More Drawing Tools

1
More Drawing Tools

• ( Canvas class Curves)
• www.cis.syr.edu/mohan/gra6.ppt

2
Canvas class

• Provides simple methods for creating screen
  window, establishing world window, mapping them,
  and simple Turtle graphics routines (moveto,
  lineto,)
• Supporting classes
• Point2 public Point2(), Point2(xx,yy),
  set(xx,yy), getX(), getY(), draw() private x,y
• IntRect, RealRect public Int/RealRect()/(ll,rr,bb
  ,tt), set(ll,rr,bb,tt), draw() private l,r,b,t

3
Canvas.h

• public Canvas(w,h,title), setWindow(l,r,b,t),
  setViewport(l,r,b,t), getViewport(), getWindow(),
  getWindowAspectRatio(), clearScreen(),
  setBackgroundColor(r,g,b), setColor(r,g,b),
  lineTo(x,y)/(p), moveTo(x,y)/(p)
• private CP, viewport, window

4
Using the Canvas class

• Create a global object cvs which initializes and
  opens the desired screen window.
• Callback functions such as display access and
  invoke cvs.methods.
• All initialization is done in the Canvas
  constructor
• main() sets the drawing and background colors,
  registers the display() callback function, and
  enters the main event loop.

5
Implementing the Canvas class

• Canvas constructor invokes glutInit,
  glutInitDisplayMode, glutInitWindowSize,
  glutInitWindowPosition, glutCreateWindow,
  setWindow, setViewport, and CP.set,
• using default values for all parameters.
• Other functions invoke appropriate gl... and glu
  functions, e.g., Fig.3.28.

6
Other functions turtle graphics

• moveRel(dx, dy)
• lineRel(dx, dy)
• turnTo(angle)
• turn(angle) //counterclockwise
• forward(dist, isVisible)//invoking lineTo and
  moveTo, conditional on isVisible
• These functions make it easy to build complex
  drawings from simple ones.

7
Examples using turtle graphics

• Ex.3.5.2, hook motif, its repetitions varying
  starting point CP and initial direction CD
• Ex.3.5.3, Polyspirals, iterating
• forward(len, 1) turn(angle) len increment
• results shown in Fig.3.35
• Meander patterns
• Drawing fractals, using F,L,R notation to
  abbreviate forward(d,1), turn(60), turn(-60)

8
Figures based on polygons

• Simple polygon only adjacent edges touch
• Regular polygon simple, equal sides, and
  adjacent sides meet at equal interior angles
  implemented by iterating for i0..n-1 to draw
  vertices at (R cos (2pi/n), R sin (2pi/n)), e.g.,
  cvs.forward(L,1) cvs.turn(60) for a hexagon
• Stellation Connecting every other vertex of a
  regular polygon
• Rosette Interconnecting all vertices of an r.p.

9
Shapes with arcs

• Teardrop patterns lines have the same slope as
  the circular arc at the intersection point
• Pie charts, e.g., with one slice exploded

10
Parametric Forms

• Graphics shapes can be described in many ways,
  each with its own disadvantages
• Implicit form F(x,y)0
• easy to test whether a point is on/inside/outside
• Explicit form yg(x) or xh(y), if single-valued
• Parametric form, use a new time parameter in
  terms of which each coordinate is expressed
  x(t)f(t), y(t)g(t)

11
Examples of parametric 2D curves

• Line from (A.x,A.y) to (B.x,B.y)
• x(t)A.x (B.x-A.x)t, y(t) A.y(B.y-A.y)t
• Ellipse of half-width W and half-height H
• x(t)W cos(t), y(t) H sin (t)
• Parabola x(t)att, y(t)2at
• Hyperbola x(t)a sec(t), y(t)b tan(t)
• To extract implicit form, we would have to
  eliminate the parameter t from the equations.

12
Drawing curves using parametric reps.

• Vary t from lower to upper extreme, take samples
  x(t), y(t) at small intervals of t
• For better appearance, use more samples where
  curve changes sharply with t
• For relatively smooth curves, generate points on
  the fly at uniform intervals of t, instead of
  first storing them.

13
Supercurves

• Superellipses, supercircles the bulge, i.e., the
  exponent 2 in the usual equations is allowed to
  vary outward bulgegt1, inward bulgelt1, rectangle
  for bulge1. Used in traffic circles and
  decorative patterns.
• Superhyperbola, similarly defined

14
Polar Forms

• Use angle ? instead of parameter t, e.g., x f(?)
  cos (?), y f(?) sin (?),
• circle f(? )K
• cardioid f(? )K(1cos (?))
• Archimedean spiral f(? )K ?
• conic sections f(? )1/(1 e cos (?))
• logarithmic spiral f(? ) K exp(a ?), cuts all
  radial lines at constant angle a, where cot(a)a
  has the same shape for any change of scale

15
3D Curves

• Parametric forms specified using three functions
  x(t), y(t), z(t), e.g.,
• Helix x(t)W cos(t), y(t)H sin(t), z(t) bt
• Conical Helix WHt
• Toroidal spiral winding a string about a torus
• x(t)(a sin(ct) b) cos(t),
• y(t)(a sin(ct) b) sin(t), z(t) a cos (ct)