TPMS - Galerie 6

---------------- Direkt zur TPMS -----------------

In dieser Galerie finden Sie für diverse TPMS (s. rechts) Einheitszellen (engl. unit cells) der Objekte

TPMS mit ϕ (x,y,z) = c als 360°-Animation
Sheet mit | ϕ (x,y,z) | ≤ d, d ∈ |R⁺
Solid A mit ϕ (x,y,z) > c
Solid B mit ϕ (x,y,z) < c

für c = 0 und weitere Grafiken. Bezüglich der Nomenklatur und Erzeugung siehe TPMS – Einführung.

Für eigene Experimente enthält die Tabelle am Ende der Seite die TPMS-Funktionen in gewohnter Syntax und MSLattice-Syntax für ein schnelles Copy & Paste.

Galerie 1

D
P
Neovius
IWP
FRD
OCTO

Galerie 2

C(D)
Gyroid
C(G)
S
C(S)

Galerie 3

Y
C(Y)
±Y
C(±Y)
I2-Y**
C(I2-Y**)

Galerie 4

D'
G'
K
Lidinoid
P+C(P)

Galerie 5

Slotted P
Split-P
Q*
W
F
Double D

Galerie 6

Double G
Double P
Tubular D
Tubular G
Tubular P

Double G

ϕ (x,y,z) = 2.75 (S_2xC_yS_z + S_2yC_xS_z + S_2zS_yC_x) − (C_2xC_2y + C_2yC_2z + C_2zC_2x)

Double Gyroid - TPMS

Double G - Sheet

Double G - Solid A

Double G - Solid B

Double P

ϕ (x,y,z) = ½ (C_xC_y + C_yC_z + C_zC_x) + 0.2 (C_2x + C_2y + C_2z)

Double P - TPMS

Double P - TPMS ('Rainbow')

Double P - Sheet

Double P - Solid A

Double P - Solid B

Tubular D

ϕ (x,y,z) = 10 (S_{x}S_{y}S_{z} + S_{x}C_{y}C_{z} + C_{x}S_{y}C_{z} + C_{x}C_{y}S_{z}) −
0.7 (C_4x +C_4y +C_4z) – 11

mit {x} = x − π/4, {y} = y − π/4, {z} = z − π/4

Tubular D - TPMS

Tubular D, p=4π - TPMS

Tubular D, p=4π, x/z-Ebene - TPMS

Tubular D - Sheet

Tubular D -Sheet, -1 ≤ z ≤ 1

Tubular G

ϕ (x,y,z) = 10 (C_xS_y + C_yS_z + C_zS_x) − 0.5 (C_2xC_2y + C_2yC_2z + C_2zC_2x) – 14

Tubular G - TPMS

Tubular D, p=4π - TPMS

Tubular G, p=4π, x/z-Ebene - TPMS

Tubular G - Sheet

Tubular G - Sheet, -1 ≤ z ≤ 1

Tubular P

10 (C_x + C_y + C_z) − 5.1 (C_xC_y + C_yC_z + C_zC_x) − 14.6

Tubular P - TPMS

Tubular P, p=4π - TPMS

Tubular P, p=4π, x/z-Ebene - TPMS

Tubular P - Sheet

Tubular P - Sheet, -1 ≤ z ≤ 1

TPMS	ϕ_TPMS \| F(x,y,z) für MSLattice	p	d
Double G	2.75(sin(2px)cos(py)sin(pz)+sin(2py)cos(px)sin(pz)+sin(2pz)sin(py)cos(px))- (cos(2px)cos(2py)+cos(2py)cos(2pz)+cos(2pz)cos(2px)) 2.75.(sin(2.2.pi.x).cos(2.pi.y).sin(2.pi.z)+ sin(2.2.pi.y).cos(2.pi.x).sin(2.pi.z)+ sin(2.2.pi.z).sin(2.pi.y).cos(2.pi.x))-(cos(2.2.pi.x).cos(2.2.pi.y)+cos(2.2.pi.y).cos(2.2.pi.z)+ cos(2.2.pi.z).cos(2.2.pi.*x))	2π	0.25
Double P	0.5(cos(px)cos(py)+cos(py)cos(pz)+cos(pz)cos(px))+0.2(cos(2px)+cos(2py)+cos(2pz)) 0.5.(cos(2.pi.x) .cos(2.pi.y)+cos(2.pi.y) .cos(2.pi.z)+ cos(2.pi.z) .cos(2.pi.x))+0.2.(cos(2.2.pi.x)+cos(2.2.pi.y)+cos(2.2.pi.z))	2π	0.1
Tubular D	10(sin(x−π/4)sin(y−π/4)sin(z−π/4)+sin(x−π/4)cos(y−π/4)cos(z−π/4)+ cos(x−π/4)sin(y−π/4)cos(z−π/4)+cos(x−π/4)cos(y−π/4)sin(z−π/4))− 0.7(cos(4x)+cos(4y)+cos(4z))−11 10.(sin(2.pi.x-pi/4).sin(2.pi.y-pi/4).sin(2.pi.z-pi/4)+ sin(2.pi.x-pi/4).cos(2.pi.y-pi/4).cos(2.pi.z-pi/4)+ cos(2.pi.x-pi/4).sin(2.pi.y-pi/4).cos(2.pi.z-pi/4)+ cos(2.pi.x-pi/4).cos(2.pi.y-pi/4).sin(2.pi.z-pi/4))- 0.7.(cos(2.pi.4.x)+cos(2.pi.4.y)+cos(2.pi.4.*z))-11	2π	0.15
Tubular G	10(cos(px)sin(py)+cos(py)sin(pz)+cos(pz)sin(px))−0.5(cos(2px)cos(2py)+ cos(2py)cos(2pz)+cos(2pz)cos(2px))−14 10.(cos(2.pi.x).sin(2.pi.y)+cos(2.pi.y).sin(2.pi.z)+ cos(2.pi.z).sin(2.pi.x))-0.5.(cos(2.2.pi.x).cos(2.2.pi.y)+ cos(2.2.pi.y).cos(2.2.pi.z)+cos(2.2.pi.z).cos(2.2.pi.x))-14	2π	0.15
Tubular P	10(cos(px)+cos(py)+cos(pz))−5.1(cos(px)cos(py)+cos(py)cos(pz)+ cos(pz)cos(px))−14.6 10.(cos(2.pi.x)+cos(2.pi.y)+cos(2.pi.z))-5.1.(cos(2.pi.x).cos(2.pi.y)+ cos(2.pi.y).cos(2.pi.z)+cos(2.pi.z).cos(2.pi.*x))-14.6	2π	0.15