Hatch

7d96eb7f-91c2-40ce-bef0-347747bb679d 41 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Min plottable

This region is now blank and probably corrupted, Why ? Below the last plot, I constructed a discrete "G", all similar to "S". It freaked the work sheet and it could no be recuperated. Can't delete the attempt "G" can't do this, can't do that ... etc. Finally, Smath crashed. ------------------------------------ The X_Y plot is interesting wrt trace colors an wrt what it can do. Otherwise, it is not a "technical plotting package". In short, X_Y make Smath gorgeous for plotting parametric f(x,y), custom bar plot, radial grid to imitate dedicated polar packages. ------------------------------------

148 / ln 3.871201 -

Smath lower ln(x) limit 1099 -^ln 227.955924 -

2 3 x * sin * x abs ln 0 3.87 - 1 2 mat 3 1 sys

RESUME: bugs/deficiencies 1. Ugly QuickPlot points is caused by 2 pixels wide 2. X_Y needs be instructed to ignore ± infinite line. 3. Can't explain/reconciliate: __ Both, QuickPlot & X_Y rejet Gamma(x __ Both, QuickPlot & X_Y accept Γ(x) 4. X_Y is missing the code to interpret ln(0)=-∞ is 'NaN' [Not a Number]. Obligation to plot ln(|x|) for dual range x ± is not technical, missing realism. Alternate proposal: Algo(ln(x),hi)

Hatch

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x f 1 x / :

x g 0 :

b 3 :

H x f x g 1 b 10 hatch :

x f x g H 3 1 sys

x Γ 1 x / 11 x n / + / (11 n / + (x^* (n 1 ∞ product * (≡

x f x 1 b int b ln 21 mat 1.098612 1.098612 21 mat

x G x Γ x Gamma : x 0 ≥ x Γ π x abs 1 + (* x abs 2 + Γ π x abs 1 + (* sin * / if 21 line :

On many counts, X_Y plot adds professionalism to Smath document. On other counts => useless : 1/x => pure zombie in finity, NO Gamma(x), rejects "if" ... "x not defined" ... then assign as NaN [Not a Number]. The min "zero" X_Y is 10e-7

Damned crappy plot point ... should plot single pixel.

x Gamma x Gamma 1 1 sys

1099 -^Gamma 1.000002 1099^*

x G x ln x sqrt

Perfect technical plot

x G

box 0.05 - 1 - 0.05 - 1 0.05 1 0.05 1 - 0.05 - 1 - 52 mat :

Scalar does not plot 'box'...Why ? => 'box is not scalar

x 0.05 - ≤ ( 0.05 x ≤ ( | ( 1 x / sin if box 2 1 sys

Assign result for compatibilies Ω xx 0.25 - 0.25 0.2495 - range : i 1 xx rows range xx i el 0.05 - ≤ (0.05 xx i el ≤ (| (Ω i el 1 xx i el / sin : if for Ω xx Ω augment : 31 line :

Technical compatible plots [discrete/scalar]

Ω box 0.01 x / 3 1 sys Ω box 0.01 x / 3 1 sys

Crappy not thechnical [±] infinite line

A technical plot

1 x /

Next: the 4 most useful X_Y applications

1. X_Y parametric companion to Smath

r 1 :

level 0.25 :

α 2 :

x y Doublet y r 2^- x 2^+ y 2^+ (* x 2^y 2^+ / :

x y Doublet_1 y r 2^- x 2^+ y 2^+ (* x 2^y 2^+ / level + :

x y Doublet_3 y r 2^- x 2^+ y 2^+ (* x 2^y 2^+ / α level * + :

x y Doublet_2 y r 2^- x 2^+ y 2^+ (* x 2^y 2^+ / level - :

x y Doublet_4 y r 2^- x 2^+ y 2^+ (* x 2^y 2^+ / α level * - :

plot Doublet Doublet_1 Doublet_2 Doublet_3 Doublet_4 51 sys :

plot

2. Radial grid [polar plot style]

Stem & RK Vector

Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem n vy length : i 1 n range q i el 3 : q n el 2 : 21 line for i 1 n range v i el i : for i 1 n range S 3 i * el vy i el : for u q v replicate : V u S augment : V V 3 V rows 12 submatrix : 71 line :

t u D u 2 el u 1 el - 21 mat : 11 mat

radial 2.5 : radial extend ≡ Ro 2 : Great circle radius ≡ r1 1.5 : inner circle radius ≡ Nradial 12 : divide in N sectors ≡ mesh 180 : mesh the circles ≡ 51 line

The core components: --------------------- 1. Rk vector D(t,u) 2. radial => replicate(,,) stem(,) 3. circles => rkfixed(,,,,) 4. X_Y plot "traces" line styles

Radial Grid Construction

Great circle for radial sol radial 021 mat 02 π * Nradial t u D rkfixed : R sol 2 col sol 3 col augment : radial R 1 col stem 2 col R 2 col stem 2 col augment : 31 line

Great circle C Ro 021 mat 02 π * mesh t u D rkfixed : C C 2 col C 3 col augment : 21 line

Inner circle c1 r1 021 mat 02 π * mesh t u D rkfixed : c1 c1 2 col c1 3 col augment : 21 line

Lissajous preparation t fX 1.5 t sin * : t fY 0.75 2 t * sin * : start 0 : end 2 π * : 12 mat t start end start 0.01 + (range : 41 line

i 1 t rows range vx i el t i el fX eval : for

i 1 t rows range vy i el t i el fY eval : for

Lissajous vx vy augment : λissajous vy vx augment : 21 line

Point Lissajous 98 row : 1.237329 0.699461 12 mat

radial C c1 Lissajous λissajous 5 1 sys

θ rot θ cos θ sin - θ sin θ cos 22 mat :

θ π - 4 / :

θ 0.7854 -

RotRadial radial θ rot * :

radial RotRadial C c1 4 1 sys

3. Custom bar plot

Custom bar Size/Fill

j v Bar data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line : ----------------------------------------------- L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx - (dx i * + : for U 41 line : --------------------------- N X j el : U N size - N size + fill xd : 21 line p i 1 U rows range Y i el v : for U Y augment 21 line : Bar p Stem : 71 line :

Pilot your project from here

fill 7 : size 0.25 : 21 line

1. If you set size = 0, set 'fill ≥ 2' 2. For 'size ≥ 0' ... fill at will.

data 02 sqrt 4 π 8212 π - 16424 2.75 62 mat :

X data 1 col : vbar data 2 col : 21 line

barplot 1 vbar 1 el Bar 2 vbar 2 el Bar 3 vbar 3 el Bar 4 vbar 4 el Bar 5 vbar 5 el Bar 6 vbar 6 el Bar 61 sys :

plot barplot 00505 - 22 mat 31 sys :

0. Specify the project above. 1. Abstract the project here.

plot

fill size 21 mat 7 0.25 21 mat

The centered XY system x y XY x y + y / (2 x y / * 1 + (- :

4. X_Y plot compatibility

# f hi Algo x 106 -^hi 0.005 range : i 1 x rows range 0 x i el ≤ (x i el hi ≤ (| (algo i el x i el f eval : Assign algo if for Assign x algo augment : 31 line :

x Gamma

Compatible x ln x sqrt x f 1 x / ≡ x Gamma NOT ≡ x Γ YES ≡ # 61 mat

x f 1 x / :

Φplot x ln 5 Algo :

x ln 15 Algo x f 2 1 sys Φplot 2 3 x * sin * XY 3 1 sys