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+--- Forum: HP Prime Software Library (/forum-15.html)
+--- Thread: Complex Plotting App (/thread-2752.html)
RE: Complex Plotting App - Han - 07-01-2017 12:17 AM
(06-30-2017 03:48 AM)jtm Wrote: While this can be easily fixed by inserting evalf or approx into the CAS call, I’m curious, as an essentially clueless Prime programmer*, why you’re building and calling a CAS function in the first place, given that, in my cursory testing at least, the original non-CAS function works fine and plots slightly (~20%) faster.
I'm not sure what you mean by "CAS call" -- I believe that the entire program/app uses only non-CAS commands. (However, it has been a while and I have yet to refer to the code.)
RE: Complex Plotting App - FrankP - 12-25-2019 12:26 PM
My personal 3D color view skills have problems interpreting complex function characteristics from the domain coloring scheme. Therefore, I played around with one imaginary and one real color intensity mapped directly linear to a given value range. Additionally the RGB color scheme is changed from ABS related black/white to real/imaginary related blue/red combination for values above a threshold value 'amin':
- ABS(f(X)) < amin:
white..black #000000..#FFFFFF = ABS(f(X)) 0 ...amin - ABS(f(X)) > amin:
red #0000xx..#FF00xx = IM(f(X)) ymin...ymax
blue #xx0000..#xx00FF = RE(f(X)) xmin...xmax
black #000000 = IM(f(X)) < ymin and RE(f(X)) < xmin
magenta #FF00FF = IM(f(X)) > ymax and RE(f(X)) > xmax
Code:
#pragma mode( separator(.,;) integer(h-32) )
//EXPORT fX:="X^3"; // X gets x+i*y
//EXPORT xmin:=-5, xmax:=5, ymin:= −5, ymax:=5;
//EXPORT rmin:=-100, rmax:=350, imin:=-100, imax:=100;
//EXPORT fX:="Zeta(X)";
//EXPORT xmin:=−2, xmax:=1, ymin:=−4, ymax:=24;
//EXPORT rmin:=-4, rmax:=6, imin:=-4, imax:=6;
EXPORT fX:="(X+2)^2*(X-1-2*)*(X+)";
EXPORT xmin:=−4, xmax:=4, ymin:=−3, ymax:=3;
EXPORT rmin:=-100, rmax:=100, imin:=-100, imax:=100;
EXPORT amin:=0.1;
LOCAL fxiy:=replace(fX,"X","(xmin+xi*x + *(ymax-yi*y))");
LOCAL dx, dy, dreal, dimag, dabs;
PlotRes(r);
EXPORT Plot()
BEGIN
LOCAL mymouse,mykey,entr,x,y;
entr:=Entry; Entry:=1; // avoid textbook entry interpretation of fX
IF input(
{ {fX, [2],{10,90,0}},
{xmin,[0],{30,15,1}},
{xmax,[0],{80,15,1}},
{ymin,[0],{30,15,2}},
{ymax,[0],{80,15,2}},
{rmin,[0],{30,15,3}},
{rmax,[0],{80,15,3}},
{imin,[0],{30,15,4}},
{imax,[0],{80,15,4}},
{amin,[0],{30,15,5}}
},
"Complex Plot Setup",
{
"f(X)",
"Xmin=", "Xmax=",
"Ymin=", "Ymax=",
"REmin", "REmax",
"IMmin", "IMmax",
"min|f(X)|"
},
{ "Enter function (X as independant)",
"Enter minimum horizontal value",
"Enter maximum horizontal value",
"Enter minimum vertical value",
"Enter maximum vertical value",
"Enter minimum real f(X) value",
"Enter maximum real f(X) value",
"Enter minimum imaginary f(X) value",
"Enter maximum imaginary f(X) value",
"Switch from BlackWhite ABS to RedBlue IM/RE"
} )
THEN
RECT();
fxiy:=replace(fX,"X","(xmin+dx*x + *(ymax-dy*y))");
dx :=(xmax-xmin)/320;
dy :=(ymax-ymin)/240;
dreal:=255/(rmax-rmin);
dimag:=255/(imax-imin);
dabs :=255/(amin);
PlotRes(16);
// PlotRes(8);
PlotRes(4);
//PlotRes(2);
//PlotRes(1);
LINE_P(G0, 320/(xmin-xmax)*xmin, 0, 320/(xmin-xmax)*xmin, 240, #0); // y axis
LINE_P(G0, 0, 240/(ymax-ymin)*ymax, 320, 240/(ymax-ymin)*ymax, #0); // x axis
TEXTOUT_P(" ESC to cancel. Tap + directional pad to show values. ",G0,0,0,2, #0h,500,#FFFFFF);
// black text shadow ...
