Utilities

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Utilities

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 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 51 line :

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 :

data Strip2 nest striped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line 0 pairs excluded if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

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 :

Contour level matrix 'ε' extract Advisor

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 must strip for convenient export. The main idea behind the contour extractor is two fold: 1. Observe/visualize the level path of 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. 3. NO MATTER how much maths you may imagine, only few "maths functions" have a symbolic contour ... your project needs more contour utilies. 4. Particularly useful for yhpersurfaces.

size 1 : a 1 : 12 mat L size - : H size : N 100 : 13 mat U L H N xd : V U : 12 mat 31 line

Observe . . .

1. The extracted contour is slightly noisy [0.25 ± 0.005].

2. More sorting is required for isolating contour(s).

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x y f 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - : M x y f U V Sym : 21 line

M min M max 21 mat 0.7165 - 1.4331 21 mat ≡

t0 1 time :

level 0.25 : ε 0.005 : 12 mat Q M ε level CONTR : XY Q Strip2 : (Export the project ≡ X XY 1 col N / : Y XY 2 col N / : 12 mat data X size 2 / - Y size 2 / - augment : contour data o 5 red plot : 61 line

contour

1 time t0 - min 3.5

data [CONTR(M,ε,level)]

data 0.48 - 0.4 - 0.48 - 0.42 0.45 - 0.38 - 0.45 - 0.4 0.4 - 0.35 - 0.4 - 0.37 0.37 - 0.33 - 0.37 - 0.35 0.35 - 0.32 - 0.35 - 0.34 0.32 - 0.3 - 0.32 - 0.32 0.3 - 0.29 - 0.3 - 0.31 0.23 - 0.25 - 0.23 - 0.27 0.21 - 0.24 - 0.21 - 0.26 0.16 - 0.22 - 0.16 - 0.24 0.14 - 0.21 - 0.14 - 0.23 0.11 - 0.2 - 0.11 - 0.22 0.08 - 0.19 - 0.08 - 0.21 0.03 - 0.18 - 0.03 - 0.2 0.02 - 0.18 - 0.02 - 0.2 0.01 - 0.18 - 0.01 - 0.2 0 0.18 - 0 0.2 0.01 0.18 - 0.01 0.2 0.02 0.18 - 0.02 0.2 0.03 0.18 - 0.03 0.2 0.04 0.18 - 0.04 0.2 0.05 0.18 - 0.05 0.2 0.1 0.19 - 0.1 0.21 0.13 0.2 - 0.13 0.22 0.16 0.21 - 0.16 0.23 0.18 0.22 - 0.18 0.24 0.23 0.24 - 0.23 0.26 0.25 0.25 - 0.25 0.27 0.32 0.29 - 0.32 0.31 0.34 0.3 - 0.34 0.32 0.37 0.32 - 0.37 0.34 0.39 0.33 - 0.39 0.35 0.42 0.35 - 0.42 0.37 0.47 0.38 - 0.47 0.4 0.5 0.4 - 0.5 0.42 702 mat :

sub-process this example [demo]

data n Decimate collect every 'n' pairs range 2 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

sub data 132 range 12 range el : C1_left sub 4 Decimate : C1_right 1 C1_left 1 col * - C1_left 2 col augment : C1 C1_left C1_right stack : C1 C1 o 4 red plot : 51 sys