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360 changes: 360 additions & 0 deletions Vectorplot_examples.wxm
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/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 22.04.0 ] */
/* [wxMaxima: input start ] */
:lisp (defvar $hexversion 0.1)
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
:lisp (defun $hex2dec (h) (parse-integer h :radix 16))
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
:lisp (defun $dec2hex (h) (write-to-string h :base 16))
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* define the names of the hexadecimal colors */
white: "#ffffff"$
black: "#000000"$
gray0: "#000000"$
grey0: "#000000"$
gray10: "#1a1a1a"$
grey10: "#1a1a1a"$
gray20: "#333333"$
grey20: "#333333"$
gray30: "#4d4d4d"$
grey30: "#4d4d4d"$
gray40: "#666666"$
grey40: "#666666"$
gray50: "#7f7f7f"$
grey50: "#7f7f7f"$
gray60: "#999999"$
grey60: "#999999"$
gray70: "#b3b3b3"$
grey70: "#b3b3b3"$
gray80: "#cccccc"$
grey80: "#cccccc"$
gray90: "#e5e5e5"$
grey90: "#e5e5e5"$
gray100: "#ffffff"$
grey100: "#ffffff"$
gray: "#bebebe"$
grey: "#c0c0c0"$
lightgray: "#d3d3d3"$
lightgrey: "#d3d3d3"$
darkgray: "#a0a0a0"$
darkgrey: "#a0a0a0"$
red: "#ff0000"$
lightred: "#f03232"$
darkred: "#8b0000"$
yellow: "#ffff00"$
darkyellow: "#c8c800"$
green: "#00ff00"$
lightgreen: "#90ee90"$
darkgreen: "#006400"$
springgreen: "#00ff7f"$
forestgreen: "#228b22"$
seagreen: "#2e8b57"$
blue: "#0000ff"$
lightblue: "#add8e6"$
darkblue: "#00008b"$
midnightblue: "#191970"$
navy: "#000080"$
mediumblue: "#0000cd"$
royalblue: "#4169e1"$
skyblue: "#87ceeb"$
cyan: "#00ffff"$
lightcyan: "#e0ffff"$
darkcyan: "#00eeee"$
magenta: "#ff00ff"$
lightmagenta: "#f055f0"$
darkmagenta: "#c000ff"$
turquoise: "#40e0d0"$
lightturquoise: "#afeeee"$
darkturquoise: "#00ced1"$
pink: "#ffc0c0"$
lightpink: "#ffb6c1"$
darkpink: "#ff1493"$
coral: "#ff7f50"$
lightcoral: "#f08080"$
orangered: "#ff4500"$
salmon: "#fa8072"$
lightsalmon: "#ffa070"$
darksalmon: "#e9967a"$
aquamarine: "#7fffd4"$
khaki: "#f0e68c"$
darkkhaki: "#bdb76b"$
goldenrod: "#ffc020"$
lightgoldenrod: "#eedd82"$
darkgoldenrod: "#b8860b"$
gold: "#ffd700"$
beige: "#f5f5dc"$
brown: "#a52a2a"$
orange: "#ffa500"$
darkorange: "#c04000"$
violet: "#ee82ee"$
darkviolet: "#9400d3"$
plum: "#dda0dd"$
purple: "#c080ff"$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* define some palettes */
Palette_RGB : [red,green,blue]$
Palette_BGR : [blue,green,red]$
Palette_RB : [red,blue]$
Palette_BR : [blue,red]$
Palette_WB : [white,black]$
Palette_01 : ["#fffcf6","#fff7db","#fff4c2","#feecae","#f8ca8c","#f0a848","#c07860","#a86060","#784860","#604860"]$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* default palette used */
GlobalPalette : Palette_RGB$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* ------------------------------------------------------------------------- */
/* ----- convert rgb hex number (e.g. FFFFFF) to 3 rgb numbers [R,G,B] ----- */
/* ------------------------------------------------------------------------- */
splithex(hex):=block([],
if not stringp(hex) then hex:string(hex),
R:hex2dec(substring(hex,1,3)),
G:hex2dec(substring(hex,3,5)),
B:hex2dec(substring(hex,5,7)),
/*print("RGB = (",R,",",G,",",B,")"),*/
return([R,G,B])
)$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* ------------------------------------------------------------------------- */
/* ----- interpolate hexadecimal colors ------------------------------------ */
/* ------------------------------------------------------------------------- */
colorinterpolate(rl,color1,color2):=block([],

if (color1 = color2) then return(color1),
/* split the hexadecimal color hRGB into R,G,B */

/* if first character is a "#", then strip it */
if (substring(color1,1,2)="#") then color1:substring(color1,2),
if (substring(color2,1,2)="#") then color2:substring(color2,2),
RGB1 : splithex(color1),
RGB2 : splithex(color2),
R1:RGB1[1],
G1:RGB1[2],
B1:RGB1[3],
R2:RGB2[1],
G2:RGB2[2],
B2:RGB2[3],

