Graphics

1. Graphics • Vector graphics 2D only. • Overview of common functions and parameters.. • Drawing in Matlab. • We will see how a common file format stores the information. • Looking at similar functions in PDF.

2. Graphics • Source of confusion. • Vectors vs Bitmaps. • Here we are concerned with vector graphics.

3. Vector Graphics • Is to pictures what MIDI is to sound. • Uses lines, predefined shapes, curves and (predefined text). • Can be very compact. • Good for plotters. • Converted to bitmap for monitor display.

4. Co-ordinate systems • Vector graphics based upon an x, y co-ordinate system. • The x co-ordinate runs from left to right across the screen. • The y co-ordinate usually runs from the bottom (= 0) of the image to the top, but sometimes from top (= 0) to the bottom.

5. Co-ordinate systems • To set up co-ordinate system in Matlab. • haxes=axes • Sets up a co-ordinate system starting at 0 on the x- and y-axes and extending to 1.0 on the x-axis and 1.0 on the y-axis. • You may now draw on this system. • You can change the axis scaling using the “axis” command. • But by default the scaling will increase to accommodate your objects.

6. Lines in Matlab • Function line used to draw lines • h = line(x, y) where x and y are x and y co-ordinates of the start and end of a line. H is a “handle” to the graphics object (used for setting properties. • Example • x=[20 50] • y=[30 80] • hline = line(x,y) Draws a line from point x=20, y=30 to the point x=50, y=80

7. Rectangles in Matlab • Function “rectangle” used to draw rectangles in Matlab. • Often (in other packages and ‘C’ routines) rectangles are defined by 2 points only • Bottom left and top right. • In Matlab • hrect = rectangle('Position', [100 100 50 25]) • (start position (x,y) then width and height.) • Also used to draw ellipses and circles • hcirc = rectangle('Position', [100 100 50 25], 'Curvature', [1 1]). • A circle is an ellipse with the same (height as its width)

8. Polygons in Matlab • h = patch(x, y, ‘c’) draws a polygon, the vertices of which are contained in x and y, and is filled by colour ‘c’. • Example draw a red filled pentagon. • Need 5 points in x and y. • x=[50 25 100 175 150] • y=[50 100 150 100 50] • hpoly = patch(x, y, ‘r’)

9. Exercises • Draw a line from point x=20, y=30 to the point x=50, y=60. • Draw a rectangle with the bottom left hand corner at point x=30, y=50 and the top right hand corner at point x=70, y=80. • Draw a circle of radius 3 and centred at point x=50, y=60. • Draw a blue filled triangle.

10. Handles • The main figure has a “handle” in the Matlab environment. • Handles allow Matlab to keep track of figures and graphic objects. • Within the main figure we have an axis object; this also also has a handle. • It is a “child” object of the figure.

11. Handles • We differentiate between or identify objects by their handles • Sort of pointer. • When we add drawing objects such as our lines, rectangles, patches, they become child objects of the axis object and are also identified by handles. • So we now have an axes with four children. • We can return there values using • Hchild=get(haxes, ‘Children’)

12. Handles • So our structure so far could be drawn as. haxes has 4 children with handles hline, hrect, hcirc, and hpoly Hfigure is the handle to the figure and has child object with handle haxes

13. Handles • Or in hierarchical form hfigure Figure ‘children’ Represents handles Axes ‘children’ line rect rect patch

14. Handles • The handle of the figure is returned in variable “hfigure”. • It gives us access to all the properties of the figure. get(h) returns a copy of the figure’s (object’s) properties including its children.

15. Handles, Try it • Type “maindetails=get(hfigure)” • maindetails lists all the properties in the figure. • The structure includes handles to the child objects. • We can use the handles to gain access to the child objects and alter their properties.

16. Properties, get() and set() • We can retrieve a copy of the values associated with a graphic object through its handle by using S=get(hrect) • The structure contains all the properties of the graphic object. • However, since it is a copy we cannot change the actual information associated with the graphic object.

