05viewing2d.ppt

Graphics

cgvr.korea.ac.kr 1 Graphics Lab @ Korea University

2D Viewing

고려대학교 컴퓨터 그래픽스 연구실

cgvr.korea.ac.kr

CGVR

2 Graphics Lab @ Korea University

Contents

3D Rendering Pipeline 2D Rendering Pipeline Clipping

Cohen-Sutherland Line Clipping Sutherland-Hodgeman Polygon Clipping

Viewport Transformation Scan Conversion Summary of Transformation

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3D Rendering Pipeline

Model TransformationModel Transformation

LightingLighting

Viewing TransformationViewing Transformation

Projection TransformationProjection Transformation

ClippingClipping

Viewport TransformationViewport Transformation

Scan ConversionScan Conversion

3D Primitives

Image

3D Modeling Coordinates

3D World Coordinates


3D Viewing Coordinates

2D Projection Coordinates


2D Device Coordinates


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Model TransformationModel Transformation

LightingLighting

Viewing TransformationViewing Transformation

Projection TransformationProjection Transformation

ClippingClipping



3D Primitives

Image

3D Modeling Coordinates








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3D Primitives

ClippingClipping



Image

Clip portions of geometric primitives residing outside window

Transform the clipped primitives from screen to image coordinates

Fill pixel representing primitives in screen coordinates

2D Primitives

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3D Primitives

ClippingClipping



Image




2D Primitives

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Clipping

Avoid Drawing Parts of Primitives Outside Window Window defines part of scene being viewed Must draw geometric primitives only inside window

WorldCoordinates

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Clipping

Avoid Drawing Parts of Primitives Outside Window Window defines part of scene being viewed Must draw geometric primitives only inside window

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Clipping

Avoid Drawing Parts of Primitives Outside Window Points Lines Polygons Circles etc.

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Point Clipping

Is Point(x,y) Inside the Clip Window?

(x, y)

wx2wx1wy1

wy2Inside =

(x>=wx1) &&

(x<=wx2) &&

(y>=wy1) &&

(y<=wy2);

Inside =

(x>=wx1) &&

(x<=wx2) &&

(y>=wy1) &&

(y<=wy2);

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Line Clipping

Find the Part of a Line Inside the Clip Window

P7

P8

P10

P9

P1

P2

P5

P4P3

P6

Before Clipping

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Line Clipping

Find the Part of a Line Inside the Clip Window

After Clipping

P4P3

P6

P’8

P’7

P’5

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Cohen-Sutherland Line Clipping

Use Simple Tests to Classify Easy Cases First

P7

P8

P10

P9

P1

P2

P5

P4P3

P6

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Classify Some Lines Quickly by AND of Bit Codes Representing Regions of Two Endpoints (Must Be 0)

P10

P5

P6

P9

0001P7

P8

0101

0100

01100010

0000

1010

1000

P1

P2

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

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P10

P5

P6

P9

0001P7

P8

0101

0100

01100010

0000

1010

1000

P1

P2

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

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P10

P5

P6

P9

0001P7

P8

0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

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Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly

P10

P5

P6

P9

0001P7

P8

0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

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P10

P5

P6

P9

0001P7

P8

0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

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P10P6

P9

0001P7

P8

0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

P’5

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P10P6

P9

0001

P8

0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

P’5

P’7

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P10P6

P9

0001 0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

P’5

P’7

P’8

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P10P6

0001 0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

P’5

P’7

P’8

P’9

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P6

0001 0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

P’5

P’7

P’8

P10P’9

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P6

0001 0101

0100

01100010

0000

1010

1000

1001

P4P3

Bit 4

Bit 3

Bit 2Bit 1

P’5

P’7

P’8

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Polygon Clipping

Find the Part of a Polygon Inside the Clip Window?

Before Clipping

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Polygon Clipping

Find the Part of a Polygon Inside the Clip Window?

After Clipping

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Sutherland-Hodgeman Polygon Clipping

Clip to Each Window Boundary One at a Time

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Clipping to a Boundary

Do Inside Test for Each Point in Sequence,

Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary

P1P2

P3

P4

P5

Inside

Outside

Window Boundary

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P1P2

P3

P4

P5

Inside

Outside

Window Boundary

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P1P2

P3

P4

P5

Inside

Outside

Window Boundary P’

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P1P2

P3

P4

P5

Inside

Outside


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P1P2

P3

P4

P5

Inside

Outside

Window Boundary P’ P”

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P1P2

Inside

Outside

Window Boundary P’ P”

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3D Primitives

ClippingClipping



Image




2D Primitives

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Viewport Transformation

Transform 2D Geometric Primitives from Screen Coordinate System (Projection Coordinates) to Image Coordinate System (Device Coordinates)

Screen Image

Viewport

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Window vs. Viewport

Window World-coordinate area selected for display What is to be viewed

Viewport Area on the display device to which a window is

mapped Where it is to be displayed

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Viewport Transformation

Window-to-Viewport Mapping

(wx, wy)

wx2wx1wy1

wy2

(vx, vy)

vx2vx1vy1

vy2Window Viewport

Screen Coordinates Image Coordinates

vx = vx1 + (wx – wx1) * (vx2 – vx1) / (wx2 – wx1);

vy = vy1 + (wy – wy1) * (vy2 – vy1) / (wy2 – wy1);

vx = vx1 + (wx – wx1) * (vx2 – vx1) / (wx2 – wx1);

vy = vy1 + (wy – wy1) * (vy2 – vy1) / (wy2 – wy1);

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3D Primitives

ClippingClipping



Image




2D Primitives

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Scan Conversion

Definition Figure out which pixels to fill

Example Filling the inside of a triangle

P1

P2P3

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Triangle Scan Conversion

Simple Algorithm Color all pixels inside a triangle Inside triangle test

A point is inside a triangle if it is in the positive halfspace of all three boundary lines

L1

L2

L3P

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Triangle Scan Conversion

Triangle Sweep-Line Algorithm Take advantage of spatial coherence

Compute which pixels are inside using horizontal spans Process horizontal spans in scan-line order

Take advantage of edge linearity Use edge slopes to update coordinates incrementally

dxdy

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Polygon Scan Conversion

Fill Pixels Inside a Polygon Triangle Quadrilateral Convex Star-Shaped Concave Self-Intersecting Holes

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Inside Polygon Rule

Need Better Test for Points Inside a Polygon “Inside triangle test” works only for convex polygon

L

1L2

L3L4

L5

L

1L2

L3L4

L5A

L5B

Convex Polygon Concave Polygon

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Inside Polygon Rule

Odd-Parity Rule Any ray from P to infinity crosses odd number of

edges

Concave Self-Intersecting With Holes

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Polygon Line-Sweep Algorithm Incremental algorithm to find spans, and determine

insideness with odd-parity rule

Triangle Polygon

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Hardware Scan Conversion Convert everything into Triangles

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Summary of Transformation

P(x, y, z)

Viewing Transformation

Viewing Transformation

Projection Transformation

Projection Transformation

Window-to-Viewport Transformation

Window-to-Viewport Transformation

P(x, y)

Modeling Transformation

Modeling Transformation

3D Object Coordinates





05viewing2d.ppt

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