# GR2 Advanced Computer Graphics AGR

## Presentation on theme: "GR2 Advanced Computer Graphics AGR"— Presentation transcript:

Reflection 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...

Phong Reflection Model
light source N R eye L V surface I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*() / dist dist = distance attenuation factor In practice, we evaluate IRED, IGREEN, IBLUE for red, green, blue intensities: IRED= KaREDIaRED + ( KdRED( L . N ) + Ks( R . V )n ) I*RED/dist Note: R.V calculation replaced by H.N for speed - H = (L+V)/2

Phong 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

Viewing Polygons We have also seen how a 3D polygon can be projected to screen space via a sequence of transformations This lecture looks at how we shade the polygon, using our reflection model

light viewer 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

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

Polygonal Models Recall that we use polygonal models to approximate curved surfaces Constant shading will emphasise this approximation because each facet will be constant shaded, with sudden change from facet to facet

Gouraud Shading Gouraud shading attempts to smooth out the shading across the polygon facets Begin by calculating the normal at each vertex N

Gouraud Shading N A feasible way to do this is by averaging the normals from surrounding facets Then apply the reflection model to calculate intensities at each vertex

Gouraud Shading We use linear interpolation to calculate intensity at edge intersection P IPRED = (1-)IP1RED + IP2RED where P divides P1P2 in the ratio 1- Similarly for Q P4 P2 P1 P3 P Q

Gouraud Shading Then we do further linear interpolation to calculate colour of pixels on scanline PQ P2 P1 P3 P Q

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

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 banding

Phong Shading N Phong shading has a similar first step, in that vertex normals are calculated - typically as average of normals of surrounding faces

Phong 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

Phong 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

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

Gouraud versus Phong

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 P3 P2 Q P P1 P4

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

Wall Lights

Wall Lights with Fewer Polygons

Final Note on Normals If a sharp polygon boundary is required, we calculate two vertex normals for each side of the joint NLEFT NRIGHT

Further Study There are excellent illustrations of Gouraud and Phong shading at a number of Web sites Please go to: and follow the link to Resources

Acknowledgements Thanks again to Alan Watt for the images
The following sequence is the famous Shutterbug from Foley et al

Simple Shading - Without Taking Account of Normals