University of British Columbia News CPSC 314 Computer Graphics � extra lab coverage: Mon 12-2, Wed 2-4 May-June 2005 � P2 demo slot signup sheet Tamara Munzner � handing back H1 today � we’ll try to get H2 back tomorrow Compositing, Clipping, Curves � we will put them in bin in lab, next to extra handouts � solutions will be posted Week 3, Thu May 26 � you don’t have to tell us you’re using grace days � only if you’re turning it in late and you do *not* want to use up grace days http://www.ugrad.cs.ubc.ca/~cs314/Vmay2005 � grace days are integer quantities � Homework 1 Common Mistakes Schedule Change � Q4, Q5: too vague � HW 3 out Thu 6/2, due Wed 6/8 4pm � don’t just say “rotate 90”, say around which axis, and in which direction (CCW vs CW) � be clear on whether actions are in old coordinate frame or new coordinate frame � Q8: confusion on push/pop and complex operations � wrong: object drawn in wrong spot! glPushMatrix(); glTranslate(..a..); glRotate(..); draw things glPop(); � correct: object drawn in right spot glPushMatrix(); glTranslate(..a..); glRotate(..); � both: nice modular function glTranslate(..-a..); that doesn’t change modelview matrix draw things � � glPop(); Poll Midterm Logistics � which do you prefer? � Tuesday 12-12:50 � P4 due Fri, final Sat � sit spread out: every other row, at least three seats between you and next person � final Thu in-class, P4 due Sat � you can have one 8.5x11” handwritten one- sided sheet of paper � keep it, can write on other side too for final � calculators ok � � Page 1 1
Midterm Topics Reading: Today � H1, P1, H2, P2 � FCG Chapter 11 � pp 209-214 only: clipping � first three lectures � topics � FCG Chap 13 � RB Chap Blending, Antialiasing, ... � Intro, Math Review, OpenGL � Transformations I/II/III � only Section Blending � Viewing, Projections I/II � � Reading: Next Time Errata � FCG Chapter 7 � p 214 � f(p) > 0 is “outside” the plane � p 234 � For quadratic Bezier curves, N=3 � w_i^N(t) = (N-1)! / (i! (N-i-1)!)... � �� Review: Illumination Review: Light Sources � directional/parallel lights � transport of energy from light sources to surfaces & points � point at infinity: (x,y,z,0) T includes direct and indirect illumination � � point lights � finite position: (x,y,z,1) T � spotlights � position, direction, angle � ambient lights Images by Henrik Wann Jensen �� �� Page 2 2
Review: Light Source Placement Review: Reflectance � geometry: positions and directions � specular : perfect mirror with no scattering � standard: world coordinate system � gloss : mixed, partial specularity � effect: lights fixed wrt world geometry � diffuse : all directions with equal energy � alternative: camera coordinate system � effect: lights attached to camera (car headlights) + + = specular + glossy + diffuse = reflectance distribution �� �� Review: Reflection Equations Review: Reflection Equations 2 n n l n h h � Blinn improvement I diffuse = k d I light (n • l) v v I specular = k s I light ( h • n ) n shiny θ l l h = ( l + v )/2 I specular = k s I light ( v • r ) n shiny � full Phong lighting model � combine ambient, diffuse, specular components # lights � k d ( n • l i ) + k s ( v • r i ) n shiny ) 2 ( N ( N · L )) – L = R I total = k s I ambient + I i ( i = 1 � don’t forget to normalize all vectors: n,l,r,v,h �� �� Review: Lighting Review: Shading Models � flat shading � lighting models � compute Phong lighting once for entire � ambient polygon � normals don’t matter � Gouraud shading � Lambert/diffuse � compute Phong lighting at the vertices and � angle between surface normal and light interpolate lighting values across polygon � Phong/specular � Phong shading � surface normal, light, and viewpoint � compute averaged vertex normals � interpolate normals across polygon and perform Phong lighting across polygon �� �� Page 3 3
