<content> <p>Rezonar's triangular mesh</p> </content>

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

Creating surface thickness with triangular meshes

The solid is formed from the initial surface, the offset surface, and the
lateral surface that connects them. The lateral surface is formed by normals
reconstructed from the boundary nodal points of the initial surface.

A pCycleC M A 1 el 11 mat : k 1 A length range n 15 range M M rows 1 + el 105^105^12 mat : for M M rows 1 + el A k el : 21 line for M mat2sys.1 eval 31 line :

γ 0.8232 - 0.4194 - 0.3827 0.5677 0.6187 - 0.543 0.009 0.6643 0.7474 33 mat :

zum 1.4 :

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

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

PMesh returns a matrix suitable for 3D plots. F pTMesh T F F F rows row stack eval : T F F F cols col augment eval : nu T rows 1 - : nv T cols 1 - : 12 mat np 5 : r.np 1 np range : r.nv 1 nv 1 - (range : 13 mat M 03 matrix eval : c 13 range : 12 mat u 1 nu range v 1 nv range r M rows : k r r.np + : 12 mat M k c el T 0010115 mat k r - el u + 0110015 mat k r - el v + el c el : 21 line for r M rows : k r r.nv + : 12 mat M k c el M u 1 - (np nv * nv + 1 - (* np v 1 - (* + k r - 1 - (np * - c el : 31 line for M eval 71 line :

PMesh returns a matrix suitable for 3D plots. F X Y pTMesh r 1 X length range : c 1 Y length range : M 0 : 13 mat M r c el F X r el Y c el feval : pTMesh eval 21 line :

m1 b 1 el b 2 el n 1 el pR : m2 b 3 el b 4 el n 2 el pR : 12 mat

x h Solid c 13 range : g c el x f x c el diff : x G g : x u x G transpose x G norme / : 14 mat k 1 initSur rows range nodeInit k el initSur k row eval : nodeOffset k el nodeInit k el h nodeInit k el u * + eval : k 1 ≡ meshOffset nodeOffset k el : meshOffset meshOffset nodeOffset k el stack : if 31 line for a F b 1 el b 1 el 1 pR m2 pTMesh : c F m1 b 3 el b 3 el 1 pR pTMesh : 12 mat d F b 2 el b 2 el 1 pR m2 pTMesh : e F m1 b 4 el b 4 el n 2 el pR pTMesh : 12 mat border a c d e stack : k 1 border rows range : nodeB k el border k row eval : 12 mat normalB k el nodeB k el nodeB k el h nodeB k el u * + stack γ * zum * eval : solid initSur γ * zum * 11 mat normalB meshOffset γ * zum * 11 mat stack eval : solid mat2sys.1 eval 91 line :

x f x 1 el (2^92^/ x 2 el (2^4.5 2^/ + x 3 el (2^32^/ + 1 - :

u v F 9 u sin * v cos * 4.5 u sin * v sin * 3 u cos * 31 mat :

b 0.5 π * 0 1.5 π * 0.5 π * 14 mat :

n 101012 mat :

initSur F m1 m2 pTMesh :

Offset surfaces on both sides of the initial surf.

x 1.5 Solid

x f x 1 el 2^22^/ x 2 el (2^12^/ + x 3 el - 5 + :

u v F 2 u * v cos * 1 u * v sin * u 2^5 - 31 mat :

b 0.3 3 1.4 π * - 014 mat :

n 151012 mat :

initSur F m1 m2 pTMesh :

Offset surfaces on both sides of the initial surf.

x 1 Solid

x f 0.5 x 1 el * 0.5 x 2 el * + sin x 3 el - :

u v F u v 0.5 u * 0.5 v * + sin 31 mat :

b 5 - 55 - 514 mat :

n 121512 mat :

initSur F m1 m2 pTMesh :

Offset surfaces on both sides of the initial surf.

x 0.8 Solid

x f 0.5 x 1 el x 2 el + sin * x 3 el - :

u v F u v 0.5 u v + sin * 31 mat :

b 5 - 55 - 514 mat :

n 121412 mat :

initSur F m1 m2 pTMesh :

Offset surfaces on both sides of the initial surf.

x 0.5 Solid

x f x 1 el 2^x 2 el 2^+ sqrt 6 - (2^22^- x 3 el 2^+ :

u v F 62 u cos * + (v cos * 62 u cos * + (v sin * 2 u sin * 31 mat :

b 040514 mat :

n 201512 mat :

initSur F m1 m2 pTMesh :

Offset surfaces on both sides of the initial surf.

x 0.6 - Solid

x f 0.5 2 πx 1 el * sin 2 πx 2 el * sin + (* x 3 el - :

u v F u v 0.5 2 π * u * sin 2 π * v * sin + (* 31 mat :

b 6 - 66 - 614 mat :

n 121412 mat :

initSur F m1 m2 pTMesh :

Offset surfaces on both sides of the initial surf.

x 0.8 Solid