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Filling Rectangles

for (y=YMIN; y<YMAX; y++) // by scan line

{

for (x=XMIN; x<XMAX; x++) // by pixel in span

{

WritePixel(x,y,color);

}

}

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Filling Polygons

• Simple version

– For each scan line

• Compute intersection points with each edge

• Generate spans

• Display spans

– Example

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Filling Examples

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Span Filling

1. Find the intersections of the scan line with al edges of thepolygon

2. Sort the intersections by increasing x coordinate

3. Fill in all pixels between pairs of intersections that lieinterior to the polygon, using the odd-parity rule (parity isinitially even, and each intersection encountered thusinverts the parity bit---draw when parity is odd, do notdraw if even)

Note: Step 1 and 2 will be discussed later

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Span-filling Strategy

• Question with Step 3:

3.1 Intersection may be at fractional x value, how todetermine which pixel one either side is interior?

3.2 How to deal with intersections at integer coordinates?

3.3 How to deal with shared vertices?

3.4 How to deal with Horizontal edges?

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Answers

3.1 If we are approaching the intersection from the left sideand are inside the polygon, we round down the xcoordinate; If we are outside, we round up to be inside.

3.2 Use these rules:

– leftmost is defined interior

– rightmost is defined exterior

3.3 Count only ymin vertex of an edge for parity calculationbut not ymax

3.4 Do not count vertices of horizontal edges

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Edge Coherence and Scan-Line Algorithm

• Many edges intersected by scan line i are also intersectedby scan line i+1 (edge coherence)

xi+1 = xi + 1/m

where m = (ymax-ymin)/(xmax-xmin)

• For polygon filling, we will step in y direction, thus 1/mwill be used to update x

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Edge Table and Active Edge Table

• ET: A (bucket) sorted table that stores list of all edges

• AET: List of edges that intersect with current scan line(sorted by x)

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Scan-line Algorithm

1. Set y to smallest coordinate

2. Initialize the AET to be empty

3. Repeat until the AET and ET are empty:

3.1 Move from ET bucket y to the AET those edges whose ymin

= y, then sort the AET on x

3.2 Fill in desired pixel on scan line y by using pairs of xcoordinates from the AET

3.3 Remove those entries for which y=ymax from the AET

3.4 Increment y by 1

3.5 For each non-vertical edge remaining in the AET, update x

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Edge Table

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Active Edge Table

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Pattern Filling (1/2)

• To fill an area with a pattern

• Transparent mode:

– perform WritePixel() with foreground color if pattern = 1

– inhibit WritePixel() if pattern = 0

• Opaque mode:

– perform WritePixel() with foreground color if pattern = 1

– perform WritePixel() with background color if pattern = 0

• Where the pattern is “anchored” ?

– Left most polygon vertex (doesn’t work with circles)

– Screen origin (fast, seamless connection

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Pattern Filling (2/2)

• Patterns are defined as small M by N bitmaps

• Assume that the Pattern [0, 0] pixel is coincident with thescreen origin, we can write a pattern in transparent modewith the following code:

if pattern[x mod M, y mod n] then WritePixel(x, y, color);

• Note: In opaque mode, a whole row can be copied atonce!

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Pattern Filling Without Repeated Scan Conversion

• Scan convert a primitive first into a rectangular work area,then write each pixel to the appropriate place in thecanvas

• Twice as much work but good for primitives that arescan-converted repeatedly (e.g. characters)

• Don’t have to worry about clipping

• Use copyPixel() (or BitBlt()) for faster speed (drawing theentire rectangle encompassing the primitive at once)

• Problem with objects with “holes” when writing in opaquemode

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Example

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Thick Primitives (1/3)

• Replicating pixels

– write multiple pixels at each selected pixel in scanconversion process

– thickness inconsistent, gaps may occur when connecting 2lines

• The moving pen

– using a rectangular pen whose center moves along thesingle-pixel outline of the primitive

– line seems thicker at endpoints

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Thick Primitives (2/3)

• Filling areas between boundaries

– A thick line is drawn as a rectangle with thickness t

– A thick circle is draw as 2 circles of radius R-t/2 and R+t/2

• Approximation by thick polyline

– decompose each primitive into rectangular pieces

– draw each piece

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Thick Primitives (3/3)

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Line Style and Pen Style

• Sample code for a write mask of 16 booleans:

if bitstring[i mod 16] then WritePixel(x, y, color);

– index i is a new variable incremented in the inner loop

• Thick lines are created as sequences of altering solid andtransparent rectangles.

• Line style is used to calculate the rectangle for each dash

• Pen style is used to fill each rectangle