<content> pMesh </content>

c74444bd-b18a-439d-860c-0ca0dd46e433 186 4 5 false false 0 decimal

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

Exploring meshes

az el pView α az : ε el : 12 mat ε ε 180 ° * + 360 ° * mod 360 ° * + 360 ° * mod 180 ° * - : ε 90 ° * > ε 180 ° * ε - : α α 180 ° * + : 12 mat ε 90 ° * - < ε 180 ° * - ε - : α α 180 ° * + : 12 mat 0 if if α α 360 ° * mod 360 ° * + 360 ° * mod : α cos ε sin α sin * - ε cos α sin * α sin ε sin α cos * ε cos α cos * - 0 ε cos ε sin 33 mat eval 51 line :

P cyl2xyz P 1 el P 2 el cos * P 1 el P 2 el sin * P 3 el 31 mat :

P ρ φ z 31 mat ≡

f# x# y# feval f# num2str (x# num2str, y# num2str) concat str2num 11 line :

x# IsMatrix x# length 0 > eval 0 try 11 line 10 if 11 line :

a b 12 mat GetType unknown

a b 12 mat IsMatrix 1

range utility a b n pR a b a - n / 0 n range * + eval 11 line :

PMesh returns a matrix suitable for 3D plots. F# F'# uo vo pTMesh F F# F# F# cols col augment eval : F' F'# eval : 12 mat nu F rows 1 - : nv F cols 1 - : M 03 matrix eval : r' 0 : 14 mat np uo length : p' np 1 + : r.np 1 np range : r.nv 1 nv 1 - (range : c 13 range : 15 mat u 1 nu range v 1 nv range r M rows : k r r.np + : r' r' 1 + : 13 mat M k c el F uo k r - el u + vo k r - el v + el c el : v nv ≡ M r p' + c el M r np + c el : M r p' + c el F' r' el c el : if 31 line for r M rows : k r r.nv + : 12 mat M k c el M u 1 - (p' nv * nv + 1 - (* p' v 1 - (* + k r - 1 - (p' * - 1 - c el : 31 line for M 51 line :

FS U V pTGrid A pr v A 2 el A 1 el - 2 / A + : v v length el A v length el : eval 21 line : FS U pr V pr pGrid 21 line :

pGrid(F,U,V) returns a length(U)*lenght(V) matrix with [u,v,F(u,v)] FS# X# Y# pGrid r# 1 X# length range : c# 1 Y# length range : M# 0 : 13 mat FS# X# 1 el Y# 1 el feval IsMatrix num2str 1 ≡ eval M# r# c# el FS# X# r# el Y# c# el feval : M# r# c# el X# r# el Y# c# el FS# X# r# el Y# c# el feval 31 mat : if eval 21 line :

pGrid(M) converts M = pGrid(F,U,V) into three matrices [X,Y,Z]with the same shape than matlab's meshgrid function M# pGrid r# 1 X# rows range : c# 1 Y# cols range : X# 0 : Y# 0 : Z# 0 : 15 mat X# r# c# el M# r# c# el 1 el : Y# r# c# el M# r# c# el 2 el : Z# r# c# el M# r# c# el 3 el : 13 mat eval 21 line :

PMesh returns a maitrx suitable for 3D plots. F# uo vo pMesh F F# eval : nu\032E\ F rows 1 - : nv F cols 1 - : 13 mat np uo length : r.np 1 np range : r.nv 1 nv 1 - (range : 13 mat M 03 matrix eval : c 13 range : 12 mat u\032E\ 1 nu\032E\ range v 1 nv range r M rows : k r r.np + : 12 mat M k c el F uo k r - el u\032E\ + vo k r - el v + el c el : 21 line for r M rows : j r r.nv + : 12 mat M j c el M u\032E\ 1 - (np nv * nv + 1 - (* np nv 1 - (* + j r - 1 - (np * - c el : 31 line for M 51 line :

S z pZoom z length 2 ≡ S 1 col z 1 el * S 2 col z 2 el * augment eval S 1 col z 1 el * S 2 col z 2 el * S 3 col z 3 el * augment eval if 11 line :

