file qdrawcode.txt

Maxima code from sections of Ch. 5 of
Maxima by Example, E.L. Woollett
Jan., 2009 version

5.1 Quick Plots for Explicit Functions: ex(...) 

(%i1) load(draw)$
(%i2) load(qdraw)$
(%i3)  qdraw( ex( [x,x^2,x^3],x,-3,3 ) )$
(%i4) qdraw( ex([x,x^2,x^3],x,-3,3 ),yr(-2,2) )$ 
(%i5) qdraw(ex([x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6))$
(%i6) qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2),lw(6),key(bottom) )$
(%i7) qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2),
                 lw(6),key(bottom), cut(grid, xyaxes) )$
(%i8) qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2),
                 lw(6), cut( all ) )$
(%i9)  qdraw( ex([x,x^2,x^3],x,-3,3 ),yr(-2,2),lw(6),
              key(bottom),pts( [ [-1,-1],[0,0],[1,1] ] ) )$
(%i10) qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6),key(bottom), 
              pts([ [-1,-1],[0,0],[1,1] ],ps(2),pc(magenta) ) )$
(%i11) qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6),key(bottom), 
           pts([ [-1,-1],[0,0],[1,1] ],ps(2),pc(magenta),pk("intersections") ) )$
(%i12) qdraw( ex( [x,x^2,x^3],x,-3,3 ),yr(-2,2), lw(6),key(bottom), 
        line(-3,0,3,0,lw(2)),line(0,-2,0,2,lw(2)),
    pts([ [-1,-1],[0,0],[1,1] ],ps(2),pc(magenta),pk("intersections")),
            pic(eps,"ch5p9") )$
(%i13) qdraw( yr(-2,2),lw(6), ex( [x,x^2,x^3],x,-3,3 ),
              key(bottom), ex(sin(3*x)*exp(x/3),x,-3,3),
              pts([ [-1,-1],[0,0],[1,1] ]) )$
(%i14) qdraw( yr(-2,2),lw(6), ex( [x,x^2,x^3],x,-3,3 ),
              key(bottom), ex(sin(3*x)*exp(x/3),x,-3,3),
              pts([ [-1,-1],[0,0],[1,1] ]) ,
               label(["qdraw at work",-2.9,1.5]),
              pic(eps,"ch5p11",font("Times-Bold",20) ) );
(%i15) qdraw( yr(-2,2),lw(6), ex( [x,x^2,x^3],x,-3,3 ),
              key(bottom), ex(sin(3*x)*exp(x/3),x,-3,3),
              pts([ [-1,-1],[0,0],[1,1] ]) ,
               label(["qdraw at work",-2.9,1.5]),
              pic(jpg,"ch5p11",font("c:/windows/fonts/timesbd.ttf",20) ) );

5.2 Quick Plots for Implicit Functions: imp(...)

(%i16) qdraw( imp( sin(2*x)*cos(y)=0.4,x,-3,3,y,-3,3 ) ,
             cut(key) );
(%i17) qdraw( imp( [sin(2*x)*cos(y)=0.4,
             sin(2*x)*cos(y)=0.7,
             sin(2*x)*cos(y)=0.9] ,x,-3,3,y,-3,3 ) ,
             cut(key) );
(%i18) g : sin(2*x)*cos(y)$
(%i19) qdraw( imp( [g = 0.4,g = 0.7,g = 0.9] ,x,-3,3,y,-3,3 ) ,
             cut(key) )$
(%i20) qdraw( imp( [g = 0.4,g = 0.7,g = 0.9] ,x,-%pi,%pi,y,-%pi,%pi ) ,
             cut(key) )$
(%i21) qdraw( imp( [g = 0.4,g = 0.7,g = 0.9] ,x,-4.2,4.2,y,-3,3 ) ,
             cut(key) )$

