CS248 Final Review Derek Chan and Abe Davis

CS248 Final Monday, December 8, 3:30 to 6:30 pm Closed book, closed notes Mainly from material in the second half of the quarter Project submission and writeups along with partner evaluations due today

CS248 Final Review Contents Topics from second half of the course – Image warping, texture mapping – Perspective – Visibility – Lighting / Shading

Texture Warps Rotation, translation Perspective Minification (decimation)‏ – unweighted average: average projected texel elements that fall within a pixel’s filter support – area-weighted average: average based on area of texel support

Texture Warps Magnification – Unweighted – Area-weighted – bilinear interpolation = texel = pixel

Textures 1.Mipmapping – multi-resolution texture – bilinear interpolation at 2 closest resolutions to get 2 color values – linear interpolate 2 color values based on actual resolution 2.Summed area tables 1. fast calculation of prefilter integral in texture space

Viewing: Planar Projections Perspective Projection – rays pass through center of projection – parallel lines intersect at vanishing points Parallel Projection – center of projection is at infinity – oblique – orthographic

Specifying Perspective Views Observer position (eye, center of projection)‏ Viewing direction (normal to picture plane)‏ Clipping planes (near, far, top, bottom, left, right)‏

Viewing: OpenGL Pipeline Object Space Eye Coordinates Projection Matrix Clipped to Frustum Homogenize to device coordinates Window coordinates Why is clipping before homogenization?

Visibility 1.6 visible-surface determination algorithms: 1. Z-buffer 2. Watkins 3. Warnock 4. Weiler-Atherton 5. BSP Tree 6. Ray Tracing

Things to know how does it work what are the necessary preconditions? asymptotic time complexity well-suited for hardware? how can anti-aliasing be done? how can shading be incorporated? parallelizable? ease of implementation best-case/worst-case scenarios

Z-buffer Project all polygons to the image plane, at each pixel, pick the color corresponding to closest polygon

Watkins Scanline + depth – progressing across scanline, if pixel is inside two or more polygons, use depth to pick – process interpenetrating polygons

Warnock Subdivision Start with area as original image – subdivide areas until either: all surfaces are outside the area only one inside, overlapping or surrounding a surrounding surface obscures all other surfaces *

Weiler-Atherton Subdivision Cookie-cutter algorithm: clips polygons against polygons – front to back sort of list – clip with front polygon

BSP Trees/List Priority Provides a data structure for back-to- front or front-to-back traversal – split polygons according to specified planes – create a tree where edges are front/back, leaves are polygons

Ray Tracing “Ray Casting” – for each pixel, cast a ray into the scene, and use the color of the closest polygon – Parametric form of a line: u(t) = a+(b-a)t – Implicit form of the object a b (0,0)‏ x y t

Lighting Photometry vs Radiometry – What's the difference?

Lighting Terminology – Radiant flux: energy/time (joules/sec = watts)‏ – Irradiance: amount of incident radiant flux / area (how much light energy hitting a unit area, per unit time)‏ – Radiant intensity (of point source): radiant flux over solid angle – Radiance: radiant intensity over a unit area

Lighting Lambertian (diffuse) surfaces – Radiant intensity has cosine fall off with respect to angle – Radiance is constant with respect to angle – Reason: the projected unit area ALSO gets smaller as a cosine fall off! – F att x I x K d x (N L)‏ N V I  length = cos(t)‏ Radiance intensity: intensity/solid angle N V

Lighting BRDF = Bidirectional Reflectance Distribution Function – Description of how the surface interacts with incident light and emits reflected light – Isotropic Independent of absolute incident and reflected angles – Anisotropic Absolute angles matter – Generalizations to the BRDF! Spatially/spectrally varying, florescence, phosphorescence, etc.

Lighting Phong specular model – Isn’t true to the physics, but works pretty well – Reflected light is greatest near the reflection angle of the incident light, and falls off with a cosine power – L spec = K s x cos n (a), a= angle between viewer and reflected ray NL R V

Shading Gouraud shading – Compute lighting information (ie: colors) at polygon vertices, interpolate those colors – Problems? Misses highlights need high resolution mesh to catch highlights

Shading Phong shading – Compute lighting normals at all points on the polygon via interpolation, and do the lighting computation on the interpolated normals (of the polygon)‏ Implicit surfacePolygon approximation N1 N2

Good Luck! Good Luck on the Final!