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CS248 Final Review CS248 Final Review


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CS248 FinalCS248 Final

Thurs, December 12, 7-10 pm, GatesB01, B03

Mainly from material in the second half of the quarter will not include material from last part of last

lecture (volume rendering, image-basedrendering)

Review session slides available fromclass website

Office hours as regularly scheduled


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CS248 Final Review ContentsCS248 Final Review Contents

Image warping, texture mappingPerspectiveVisibilityLighting / Shading


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T exture Mapping T exture Mapping

Coordinate systems [u,v,q] => [x o, y o zo, wo] => [x w, y w zw, w w]

=> [x, y, w] Assuming all transforms are linear, then

[A][u, v, q] = [x, y, w]

Common mappings forward mapping (scatter), texture->screen backward mapping (gather)


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T exture Warps T exture Warps

Rotation, translationperspectiveMinification (decimation) unweighted average: average projected

texel elements that fall within a pixels filter

support area-weighted average: average based on

area of texel support


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T exture Warps T exture Warps

Magnification Unweighted Area-weighted bilinear interpolation

= texel= pixel


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T extures T extures

1. Mipmapping1. multi-resolution texture2. bilinear interpolation at 2 closest

resolutions to get 2 color values3. linear interpolate 2 color values based on

actual resolution

2. Summed area tables1. fast calculation of prefilter integral in

texture space


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V iewing: Planar Projections V iewing: Planar Projections

Perspective Projection rays pass through center of projection

parallel lines intersect at vanishing pointsParallel Projection center of projection is at infinity

oblique orthographic

How many vanishing points are there in an image

produced by parallel projection ?


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Specifying Perspective V iewsSpecifying Perspective V iews

Observer position (eye, center of projection)Viewing direction (normal to picture plane)

Clipping planes (near, far, top, bottom, left,right)


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V iewing: OpenGL Pipeline V iewing: OpenGL Pipeline

Object SpaceEye Coordinates

Projection MatrixClipped to FrustumHomogenize to normalized devicecoordinatesWindow coordinates


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V isibility V isibility

1. 6 visible-surface determinationalgorithms:

1. Z-buffer 2. Watkins3. Warnock

4. Weiler-Atherton5. BSP Tree6. Ray Tracing


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Th ings to know Th ings to know

how does it workwhat are the necessary preconditions?

asymptotic time complexityhow can anti-aliasing be done?how can shading be incorporated?well-suited for hardware?

parallelizable?ease of implementationbest-case/worst-case scenarios


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ZZ--bufferbuffer

Project all polygons to the image plane,at each pixel, pick the color

corresponding to closet polygon


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Watkins Watkins

Scanline + depth progressing across scanline, if pixel is

inside two or more polygons, use depth topick

process interpenetrating polygons, addthose events


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Warnock Subdivision Warnock Subdivision

Start with area as original image subdivide areas until either:

all surfaces are our outside the areaonly one inside, overlapping or surroundinga surrounding surface obscures all other surfaces

*


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Weiler Weiler --A th erton Subdivision A th erton Subdivision

Cookie-cutter algorithm:clips polygonsagainst polygons

front to back sort of list clip with front polygon


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B SP T reesB SP T rees

Provides a data structure for back-to-front or front-to-back traversal

split polygons according to specifiedplanes

create a tree where edges are front/back,leaves are polygons


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Ray T racing Ray T racing

Ray Casting for each pixel, cast a ray into the scene,

and use the color of the point on theclosest polygon

Parametric form of a line: u(t) = a+(b-a)t

a b

(0,0) x

y t


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Sphere: | P -P c|2 r 2 = 0Plane: N P = -DCan you compute the intersection of aray and a plane? A ray and a sphere?


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Point in polygon tests Odd, even rule

draw a line from point to infinity in one directioncount intersections: odd = inside, even =outside

Non-zero winding rulecounts number of times polygon edges windaround a point in the clockwise directionwinding number non zero = inside, else outside


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Lig h ting Lig h ting

Terminology Radiant flux: energy/time (joules/sec =

watts) Irradiance: amount of incident radiant flux /

area (how much light energy hitting a unitarea, per unit time)

Radiant intensity (of point source): radiantflux over solid angle

Radiance: radiant intensity over a unit area


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Point to area transport Computing the irradiance to a surface

Cos falloff: N L E = F att x I x (N L)


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Lambertian (diffuse) surfaces Radiant intensity has cosine fall off with

respect to angle Radiance is constant with respect toangle Reason: the projected unit area ALSO gets

smaller as a cosine fall off! F att x I x K d x (N L)

NV

I w length = cos(t)

Radiance intensity: intensity/solid angle

NV


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BRDF = Bidirectional Reflectance DistributionFunction

description of how the surface interacts withincident light and emits reflected light Isotropic

Independent of absolute incident and reflected angles

AnisotropicAbsolute angles matter

Dont forget the generalizations to the BRDF!Spatially/spectrally varying, florescence,phosphorescence, etc.


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Phong specular model Isnt true to the physics, but works pretty

well reflected light is greatest near thereflection angle of the incident light, andfalls off with a cosine power

Lspec = K s x cosn

(a), a= angle betweenviewer and reflected ray how do you compute the reflected ray

vector?

N LR

V


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Local vs. infinite lights Understand them! Know how to draw the

goniometric diagrams for variouslight/viewer combinations

N H model

H is the halfway vector between the viewer and the light

What is the difference in specular highlight?

N

V

R H L


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Sh ading Sh ading

Gouraud shading Compute lighting information (ie: colors) at

polygon vertices, interpolate those colors Problems?

Misses highlightsneed high resolution mesh to catch highlightsmach bands!


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Sh ading Sh ading

Angle interpolation interpolate normal angles according to the implicit

surface compute shading at each point of the implicit

surface CORRECT! But very expensive


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Sh ading Sh ading

Phong shading Compute lighting normals at all points on the

polygon via interpolation, and do the lightingcomputation on the interpolated normals (of thepolygon)

Problems? Difference with angle interpolation?

Implicit surfacePolygon approximationN1 N2


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Lig h ting and S h ading Lig h ting and S h ading

Know the OpenGL 1.1, 1.2 lightequations


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E xotic uses of texturesE xotic uses of textures

Environment/reflection mapping Alphas for selecting betweentextures/shading parametersBump mappingDisplacement mapping

Object placement3d textures


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Good Luck!Good Luck!

Good Luck on the Final!

More review questions at:http://graphics.stanford.edu/courses/cs248-99/final_review

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