CS430 Computer Graphics

1. CS430 Computer Graphics Lighting and Shading Chi-Cheng Lin, Winona State University

2. Topics • Introduction • Geometric Model in Lighting • Colored Surfaces and Lights • Shading and Graphics Pipeline • Flat Shading and Smooth Shading

3. Introduction • Lighting • Process of computing the luminous intensity reflected from a specific 3-D point • Shading • Process of assigning colors to pixels • Shading model dictates how light is scattered or reflected from a surface • We will begin with achromatic light then colored lights

4. Introduction • Two types of light sources • Point light source • Ambient light • Light interacts surfaces in different ways • Absorbed by surface • Reflected by surface • Transmitted into the interior • What absorbs all of the incident achromatic light?

5. Introduction • Types of reflection of incident light • Diffuse scattering • Some of the incident light penetrates the surface slightly and is re-radiated uniformly in all directions • Scattering light interacts strongly with surface  color is affected by nature of surface material • Specular reflections • Incident light does not penetrate the surface • Reflected directly from the surface • More mirror like and highly directional • Highlight, shiny, plastic like

6. Introduction • Total light reflected from the surface in a certain direction is the sum of • Diffuse components • Specular components • We calculate the size of each component that reaches the eye for each point of interest on surfaces

7. Geometric Model in Lighting • Principle vectors to find amount of light reaching the eye from a point P • m: normal vector of surface at P • v: from P to the eye • s: from P to light source • Angles between vectors are calculated in the world coordinates • Is: intensity of light source m eye s v P

8. Diffuse Component • Id: intensity of the diffused component • Scattering is uniform in all directions • Independent of v • unless m  v 0, where Id = 0 (why?) • Lambert’s law: brightness is proportional to the area subtended (= fraction cos()) •   0: brightness varies slightly with angle •  90°: brightness falls rapidly to 0 m s 

9. Diffuse Component • cos() = • How do we calculate/obtain the value for d ? By experiments.

10. Specular Reflection • Isp: intensity of specular reflection • Phong model is used to approximate highlight • Amount of light reflected is greatest in the direction of perfect mirror reflection, r • Amount of light reflected diminished rapidly at the nearby angles • Beam pattern r m s P

11. Specular Reflection • Remember ? • Amount of light reflected falls off as  increases and is approximately cosf(), where f is the Phong exponent • Problem: expensive to compute as r has to be found and normalized r m s  eye v

12. =0 m h m =h s s v  v Specular Reflection • Solution (proposed by Jim Blinn) • Calculate h = s + v • Let  be the angle between h and m • Use  to calculate the falloff of specular intensity as  has the same property as  •   , but can be compensated by different value of f

13. Ambient Light • A uniform background glow in the environment • Source is not situated at any particular place • Light spreads uniformly in all directions • Ia: intensity of light source • Iaa is added to the light reaching the eye • a: ambient reflection coefficient • a is often the same as d

14. Combining Light Contributions • I = Ia a + Id d  lambert+ Isp s  phongf • lambert = • phong = • Implications for different points P on a facet • Ambient is not changed for different P • m is the same for all point on the facet • If the light is far far away, s will change slightly as P changes  diffuse will change slightly on different P • If the light or/and eye is/are close, s and h will change a lot as P changes  specular changes significantly over the facet

15. Colored Surfaces and Lights • Colored surface • Ir = Iar ar + Idr dr  lambert+ Ispr sr  phongf • Ig = Iag ag + Idg dg  lambert+ Ispg sg  phongf • Ib = Iab ab + Idb db  lambert+ Ispb sb  phongf • lambert and phong terms do not depends on color component • We have to define 9 reflection coefficients • Ambient and diffuse reflection are based on the color of surface

16. Colored Surfaces and Lights • Colored light (Isr,Isg,Isb) • If the color of a surface is (r, g, b), then it is reasonable to set (ar, ag, ab) = (dr, dg, db) = (rK, gK, bK), where K is the fraction of light reflected • The diffusion of the surface = (Isrdr, Isgdg, Isbdb) = (IsrrK, IsggK, IsbbK) • Example: white light • Isr =Isg = Isb = I, (r, g, b) = (0.3, 0.45, 0.25) then diffusion = (0.3IK, 0.45IK, 0.25IK)  the surface is seen as its color

17. Colored Surfaces and Lights • Color of specular light • Often the same as that of light source • Example: sunlight • Highlight on plastic caused by sunlight is white • Set (sr, sg, sb) = (s, s, s) • s = 0.5  slightly shiny • s = 0.9  highly shiny • Different coefficients are selected for specific materials. (Fig 8.17)

19. Shading and Graphics Pipeline • Vertices are sent down the pipeline along with their associated normals • All shading calculations are done on vertices v1, m1 v2, m2 projection matrix viewport matrix VM clip v0, m0 shading is applied here

20. Shading and Graphics Pipeline • Lights are objects and the positions of light sources are also transformed by the modelview matrix • After all quantities are expressed in camera coordinates, colors are attached to vertices using the formula • If an object is clipped, normals of newly generated vertices are calculated by interpolation

21. Flat Shading and Smooth Shading • Polygonal face in 3D space • Individual face • Underlying surface approximated • Shading methods • Flat shading • Smooth shading • Gouraud shading • Phong shading

22. Comparison of Shading Methods

23. Flat Shading • Entire face is drawn with the same color • Lateral inhibition • When there is a discontinuity across an object, the eye manufactures a Mach band at the discontinuity and a vivid edge is seen • Specular highlights are rendered poorly • Either no highlight at all • Or highlight on the entire face

24. Smooth Shading • Smooth shading computes colors at more points on each face to de-emphasize edges between adjacent faces • Use linear interpolation • Gouraud shading • Interpolate vertex colors • Phong shading • Interpolate vertex normals • Interpolate normal for each pixel

25. Gouraud Shading • Used by OpenGL • Example • colora: by interpolating color3 and color4 • colorb: by interpolating color1 and color2 • Colors of pixels on the horizontal line segment is obtained by interpolating colora and colorb • Does not picture highlights well color3 color2 colora colorb color4 color1

26. Phong Shading • Compute normal at each pixel by interpolating the normals at the vertices • Apply the shading model to to every point to find the color • Example • ma: by interpolating m3 and m4 • mb: by interpolating m1 and m2 • Normals of pixels on the horizontal line segment is obtained by interpolating ma and mb • Colors of the pixels are then computed m3 m2 ma mb m4 m1

27. Phong Shading • Very smooth appearance • Highlights are approximated better • Principle drawback • Heavy computation  slow speed • Not supported by OpenGL • Can be approximated using texture mapping • Phong shading  Phong model Don’t be confused!!