Shading 1: basics Christian Miller CS Fall 2011

Transcription

1 Shading 1: basics Christian Miller CS Fall 2011

2 Picking colors Shading is finding the right color for a pixel This color depends on several factors: The material of the surface itself The color and angle of incoming light The angle of outgoing light to the eye There are several types of shading

3 Emissive light Sometimes objects emit their own light [WP]

4 Diffuse reflection Incoming light is reflected in all directions Completely uniform reflection is called Lambertian Pattern of light and dark does not change with viewing angle, only the locations of object and light[wp]

5 Specular reflection Light that is reflected (mostly) coherently View dependent: the reflection you see depends on where you, the object, and the light are [WP]

6 Diffuse and specular There s a continuum of sorts between the two You can have both effects at once as well [RTR]

7 The rendering equation Computer graphics didn t really know what it was doing with shading until 1986 Tons of models had been proposed, that looked good in different circumstances Jim Kajiya came along with the rendering equation, which formalized what the heck we were trying to do

8 The rendering equation [WP]

9 Definitions x is the point at which we re evaluating shading ω is the normalized outgoing light direction (to eye) λ is the wavelength of the light t is the time n is the surface normal at x Lo is the outgoing light from x to the eye Le is emitted light from the surface, going to the eye

10 Inside the integral Ω is the hemisphere centered around n at x This means the integral is over all incoming light directions ω is one particular normalized incoming light direction Li is the incoming light along ω (-ω n) is the cosine of the angle between the normal and the incoming light direction

11 Cosine weighting cos(0 ) = 1 cos(45 ).71 cos(70 ).34 At sharper angles, incoming light is spread out over a wider area, and thus gets dimmer Hence the cosine weighting term

12 BRDF fr is called the BRDF: Bidirectional Reflectance Distribution Function Captures how much light is reflected by every surface point at every incoming and outgoing angle, at every wavelength and time Always positive (there no negative light) Bidirectional: fr(x, ω, ω,...) = fr(x, ω, ω,...) Incredibly general, most BRDFs have much simpler form

13 Rendering equation This is the gold standard: perfect rendering But evaluating it is impossibly expensive Especially considering light bouncing around Every shading model we make in graphics is an approximation to the rendering equation This version is only for opaque surfaces, there are other versions for transparent ones

14 Local shading Make some simplifying assumptions to make the rendering equation more tractable When evaluating a point s shading, ignore everything except the eye, the surface, and the light(s) No multiple bounces, shadows, refractions, etc. Lights are just points in space (no area) We ll use this to build a very simple approximation of the real thing

15 Some terminology v is a normalized vector to eye, l is same to light, n is the surface normal, p is the point on the surface L is incoming light, k are constants between 0 and 1, and I is outgoing light (one set for each RGB) [RTR]

16 Approximation 1: ambient Every point on the object is a constant color Completely ignore all angles and surface geometry [WP]

17 Approx. 2: diffuse Add in the cosine weighting term from the rendering equation, gives a Lambertian surface Smooth changes in brightness if n changes smoothly, does not depend on v Clamp dot product to [0, 1]! [WP]

18 Approx. 3: specular We d like to add some specular reflection Highlights shift around with both light and viewer Perfect specular isn t interesting for point lights; we d like to widen the reflections a bit [WP]

19 Blinn-Phong specular This is a simpler specular approximation Uses the halfway vector h = norm(v + l) α is the specular exponent or shininess parameter Again, clamp dot product to [0, 1]! [RTR]

20 Shininess exponent Lower exponents make a wider highlight, higher ones make a sharper highlight [RTR]

21 Adding it all together Combine the ambient, diffuse, and specular approximations to get a decent local lighting model 3 of these equations: one for each R, G, and B [WP]

22 Blinn-phong lighting If you have multiple lights, just sum them up This local lighting model has pretty much been the standard for real-time graphics for the last 20 years The default lighting model in OpenGL Tends to make everything look like plastic Much better local models exist for certain types of renderings, but it s still the most common by far

23 Light types We ve assumed point lights so far, but there s more stuff you can add for different behavior

24 Directional lights Treated like point lights placed an infinite distance away Light rays are always parallel, l never changes [RTR]

25 Light attenuation If a light emits a certain amount of energy, then the energy received on a surface should fall off as 1/r 2, where r is distance from the light [RTR]

26 Light attenuation The quadratic falloff law tends to look unnaturally dark on its own, so we represent it instead as the reciprocal of a general quadratic function This allows us to give it a softer falloff Just multiply the light parameters by the falloff

27 Spotlight You can also define a spotlight, which is like a cross between direction and point lights They point in a direction, but fall off as a function of both distance and angle from their direction d is the direction the spotlight points, p is the sharpness of the beam (works like shininess) Again, must clamp dot product to [0, 1]

28 Light type comparison Directional, point with falloff, spotlight with falloff [RTR]

29 Applying the lighting model Evaluating a shading model is generally expensive We can occasionally get away with evaluating it sparsely and reusing the results somehow

30 Flat shading Evaluate your lighting model at the center of each face, then fill the entire face with that color Gives a sparkly or gemstone like appearance [RTR]

31 Gouraud shading Evaluate lighting just at vertices, then interpolate those colors across the faces of each triangle Gives a much smoother appearance, but is dependent on resolution of mesh [RTR]

32 Flat vs. Gouraud [ICG]

33 Mesh resolution Gouraud can miss detail at low resolution Leads to popping when meshes are moved around [RTR]

34 Phong shading Interpolate vertex normals along triangles, then use those normals to evaluate per-pixel lighting model Most expensive, but has best results [RTR]

35 Interpolating normals Linear interpolation will cause non-unit-length normals to be generated You must renormalize your interpolated normals before using them in the lighting calculation [RTR]

36 figures courtesy... Real-Time Rendering, 3rd ed. [RTR] Tomas Akenine-Moller, Eric Haines, Naty Hoffman Mathematics for 3D Game Programming and Computer Graphics, 3rd ed. [M3D] Eric Lengyel Interactive Computer Graphics: A Top-Down Approach Featuring Shader-Based OpenGL, 6th ed. [ICG] Edward Angel, Dave Shreiner Wikipedia [WP]