Page 1 1 Review: Projection Taxonomy Review: Midpoint Algorithm - PDF document

University of British Columbia News CPSC 314 Computer Graphics � P1 demos if you missed them May-June 2005 � 3:30-4:30 today Tamara Munzner Lighting/Shading I, II, III Week 3, Tue May 24 http://www.ugrad.cs.ubc.ca/~cs314/Vmay2005 � Homework 2 Clarification Clarification: N2D General Formulation � translate, scale, reflect � off-by-one problem in Q4-6 glViewport(c,d,a,b); � Q4 should refer to result of Q1 (1,1) (1,1) (w,h) (w,h) � Q5 should refer to result of Q2 � Q6 should refer to result of Q3 DCS DCS b NDCS NDCS � acronym confusion a d (-1,-1) � Q1 uses W2C, whereas notes say W2V c (0,0) (0,0) � world to camera/view/eye � x D = (a*x N )/2 + (a/2)+c � Q2 uses C2P, whereas notes say V2C, C2N � y D = - ((b*y N )/2 + (b/2)+d) � Q3 uses N2V, whereas notes say N2D � z D = z N /2 + 1 � normalized device to viewport/device � � Reading: Today Reading: Next Time � FCG Chap 8, Surface Shading, p 141-150 � FCG Chap 11.1-11.4 � RB Chap Lighting � FCG Chap 13 � RB Chap Blending, Antialiasing, Fog, Polygon Offsets � only Section Blending � � Page 1 1

Review: Projection Taxonomy Review: Midpoint Algorithm � moving horizontally along x direction planar planar projections projections � draw at current y value, or move up vertically to y+1? � check if midpoint between two possible pixel centers perspective: perspective: above or below line 1,2,3 1,2,3-point point parallel parallel � candidates � top pixel: (x+1,y+1) � bottom pixel: (x+1, y) orthographic orthographic oblique oblique � midpoint: (x+1, y+.5) cabinet cabinet cavalier cavalier � check if midpoint above or below line � below: top pixel axonometric: axonometric: � above: bottom pixel top, top, http://ceprofs.tamu.edu/tkramer/ENGR%20111/5.1/20 isometric isometric front, front, � key idea behind Bresenham dimetric dimetric side side trimetric trimetric � [demo] � � Review: Flood Fill Review: Scanline Algorithms � simple algorithm � scanline: a line of pixels in an image � draw edges of polygon � set pixels inside polygon boundary along horizontal lines one pixel apart vertically � use flood-fill to draw interior 3 1 P 5=0 2 P 4 � �� Review: General Polygon Rasterization Review: Making It Fast: Bounding Box � smaller set of candidate pixels � loop over xmin, xmax and ymin,ymax instead of all x, all y � idea: use a parity test for each scanline edgeCnt = 0; for each pixel on scanline (l to r) if (oldpixel->newpixel crosses edge) edgeCnt ++; // draw the pixel if edgeCnt odd if (edgeCnt % 2) setPixel(pixel); �� Page 2 2

Review: Bilinear Interpolation Review: Barycentric Coordinates ( α,β,γ α,β,γ ) = α,β,γ ) = ( α,β,γ α,β,γ α,β,γ α,β,γ α,β,γ P (1,0,0) (1,0,0) � interpolate quantity along L and R edges, � weighted combination of vertices 1 as a function of y β = 0 � smooth mixing ( α,β,γ α,β,γ ) = α,β,γ ) = ( α,β,γ α,β,γ α,β,γ α,β,γ α,β,γ (0,0,1) (0,0,1) β = 0 . 5 � then interpolate quantity as a function of x � speedup P 3 � compute once per triangle P 1 P P β = 1 = α ⋅ + β ⋅ + γ ⋅ P P P P P 1 2 3 ( ( α,β,γ α,β,γ α,β,γ α,β,γ α,β,γ α,β,γ ) = ) = α,β,γ α,β,γ 2 (0,1,0) (0,1,0) α + β + γ = 1 P 3 P P(x,y) P(x,y) 0 ≤ α , β , γ ≤ 1 for points inside triangle P L P P R P y y “convex combination convex combination “ of points” of points” P P 2 �� �� Correction/Review: Deriving Barycentric Review: Deriving Barycentric Coordinates Coordinates P (1,0,0) (1,0,0) 1 ( α,β,γ ( α,β,γ ) = α,β,γ α,β,γ α,β,γ α,β,γ ) = � non-orthogonal � 2D triangle area α,β,γ α,β,γ P (1,0,0) (1,0,0) 1 coordinate system α = A P1 A / A (0,0,1) (0,0,1) P � P 3 is origin, P 2 -P 3 , P 1 - 3 ( α,β,γ α,β,γ ) = α,β,γ ) = ( α,β,γ α,β,γ α,β,γ α,β,γ α,β,γ P β = A / A A P 3 are basis vectors (0,0,1) (0,0,1) 3 P P 2 2 A P P P γ = 3 A / A A P3 3 P P 1 P A (0,1,0) (0,1,0) P 1 P � from bilinear 2 P A = + A + A + A 1 P P P P 3 2 1 ( ( α,β,γ α,β,γ α,β,γ ) = α,β,γ α,β,γ α,β,γ ) = α,β,γ α,β,γ 2 interpolation of point P (0,1,0) (0,1,0) on scanline P P 3 P L P P P P P R d d 2 2 : : d d 1 1 �� �� P P 2 Review: Simple Model of Color Review: Trichromacy and Metamers � simple model based on RGB triples � three types of cones � component-wise multiplication of colors � color is combination of cone stimuli � (a0,a1,a2) * (b0,b1,b2) = (a0*b0, a1*b1, a2*b2) � metamer: identically perceived color caused by very different spectra � why does this work? �� �� Page 3 3

