Just for shits and giggles. Here is: \(f(z) = \sin(z)\). Where \(-1 \le \Re(z) \le 1\) and \(-1 \le \Im(z) \le 1\). And let's make a 500 by 500 pixel graph. But let's only choose 125 x 125 reference points; which is a "blur factor" of 0.25.
We have to run:
E = for X; for Y; write(X,Y);
For all X,Y in 500 by 500; which creates our default starter speed.
P = for X/0.25; for Y/0.25; F(X,Y)
Where, X only ends up doing 125 loops, same with Y. Because 500*0.25 = 125.
So we write 500x500 times; but we only calculate F 125x125 times.
Then the total time is just:
E + P
Which with large graphs, and large values, reduces times tenfold!!!!! Assuming we don't lose accuracy, or quality of the graph, is a purist's question. Everything looks good enough!
This does E = WRITE(500 BY 500) time, plus the addition of O(F(125,125))
And god its fast as fuck, and there's zero difference
The code is simple as:
P =
For X=0, 125:
For Y=0, 125:
F(X,Y)
E =
For X = 0, 500:
For Y=0, 500:
WRITE(X,Y)
Total time to compile is:
E + P
Mike3's time would be written:
MIKE =
For X=0,500:
For Y=0, 500:
P = F(X,Y);
WRITE(P);
Which causes 500 BY 500 evaluations of F(X,Y). Rather than my modest 125 BY 125. And the graphs are indistinguishable.... What I call "blur factor" isn't a jpeg blur. The splining, and graphing, is indistinguishable. So if you take a nice function like F(X,Y) = sin(X + iY), everything behaves perfectly. And even choosing a blur factor of 0.25 still keeps everything beautiful!
We have to run:
E = for X; for Y; write(X,Y);
For all X,Y in 500 by 500; which creates our default starter speed.
P = for X/0.25; for Y/0.25; F(X,Y)
Where, X only ends up doing 125 loops, same with Y. Because 500*0.25 = 125.
So we write 500x500 times; but we only calculate F 125x125 times.
Then the total time is just:
E + P
Which with large graphs, and large values, reduces times tenfold!!!!! Assuming we don't lose accuracy, or quality of the graph, is a purist's question. Everything looks good enough!
This does E = WRITE(500 BY 500) time, plus the addition of O(F(125,125))
And god its fast as fuck, and there's zero difference
The code is simple as:
P =
For X=0, 125:
For Y=0, 125:
F(X,Y)
E =
For X = 0, 500:
For Y=0, 500:
WRITE(X,Y)
Total time to compile is:
E + P
Mike3's time would be written:
MIKE =
For X=0,500:
For Y=0, 500:
P = F(X,Y);
WRITE(P);
Which causes 500 BY 500 evaluations of F(X,Y). Rather than my modest 125 BY 125. And the graphs are indistinguishable.... What I call "blur factor" isn't a jpeg blur. The splining, and graphing, is indistinguishable. So if you take a nice function like F(X,Y) = sin(X + iY), everything behaves perfectly. And even choosing a blur factor of 0.25 still keeps everything beautiful!