Review: Non-Photorealistic Shading Correction/Review: Computing Normals k w = 1 + n ⋅ l � cool-to-warm shading , c = k w c w + (1 − k w ) c c 2 � per-vertex normals by interpolating per-facet � draw silhouettes: if , e =edge-eye vector ( e ⋅ n 0 )(e ⋅ n 1 ) ≤ 0 normals ( n 0 ⋅ n 1 ) ≤ threshold � draw creases: if � OpenGL supports both � computing normal for a polygon � three points form two vectors � pick a point b (a-b) x (c-b) � vectors from � A: point to previous � B: point to next c-b � AxB: normal of plane direction a-b � normalize: make unit length c � which side of plane is up? � counterclockwise a point order convention �� http://www.cs.utah.edu/~gooch/SIG98/paper/drawing.html �� End of Class Last Time � use version control for your projects! � CVS, RCS � partially work through problem with lighting Compositing �� �� Compositing Premultiplying Colors specify opacity with alpha channel: (r,g,b, α ) � � how might you combine multiple elements? α =1: opaque, α =.5: translucent, α =0: transparent � � foreground color A , background color B A over B � C = α A + (1- α ) B � but what if B is also partially transparent ? � C = α A + (1- α ) β B = β B + α A + β B - α β B � γ = β + (1- β ) α = β + α – αβ � � 3 multiplies, different equations for alpha vs. RGB premultiplying by alpha � � C’ = γ C, B’ = β B, A’ = α A � C’ = B’ + A’ - α B’ � γ = β + α – αβ � 1 multiply to find C, same equations for alpha and RGB �� �� Page 4 4
Rendering Pipeline Geometry Geometry Model/View Model/View Model/View Perspective Perspective Geometry Perspective Lighting Lighting Lighting Clipping Clipping Clipping Transform. Transform. Transform. Transform. Database Database Database Transform. Transform. Clipping Frame- Frame Frame- Scan Scan Scan Depth Depth Depth Texturing Texturing Texturing Blending Blending Blending buffer buffer Conversion Conversion Conversion Test Test buffer Test �� �� Next Topic: Clipping Clipping � we’ve been assuming that all primitives (lines, � analytically calculating the portions of triangles, polygons) lie entirely within the viewport primitives within the viewport � in general, this assumption will not hold: �� �� Why Clip? Line Clipping � bad idea to rasterize outside of framebuffer � 2D bounds � determine portion of line inside an axis-aligned rectangle (screen or window) � also, don’t waste time scan converting pixels outside window � 3D � could be billions of pixels for very close � determine portion of line inside axis-aligned objects! parallelpiped (viewing frustum in NDC) � simple extension to 2D algorithms �� �� Page 5 5
Clipping Trivial Accepts � big optimization: trivial accept/rejects � naïve approach to clipping lines: � Q: how can we quickly determine whether a line for each line segment segment is entirely inside the viewport? for each edge of viewport � A: test both endpoints find intersection point pick “nearest” point if anything is left, draw it B � what do we mean by “nearest”? D � how can we optimize this? C A �� �� Trivial Rejects Clipping Lines To Viewport � Q: how can we know a line is outside � combining trivial accepts/rejects � trivially accept lines with both endpoints inside all edges viewport? of the viewport � A: if both endpoints on wrong side of same � trivially reject lines with both endpoints outside the same edge, can trivially reject line edge of the viewport � otherwise, reduce to trivial cases by splitting into two segments �� �� Cohen-Sutherland Line Clipping Cohen-Sutherland Line Clipping � assign outcode to each vertex of line to test � outcodes � line segment: ( p1,p2 ) � 4 flags encoding position of a point relative to � trivial cases top, bottom, left, and right boundary � OC( p1 )== 0 && OC( p2 )==0 1010 1000 1001 1010 1000 1001 � both points inside window, thus line segment completely � OC( p1 )=0010 y=y y max y= p3 p3 max visible (trivial accept) p1 p1 � OC( p2 )=0000 � (OC( p1 ) & OC( p2 ))!= 0 0010 0010 0000 0000 0001 0001 � OC( p3 )=1001 � there is (at least) one boundary for which both points are outside (same flag set in both outcodes) p2 p2 y=y y min y= min � thus line segment completely outside window (trivial 0110 0110 0100 0100 0101 0101 reject) x=x x min x=x x= x max x= max min �� �� Page 6 6
Recommend
More recommend
