 Rasterization. Geometry. Scan Conversion. Rasterization


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1 Computer Graphics  The graphics pipeline  Geometry Modelview Geometry Processing Lighting Perspective Clipping Scan Conversion Texturing Fragment Tests Blending Framebuffer Fragment Processing  So far, projection of vertices into view space (done in the geometry stage)  Now, conversion of geometric primitives into fragments  Fragment:  Represents a point of geometry  Has color, texcoord, depth etc.  Associated with a pixel  But not yet a pixel (not stored in the framebuffer)  Scan conversion of geometric primitives  For each covered pixel a fragment is generated  Attributes like color, depth, texture coordinates etc. are generated from projected vertex attributes  During fragment generation OpenGL states, e.g. shading model, line width, polygon mode etc. are taken into account  Pixel:  Color of a pixel in the framebuffer  of geometric data Geometry processing Vertex transformation Lighting Clipping... Screen coord (X,Y) Depth (z) Color (RGBα) TexCoords (u,v,w)... Fragment Processing Texturing Perfragment tests Perfragment comparison Blending...  of triangles  Using OpenGL, everything is broken into triangles  Find all fragments covered by a triangle // most simple rasterizer Rasterize(vertex v[3]) { int x, y; bbox b; getbbox(v,, &b); for (y= b.ymin; ; y < b.ymax; ; y++) for (x= b.xmin; ; x < b.xmax; ; x++) if (inside(v,, x, y)) fragment(x,y); }
2  Scanline algorithm  Edge table:  Stores list of all edges in increasing y min order y min, x min, y max, dx/dy  Active edge table:  Contains all edges that intersect current scanline in increasing xorder x, y max, dx/dy  Scanline algorithm scanconvert(vertex v0, v,... vn) { AEL = NULL; foreach(scanline y) { remove edges from AEL with y max y; foreach(edge AEL) x = x + dx/dy; insert edges into AEL with y min == y; sort AEL by increasing x; draw scanline segments xx, x3x4,... } }  Once a fragment is generated, pervertex attributes need to be assigned properly  Determination of color and other properties for all pixels along a scanline is called Shading  This is done via interpolation (see exercise for more information) wire frame scanline v 0 v v  Flat shading  Per surface (polygon) lighting  Take normal of one distinct vertex as triangle normal  Constant color for polygon  Mach band effect flat shading
3  Smooth or Gouraud shading (97)  Idea: better quality by respecting color variations on the polygon  Per vertex lighting  Linear interpolation of color using barycentric interpolation in triangles  In object space during raytracing  In screen space during scan conversion (OpenGL)  How to determine barycentric coordinates efficiently for every pixel A a D a C P E B a D = A + ( C A) a + a a a = A C a a + + a + a a a = A + C a + a a + a  Similar  Similar C C A a a b b b D P E E = B + C b + b b + b b B A a a b c c D P E P = D + E c + c c + c c c b B Gouraud shading Polygon shading  Does this algorithm work for polygons, i.e. non triangles? 3
4  Problems of Gouraud shading:  Loosing surface structure  No internal highlights  Phong shading (975): higher quality shading by interpolating normals rather than colors  Evaluates lighting model for every pixel Has to be done in object space Not supported by OpenGL Phong shading  Shading problems  Smooth surfaces, but polygonal borders (silhouette)  Inconsistencies in vertices  Tvertex (hanging node)  OpenGL shading Phong lighting Gouraud shading Phong lighting and shading  Scan conversion of primitives scanline v 0 Interpolation of pervertex attributes along scanlines v v z Depth values: nonlinear in [Z near, Z far ] due to perspective projection Z near Z far 4
5  For perspective views,, linear interpolation of vertex parameters like color, texcoords, normals in screen space leads to wrong results  Linear (left( left) ) and rational linear (right) interpolation of texture coordinates in screen space Wrong interpolation in screen space P a A P A=0.5 Line with parameters P 0,P at vertices viewpoint P b B P =0.5 (P + P ) viewplane P B=0.5 P  Texture interpolation without perspective correction  Refinement in,4,64 Quads (=,8,8 Tris)  Relationship between spaces in CG Objectaffine spaces Screenaffine spaces Object space World space Texture space (u,v) Homogeneous screen space (xw,yw,w) divby/w divbyw Homogeneous texture space (u/w,v/w,/w) Screen space (x,y)  Perspective correction (given:a,b; looking for A,B) a b P ' P = P + P ; P = a + b a + b w A B Aw + Bw P ' = P ' + P ' w = A + B A + B A + B ap ' / w + bp ' / w AP ' + BP ' P = = A = a + b Aw + Bw a / wp ' + b / w P ' P ' = a / w + b / w a w, B = b w Interpolate x/w, y/w, z/w, /w and divide through /w per pixel  (Wrong) algorithm for polygon rendering with linear interpolation  Associate parameters p,...,p n with each vertex  vertex object space coords to homogeneous screen space coords (xw,yw,zw,w)  Perform homogeneous division (x,y,z,)  Scan convert in screen space by linear interpolation of all parameters 5
6  (Correct) algorithm for polygon rendering with linear interpolation Next: fragment processing  Operations on fragments before the become pixels  Associate parameters p,...,p n with each vertex  vertex object space coords to homogeneous screen space coords (xw,yw,zw,w)  At each vertex construct variable list (x,y,z,s,...,s n+ ) with s i =p i /w, s n+ =/w  Scan convert in screen space by linear interpolation of all parameters; ; at each pixel compute p i =s i /s /s n+ Geometry Scan Conversion Modelview Texturing Geometry Processing Lighting Fragment Tests Perspective Blending Clipping Framebuffer Fragment Processing 6
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