CSCE 441: Computer Graphics Scan Conversion of PolygonsOpenGL Geometric PrimitivesSlide 3Slide 4Drawing General PolygonsDrawing Curved ObjectsOutlineDrawing RectanglesSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14General Polygons – Basic IdeaSlide 16Slide 17Slide 18Slide 19Slide 20How to store polygon edges?General Polygons – Data StructuresGeneral Polygons – ExampleSlide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Scan line intersectionSlide 36Slide 37General Polygons – AlgorithmSlide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Pixel Fill-inSlide 67General Polygons – ProblemsCurved BoundariesBoundary FillSlide 71Slide 72Slide 73Slide 74Boundary Fill – ExampleSlide 76Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82How to deal with this?Slide 84Flood FillFlood Fill – ExampleSlide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 981CSCE 441: Computer GraphicsScan Conversion of PolygonsJinxiang Chai2/95OpenGL Geometric PrimitivesAll geometric primitives are specified by verticesGL_QUAD_STRIPGL_QUAD_STRIPGL_POLYGONGL_POLYGONGL_TRIANGLE_STRIPGL_TRIANGLE_STRIPGL_TRIANGLE_FANGL_TRIANGLE_FANGL_POINTSGL_POINTSGL_LINESGL_LINESGL_LINE_LOOPGL_LINE_LOOPGL_LINE_STRIPGL_LINE_STRIPGL_TRIANGLESGL_TRIANGLESGL_QUADSGL_QUADS3/95OpenGL Geometric PrimitivesAll geometric primitives are specified by verticesGL_QUAD_STRIPGL_QUAD_STRIPGL_POLYGONGL_POLYGONGL_TRIANGLE_STRIPGL_TRIANGLE_STRIPGL_TRIANGLE_FANGL_TRIANGLE_FANGL_POINTSGL_POINTSGL_LINESGL_LINESGL_LINE_LOOPGL_LINE_LOOPGL_LINE_STRIPGL_LINE_STRIPGL_TRIANGLESGL_TRIANGLESGL_QUADSGL_QUADS4/95OpenGL Geometric PrimitivesAll geometric primitives are specified by verticesGL_QUAD_STRIPGL_QUAD_STRIPGL_POLYGONGL_POLYGONGL_TRIANGLE_STRIPGL_TRIANGLE_STRIPGL_TRIANGLE_FANGL_TRIANGLE_FANGL_POINTSGL_POINTSGL_LINESGL_LINESGL_LINE_LOOPGL_LINE_LOOPGL_LINE_STRIPGL_LINE_STRIPGL_TRIANGLESGL_TRIANGLESGL_QUADSGL_QUADS5/95Drawing General PolygonsHow to draw every interior pixels??6/95Drawing Curved ObjectsHow to draw every interior pixels??7/95OutlineMethods for drawing polygons or curved objects - Scanline conversion of polygons - Boundary-fill - Flood-fillRequired readings: - HB 4-9 to 4-148/95Drawing RectanglesWhich pixels should be filled?9/95Drawing RectanglesIs this correct?10/95Drawing RectanglesWhat if two rectangles overlap?11/95Drawing RectanglesIs this correct?12/95Drawing RectanglesIs this correct?Overlap!!!13/95Drawing RectanglesSolution: Exclude pixels on top and right14/95Drawing RectanglesArtifacts are possible15/95General Polygons – Basic IdeaHow to draw every interior pixels?16/95General Polygons – Basic IdeaHow to draw every interior pixels for a scan line?17/95General Polygons – Basic IdeaIntersect scan lines with edgesFind ranges along xFill interior of those ranges Don’t fill top/right Edges may NOT matchwith line drawing algo18/95General Polygons – Basic IdeaIntersect scan lines with edgesFind ranges along xFill interior of those ranges Don’t fill top/right Edges may NOT matchwith line drawing algoUse coherence to speed up19/95General Polygons – Basic IdeaIntersect scan lines with edgesFind ranges along xFill interior of those rangesUse coherence to speed upEdges intersecting one scan line are mostly same as those intersecting previous scan line20/95General Polygons – Basic IdeaIntersect scan lines with edgesFind ranges along xFill interior of those rangesUse coherence to speed upThe x-value of an intersection with one scan line is close to the intersection with the previous one21/95How to store polygon edges?22/95General Polygons – Data StructuresSorted Edge Table:01234567Scan LinesEdgesStore a linked-list per scan-line.Insert edges into table at scan-line associated with lowest end-point.23/95General Polygons – Example0123456 701234567ABCDEFG01234567Sorted Edge Table24/95General Polygons – Example0123456 701234567ABCDEFG01234567Sorted Edge Table25/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGSorted Edge Table26/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGSorted Edge TableExclude horizontal edges!27/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGFG EDSorted Edge Table28/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGFG EDCDSorted Edge Table29/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGFG EDCDBCSorted Edge Table30/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGFG EDCDBCSorted Edge TableWhich edges are intersecting with the current scan line?31/95General Polygons – Data StructuresActive Edge List:EdgesList of all edges intersecting current scan-line sorted by their x-values32/95General Polygons – Data StructuresActive Edge List:EdgesList of all edges intersecting current scan-line sorted by their x-valuesImplement active edge list with linked list33/95General Polygons – Data StructuresActive Edge List:EdgesList of all edges intersecting current scan-line sorted by their x-valuesImplement active edge list with linked listSo what kind of information should be stored in the linked list for our polygon drawing algorithm?34/95General Polygons – Data StructuresEdge:maxY: highest y-valuecurrentX: x-value of end-point with lowest y-valuexIncr: 1 / slopemazYcurrentXxIncrEdge35/95Scan line intersectionkkkkxxyym11Scan line yk+1Scan line ykmxxkk11),(00yxmkxxk0),(endendyx),(11  kkyx),(kkyx36/95Scan line intersection),(11  kkyx),(kkyxkkkkxxyym11Scan line yk+1Scan line ykmxxkk11),(00yxmkxxk0),(endendyx37/95General Polygons – Data StructuresEdge:maxY: highest y-valuecurrentX: x-value of end-point with lowest y-valuexIncr: 1 / slopemazYcurrentXxIncrEdgeHorizontal edges will not be used!!!38/95General Polygons – Algorithmline = 0While (line < height )Add edges to Active Edge List from Sorted Edge Table starting at lineRemove edges that end at lineFill pixelsIncrement x-values on edges in Active Edge ListIncrement line39/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGFG EDCDBCSorted Edge TableActive Edge List40/95General Polygons – Example0123456 701234567ABCDEFG01234567AB AGFG