5.3 Contour Plots with contour(...)

(%i22) qdraw( contour(g, x,-4.2,4.2, y,-3,3, cvals(0.4,0.7,0.9) ) )$
(%i23) qdraw( contour(g,x,-4.2,4.2,y,-3,3,cvals(0.4,0.7,0.9),
        lw(2),lc(brown) ), ipgrid(15) )$
(%i24) qdraw( contour(g,x,-4.2,4.2,y,-3,3,crange(4,0.2,0.9),
        lw(2),lc(brown) ), ipgrid(15)  )$
(%i25) qdraw( contour(sin(x)*sin(y),x,-2,2,y,-2,2,crange(4,0.2,0.9),
              lw(3),lc(blue),add(xyaxes) ), ipgrid(15) )$

5.4 Density Plots with qdensity(...)

(%i26) qdensity(x*y,[x,0,1,0.2],[y,0,1,0.2] )$
(%i27) qdensity(x*y,[x,0,1,0.2],[y,0,1,0.2],
                 palette(gray) )$
(%i28) qdensity(x*y,[x,0,1,0.05],[y,0,1,0.05] )$
(%i29) qdensity(sin(x)*sin(y),[x,-2,2,0.05],[y,-2,2,0.05] )$

5.5 Explicit Plots with Greater Control: ex1(...)

(%i30) qdraw( xr(-1.4,2.8),yr(-1,2),
        ex1(x^2,x,-2,2,lw(5),lc(brown),lk("X^2")),
        ex1(2*x-1,x,-2,2,lw(2),lc(blue),lk("TANGENT")),
        ex1(-x/2 + 3/2,x,-2,2,lw(2),lc(magenta),lk("NORMAL") ) ,
         pts( [ [1,1] ],ps(2),pc(red) ) )$

(%i31) qdraw( ex1(bessel_j(0,x),x,0,20,lc(red),lw(6),lk("bessel_j ( 0, x)") ),
          ex1(bessel_j(1,x),x,0,20,lc(blue),lw(5),lk("bessel_j ( 1, x)")),
          ex1(bessel_j(2,x),x,0,20,lc(brown),lw(4),lk("bessel_j ( 2, x)") ),
          ex1(bessel_j(3,x),x,0,20,lc(green),lw(3),lk("bessel_j ( 3, x)") ) )$
          
(%i32) qdraw( ex1(bessel_j(0, sqrt(x)),x,0,50 ,lc(blue),
              lw(7),lk("J0( sqrt(x) )") ) , 
         line(0,0,50,0,lc(red),lw(2) ) )$
         

5.6 Explicit Plots with ex1(...) and Log Scaled Axes

(%i33) g : x*exp(-x)$
(%i34) qdraw( ex1( log(g),x,0.001,10, lc(red) ),yr(-8,0)  )$

(%i35) qdraw( ex1(g, x, 0.001,10,lc(red) ),
                 yr(0.0001, 1), log(y) )$

(%i36) qdraw( ex1(g, x, 0.001,10,lc(red),lw(7) ),
                 yr(0,0.4), log(x) )$
                 
(%i37) qdraw( ex1(g, x, 0.001,10,lc(red) ),
                  yr(0.0001,1), log(xy) )$
                  
5.7 Data Plots with Error Bars: pts(...) and errorbars(...)

(%i38) printfile("fit1.dat")$
(%i39) plist : read_nested_list("fit1.dat");
(%i40) qdraw( pts(plist) )$
(%i41) qdraw( pts(plist, ps(2)), xr(0,12),yr(0,15) )$
(%i42) qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, 1) )$
(%i43) qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, 1, lw(3),lc(red) )  )$

(%i44) dyl : [0.2,0.3,0.5,1.5,0.8,1,1.4,1.8,2,2]$
(%i45) map(length,[plist,dyl] );
(%i46) qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, dyl, lw(3),lc(red) )  )$
          
