# CPSC / Illumination and Shading

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1 CPSC /

2 Rendering Pipeline usually in one step modelling of geometry transformation into world coordinate system placement of cameras and light sources transformation into camera coordinate system backface culling projection clipping w.r.t. view volume hidden surface removale (hsr) rasterization illumination and shading

3 Overview illumination models light sources light interaction with surfaces illumination model by Phong shading application of illumination models to rendering polygons efficiency vs. quality flat, Gouraud, Phong shading

4 Illumination Models real world: surfaces emit, absorb, reflect, and scatter light light intensity and color dependent on surface position and orientation w.r.t. the light source light is usually reflected or refracted several times usually several sources of light final intensity/color at a point is sum of several light paths ending at that point Angel (2000)

5 Illumination Models computer graphics world: mathematical description necessary leads to equation using integrals: the rendering equation it s usually not solvable we need approximation! simplifying light sources simplifying materials simplifying computation speed-up

6 Illumination Models description of the factors that influence the color and light intensity at a point global illumination models: considering all objects of a scene to compute light at a specific point e.g., radiosity and raytracing local illumination models: only object-light interaction, pipeline approach heuristic approximation, simpler than global Phong illumination model & polygonal shading

7 Light Sources in Computer Graphics point light source: has only position and no size, sends light equally in all directions point in 3D & intensity spot light source: point light source sending out a cone of light with light intensity decreasing towards cone border point + vector in 3D, angle, attenuation directional light source: sends directed, parallel light rays, has no position vector in 3D & intensity

8 Light Sources in Computer Graphics Angel (2000) point light spot light directional light spot light intensity defined by cosine function depending on angle from center ray, exponent

9 Light Sources in Computer Graphics results from simplification to point light sources? sharp contrast between light and shade, no gradual change (penumbra) aerial light sources have to be approximated by several point lights to have a penumbra Angel (2000)

10 Light Sources in Computer Graphics light attenuation light intensity reduces with growing distance theoretically: I ~ 1/d² reality does not follow exactly this why? CG: I ~ 1/(a+bd+cd²), often only linear: a,c = 0 light color heuristic: color modeled using RGB values approximation because light behavior depends on wave length examples?

11 Light Interaction with Surfaces angle θ between L & N determines diffuse reflection reflection angle equals θ angle Φ between R & V determines perceived brightness maximal reflection if R = V (Φ = 0) L θ N R Φ L vector to light source N surface normal vector R reflected light ray V vector to viewer/observer V

12 Light Interaction with Surfaces directed reflection: reflection only for small Φ: smooth surfaces examples? physical reality non-symmetric reflection around R materials with anisotropic reflection (reflection depends on angle Φ AND direction of L w.r.t. surface) L N R Φ V

13 Light Interaction with Surfaces light attenuation depending on angle between R and V: shininess modeled using cosine function and exponent: I ~ cos (Φ) e metals: e 100 e=2 e=1 L N R Φ V e=5 Angel (2000)

14 Light Interaction with Surfaces diffuse reflection: equal reflection in all directions on rough surfaces, depends only on θ and not observer examples? due to light scattering on rough surfaces on randomly oriented microscopic facets Angel (2000)

15 Light Interaction with Surfaces diffuse reflection modeled according to Lambert s law by cosine function: I ~ cos θ = L N for normalized L, N because light distributes over larger area Angel (2000) θ = 0º max. intensity θ = 90º 0 intensity L θ N R V

16 Light Interaction with Surfaces combined effects of diffuse and directed reflection make up material properties in reality very complex function, can be captured with BRDFs (Bidirectional Reflectance Distribution Function) Bender/Brill (2003)

17 Phong Illumination Model most common CG model for illumination I Phong = I a + I d + I s ambient light: base illumination of scene simulates light scattering on objects necessary because repeated diffuse reflection is not considered in local illumination model depends on color of all objects in scene should always be kept very small diffuse light: light from diffuse reflection specular light: light from directed reflection

18 Phong Illumination Model I ( e L k (L N) + L k (R ) Phong = La ka + d d s s V) 2 a N 1 + bd + cd L R V L vector to light source N surface normal vector R reflected light ray V vector to viewer/observer has to be evaluated for all light sources and for each of the base colors

19 Phong Illumination Model ideally specular, mixed, and ideally diffuse imperfect specular and ideally diffuse reflection as 3D functions Angel (2000) Bender/Brill (2003)

20 Phong Illumination Model 3D reflection functions for θ=10, 45, 70 Bender/Brill (2003)

21 Phong Illumination Model 3D reflection functions for different specular exponents: e = 2, 20, 100 Bender/Brill (2003)

22 Shading of Polygonal Models status: we can approximate color at a point goal: we want to render the whole model constraint: efficiency and quality approach: shade all pixel of a triangle based on color computation at a few points three techniques: flat shading Gouraud shading Phong shading ( Phong illumination)

23 Flat Shading no interpolation all pixels same color two methods: one point per triangle/quad average of triangle s/quad s vertices low quality: single primitives easily visible fast computation & easy implementation

24 Flat Shading: Edge Perception discontinuities easily visible and distracting reason in human perception contrast are enhanced by visual system (remember the saber tooth tigers ;-) perceived brightness differences are bigger than the physical reality Mach band effect Angel (2000)

25 Gouraud Shading computation of colors at all vertices linear interpolation of colors over primitive more computation but better quality than flat shading usually implemented in graphics hardware problem: highlights in the middle of triangles

26 Gouraud Shading: Vertex Normals prerequisite: normal vectors at vertices need to be interpolated from face normals n = n n n n n n n n 4 4 requires data structure supporting crossreferencing of vertices, normals, faces etc. otherwise (no normal interpolation)?

27 Phong Shading linear interpolation of normals for each pixel color computation for each pixel separately best quality but computationally more expensive, highlights are shown correctly problems: polygons still visible at silhouettes (image above is no real Phong shading) typically not implemented in hardware

28 Phong Shading: Normal Interpolation first: normal vector interpolation along edges on per-scanline basis second: normal vector interpolation between edges along scanlines on per-pixel basis Angel (2003)

29 Phong Shading: Normal Interpolation alternative: quadratic interpolation (van Overveld and Wyvill, 1997)

30 Polygonal Shading when in the pipeline? typically last step together with rasterization and z-buffering problem: normals would be perspectively projected normals not perpendicular to surface anymore light position w.r.t. surface may change determine illumination before projection! shading after projection

32 Polygonal Shading: Comparison Flat Gouraud Phong N I 2 N 2 N 3 I 2 N 2 N 3 I N 1 N 1 I 3 I 3 one color value for entire polygon I 1 one color value per vertex & interpolation inside I 1 vertex normals interpolated and one color value per pixel

33 Summary Phong illumination model: heuristic to compute color at one surface point ambient, diffuse, and specular components only computes direct (local) illumination three shading methods to color polygons flat, Gouraud, and Phong shading not physically based speed vs. quality tradeoff illumination computation in world coordinates (before projection)!

34 Sources: Computer Graphics I lecture by Berhard Preim, Department of Simulation and Graphics, Otto-von-Guericke University of Magdeburg, Germany CPSC 407 and CPSC 453 lectures by Brian Wyvill, Department of Computer Science, University of Calgary, Canada

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Chapter 7 - Light, Materials, Appearance Types of light in nature and in CG Shadows Using lights in CG Illumination models Textures and maps Procedural surface descriptions Literature: E. Angel/D. Shreiner,