Computer Graphics
2D Graphic Systems
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Understanding Window-to-Viewport Mapping in Computer Graphics, Slides of Computer Graphics
The concept of window-to-viewport mapping in computer graphics, which is used to transform points from world coordinates to screen coordinates. The basics of screen and world coordinate systems, the need for window-to-viewport mapping, and the steps to calculate the corresponding screen coordinates for a given world coordinate. It also includes an example using opengl and a more detailed explanation of the calculation process.
Typology: Slides
2012/2013
1 / 15
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Computer Graphics
2D Graphic Systems
2D Graphics: Coordinate Systems
n Screen coordinate system
n World coordinate system
n World window
n Viewport
n Window to Viewport mapping
Screen Coordinate System
Insert screen
dump from
OHIO
World Coordinate System
- Problems with drawing in screen coordinates:
- Inflexible
- Difficult to use
- One mapping: not application specific
- World Coordinate system: application-specific
- Example: drawing dimensions may be in meters, km, feet,
etc.
Definition: Viewport
•Rectangular region in the screen used to display drawing
•Defined in screen coordinate system
V.L V.R
V.B
V.T
Window to Viewport Mapping
n Would like to:
n Specify drawing in world coordinates
n Display in screen coordinates
n Need some sort of mapping
n Called Window-to-viewport mapping
n Basic W-to-V mapping steps:
n Define a world window
n Define a viewport
n Compute a mapping from window to viewport
Window to Viewport Mapping (Our Way)
n How is window-to-viewport mapping done?
n Trigonometry: derive Window-to-Viewport mapping
n Basic principles:
n Calculate ratio: proportional mapping ratio (NO distortion)
n Account for offsets in window and viewport origins
n You are given:
n World Window: W.R, W.L, W.T, W.B
n Viewport: V.L, V.R, V.B, V.T
n A point (x,y) in the world
n Required: Calculate corresponding point (s.x, s.y) in screen
coordinates
Window to Viewport Mapping (Our Way)
(x,y) (sx,sy)
V R V L
Sx V L
W R W L
x W L
V T V B
Sy V B
W T W B
y W B
W.T-W.B
W.R-W.L
V.T-V.B
V.R-V.L
Window to Viewport Mapping (Our Way)
Solve, given the formulas:
Sx = Ax −^ (^ A ( W .L ) − V .L )
Sy = By −^ (^ B ( W .B ) − V .B )
W = (W .L,W.R,W.B,W.T) = ( 0 , 4 , 0 , 2 )
What is (Sx,Sy) for point (3.4,1.2) in world coordinates if:
V = (V .L,V.R,V.B,V.T) = ( 60 , 380 , 80 , 240 )
Window to Viewport Mapping (Our Way)
Solution:
W R W L
V R V L
A
Sx Ax A W L V L
W T W B
V T V B
B
Sy By B W B V B
Sx = 80 x + 60 = 332 Sy =^80 y +^80 =^176
Hence, point (3.4,1.2) in world = point (332,176) on screen