(%i47) display2d:false$
(%i48) pmatrix : apply( 'matrix, plist );
(%i49) load(lsquares);
(%i50) soln : (lsquares_estimates(pmatrix,[x,y],y=a*x+b,
                   [a,b]), float(%%) );
(%i51) [a,b] : (fpprintprec:5, map( 'rhs, soln[1] ) )$
(%i52) [a,b];
(%i53) qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, dyl, lw(3),lc(red) ),
         ex1( a*x + b,x,0,12, lc(brown),lk("linear fit") )  )$
         
(%i54) printfile("fit2.dat");
(%i55) p2list: read_nested_list("fit2.dat");
(%i56) qdraw( pts(plist,pc(blue),pk("fit1"), ps(2)), xr(0,12),yr(0,15),
          key(bottom), errorbars( plist, dyl, lw(3),lc(red) ),
         ex1( a*x + b,x,0,12, lc(brown),lk("linear fit 1") ),
         pts(p2list, pc(magenta),pk("fit2"),ps(2)),
         errorbars( p2list,0.5,lw(3) ) )$
         

5.8 Implicit Plots with Greater Control: imp1(...)

(%i1) eqn1 : 5*x^2 + 4*x*y + 8*y^2 - 16*x + 8*y - 16 = 0$
(%i2) eqn2 : y+1 = 2*(x-2)$
(%i3) eqn3 : y+1 = -(x-2)/2$
(%i4) qdraw( imp1(eqn1,x,-2,6.4,y,-4,2,lc(red),lw(6),lk("ELLIPSE")),
              imp1(eqn2,x,-2,6.4,y,-4,2,lc(blue),lw(4),lk("ROT X AXIS")),
              imp1(eqn3,x,-2,6.4,y,-4,2,lc(brown),lw(4),lk("ROT Y AXIS") ),
          pts([ [2,-1] ],ps(2),pc(magenta),pk("TRANSLATED ORIGIN") ) )$
          
(%i5) qdraw( imp1(y^3=x^2,x,-3,3,y,-1,3,lw(10),lc(dark-blue)) )$


5.9 Parametric Plots with para(...)

(%i6) qdraw(xr(-1.5,2),yr(-2,2), 
         para(sin(t),sin(2*t),t,0,2*%pi ) ,
         pts( [ [sin(%pi/8),sin(%pi/4)] ],ps(2),pc(blue),pk("t = pi/8")),
         pts( [ [1,0] ],ps(2),pc(red),pk("t = pi/2")) )$
         
(%i7) qdraw(xr(-3,4),yr(-1,40), para(2*cos(u),u^2,u,0,2*%pi) ,
         pts([ [2,0] ],ps(2),pc(blue),pk("u = 0")),
         pts( [ [0,(%pi/2)^2] ],ps(2), pc(red), pk("u = pi/2")),
         pts([ [-2,%pi^2]],ps(2),pc(green),pk("u = pi")),
         pts( [[0,(3*%pi/2)^2]],ps(2),pc(magenta),pk("u = 3*pi/2")) )$
         

5.10 Polar Plots with polar(...)  

(%i8) qdraw( polar(10/t,t,1,3*%pi,lc(brown),lw(5)),nticks(200),
            xr(-4,6),yr(-3,9),key(bottom) ,
       pts( [[10*cos(1),10*sin(1)]],ps(3),pc(red),pk("t = 1 rad")),         
     pts([[5*cos(2),5*sin(2)]],ps(3),pc(blue),pk("t = 2 rad") ),
              line(0,0,5*cos(2),5*sin(2)) )$
              
5.11 Geometric Figures: line(...)  

(%i9) qdraw( line(0,0,1,1) )$
(%i10) qdraw( line(0,0,1,1,lc(blue),lw(6),lk("radius") ),
              xr(0,2),yr(0,2),key(bottom),
              pts([ [1,1] ] ,pc(red),pk("point")) )$
(%i11) load(doplot1)$
(%i12) doplot1(20)$


