Rasterizing Polygons

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# Rasterizing Polygons - PowerPoint PPT Presentation

Rasterizing Polygons. Lecture 29 Wed, Dec 7, 2005. Rasterizing Polygons. Given a the vertices of a polygon, in viewport coordinates, which pixels should be shaded? How do we determine them efficiently?. Rasterizing Polygons. Rasterizing Polygons.

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### Rasterizing Polygons

Lecture 29

Wed, Dec 7, 2005

Rasterizing Polygons
• Given a the vertices of a polygon, in viewport coordinates, which pixels should be shaded?
• How do we determine them efficiently?
Rasterizing Polygons
• Obviously, any pixel lying entirely within the polygon should be shaded.
• What about the pixels that are partially within the polygon?
• Rule: Shade them if their center is within the polygon.
• What about the pixels whose center is exactly on the edge?
Neighboring Polygons
• When two polygons share an edge, which one “owns” the pixels on the edge?
• Rule
• A polygon owns all pixels whose centers are within its interior.
• A polygon owns all pixels whose centers lie on one of its left edges.
Neighboring Polygons
• Fill in all pixels whose centers are within the polygon.
Neighboring Polygons
• Fill in all pixels whose centers are on a left edge of the polygon.
A Rasterization Algorithm
• To rasterize a polygon, first determine its bounding box.
A Rasterization Algorithm
• To rasterize a polygon, first determine its bounding rectangle.
A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.
A Rasterization Algorithm
• When an edge is encountered,
• If we were on the outside, we move to the inside.
• If we were on the inside, we move to the outside.
• Thus, we stop or resume shading accordingly.
A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 0

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 1

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 2

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 3

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 4

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 5

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 6

A Rasterization Algorithm
• Then scan each row of pixels in the bounding rectangle, left to right, bottom to top.

row 7

A Rasterization Algorithm
• The following algorithm is designed to allow rapid shading of the pixels.
• As the vertices are given, create a list of the vertices. (The order matters!)
• {(1, 0), (4, 3), (6, 1), (12, 1), (11, 8), (7, 8), (6, 5), (4, 8), (0, 7), (1, 0)}.
• From the list of vertices, form an edge table.
• {{(1, 0), (4, 3)}, {(4, 3), (6, 1)}, …, {(0, 7), (1, 0)}}.
A Rasterization Algorithm
• Organization of the edge table.
• Eliminate any horizontal edges.
• Sort the edges in the edge table by the y-coordinate of the lower endpoint.
• Begin scanning with the bottom scan line.
The Active Edge Table
• Create the active edge table (AET).
• For each edge in the edge table whose lower endpoint is on the scan line,
• Create an active-edge-table entry.
• Add it to the active edge table.
• Delete the edge from the edge table.
The Active Edge Table
• Organization of an active-edge-table entry:
• y-coordinate of upper endpoint.
• Reciprocal of the slope.
• x-intercept with the horizontal line ½ unit above the current scan line.
The Active Edge Table

Active

edges

Scan

line

The Active Edge Table

(7, -1/7, 13/14)

Scan

line

(3, 1, 1-1/2)

The Active Edge Table
• Sort the AET entries by their x-intercepts.
• The AET must contain an even number of entries.
• Why?
• Shade pixels from the 1st to the 2ndx-intercepts, 3rd to 4thx-intercepts, etc., in the AET.
The Active Edge Table

(7, -1/7, 13/14)

this scan line)

Scan

line

(3, 1, 1-1/2)

The Active Edge Table
• Update the AET.
• Increment the scan line number.
• Delete from the AET any entries for which the upper endpoint is on the scan line.
• Update the x-intercepts of all AET entries.
• Add the reciprocal slope to the x-intercept.
• Create and add entries from the edge table for edges whose lower endpoint is on the scan line.
A Rasterization Algorithm

(7, -1/7, 13/14)

Scan

line

(3, 1, 1-1/2)

A Rasterization Algorithm

(7, -1/7, 11/14)

Scan

line

(8, -1/7, 11-13/14)

(3, -1, 5-1/2)

(3, 1, 2-1/2)

A Rasterization Algorithm

(7, -1/7, 11/14)

Scan

line

(8, -1/7, 11-13/14)

(3, -1, 5-1/2)

(3, 1, 2-1/2)

A Rasterization Algorithm

(7, -1/7, 9/14)

Scan

line

(8, -1/7, 11-11/14)

(3, -1, 4-1/2)

(3, 1, 3-1/2)

A Rasterization Algorithm

(7, -1/7, 9/14)

Scan

line

(8, -1/7, 11-11/14)

(3, -1, 4-1/2)

(3, 1, 3-1/2)

A Rasterization Algorithm

(7, -1/7, 1/2)

Scan

line

(8, -1/7, 11-9/14)

A Rasterization Algorithm

(7, -1/7, 1/2)

Scan

line

(8, -1/7, 11-9/14)

A Rasterization Algorithm

(7, -1/7, 5/14)

Scan

line

(8, -1/7, 11-1/2)

A Rasterization Algorithm

(7, -1/7, 5/14)

Scan

line

(8, -1/7, 11-1/2)

A Rasterization Algorithm

(8, -2/3, 5-5/6)

(8, 1/3, 6-1/6)

(7, -1/7, 3/14)

Scan

line

(8, -1/7, 11-5/14)

A Rasterization Algorithm

(8, -2/3, 5-2/3)

(8, 1/3, 6-1/6)

(7, -1/7, 3/14)

Scan

line

(8, -1/7, 11-5/14)

A Rasterization Algorithm

(8, -2/3, 5)

(8, 1/3, 6-1/2)

(7, -1/7, 1/14)

Scan

line

(8, -1/7, 11-3/14)

A Rasterization Algorithm

(8, -2/3, 5)

(8, 1/3, 6-1/2)

(7, -1/7, 1/14)

Scan

line

(8, -1/7, 11-3/14)

A Rasterization Algorithm

(8, -2/3, 5)

(8, 1/3, 6-1/2)

(8, 4, 2)

Scan

line

(8, -1/7, 11-3/14)

A Rasterization Algorithm

(8, -2/3, 5)

(8, 1/3, 6-1/2)

(8, 4, 2)

Scan

line

(8, -1/7, 11-3/14)