Complex Plotting App

[dwgg]

(02-13-2015 10:04 PM)Han Wrote:  Your coloring function could be made to run faster. It's essentially the same algorithm repeated three times. Your k value can be computed using logarithms which would be much faster than using a while loop.

Code:


k:=2*m; // k:=(m-0)/(0.5-0) as the initial k value; if m>0.5 then modify k accordingly
if m>0.5 then
  k:=m/(.5e^FLOOR(LN(m)-LN(.5))*(e-1)) - 1/(e-1);
end;

If ranges:=0 and rangee:=C (C is a constant) then we are essentially finding the exponent x such that \(Ce^x < m \le Ce^{x+1} \).

\[ Ce^x = m \Rightarrow \ln C + x = \ln m \Rightarrow x = \ln m - \ln C \]

Secondly, k:=(m-ranges)/(rangee-ranges) simplifies to:
\[ k = \frac{m-Ce^x}{Ce^{x+1}-Ce^x} = \frac{m-Ce^x}{Ce^x(e-1)}
= \frac{m}{Ce^x(e-1)} - \frac{Ce^x}{Ce^x(e-1)} = \frac{m}{Ce^x}-\frac{1}{e-1} \]

The code could be made smaller by creating a function that computes and returns v.

Thank you for the recommendation. That part of code was just a port of Domain coloring code from wiki commons. I tried the modification and I think I see improvement of couple of seconds (for the same previous plot of (X+2)^2*(X-1-2*i)*(X+i)) in the simulator. I have not tried on actual HP Prime yet since I left it at home today.

Code:


// SetHSV() and GetColor() based on a
// c++ program from :
// http://commons.wikimedia.org/wiki/File:Color_complex_plot.jpg
// by Claudio Rocchini
// http://en.wikipedia.org/wiki/Domain_coloring

SetHSV(h,s,v);
GetColor(v);
EvalF();

EXPORT Plot()
BEGIN
  local x1,x2,y1,y2,co;
  local dx:=(Xmax-Xmin)/320;
  local dy:=(Ymax-Ymin)/240;
  local z1;
  local a,b,b1,d,k,x,y;
  local r:=4;  //r is size of initial square which is 2^r by 2^r pixels

  d:=2^r;
  FOR x FROM 0 TO 320-d STEP d DO
    FOR y FROM 0 TO 240-d STEP d DO
      z1:=Xmin+x*dx+i*(Ymin+(240-d-y)*dy);
      co:=EvalF(z1);
      RECT_P(G0,x,y,x+d-1,y+d-1,co); 
    END;
  END;
IF r THEN
  FOR k FROM 1 TO r DO
    d:=2^(r-k);
    FOR x FROM 0 TO 160/d-1 DO
      FOR y FROM 0 TO 120/d-1 DO
        a:=x*2*d; b:=y*2*d; b1:=(120/d-1-y)*2*d+d;
        z1:=Xmin+a*dx+i*(Ymin+b1*dy);
        co:=EvalF(z1);
        RECT_P(G0,a,b,a+d-1,b+d-1,co);
        z1:=z1+d*dx;
        co:=EvalF(z1);
        RECT_P(G0,a+d,b,a+2*d-1,b+d-1,co);
        z1:=z1+i*d*dy;
        co:=EvalF(z1);
        RECT_P(G0,a+d,b-d,a+2*d-1,b-1,co);
      END;
    END;
  END;
END;
WHILE 1 DO
  FREEZE;
END;
//  WAIT(-1);
END;

EvalF(z)
BEGIN
  IF RE(z) THEN
    RETURN(GetColor(F1(z)));
  ELSE
    RETURN(GetColor(F1(z+.001)));
  END;
END;

SetHSV(h, s, v)
BEGIN
    LOCAL r, g, b;
    LOCAL z, f, p, q, t, i;

    IF(s==0) THEN
       r:=v;
       g:=v;
       b:=v;
    ELSE
        IF(h==1) THEN h := 0; END;
        z := FLOOR(h*6);
        i := IP(z);
        f := h*6 - z;
        p := v*(1-s);
        q := v*(1-s*f);
        t := v*(1-s*(1-f));

        CASE
        IF i==0 THEN r:=v; g:=t; b:=p; END;
        IF i==1 THEN r:=q; g:=v; b:=p; END;
        IF i==2 THEN r:=p; g:=v; b:=t; END;
        IF i==3 THEN r:=p; g:=q; b:=v; END;
        IF i==4 THEN r:=t; g:=p; b:=v; END;
        IF i==5 THEN r:=v; g:=p; b:=q; END;
        END;
    END;

    r :=MIN(255,IP(256*r));
    g :=MIN(255,IP(256*g));
    b :=MIN(255,IP(256*b));
    RETURN RGB(r,g,b);
END;

GetColor(v)
BEGIN
    LOCAL a:=0;
    LOCAL m,k,sat,val;
    LOCAL c:=.01;

    IF v≠0 THEN a:=ARG(v); END;
    WHILE (a<0) DO a := a+ (2*π); END;
    a := a/(2*π);

// RE Contour
    m := ABS(RE(v));
    IF m>c then
      k:=m/(c*e^FLOOR(LN(m)-LN(c))*(e-1)) - 1/(e-1);
    ELSE
      k:=m/c;
    END;
    IF (k<0.5) THEN
        sat:=k*2;
    ELSE
        sat:=1 -(k -0.5) *2;
    END;
    val := sat;

    sat := 1 - (1-sat)^3; sat := 0.4 + sat*0.6;

    val := 1 - val;
    val := 1 - (1-val)^3;
    val := 0.6 + val*0.4;
    IF (val > 0.9999) OR (sat >0.9999) THEN 
      return SetHSV(a/6,sat,val);
      //return RGB(200,200,200); 
    END;

//IM Contour
    m := ABS(IM(v));
    IF m>c then
      k:=m/(c*e^FLOOR(LN(m)-LN(c))*(e-1)) - 1/(e-1);
    ELSE
      k:=m/c;
    END;
    IF (k<0.5) THEN
        sat:=k*2;
    ELSE
        sat:=1 -(k -0.5) *2;
    END;
    val := sat;

    sat := 1 - (1-sat)^3; sat := 0.4 + sat*0.6;

    val := 1 - val;
    val := 1 - (1-val)^3;
    val := 0.6 + val*0.4;
    IF (val > 0.9999) OR (sat >0.9999) THEN 
      return SetHSV(a/6,sat,val);
      //return RGB(255,255,255); 
    END;

//Domain Coloring
    m := ABS(v); 
    IF m>c then
      k:=m/(c*e^FLOOR(LN(m)-LN(c))*(e-1)) - 1/(e-1);
    ELSE
      k:=m/c;
    END;
    IF (k<0.5) THEN
        sat:=k*2;
    ELSE
        sat:=1 -(k -0.5) *2;
    END;
    val := sat;

    sat := 1 - (1-sat)^3; sat := 0.4 + sat*0.6;

    val := 1 - val;
    val := 1 - (1-val)^3;
    val := 0.6 + val*0.4;

    return SetHSV(a/6,sat,val);
END;