5.12 Geometric Figures: rect(...)  

(%i13) qdraw( xr(-1,2),yr(-1,2),rect(0,0,1,1) )$
(%i14) qdraw( xr(-1,2),yr(-1,2),
            rect(0,0,1,1,lw(5),lc(brown),fill(khaki) ) )$

(%i15) qdraw( xr(-3,3),yr(-3,3), rect( -2.5,-2.5,2.5,2.5,lw(4),lc(blue) ),
         rect( -2,-2,2,2,lw(4),lc(red) ),
         rect( -1.5,-1.5,1.5,1.5,lw(4),lc(green) ),
         rect( -1,-1,1,1,lw(4),lc(brown) ),
         rect( -.5,-.5,.5,.5,lw(4),lc(magenta) ),
           cut(all) )$
           
5.13 Geometric Figures: poly(...)  

(%i16) qdraw( xr(-2,2),yr(-1,2),cut(all),
            poly([ [-1,-1],[1,-1], [2,2] ]  ) )$
            
(%i17) load(doplot2)$
(%i18) doplot2()$


5.14 Geometric Figures: circle(...) and ellipse(...)  

(%i19) qdraw( xr(-2, 2), yr(-2, 2), circle( 0, 0, 1 ) )$

(%i20) qdraw(xr(-2.1,2.1),yr(-1.5,1.5),cut(all),
            circle(0,0,1,lw(5),lc(brown),fill(khaki) ),
              line(-1.5,-1.5,1.5,1.5,lw(8), lc(red) ),
                key(bottom) )$
                
(%i21) qdraw(xr(-2.1,2.1),yr(-1.5,1.5),cut(all),
            line(-1.5,-1.5,1.5,1.5,lw(8),lc(red) ),
            circle(0,0,1,lw(8),lc(brown),fill(khaki) ),
                key(bottom) )$
                
(%i22) qdraw( xr(-4.2,4.2),yr(-3,3),
         ellipse(0,0,3,2,90,270) )$
         
(%i23) qdraw( xr(-5.6,5.6),yr(-4,4),ex1(x,x,-4,4,lc(blue),lw(5)),
                  ex1(4*cos(x),x,-4,4,lc(red),lw(5) ),
         ellipse(0,0,3,1,90,270,lc(brown),lw(5),fill(khaki)) ,
             cut(all) )$
             

5.15 Geometric Figures: vector(..)  

(%i24) qdraw( xr(-2,2), yr(-2,2), vector( [-1,-1], [2,2] ) )$ 

(%i25) qdraw(xr(-2,2),yr(-2,2),
           vector([-1,-1],[2,2],lw(5),lc(brown),lk("vec 1")),
            key(bottom) )$
            
(%i26) qdraw(xr(-2,2),yr(-2,2),
           vector([0,0],[1,1],lw(5),lc(blue),lk("vec 1"),
                  ht(e),hb(t),ha(45) ), key(bottom) )$
                  
(%i27) qdraw(xr(-2.8,2.8),yr(-2,2),
           vector([0,0],[1,1],lw(5),lc(blue),lk("vec 1"),
                       ht(e),hb(t),ha(45) ),
           vector([0,0],[-1,-1],lw(5),lc(red),lk("vec 2")),
            key(bottom) )$
            

5.16 Geometric Figures: arrowhead(..)  

(%i28) qdraw(xr(-2.8,2.8),yr(-2,2),
            arrowhead(1.5,0,180,.3),arrowhead(0,1,270,.3),
            arrowhead(-1.5,0,0,.3),arrowhead(0,-1,90,.3) )$
            

5.17 Labels with Greek Letters

5.17.1 Enhanced Postscript Methods
     
(%i29) qdraw(xr(0,2.8),yr(0,2),
             line(0,0,2.8,0,lw(2)),
             line(0,0,2,2,lc(blue),lw(8) ),
           ellipse(0,0,1,1,0,45 ),
           arrowhead(0.707,0.707,135,0.15),
   label(["{/=36 {/Symbol q   \\254 }  The Incline Angle}",1,0.4]),
            cut(all),
           pic(eps,"ch5p52" ) );
           
