7.1 si31_2001 SI31 Advanced Computer Graphics AGR Lecture 7 Polygon Shading Techniques

7.2 si31_2001 Reflection Models n 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 n A reminder of the Phong reflection model...

7.3 si31_2001 Phong Reflection Model light source N L R V eye surface I( ) = K a ( )I a ( ) + ( K d ( )( L. N ) + K s ( R. V ) n ) I*( ) / dist In practice, we evaluate I RED, I GREEN, I BLUE for red, green, blue intensities: I RED = K a RED I a RED + ( K d RED ( L. N ) + K s ( R. V ) n ) I* RED /dist Note: R.V calculation replaced by H.N for speed - H = (L+V)/2 dist = distance attenuation factor

7.4 si31_2001 Phong Reflection Model n Remember calculation depends on: – surface normal at a point – light source intensity and position – material properties – viewer position n L.N and H.N constant if L, V taken to be far away

7.5 si31_2001 Viewing Polygons n 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

7.6 si31_2001 Constant (or Flat) Shading n Calculate normal (how?) n Assume L.N and R.V constant (light & viewer at infinity) n Calculate I RED, I GREEN, I BLUE using Phong reflection model n Use scan line conversion to fill polygon N light viewer

7.7 si31_2001 2D Graphics - Filling a Polygon n 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: Hearn&Baker, Ch 3 - or try applet at: ~chinkw/FillPoly

7.8 si31_2001 Polygonal Models n 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

7.9 si31_2001 Flat Shading

7.10 si31_2001 Gouraud Shading n Gouraud shading attempts to smooth out the shading across the polygon facets n Begin by calculating the normal at each vertex N

7.11 si31_2001 Gouraud Shading averaging n A feasible way to do this is by averaging the normals from surrounding facets intensities n Then apply the reflection model to calculate intensities at each vertex N

7.12 si31_2001 Gouraud Shading linear interpolation n We use linear interpolation to calculate intensity at edge intersection P I P RED = (1- I P1 RED + I P2 RED where P divides P1P2 in the ratio n Similarly for Q P4 P2 P1 P3 P Q 1-

7.13 si31_2001 Gouraud Shading n Then we do further linear interpolation to calculate colour of pixels on scanline PQ P2 P1 P3 P Q

7.14 si31_2001 Gouraud Shading

7.15 si31_2001 Gouraud Shading Limitations - Specular Highlights n 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

7.16 si31_2001 Gouraud Shading Limitations - Mach Bands n The rate of change of pixel intensity is even across any polygon, but changes as boundaries are crossed Mach banding n 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

7.17 si31_2001 Phong Shading n Phong shading has a similar first step, in that vertex normals are calculated - typically as average of normals of surrounding faces N

7.18 si31_2001 Phong Shading n However rather than calculate intensity at vertices and then interpolate intensities as we do in Gouraud shading... n In Phong shading we interpolate normals at each pixel... P4 P2 P1 P3 P Q N2 N1 N

7.19 si31_2001 Phong Shading n... and apply the reflection model at each pixel to calculate the intensity - I RED, I GREEN, I BLUE P4 P2 P1 P3 P Q N2 N1 N

7.20 si31_2001 Phong Shading

7.21 si31_2001 Phong versus Gouraud Shading 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 n Also Mach banding greatly reduced n The cost is a substantial increase in processing time because reflection model applied per pixel n But there are limitations to both Gouraud and Phong

7.22 si31_2001 Gouraud versus Phong

7.23 si31_2001 Interpolated Shading Limitations - Perspective Effects n Anomalies occur because interpolation is carried out in screen space, after the perspective transformation n Suppose P2 much more distant than P1. P is midway in screen space so gets 50 : 50 intensity (Gouraud) or normal (Phong) n... but in world coordinates it is much nearer P1 than P2 P4 P2 P1 P3 P Q

7.24 si31_2001 Interpolated Shading Limitations - Averaging Normals n Averaging the normals of adjacent faces usually works reasonably well n But beware corrugated surfaces where the averaging unduly smooths out the surface

7.25 si31_2001 Wall Lights

7.26 si31_2001 Wall Lights with Fewer Polygons

7.27 si31_2001 Final Note on Normals n If a sharp polygon boundary is required, we calculate two vertex normals for each side of the joint N LEFT N RIGHT

7.28 si31_2001 Simple Shading - Without Taking Account of Normals

7.29 si31_2001 Constant or Flat Shading - Each Polygon has Constant Shade

7.30 si31_2001 Gouraud Shading

7.31 si31_2001 Phong Shading

7.32 si31_2001 Phong Shading with Curved Surfaces

7.33 si31_2001 Better Illumination Model

7.34 si31_2001 Further Study n Hearn and Baker, section 14-5 n Watt, chapter 6 n Think about the relative computational costs of flat, Gouraud and Phong

7.35 si31_2001 Acknowledgements n Thanks again to Alan Watt for the images n The following sequence is the famous Shutterbug from Foley et al