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vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Contour level extract

This document demonstrates how to extract the points of a plane cutting a surface matrix. The program sorts the points in the X direction in ascending order and 'pair wise' or 'uniquely' in the Y direction depending upon the cutting path. The 'Q' data pairs is a huge vector(2) filled of 0's, that you can strip for convenient export, but this stripping operation takres eternity ! Whereas we generate a symmetric matrix and whereas the extraction is on the running indices, the plotting arguments are re-centered to give reality to the project. Set 'N'= even. Note that the extracted Gaussian points are unique [a closed cntr] they don't "tartine" the pixels. The Nova image below is from Mathcad 11, delicious in rich colors. The main idea behind the contour extractor is two fold: 1. Observe/visualize the level path on an 'Engineering surface' you may have obtained from sampled data [a square matrix]. 2. From functions that have no symbolic level solution(s), but from which functions you can generate a square matrix.

-------- 1. Nova fnct -------- 2. Gaussian -------- N [100] N[100] ~ 1.5 min. ~ 2 min. Strip0 ~ 16 min.

cntr 0.25 ≡

ε 0.0025 ≡

cntr 0.25 ≡

ε 0.0025 ≡

1 x y * x 2^y 2^+ / *

0.5 021 line

1 x 2^y 2^+ (- 0.25 / exp *

1 0.0003 21 line

Mesh U, V  within the bounds L, H L H N xd N intervals U 0 : dx H L - N / : i 1 N 1 + range U i el L dx i * dx - (+ : for U 21 line 41 line :

L 1 - :

H 1 :

N 100 :

U L H N xd :

V U :

x y f 1 x 2^y 2^+ (- 0.25 / exp * :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

t0 1 time :

M x y f U V Sym :

M max 1

M min 3104 -^*

The contour extractor , pair wise in X direction M ε cntr CONTR count 1 : i 1 M rows range j 1 M cols range M i j el cntr - abs ε ≤ u count el i : v count el j : 21 line count count 1 + : if for for u v augment 31 line :

ε 0.0025 :

cntr 0.25 :

Q M ε cntr CONTR :

Q rows 8004

M i j el cntr - abs ε ≤

FRAME N 2 / - N 2 / - N 2 / - N 2 / N 2 / N 2 / N 2 / N 2 / - N 2 / - N 2 / - 52 mat :

XY Q 1 col N 2 / - Q 2 col N 2 / - augment :

X FRAME 1 col :

Y FRAME 2 col :

FRAME X Y + 50 black plotG :

c 00 + N red 15 mat :

XY FRAME c 3 1 sys

1 time t0 - 342 sec *

- Nova -

N 100 ≡ 22462256234223602537256527342768342734753725377742234279462246805622568060236079652565776827687575347568773777657942796080468056322 mat ≡

jmGiraud: 2015_08_13

Strip 0's in vector v Strip0 k 0 : i 1 v rows range v i el 0 ≠ R k k 1 + : el v i el : 11 line undefined if 11 line for R 31 line :

v 10305616 mat transpose :

v Strip0 transpose 135614 mat

t0 1 time :

ExportX Q 1 col Strip0 :

ExportY Q 2 col Strip0 :

Exp ExportX ExportY augment :

1 time t0 - 0 sec *

N 100 ≡ 1000 sec * ≡

Publish your project

cntr 22462256234223602537256527342768342734753725377742234279462246805622568060236079652565776827687575347568773777657942796080468056322 mat :

Plug your vector definition cntr:= above the first plotting argument. Once you have pasted data, Smath slides it down, a wise and very practical convenience.

X cntr 1 col :

Y cntr 2 col :

c 00 + 100 red 15 mat :

CNTR X 50 - Y 50 - . 8 blue plotG :

CNTR c 2 1 sys

Functions that 'respond' Extractor

Not very nice looking, but carrying some truth. The contour extract Advisor is a tool to have. For low populated Engineering matrices, spline and plug to populate via Sym[f(,x,y),U,V]

x y f 11 x + (3^+ 3 y * 1 x + (* - y 3^+ abs ln :

<= numeric

x y f U V Sym

U i el V j el f eval

<= numeric

[± 6], 151, ε=0.125, cntr=0 ... (13 min)

x y μ ψ μ y * x 2^y 2^+ / (- :

a 1 :

R 5 :

μ 0 :

x y f a y R 2^y * x 2^y 2^+ / - (* x y μ ψ - :

x y f y 25 - x 2^+ y 2^+ (* x 2^y 2^+ / :

<= numeric

x y f U V Sym

U i el V j el f

<= numeric

[± 1], 100, ε=0.1, cntr=20

x y f