<content> pMesh </content>

c74444bd-b18a-439d-860c-0ca0dd46e433 97 4 5 false false 0 decimal

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

Offset surface creation

f\032E\ x\032E\ y\032E\ feval f\032E\ num2str (x\032E\ num2str, y\032E\ num2str) concat str2num 11 line :

a\032E\ b\032E\ n\032E\ pRange a\032E\ b\032E\ a\032E\ - n\032E\ / 0 n\032E\ range * + eval 11 line :

PMesh returns a matrix suitable for 3D plots. F pMesh nu F rows 1 - : nv F 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 : r 0 : 13 mat u 1 nu range v 1 nv range r M rows : k r r.np + : 12 mat M k c el F 0011015 mat k r - el u + 0110015 mat k r - el v + el c el : r r np + : 31 line for nv 1 > r M rows : j r r.nv + : 12 mat M j c el M u 1 - (np nv * nv + 1 - (* np v 1 - (* + j r - 1 - (np * - c el : 21 line continue if 21 line for M eval 51 line :

n u 1 - (n.p n.v * n.v + 1 - (* n.p v 1 - (* + k n.p * - :

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

Generate the unitary normal vectors to F arranged in the same way that pMesh F U V pNo u v G Clear Φ F u v feval : 12 mat g Φ u diff vectorize Φ v diff vectorize † : u v G g nznorm 11 line : 12 mat G U V pMesh eval 31 line :

Returns a mesh matrix with the mesh in M and the displaced nodes by h M N h pNoMesh A M M h N * + vectorize M 13 mat : r 13 M rows * (range : c 13 range : No 0 : 13 mat No r c el A 1 r 1 - 3 mod + el (1 r 1 - 3 / trunc + c el : eval 31 line :

Returns a mesh for a solid generated by the surface F, the displacements in h and the displaced surface M' = M+h*N F U V h pNoSolid M F U V pMesh : N F U V pNo : 12 mat h IsDefined M N h pNoMesh M h N * + stack eval u v H Clear u v H 31 matrix h u v feval + : H H U V pMesh : M N H pNoMesh M H N * + vectorize stack eval 41 line if 21 line :

Shorthands

zum 1.7 :

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

x# nznorm x# x# norme / x# try 11 line :

01012 -^:

Solid between a surface and its displaced a fixed distance h in the direction of the surfaces normals

u v F.1 9 u sin * v cos * 4.5 u sin * v sin * 3 u cos * 31 mat :

U.1 0.5 π * 016 pRange 0 + :

h.1 1 :

V.1 1.5 π * 0.5 π * 16 pRange :

M.1 F.1 U.1 V.1 pMesh : N.1 F.1 U.1 V.1 pNo : MN.1 M.1 N.1 h.1 pNoMesh : 31 line

The surface

M.1 γ * 1.2 *

The surface with the normals

MN.1 γ * 1.2 *

M'.1 M.1 h.1 N.1 * + : A MN.1 M'.1 stack : 21 line

Both toghether

M'.1 γ * 1.2 * MN.1 γ * 1.2 * 2 1 sys

The Solid as only one matrix

A γ 1.2 * *

Putting all toghether

u v F.2 u v 0.3 u sin * v cos * 31 mat : U.2 5 - 510 pRange : V.2 5 - 511 pRange : B F.2 U.2 V.2 0.8 pNoSolid : 41 line

B γ * zum * <content> Case 2 </content>

Solid between a surface and its displaced a variable distance h(u,v) in the direction of the surface normals

u v F.3 u v 0.5 u * 0.5 v * + sin 31 mat :

U.3 5 - 510 pRange :

u v h.3 u v + abs sqrt :

V.3 5 - 510 pRange :

u v H.3 31 matrix u v h.3 + 11 line :

For generating the same structure for the scalar function h.3 we use the following cheat

h.3 H.3 U.3 V.3 pMesh :

M.3 F.3 U.3 V.3 pMesh : N.3 F.3 U.3 V.3 pNo : MN.3 M.3 N.3 h.3 pNoMesh : M'.3 M.3 h.3 N.3 * + vectorize : C MN.3 M'.3 stack : 51 line

The surface with the normals

MN.3 γ * 1.2 *

The Solid

C γ * 1.2 *

Putting all toghether

u v h.4 0.5 v * : u v F.4 2 u * v cos * 1 u * v sin * u 2^5 - 31 mat : U.4 0.3 310 pRange : V.4 1.4 π * 010 pRange : D.1 F.4 U.4 V.4 h.4 pNoSolid : 51 line

D.1 γ * zum *

Compare it with the "not distorted" solid

D.2 F.4 U.4 V.4 1 pNoSolid :

D.2 γ * zum *