TEXTOUT_P(xmin+","+ymax, G0, 0+1, 13+1, 1, #0);
TEXTOUT_P(xmin+","+ymin, G0, 0+1, 240-10+1, 1, #0);
TEXTOUT_P(xmax+","+ymax, G0, 320-size(str(xmax+","+ymax))*4+1, 13+1, 1, #0);
TEXTOUT_P(xmax+","+ymin, G0, 320-size(str(xmax+","+ymin))*4+1, 240-10+1, 1, #0);
// ... and white text to sign (x,y) edge values
TEXTOUT_P(xmin+","+ymax, G0, 0 , 13 , 1, #FFFFFF);
TEXTOUT_P(xmin+","+ymin, G0, 0 , 240-10 , 1, #FFFFFF);
TEXTOUT_P(xmax+","+ymax, G0, 320-size(str(xmax+","+ymax))*4 , 13 , 1, #FFFFFF);
TEXTOUT_P(xmax+","+ymin, G0, 320-size(str(xmax+","+ymin))*4 , 240-10 , 1, #FFFFFF);
x:=−3; y:=-3; // avoid 1st inversion by position out of screen
WHILE 1 DO
mymouse:= mouse();
mykey:=getkey();
IF size(mymouse(1)) OR mykey≠−1 then // mouse activ
INVERT_P(G0, x-1,y-1,x+1,y+1); // revert previous mark
CASE
IF mykey== 2 THEN y := y-2; END; // up
IF mykey==12 THEN y := y+2; END; // down
IF mykey== 7 THEN x := x-2; END; // left
IF mykey== 8 THEN x := x+2; END; // right
IF mykey== 4 THEN RETURN; END; // esc
IF mykey==-1 THEN // no key thus we arrived here by a tap
x := mymouse(1,1);
y := mymouse(1,2);
END;
END;
TEXTOUT_P(" ESC to cancel. f ( "+TRUNCATE(xmin+dx*x + *(ymax-dy*y),-3)+" ) = "+
TRUNCATE( CAS(EVAL(fxiy)),-3 )+" ",
G0,0,0,2, #0h,500,#FFFFFFh );
INVERT_P(G0, x-1,y-1,x+1,y+1); // mark by color inversion
END;
END; // while
END; // input
Entry:=entr;
END;
LOCAL PlotRes(r)
BEGIN
LOCAL x,y,color;
FOR x FROM 0 TO 320-r STEP r DO
FOR y FROM 0 TO 240-r STEP r DO
TEXTOUT_P(" ESC to cancel. Plot col "+x+"/320, row "+y+"/240, resolution "+r+". ", G0,0,0,2, #0h,500,#FFFFFFh );
CASE
IF ( ABS( CAS(EVAL( fxiy )) ) < amin ) THEN
color:=RGB( MIN( 255, 255-(ABS( CAS(EVAL( fxiy )) )*dabs) ),
MIN( 255, 255-(ABS( CAS(EVAL( fxiy )) )*dabs) ),
MIN( 255, 255-(ABS( CAS(EVAL( fxiy )) )*dabs) ) );
END;
DEFAULT
color:=RGB( MIN( 255, MAX(0, ( IM( CAS(EVAL(fxiy)) )-imin )*dimag) ),
0,
MIN( 255, MAX(0, ( RE( CAS(EVAL(fxiy)) )-rmin )*dreal) ) );
END;
RECT_P(G0,x,y,x+r-1,y+r-1,color);
IF ISKEYDOWN(4) THEN RETURN; END;
END;
END;
END;[attachment=7959]