Review: Color Constancy Clarification/Review: Stroop Effect � blue � green � purple � red � orange � say what color the text is as fast as possible � interplay between cognition and perception �� �� Review: Measured vs. CIE Color Spaces Review: Device Color Gamuts � compare gamuts on CIE chromaticity diagram � gamut mapping measured basis � � transformed basis monochromatic lights � � “imaginary” lights physical observations � � all positive, unit area negative lobes � � Y is luminance �� �� Review: RGB Color Space Review: Additive vs. Subtractive Colors � define colors with (r, g, b) � additive: light � � � � � � C 1 R amounts of red, green, and � monitors, LCDs � � � � � � blue M = 1 − G � � � � � � � RGB model � used by OpenGL � � � � � � � � � � � � Y 1 B � subtractive: pigment � printers � CMY model � RGB color cube sits within CIE color space � subset of perceivable colors �� �� Page 4 4

Review: HSV Color Space Review: YIQ Color Space I � color model used for color TV � hue: dominant wavelength, “color” Q � saturation: how far from grey � Y is luminance (same as CIE) � value/brightness: how far from � I & Q are color (not same I as HSI!) black/white � using Y backwards compatible for B/W TVs � cannot convert to RGB with matrix � conversion from RGB is linear alone � � � � � � Y 0 . 30 0 . 59 0 . 11 R � � � � � � = − − I 0 . 60 0 . 28 0 . 32 G � � � � � � � � � � � � � Q � � 0 . 21 − 0 . 52 0 . 31 � � B � � green is much lighter than red, and red lighter than blue �� �� Review: Monitors � monitors have nonlinear response to input � characterize by gamma γ (maxIntensity) � displayedIntensity = a γ γ γ � gamma correction γ � γ � � 1 / Lighting I � a � displayedIntensity = (maxIntensity) � � = a (maxIntensity) �� �� Goal Photorealistic Illumination model interaction of light with matter in a way that appears realistic and is fast � phenomenological reflection models � ignore real physics, approximate the look � simple, non-physical � Phong, Blinn-Phong � physically based reflection models � simulate physics � BRDFs: Bidirectional Reflection Distribution Functions [ [electricimage.com electricimage.com] ] �� �� Page 5 5

Photorealistic Illumination Fast Local Illumination [ [electricimage.com electricimage.com] ] �� �� Illumination Components of Illumination � two components: light sources and surface properties � transport of energy from light sources to � light sources (or emitters ) surfaces & points spectrum of emittance (i.e., color of the light) � includes direct and indirect illumination � geometric attributes � � position � direction � shape � directional attenuation � polarization Images by Henrik Wann Jensen �� �� Components of Illumination Illumination as Radiative Transfer � radiative heat transfer approximation � surface properties � substitute light for heat reflectance spectrum (i.e., color of the surface) � � light as packets of energy (photons) � subsurface reflectance � particles not waves � geometric attributes � model light transport as packet flow � position � orientation � micro-structure thermometer/eye energy packets heat/light source reflective objects �� �� Page 6 6