17. Properties, get() and set() • So in true “OO’” style we must use an access method/function to adjust parameters.. • Set(h,'PropertyName',PropertyValue) • Get(h) or Get(h, ‘PropertyName’) returns the property. • Note ‘quotes’

18. Order of objects • As an drawing object is added to the axes object an entry (drawing object’s handle) is placed in the “children” array of the axis object. • We can rearrange this array to change which object is on top. • Again we are simply swapping handles • We need to call “refresh” to see it.

19. Order of objects • So we get the axes objects “children” array. • hchild=get(haxes, ‘children’) • Make a copy • htemp=hchild • Rearrange the handles to the objects • htemp(4)=hchild(1) • htemp(1)=hchild(4) And set the axes “children: array to our new values set(haxes,’children’, htemp)

20. Deleting objects. • We can delete an object using its handle. • delete(hpoly) • Better put it back! • hpoly = patch(x, y, ‘r’)

21. Stroke, Fill and Colour • All vector graphic shapes have stroke and fill “properties”. • They affect how the graphic is drawn. • Stroke is how lines (and outlines are drawn) fill is how shapes are filled in. • One property is “colour” (‘color’ in Matlab. • Some other properties for stroke are: • Width ‘LineWidth’ • style (dotted dashed etc.) ‘LineStyle’

22. Stroke, Fill and Colour • To alter the fill and edge colour of a shape in Matlab: • set(hrect, 'FaceColor', [1 0 0]) for fill colour • set(hrect, 'EdgeColor', [1 0 0.5]) for stroke colour. • Where hr is a handle to the shape. • Line width and style may also be applied to the shape’s outline.

23. Transparency and “alpha” channels. • Another property of vector graphics is the ability to add transparency. • Many packages allow the adjustment of transparency from 0% to 100%. • An “alpha channel” (in addition to the colour channels id s provided with the objects for this purpose.

24. Transparency and “alpha” channels. • We can access the alpha channel of our shapes by the alpha property of the “patch” drawing object in Matlab. • Face and edge (fill and stroke) have separate alpha channels. • It has values between 0 and 1. • Defaults to 1 • set(hpoly, ‘FaceAlpha’, 0.5)

25. Text • Text may be added to vector graphics. • htext=text(50,100, ‘Dogs and cats’) • Properties “font” and “colour” (at least) may be changed.

26. Exercises • Draw the rectangle as above but change the outline to red and fill the rectangle with cyan.

27. Curves • Described mathematically. • Polynomial equations. • Degree of equations is the highest power of x. • Linear y = ax + b • degree 1 • Quadratic. y = ax2 + bx + c. • degree 2 • Cubic. y = ax3 + bx2 + cx + d • degree 3

28. Exercises • Linear degree 1 e.g. y = 2x + 5. x = [-10 :10]; plot(x, 2*x + 5) • Quadratic degree 2 e.g. y = x2 + 0x + 5. x = [-10 : 10]; plot(x, (x.^2) + 5) • Cubic degree 3 e.g. y = 2x3 + 20x2 + 3x +2 . x = [-10 : 10]; plot(x, 2*(x.^3) + 20*(x.^2) + 3*x + 2)

29. Bezier curves • P(t) = P0 (1-t)3 + P13t(1-t)2 + P23t2(1-t)+ P3t3 • As t takes values between 0 and 1. P’s are x, y points • Really two equations. • x(t) = x0 (1-t)3 + x13t(1-t)2 + x23t2(1-t)+ x3t3. • y(t) = y0 (1-t)3 + y13t(1-t)2 + y23t2(1-t)+ y3t3

30. Bezier curves • Consider t=0 then (1-t) = 1 • P(0) = (x0, y0) = P0 so curve goes through first point. • Consider t=1 then (1-t) = 0 • P(1) = (x3, y3) = P3 so curve goes through last point. • In between curve is pulled towards P1 and P2.,

31. Exercises • Try Matlab function mybezier.m • Examine the function. • Set up four points P0, P1, P2, P3. • e.g. P0 = [2, 3] • Run the function. • Experiment with different points.