(%i30) qdraw(xr(-3,3),yr(-2,2),label_align(c),
         label( ["{/=48 a b c d e f g h i j k l m}",0,1.5] ),
        label( ["{/Symbol=48 a b c d e f g h i j k l m}",0,0.5] ),
        label( ["{/=48 n o p q r s t u v w x y z}",0,-.5] ),
         label( ["{/Symbol=48 n o p q r s t u v w x y z}",0,-1.5] ),   
        cut(all), pic(eps,"ch5p53") )$
        
(%i31) qdraw(xr(-3,3),yr(-2,2),label_align(c),
         label( ["{/=48 A B C D E F G H I J K L M}",0,1.5] ),
        label( ["{/Symbol=48 A B C D E F G H I J K L M}",0,0.5] ),
        label( ["{/=48 N O P Q R S T U V W X Y Z}",0,-.5] ),
         label( ["{/Symbol=48 N O P Q R S T U V W X Y Z}",0,-1.5] ),   
        cut(all), pic(eps,"ch5p54") )$
        
(%i32) s1 : "{/Symbol=48 \\243   \\245   \\253   \\254   \\256}"$
(%i33) s2 : "{/Symbol=48 \\261   \\263   \\264   \\271   \\273   \\345   \\362}"$
(%i34) qdraw(xr(-3,3),yr(-2,2),label_align(c),
        label( [s1,0,1] ), label( [s2,0,-1] ), cut(all), pic(eps,"ch5p55") )$
        


5.17.2 Windows Fonts Methods with jpeg Files                                   
     
(%i35) qdraw(xr(0,2.8),yr(0,2),
             line(0,0,2.8,0),
             line(0,0,2,2,lc(blue),lw(5) ),
           ellipse(0,0,1,1,0,45 ),
           arrowhead(0.707,0.707,135,0.15),
            label(["q",1,0.4]), cut(all),
           pic(jpg,"ch5p52p",font("c:/windows/fonts/grii.ttf",36)) );  
           
(%i36) qdraw(xr(-3,3),yr(-2,2), 
     label(["a b c d e f g h i j k l m",-2.5,1.5],
             ["n o p q r s t u v w x y z",-2.5,0.5],
              ["A B C D E F G H I J K L M",-2.5,-0.5],
                ["N O P Q R S T U V W X Y Z",-2.5,-1.5]  ),     
            cut(all),
           pic(png,"ch5p60",font("c:/windows/fonts/grii.ttf",24)) );
           

5.17.3 Using Windows Fonts with the Gnuplot Console Window

  (See text for converting "q" to Greek letter theta.)

(%i37) qdraw(xr(0,2.8),yr(0,2),
             line(0,0,2.8,0),
             line(0,0,2,2,lc(blue),lw(5) ),
           ellipse(0,0,1,1,0,45 ),
           arrowhead(0.707,0.707,135,0.15),
            label(["q",1,0.4]), cut(all) )$
            

5.18 Even More with more(...)                           


(%i38)  qdraw( lw(8), ex([x,x^2,x^3],x,-2,2),
          more(xlabel = "X AXIS", title="intersections of x, x^2, x^3" ),
		   cut(key),line(-2,0,2,0,lw(2)),line(0,-8,0,8,lw(2)),
               vector([-1,5],[-0.4,-2.7],lc(red),hl(0.1) ),
               label(["x^2",-0.9,6]),
               vector([-1.2,-6],[-0.5,0],lc(turquoise),lw(8)),
               label( ["x^3", -1,-5.5] ),
              pts( [[-1,-1],[0,0],[1,1]],ps(2),pc(magenta)  ),
              pic(eps,"ch5p56",font("Times-Roman",28)) )$