Subodh Kumar IIT Delhi - ERNETsubodh/courses/CSL781/pdfslides/... · 2010. 2. 4. · Subodh Kumar...

Computer Graphics

Subodh Kumar

Dept of Computer Sc. & Engg.IIT Delhi

Thursday 4 February 2010

Pixel/Screen Coordinates



Xscreen = 0 1 w-1



Xscreen = 0 1 w-1

Caution: In OpenGL this is X = 0, pixel centers are at int + .5


Polygon RasterizationDraw pixels “intersected” by polygon

But one color per pixel..And 2D polygon?

Can iterate over rows (scan lines) Find intersection of scan-lines with edges

All lines and edges?


Triangle Rasterization Issues

Sliver problem


Animating Slivers




Shared Edge Ownership


Polygon Rasterization Rules

Draw pixel, if center inside polygonWhat if it is at an edge?Draw on left edge, Skip on right edgeUnless Horizontal

Then, draw a bottom edge, skip a top edge

Find lo, hi y (scanline)For y=lo to hi: Find left extreme (of span) Find right extreme (of span) For left to right, draw pixel


Triangle Rasterization



For a scan line: find Left extreme



For a scan line: find Left extremeRemember from previous line:




StartX = StartXprevious+ 1/m





Similarly find Right extreme





Similarly find Right extreme Extrema are on two edges






(sometimes at vertices)






(sometimes at vertices)Which two?







Start with two at the lowest vertex







Start with two at the lowest vertex What if there are two lowest vertices?








When an edge ends (at a vertex), replace edge








When an edge ends (at a vertex), replace edge What if both edges end?


General Polygon Rasterization



Multiple spans



Multiple spans

B

CD

E

FG

I H

J

AThursday 4 February 2010


Multiple spansCount parity

B

CD

E

FG

I H

J




How do you count vertex intersections?

B

CD

E

FG

I H

J




How do you count vertex intersections?

Divide into triangles

B

CD

E

FG

I H

J


Triangulation

Draw horizontal line at each vertexAssume no two vertices have the

same YPerturb if assumption not true

Draw diagonals of trapezoids Decomposed into monotone

polygons Triangulate monotone polygon O(n lg* n)


Triangulating Monotone Polygons Process vertices from low to high Push first (lowest two) vertices on a stack For each vi

If vi and top are on the same chain: Form diagonal with the top and pop until possible Finally, push vi

Otherwise savetop := top Form diagonal with the top and pop until possible Finally, push savetop and vi

O(n)


Edge Equations

Edge equation (line equation)Defines two half-spaces:


Triangle Evaluation

Triangle = intersection of three positive half-spaces:

A1x + B1y + C1 < 0

A2x + B

2y + C2 < 0

A 3x +

B3y

+ C

3 < 0

A1x + B1y + C1 > 0

A 3x +

B3y

+ C

3 > 0 A

2x + B2y + C

2 > 0


Evaluate Edge Equations

Plug in pixels’ x,y into the equationIf F(x,y) > 0, draw

+++-

--


Triangle Rasterization Setup:

Find inverse of edge slopesFind bounding box




Rasterize: Initialize left, right intersectionFrom Bounding Box bottom to Top:

Update left, right intersectionRound up or downFill span




Rasterize: Initialize left, right intersectionFrom Bounding Box bottom to Top:

Update left, right intersectionRound up or downFill span

Interpolate Z, Color?Do in fragment shaderFill span = create fragment


Triangle Rasterization, Really

Multiple rasterizers?Blocked or Strided

Create tiles of fragmentsIn parallel, divide tiles into

sub-tilesEach sub-tile shaded

togetherMask to turn off uncovered

tiles


Triangle Rasterization, Really

Multiple rasterizers?Blocked or Strided

Create tiles of fragmentsIn parallel, divide tiles into

sub-tilesEach sub-tile shaded

togetherMask to turn off uncovered

tiles

Partially covered sub-tile

Fully covered sub-tile


Multi-sampling

An attempt to increase resolutionAnti-aliasing: more on this later


Point Drawing

Draw [X0, Y0]


Point Drawing

Draw [X0, Y0] of a certain size


Line Drawing

Draw a lineStart at [X0, Y0]

End at [X1, Y1]


Subodh Kumar IIT Delhi - ERNETsubodh/courses/CSL781/pdfslides/... · 2010. 2. 4. · Subodh Kumar...

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