32. Other mathematical curves • B-splines • NURBS

33. Storage of Vector Graphics. • Many formats • Autocad DXF. • Photoshop PSD. • Paintshop Pro PSP. • We will consider PDF’s implementation because it may be viewed easily.

34. PDF format • Portable Document Format • Developed by Adobe. • Developed from PostScript (and EPS (Encapsulated PostScript)). • PostScript describes pages as vector graphics.

35. Graphics in PDF • Similar operations to Matlab (and other). • PDF allows many complex graphics operations. • Lines • Rectangles • Curves • No direct method for circles. • We will look at a small selection to see that the PDF file can store vector graphics.

36. PDF graphic instructions. • All PDF graphic instructions use postfix notation where parameters are followed by the graphics operation instruction. • Fill and stroke parameters are set before the object is drawn. • To see a created object we must “fill” and “stroke” it.

37. PDF graphic instructions. • After adding to the PDF file we should really adjust the “Length” parameter of the stream and the “startxref” pointer at the end of the file. (see example file test.pdf) • When counting additions a new line (in Windows/Dos) counts as 2 characters. • However, Acrobat seems quite tolerant of errors in these fields. • (Ghostscript is not)

38. Lines in PDF • We must firstly move to the start of the path. (see test.pdf) • 150 250 m • Then we draw a line from this point to the end of line. • 400 250 l • To see the line we must draw the stroke • S • Try your own using note pad saving the file by some different name.

39. Rectangles in PDF • We set up the start point (x, y), then specify the width and height of the rectangle. • Then use the re operator to create the rectangle. • 200 300 50 75 re • We must then draw the stroke and fill the rectangle. “B” does this in one operation. • B

40. Rectangles in PDF • We set up the start point (x, y), then specify the width and height of the rectangle. • Then use the re operator to create the rectangle. • 200 300 50 75 re • Creates a rectangle starting at point x=200 y=300 width=50, height = 75. • We must then draw the stroke and fill the rectangle. “B” does this in one operation. • B

41. Bezier curve in PDF • Set starting point (x, y) for curve using m operator • 300 300 m • Add the two “control points” (x, y pairs) and the end point and create the curve using the c operator: • 300 400 400 400 400 300 c • Draw and fill the curve. • The example also closes (joins the ends together) using the b operator (which also draws the stroke and fills the closed shape) • b

42. Stroke and fill in PDF • Note that fill and stroke colours are set up before the affected object is drawn. In PDF terms we set the “graphics state”. • Some “graphics state” commands: • Set line width • Number w. • Set line style • [ a b ] 0 d ( [ ] is solid line) • Set stroke colour • R G B RG • Set fill colour • R G B rg

43. Graphic manipulations • Explained in detail in separate lecture. • Translation, scaling, rotation. • May be applied to vector or bitmap images. • Less artefacts with vectors. • This is set up as a “graphics state” in PDF using the cm operator.

44. Scaling • Making objects larger or smaller • In PDF we change the “current transformation matrix” of the “graphics state” using the cm operator. • For scaling: • sx 0 0 sy 0 0 cm

45. Translation • Moving objects left/right and up/down • In PDF we change the “current transformation matrix” of the “graphics state” using the cm operator. • For translation: • 10 0 1 tx ty cm

46. Rotation • Making objects larger or smaller • In PDF we change the “current transformation matrix” of the “graphics state” using the cm operator. • For rotation: • cos(q) sin(q) -sin(q)cos(q) 0 0 cm • Eg • 0.707 0.707 –0.707 0.707 0 0 cm rotates the current co-ordinates by 45o

47. Further information • Hill, Computer Graphics. Prentice Hall. • Adobe specifications available from www.adobe.com • Postscript • PDF