– from ymin to ymax do:– find intersection with
polygon edges– fill in pixels between
intersections using specified colour
– See lecture 6 for details of algorithm with edge tables etc
See alsoHearn&Baker, Ch 3
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Polygonal ModelsPolygonal Models
Recall that we use polygonal models to approximate curved surfaces
Constant shading will emphasise this approximation becauseeach facet will be constant shaded, with sudden change fromfacet to facet
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Flat ShadingFlat Shading
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Gouraud ShadingGouraud Shading
Gouraud shading attempts to smooth out the shading across the polygon facets
Begin by calculating the normal at each vertex
N
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Gouraud ShadingGouraud Shading
A feasible way to do this is by averagingaveraging the normals from surrounding facets
Then apply the reflection model to calculate intensitiesintensities at each vertex
N
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Gouraud ShadingGouraud Shading
We use linear linear interpolation interpolation to calculate intensity at edge intersection P
IPRED = (1-IP1
RED + IP2
RED
where P divides P1P2 in the ratio
Similarly for Q
P4
P2
P1
P3
PQ
1-
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Gouraud ShadingGouraud Shading
Then we do further linear interpolation to calculate colour of pixels on scanline PQ
P2
P1
P3
PQ
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Gouraud ShadingGouraud Shading
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Henri GouraudHenri Gouraud
Henri Gouraud is another pioneering figure in computer graphics
http://www.univ-reims.fr/Labos/LERI/Afig99/biographie.html
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Gouraud Shading Limitations - Specular
Highlights
Gouraud Shading Limitations - Specular
Highlights
Gouraud shading gives intensities within a polygon which are a weighted average of the intensities at vertices– a specular highlight at a vertex
tends to be smoothed out over a larger area than it should cover
– a specular highlight in the middle of a polygon will never be shown
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Gouraud Shading Limitations - Mach Bands
Gouraud Shading Limitations - Mach Bands
The rate of change of pixel intensity is even across any polygon, but changes as boundaries are crossed
This ‘discontinuity’ is accentuated by the human visual system, so that we see either light or dark lines at the polygon edges - known as Mach bandingMach banding
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Phong ShadingPhong Shading
Phong shading has a similar first step, in that vertex normals are calculated - typically as average of normals of surrounding faces
N
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Phong ShadingPhong Shading
However rather than calculate intensity at vertices and then interpolate intensities as we do in Gouraud shading ...
In Phong shading we interpolate normals at each pixel ...
P4
P2
P1
P3
P Q
N2
N1
N
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Phong ShadingPhong Shading
... and apply the reflection model at each pixel to calculate the intensity - IRED, IGREEN, IBLUE
P4
P2
P1
P3
P Q
N2
N1
N
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Phong ShadingPhong Shading
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Phong versus Gouraud Shading
Phong versus Gouraud Shading
A major advantage of Phong shading over Gouraud is that specular highlights tend to be much more accurate– vertex highlight is much sharper– a highlight can occur within a polygon
Also Mach banding greatly reduced The cost is a substantial increase in
processing time because reflection model applied per pixel
But there are limitations to both Gouraud and Phong
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Gouraud versus PhongGouraud versus Phong
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Interpolated Shading Limitations - Perspective
Effects
Interpolated Shading Limitations - Perspective
Effects
Anomalies occur because interpolation is carried out in screen space, after the perspective transformation
Suppose P2 much more distant than P1. P is midway in screen space so gets 50 : 50 intensity (Gouraud) or normal (Phong)
... but in world coordinates it is much nearer P1 than P2
P4
P2
P1
P3
PQ
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Interpolated Shading Limitations - Averaging
Normals
Interpolated Shading Limitations - Averaging
Normals
Averaging the normals of adjacent faces usually works reasonably well
But beware corrugated surfaces where the averaging unduly smooths out the surface
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Wall LightsWall Lights
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Wall Lights with Fewer Polygons
Wall Lights with Fewer Polygons
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Final Note on NormalsFinal Note on Normals
If a sharp polygon boundary is required, we calculate two vertex normals for each side of the joint
NLEFT NRIGHT
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Simple Shading -Without Taking Account of
Normals
Simple Shading -Without Taking Account of
Normals
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Constant or Flat Shading -Each Polygon has Constant
Shade
Constant or Flat Shading -Each Polygon has Constant
Shade
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Gouraud ShadingGouraud Shading
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Phong ShadingPhong Shading
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Phong Shading with Curved Surfaces
Phong Shading with Curved Surfaces
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Better Illumination ModelBetter Illumination Model
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Further StudyFurther Study
Hearn and Baker, section 14-5 Think about the relative
computational costs of flat, Gouraud and Phong
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AcknowledgementsAcknowledgements
Thanks again to Alan Watt for the images
The following sequence is the famous Shutterbug from Foley et al