/* interpolate between the colors */
R:round(R1+rl*(R2-R1)),
G:round(G1+rl*(G2-G1)),
B:round(B1+rl*(B2-B1)),
/* convert the colors back to hex */
Rh:dec2hex(R),
Gh:dec2hex(G),
Bh:dec2hex(B),
if(slength(Rh)=1) then Rh:concat("0",Rh),
if(slength(Gh)=1) then Gh:concat("0",Gh),
if(slength(Bh)=1) then Bh:concat("0",Bh),
return(concat("#",Rh,Gh,Bh))
)$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* ------------------------------------------------------------------------- */
/* ----- -------- */
/* ------------------------------------------------------------------------- */
v2hex(v) := block([p, nc],

/* write here your palette of colors */
/*1 2 3 4 5 6 7 8 9 10 */
p: GlobalPalette,
if not listp(p) then return(p), /* if there is only one color, and it's not in a list*/
nc: length(p),
if nc=1 then return(p[1]), /* there is only 1 color in the palette */

/* map range to color palette range */
ratio: 1 + (nc-1)*(v-minv)/(maxv-minv),
fr: floor(ratio),
fc: ceiling(ratio),
rl: ratio-fr,
color1:p[fr],
color2:p[fc],
colorinterpolate(rl,color1,color2)
)$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
/* streamplot */


/* ------------------------------------------------------------------------- */
/* draw a vector plot*/
/* input: fxy: list [fx,fy] with the x and y parts of the vector */
/* xrange,yrange: list [a,b] with the range in x and y direction */
/* vectorpoints: nr of vectors in x and y direction */
/* optional argument : vectorscale */
/* ------------------------------------------------------------------------- */
Vectorplot(fxy,xrangeV,yrangeV,[opt]):=block([x,y,fx,fy,Nx,Ny,Nxy,x1,x2,y1,y2,v,vectorscale],

/* ----- which optional arguments do we want: */
/* make xynr optional, default 10x10 */
/* scale = 1.0 scales the final vector size scale=none means all vectors have the same size*/
/* we should also have a user-defined scaling from Vmin to Vmax */
/* we should also have a user-defined scaling for the colors */
/* color = black,red,green,blue, #ffffff, gives all arrows a constant color */
/* staggered, for staggered grid */
/* grid = list of gridpoints */

/*if length(opt) = 1 then scale:opt[1] else if length(opt)>1 then error("too many arguments found:",opt),*/

vectorscale : assoc(vectorscale,opt,1.0), /* scaling of vectors */
vectorpoints: assoc(vectorpoints,opt,[10,10]), /* [Nx,Ny] number of vectors in x and y direction*/
terminalsetting: assoc(terminal,opt,wxt), /* set terminal (screen, png file, etc)*/
filename : assoc(filename,opt,"maxima_out"),/* filename of figure when terminal is a file (png, etc) */
user_preamble: assoc(user_preamble,opt,"set style line 11 lc rgb '#555555' lt 1; set border back ls 11 lw 2 "),
xrange: assoc(xrange,opt,1.2*xrangeV), /* the actual xrange of the figure (shown on the axes), default=1.2*xrangeV */
yrange: assoc(yrange,opt,1.2*yrangeV), /* note that xrangeV is the range in which the vectors are being plotted. */

print("terminal = ",terminalsetting),
Lv: sort(listofvars(fxy)), /* we assume that the variable on the x-axis is also alphabetically first */
if length(Lv)#2 then error("Vectorplot needs 2 variables, found ",Lv),
x: assoc(xvar,opt,Lv[1]), /* xvar determines the variable on the x-axis*/
y: assoc(yvar,opt,Lv[2]), /* yvar determines the variable on the y-axis*/

/* split the list of vectors */
fx:fxy[1], fy:fxy[2],
/* define fx,fy as functions of x,y */
define(dx(x,y),fx),
define(dy(x,y),fy),

/* by default, color by norm */
colorfunction : assoc(colorfunction,opt,sqrt(fx*fx+fy*fy)),
print("colorfunction = ",colorfunction),
/* vecColors is the local norm(strength) of the vector */
define(vecColors(x,y),colorfunction),
print("veccolors = ",fundef(vecColors)),

colorpalette : assoc(colorpalette,opt,GlobalPalette),
print("palette = ",colorpalette),
oldGlobalPalette:GlobalPalette,
GlobalPalette : colorpalette,

/* the plot domain to plot the vectors in is (x1,x2) - (y1,y2) */
x1:xrangeV[1], x2:xrangeV[2],
y1:yrangeV[1], y2:yrangeV[2],
AspectRatio : (y2-y1)/(x2-x1),
Nx:vectorpoints[1]-1, Ny:vectorpoints[2]-1,
Nxy:(Nx+1)*(Ny+1),

