<content> <p>pMesh</p> </content>

c74444bd-b18a-439d-860c-0ca0dd46e433 59 4 5 false false 0 decimal

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

Offset surface creation

An initial surface is given, given by the "createmesh" function, which forms a network with nodes. Dyou want to create an offset surface, offset by an amount h from the initial.The direction of displacement surface epends on the sign of h.

Sequence of calculation:
1.Restoring the normal from the nodal points of the initial surface and we get the nodal points of the displaced surface.
2.We connect the resulting node points

Notation :
initSur-initial surface
nodeInit , nodeOffset -corner points of start and offset surfaces respectively
unitNorm ,No - unit normal and surface normal respectively
meshOffset - offset surface mesh
±h - offset distance

https://www.mapleprimes.com/posts/211000-Preparing-A-Parametrized-Surface-For

The image is built on three-dimensional graphics and can be rotated with the mouse

<content> <p>pMesh</p> </content>

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 : c 13 range : 12 mat u\032E\ 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\032E\ + 0110015 mat 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 :

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 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 31 line :

Returns a mesh matrix with the mesh in M and the unitary normals in N M N h pNoMesh A M M h N * + 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 : 31 line :

Shorthands

plot.1 M N h pNoMesh γ * zum * 31 sys 11 line :

plot.2 M h N * + (γ * zum * M h N * - (γ * zum * 21 sys 11 line :

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 :

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

Issue at origin?

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

U 0.5 π * 010 pRange :

V 1.5 π * 0.5 π * 10 pRange :

h 1 :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2

x f 0.3 x 1 el sin * x 2 el cos * x 3 el - :

u v F u v 0.3 u sin * v cos * 31 mat :

U 5 - 510 pRange :

V 5 - 510 pRange :

h 0.8 - :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2

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 :

U 5 - 510 pRange :

V 5 - 510 pRange :

h 0.8 - :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2

x f 0.2 2 πx 1 el * sin 2 πx 2 el * sin + (* x 3 el - :

πx it's wrong.

u v F u v 0.2 2 π * u * sin 2 π * v * sin + (* 31 mat :

U 6 - 610 pRange :

V 3 - 310 pRange :

h 0.8 :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2

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 :

U 0.3 310 pRange :

V 1.4 π * 010 pRange :

h 0.8 - :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2

x f 9 0.01 e x 1 el^* 0.094 x 1 el (4^+ x 2 el (4^+ / * x 3 el - :

u v F u v 0.3 u v + sin * 2 - 31 mat :

U 6 - 610 pRange :

V 6 - 610 pRange :

h 0.8 - :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2

x f 9 0.01 e x 1 el^* 0.094 x 1 el (4^+ x 2 el (4^+ / * x 3 el - :

u v F 9 u * 9 v * 9 0.01 e u^* 0.0094 u (4^+ v (4^+ / * 31 mat :

U 0 0.5 10 pRange :

V 0.8 - 0.8 10 pRange :

h 0.8 - :

M F U V pMesh :

N F U V pNo :

Ns M N h pNoMesh :

Normals from nodal points of initial surface

plot.1

Offset surfaces on both sides of the initial surf.

plot.2