P cl ls w cs pLine cs 0 ≡ polyline P 11 mat cl ls w stack polygon P 11 mat cl ls w cs stack if 11 line :

S# CM γ2 pMeshShow S S# eval : k 2 S rows (range : cm S 3 col CM pClr : 13 mat γ γ2 13 range 12 range el : S2 S γ * eval : 12 mat L k el S2 k row S2 k 1 - row stack cm k el solid 10 pLine : 11 mat eval 31 line :

M# G pClr M M# eval : C 0 : r 1 M length range : 13 mat G 0 ≡ M length 1 matrix G IsString C r el G : a b n 13 mat M min M max G length 13 mat eval : 11 mat C r el G M r el a - (n 1 - b a - / (* 0 round 1 + el eval : 21 line if if 21 line :

n a pCmapJet r 1 n range : m 0.25 n * trunc : M 0 : 13 mat v z v rows 1 matrix : o 255 m 1 matrix + : 12 mat x 2551 m range m / * trunc vectorize : y 255 m / m 2 / m range (* trunc vectorize : 12 mat R y z o z x o y reverse stack : G y z x o x reverse y z stack : B y o x reverse o z y z stack : k R length n - : M r el B r k + el 256 G r k + el * + 2562^R r k + el * + 2563^255 a * trunc * + : M r el M r el 232^2 M r el * 232^1 - ≥ (* - eval : 91 line :

CM 32 0.8 pCmapJet :

Matlab default view γ 37.5 ° * - 30 ° * pView :

Playing with mesh creation. Notice that the functions calls are in pGrid and pTGrid. The others are only for arrange the data. Try to change uo and vo.

Targets are 3:

1. For visualization, get the best view with less matrix size.
2. For solving PDE's, get the best mesh for the algorithm.
3. For the 3D printer, get the faster path for the printer head.

<content> peaks </content>

x y peaks 31 x - (2^e x 2^y 1 + (2^+^/ * 10 x 5 / x 3^- y 5^- e x 2^y 2^+^/ * - 13 e x 1 + (2^y 2^+^* / - :

U 3 - 325 pR : V 3 - 325 pR : G peaks U V pGrid : z 32113 mat : 41 line

<content> pMesh </content>

uo 0011015 mat : vo 0110015 mat : S G uo vo pMesh : S.1 S z pZoom : 41 line

uo 0012 mat : vo 1112 mat : S G uo vo pMesh : S.2 S z pZoom : 41 line

uo 0012 mat : vo 1112 mat : S G transpose uo vo pMesh : S.3 S z pZoom : 41 line

S.1 rows 3725

S.2 rows 1850

S.3 rows 1850

Viacheslav original mesh

S.1 γ *

waterfall along x

S.2 γ *

waterfall along y

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow

uo 1012 mat : vo 0112 mat : S G uo vo pMesh : S.1 S z pZoom : 41 line

uo 00113 mat : vo 01113 mat : S G uo vo pMesh : S.2 S z pZoom : 41 line

uo 0010115 mat : vo 0110015 mat : S G uo vo pMesh : S.3 S z pZoom : 41 line

S.1 rows 1850

S.2 rows 2475

S.3 rows 3725

fake but fast trimesh

S.1 γ *

something else

S.2 γ *

fake but nice trimesh

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow <content> Trimesh </content>

Trimesh

TG peaks U V pTGrid :

uo 0010115 mat : vo 0110015 mat : S G TG uo vo pTMesh : S.1 S z pZoom : 41 line

uo 01013 mat : vo 01113 mat : S G TG uo vo pTMesh : S.2 S z pZoom : 41 line

uo 0112 mat : vo 0112 mat : S G TG uo vo pTMesh : S.3 S z pZoom : 41 line

S.1 rows 4525

S.2 rows 3225

S.3 rows 2575

true tri mesh

S.1 γ *

intermediate variation

S.2 γ *

fast variation

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow <content> torus </content>

