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GR2Advanced Computer

GraphicsAGR

GR2Advanced Computer

GraphicsAGR

Lecture 7Polygon Shading Techniques

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Reflection ModelsReflection Models

We have seen how the reflected intensity at a point may be calculated– either by the Phong model or the

physically based Cook and Torrance model

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

Note: R.V calculation replaced by H.N for speed - H = (L+V)/2

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 H.N 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

Use scan line conversion to fill polygon

N

lightviewer

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2D Graphics - Revision!2D Graphics - Revision!

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

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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

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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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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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Further StudyFurther Study

There are excellent illustrations of Gouraud and Phong shading at a number of Web sites

Please go to:http://www.scs.leeds.ac.uk/kwb/

GR2and follow the link to Resources

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AcknowledgementsAcknowledgements

Thanks again to Alan Watt for the images

The following sequence is the famous Shutterbug from Foley et al

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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