1. Semantics For Pictures COS 441 Princeton University Fall 2004

2. A Simple Picture Language Provide rigorous denotational semantics –Resolution and device independent specification Not about how to draw a picture but about what a picture is Start with informal concepts then dive into semantics

3. Concepts Point – A location on R 2 Shape – A set of points Color – red, blue, green, etc… Texture – An assignment of color to every point on the plane Layer – A partial assignment of colors to points on the plane

4. Concepts (cont.) Picture – An order collection of layers Image – A total assignment of colors to every point on the plane. e.g. A picture with a default background

5. Picture Syntax

6. Points (1,1) (0,0)

7. Shapes: Everything

8. Shapes: Nothing

9. Shapes: Ellipse (0,0) 2 1 ellipse((0,0),1,2)

10. Shapes: Half Planes (1,1) (0,0) halfplane((0,0),(1,1))

11. Shapes: Half Plane (1,1) (0,0) halfplane((1,1),(0,0))

12. Composite Shapes (0,0) 1 1 (0,1) intersect(ellipse((0,0),1,1),halfplane((0,0),(0,1))

13. Polygon as Shapes intersect(halfplane((0,0),(0,1), intersect(halfplane((0,1),(1,1), halfplane((1,1),(0,0)))

14. Red Texture

15. Layer (0,0) 1 1 layer(ellipse((0,0),1,1),red)

16. Picture 1 layer(ellipse((0,0),1,1),red) B layer(ellipse((1,0),1,1),green)

17. Miscellaneous Operators Set operators on shapes –Intersection, Union, Difference Scaling and Translation on shape coordiates

18. Formal Semantics

19. Formal Semantics (cont.)

20. A Simple Theorem

21. More Theorems

23. Scaling and Translation Thms.

25. Optimizations We can systematically remove every scaling and translation operation to obtain an equivalent picture Removing scaling and translation can speed up rasterizing of image by removing unneeded computations