R 6 : r 2 : 12 mat u v torus R r u cos * + (v cos * R r u cos * + (v sin * r u sin * 31 mat : 21 line

U 1.25 π * - 016 pR : V 0 1.75 π * 32 pR : G torus U V pGrid : z 11213 mat : 41 line

<content> pMesh </content>

uo 0011015 mat : vo 0110015 mat : S G uo vo pMesh : S.1 S z pZoom : 41 line

uo 0012 mat : vo 1112 mat : S G uo vo pMesh : S.2 S z pZoom : 41 line

uo 0012 mat : vo 1112 mat : S G transpose uo vo pMesh : S.3 S z pZoom : 41 line

S.1 rows 3056

S.2 rows 1520

S.3 rows 1504

Viacheslav original mesh

S.1 γ *

waterfall along x

S.2 γ *

waterfall along y

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow

uo 1012 mat : vo 0112 mat : S G uo vo pMesh : S.1 S z pZoom : 41 line

uo 00113 mat : vo 01113 mat : S G uo vo pMesh : S.2 S z pZoom : 41 line

uo 0010115 mat : vo 0110015 mat : S G uo vo pMesh : S.3 S z pZoom : 41 line

S.1 rows 1520

S.2 rows 2032

S.3 rows 3056

fake but fast trimesh

S.1 γ *

something else

S.2 γ *

fake but nice trimesh

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow <content> Trimesh </content>

Trimesh

TG torus U V pTGrid :

uo 0010115 mat : vo 0110015 mat : S G TG uo vo pTMesh : S.1 S z pZoom : 41 line

uo 01013 mat : vo 01113 mat : S G TG uo vo pTMesh : S.2 S z pZoom : 41 line

uo 0112 mat : vo 0112 mat : S G TG uo vo pTMesh : S.3 S z pZoom : 41 line

S.1 rows 3680

S.2 rows 2624

S.3 rows 2096

true tri mesh

S.1 γ *

intermediate variation

S.2 γ *

fast variation

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow <content> wave </content>

r f 0.5 4 r * cos * : r θ wave r θ r f 13 mat cyl2xyz : 21 line

U 0520 pR : V 0 1.5 π * 30 pR : G wave U V pGrid : z 22213 mat : 41 line

<content> pMesh </content>

uo 0011015 mat : vo 0110015 mat : S G uo vo pMesh : S.1 S z pZoom : 41 line

uo 0012 mat : vo 1112 mat : S G uo vo pMesh : S.2 S z pZoom : 41 line

uo 0012 mat : vo 1112 mat : S G transpose uo vo pMesh : S.3 S z pZoom : 41 line

S.1 rows 3580

S.2 rows 1780

S.3 rows 1770

Viacheslav original mesh

S.1 γ *

waterfall along x

S.2 γ *

waterfall along y

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow

uo 1012 mat : vo 0112 mat : S G uo vo pMesh : S.1 S z pZoom : 41 line

uo 00113 mat : vo 01113 mat : S G uo vo pMesh : S.2 S z pZoom : 41 line

uo 0010115 mat : vo 0110015 mat : S G uo vo pMesh : S.3 S z pZoom : 41 line

S.1 rows 1780

S.2 rows 2380

S.3 rows 3580

fake but fast trimesh

S.1 γ *

something else

S.2 γ *

fake but nice trimesh

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow <content> Trimesh </content>

Trimesh

TG wave U V pTGrid :

uo 0010115 mat : vo 0110015 mat : S G TG uo vo pTMesh : S.1 S z pZoom : 41 line

uo 01013 mat : vo 01113 mat : S G TG uo vo pTMesh : S.2 S z pZoom : 41 line

uo 0112 mat : vo 0112 mat : S G TG uo vo pTMesh : S.3 S z pZoom : 41 line

S.1 rows 4320

S.2 rows 3080

S.3 rows 2460

true tri mesh

S.1 γ *

intermediate variation

S.2 γ *

fast variation

S.3 γ * S.1 CM γ pMeshShow S.2 CM γ pMeshShow S.3 CM γ pMeshShow

Alvaro