1. Handwritten Fonts Modeling Based on Fat Lines of Variable Width Stanislav Klimenko Moscow Physicotechnical Institute Moscow, Russia klimenko@sim.ol.ru Leonid Mestetskiy Moscow State University Moscow, Russia l.mest@ru.net Andrey Semenov Tver State University Tver, Russia semenov@tversu.ru klimenko@sim.ol.ru l.mest@ru.net semenov@tversu.ru

2. Fonts Describing The 16-th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2008 Outline description is union of Bezier curves 2

3. Fonts Describing Disadvantages of outline description: 1. Implementation of “alive” handwriting is difficulty 2. Doesn’t allow implementing variations of stroke width of pen 3. The problem of preservation of contour smoothness ? 3

4. Handwritten Fonts 4

5. 1.Representation of a font as a trace of pen «with a variable width» 2.Obtaining of a font in the form of curves with a width on the scanned image Our approach 5

6. - Fat curve with axis P(t)=(u(t),v(t)) and thickness r(t) Fat Curve is family of circles of variable radius with centers on smooth curve 6

7. Elementary Fat B-Spline Curve 7

8. Composite Fat B-Spline Curve 8

9. The hand-written alphabet (Russian) Personal hand-written font Our task 9

10. Step 1 The person writes separate letters by ink pen on a paper, for example, the alphabet The method description Step 2 The image is digitized by the scanner 10

11. The method description Binary image Polygonal figure Step 3 Construction of piecewise-linear boundary as a polygon of minimal perimeter 11

12. The method description Polygonal figure Continuous skeleton Step 4 Construction of continuous skeleton as a set of medial axes of polygonal figure 12

13. The method description Step 5 Construction of a base skeleton Continuous skeletonBase skeleton 13

14. The method description Step 6 Decomposition branches of base skeleton Base skeleton Base skeleton with circles 14

15. The method description Step 7 Approximation of base skeleton by a circular figure Circular figure Base skeleton with circles 15

16. Fat Curve Outline Smoothing Recalculation radius value for each control circle: 16

17. Fat Curve Axis Smoothing Recalculation center coordinates for each control circle: 17

18. Fat Curve Sewing 18

19. Kerning task What is better ? 19

20. Alignment of letter spacing Kerning - is a visual alignment of letter spacing in process of text on raster devices. How is near ? 20

21. Method of Automatic Kerning 1. Rasterization of kerning pair of characters on a common base line of raster 21

22. Method of Automatic Kerning 2. Scanning by a horizontal line "from top to bottom" with step of 1 pixel 22

23. Method of Automatic Kerning 3. At each position of a scanning line 23

24. 4. Defining position of a scanning line at which distance between the points is minimum Method of Automatic Kerning Minimal distance 24

25. 5. Defining minimal kerning distance Method of Automatic Kerning Minimal kerning distance Is negative kerning 25

26. 5. Defining minimal kerning distance Method of Automatic Kerning Minimal kerning distance Is positive kerning 26

27. Some examples KERNING[я][б] = 15 KERNING[в][а] = -72 Method of Automatic Kerning Minimal kerning distance is 20 27

28. Kerning table абвг.. эюя а1915812..-31119 б-13-17-5-8.. -7-29-21 в-721-62-67.. -66-88-80 г1915810.. -91019.. э4019.. 10-13-5 ю161263.. 19212 я19151117.. 919 Method of Automatic Kerning 28

29. Method of Automatic Kerning KERNING[в][ю] = -88What does it mean ? Length of this segment is 88 It means how many pixels to the left it is necessary to move the right character 29

30. Some examples Method of Automatic Kerning It’s A.S. Pushkin No kerning 30

31. Some examples Method of Automatic Kerning It’s A.S. Pushkin Kerning is 20 pixels 31

32. Some examples Method of Automatic Kerning It’s A.S. Pushkin Kerning is 40 pixels 32

33. Thickness Pen Modeling 33

34. 3D Modeling 34 Modeling of 3D effect by layer painting

35. “Alive” Handwriting Modeling - is noise Adding of small noise into values of radiuses 35

36. Adding of small noise into values of radiuses “Alive” Handwriting Modeling 36

37. Converting fat curve representation to outline description Export to famous description 37 Fat curves descriptionPostScript description

38. Summary The method of fat curves is efficient tool for modeling of hand-written characters; There is possibility of letterspacings controlling (zoom in/out letterspacing); There is easy way to modeling “alive” handwriting; Our approach can be used as embedded module (plug-in) in font editors. 38