/* smallest vector */
/* largest vector should have the size of a cell*/
if listp(vectorscale) then (
Vmin : vectorscale[1],
Vmax : vectorscale[2],
vectorscale : 1.0
) else (
Vmax : min( (x2-x1)/Nx, (y2-y1)/Ny),
Vmin : 0.05*Vmax /* nonzero Vmin*/
),
print("Vmin,Vmax=",Vmin,Vmax),


/* initialization of the minimum and maximum values of the norm */
Nmin:sqrt(dx(x1,y1)*dx(x1,y1)+dy(x1,y1)*dy(x1,y1)), Nmax:Nmin,
/* norm contains the norm of the vector, used as the size of the arrow */
norm:makelist((_x:(x2-x1)*(mod(i-1,(Nx+1))/Nx)+x1,
_y:(y2-y1)*(quotient(i-1,(Nx+1))/Ny)+y1,
tmpx:errcatch(dx(_x,_y)),
tmpy:errcatch(dy(_x,_y)),
if length(tmpx)=0 then _dx:0 else _dx:tmpx[1],
if length(tmpy)=0 then _dy:0 else _dy:tmpy[1],
R:max(float(sqrt(_dx*_dx + _dy*_dy)),1.0e-6), /* make sure that the norm is nonzero */
Nmin:min(Nmin,R),Nmax:max(Nmax,R),
R),i,1,Nxy),
/* Now scale the norm from [Nmin,Nmax] -> [0,Vmax] */
/* (norm-Nmin)/(Nmax-Nmin) = (p-Vmin)/(Vmax-Vmin) */
/*
print("Nmin,Nmax = ",Nmin,Nmax),
vectorclip : assoc(vectorclip,opt,[Nmin,Nmax]), /* clip the vector size */
("vectorclip = ",vectorclip[1],vectorclip[2]),
*/
normp:(norm-Nmin)*(Vmax-Vmin)/(Nmax-Nmin) + Vmin,

print("Nmin,Nmax = ",Nmin,Nmax,vectorscale),
dxdy:makelist((_x:(x2-x1)*(mod(i-1,(Nx+1))/Nx)+x1,
_y:(y2-y1)*(quotient(i-1,(Nx+1))/Ny)+y1,
tmpx:errcatch(dx(_x,_y)),
tmpy:errcatch(dy(_x,_y)),
if length(tmpx)=0 then _dx:0 else _dx:tmpx[1],
if length(tmpy)=0 then _dy:0 else _dy:tmpy[1],
[float(_dx),float(_dy)]),i,1,Nxy),

/* scale dxdy with the norm */
/* also, use scale factor in case you want larger/smaller than default */
/* also, clipping activated */
/*dxdy:vectorscale*min(max(normp*dxdy/norm,vectorclip[1]),vectorclip[2]),*/
dxdy:vectorscale*normp*dxdy/norm,

xy:makelist((_x:(x2-x1)*(mod(i-1,(Nx+1))/Nx)+x1,
_y:(y2-y1)*(quotient(i-1,(Nx+1))/Ny)+y1,
[float(_x),float(_y)]),i,1,Nxy),

v1:xy-dxdy/2.0,
v2:dxdy,

/* find minimum and maximum for colors */
v_values: makelist(apply(vecColors, xy[i]),i,1,Nxy),
minv: lmin(v_values),
maxv: lmax(v_values),
print("minv,maxv = ",minv,maxv),
veclist:makelist(['color = v2hex(apply(vecColors, xy[i])), vector(v1[i],v2[i])],i,1,Nxy),

GlobalPalette:oldGlobalPalette,
/* draw the list of vectors */
header : ['terminal = terminalsetting,
'file_name = filename,
'font_size = 16,
'dimensions = [800,AspectRatio*800],
'xrange = [xrange[1],xrange[2]],
'yrange = [yrange[1],yrange[2]],
'line_width = 2,
'head_angle = 20,
'head_length = 0.30*Vmax,
'user_preamble = concat("set term ",terminalsetting," enhance font \"Charter,16\"; ",user_preamble)
],
draw2d(header, veclist)
)$
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
Vectorplot([y,-x],[-2,2],[-2,2],vectorpoints=[10,10],colorpalette=[green,red,blue,black,gold],vectorscale=[0.3,0.3]);
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
Vectorplot([y,-x],[-2,2],[-2,2],vectorpoints=[10,10],colorpalette=Palette_BGR,vectorscale=[0.3,0.3]);
/* [wxMaxima: input end ] */


/* [wxMaxima: input start ] */
Vectorplot([y,-x],[-2,2],[-2,2],vectorpoints=[10,10],colorpalette=["#fffcf6","#fff7db","#fff4c2","#feecae","#f8ca8c","#f0a848","#c07860","#a86060","#784860","#604860"],vectorscale=[0.3,0.3]);
/* [wxMaxima: input end ] */



/* Old versions of Maxima abort on loading files that end in a comment. */
"Created with wxMaxima 22.04.0"$