TPMS - Galerie 5

---------------- 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

Slotted−P

ϕ (x,y,z) = −2 (C_xC_y + C_yC_z + C_xC_z) − 2(C_2x + C_2y + C_2z) + (C_2xC_y + C_2yC_z + C_xC_2z) −
(C_xC_2y + C_yC_2z + C_2xC_z)

Slotted-P - TPMS

Slotted-P - Sheet

Slotted-P - Solid A

Slotted-P - Solid B

Split−P

ϕ (x,y,z) = 1.1 (S_2xC_yS_z + S_2yC_zS_x + S_2zC_xS_y) − 0.2 (C_2xC_2y + C_2yC_2z + C_2zC_2x) −
0.4 (C_2x + C_2y +C_2z)

Split-P - TPMS

Split-P - Sheet

Split-P - Solid A

Split-P - Solid B

Q*

ϕ (x,y,z) = (C_x – 2 C_y) C_z − √3 S_z (C_x−y − C_x) + C_x−yC_z

Q* - TPMS

Q* - Sheet

Q* - Solid A

Q* - Solid B

W • W*

ϕ (x,y,z) = (C_2xC_y + C_2yC_z +C_xC_2z) − (C_xC_2y + C_yC_2z + C_2xCz)

W - TPMS

W - Sheet

W - Solid A

W - Solid B

F • F*, Tripleplane 1

ϕ (x,y,z) = C_x C_y C_z

F - TMPS

F - Sheet

F - Solid A

F - Solid B

Double D

ϕ (x,y,z) = (S_2xS_2y + S_2yS_2z +S_2zS_2x) + C_2xC_2yC_2z

Double D - TPMS

Double D - Sheet

Double D - Solid A

Double D - Solid B

Variante: ϕ (x,y,z) = C_2xC_2y + C_2yC_2z + C_2xC_2z + S_2xS_2yS_2z

Double D₂ - TPMS

Double D₂ - Sheet

Double D₂ - Solid A

Double D₂ - Solid B

TPMS	ϕ_TPMS \| F(x,y,z) für MSLattice	p	d
Slotted-P	−2(cos(px)cos(py)+cos(py)cos(pz)+cos(px)cos(pz))−2(cos(2px)+cos(2py)+ cos(2pz))+(cos(2px)cos(py)+cos(2py)cos(pz)+cos(px)cos(2pz))− (cos(px)cos(2py)+cos(py)cos(2pz)+cos(2px)cos(pz)) -2.(cos(2.pi.x).cos(2.pi.y)+cos(2.pi.y).cos(2.pi.z)+cos(2.pi.x).cos(2.pi.z))- 2.(cos(2.2.pi.x)+cos(2.2.pi.y)+cos(2.2.pi.z))+(cos(2.2.pi.x).cos(2.pi.y)+ cos(2.2.pi.y).cos(2.pi.z)+cos(2.pi.x).cos(2.2.pi.z))-(cos(2.pi.x).cos(2.2.pi.y)+ cos(2.pi.y).cos(2.2.pi.z)+cos(2.2.pi.x).cos(2.pi.z))	2π	0.75
Split-P	1.1(sin(2px)cos(py)sin(pz)+sin(2py)cos(pz)sin(px)+sin(2pz)cos(px)sin(py))− 0.2(cos(2px)cos(2py)+cos(2py)cos(2pz)+cos(2pz)cos(2px))−0.4(cos(2px)+ cos(2py)+cos(2pz)) 1.1.(sin(2.2.pi.x).cos(2.pi.y).sin(2.pi.z)+ sin(2.2.pi.y).cos(2.pi.z).sin(2.pi.x)+sin(2.2.pi.z).cos(2.pi.x).sin(2.pi.y))- 0.2.(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))-0.4.(cos(2.2.pi.x)+cos(2.2.pi.y)+ cos(2.2.pi.z))	2π	0.25
Q*	(cos(px)-2cos(py))cos(pz)-sqrt(3)sin(pz)(cos(px-py)-cos(px))+cos(px-py)cos(pz) (cos(2.pi.x)-2.cos(2.pi.y)).cos(2.pi.z)-sqrt(3).sin(2.pi.z).(cos(2.pi.(x-y))-cos(2.pi.x))+cos(2.pi.(x-y)).cos(2.pi.*z)	2π	0.25
W	(cos(2px)cos(py)+cos(2py)cos(pz)+cos(px)cos(2pz))-(cos(px)cos(2py)+cos(py)cos(2pz)+cos(2px)cos(pz)) (cos(2.2.pi.x).cos(2.pi.y)+cos(2.2.pi.y).cos(2.pi.z)+ cos(2.pi.x).cos(2.2.pi.z))-(cos(2.pi.x).cos(2.2.pi.y)+ cos(2.pi.y).cos(2.2.pi.z)+cos(2.2.pi.x).cos(2.pi.z))	2π	0.1
F	cos(px) cos(py) cos(pz) cos(2.pi.x).cos(2.pi.y).cos(2.pi.z)	2π	0.1
Double D	(sin(2px)sin(2py)+sin(2py)sin(2pz)+sin(2pz)sin(2px))+cos(2px)cos(2py)cos(2pz) (sin(2.2.pi.x).sin(2.2.pi.y)+sin(2.2.pi.y).sin(2.2.pi.z)+ sin(2.2.pi.z).sin(2.2.pi.x))+cos(2.2.pi.x).cos(2.2.pi.y).cos(2.2.pi.z) Variante: cos(px)cos(py)+cos(py)cos(pz)+cos(px)cos(pz)+sin(2px)sin(2py)sin(2pz) cos(2.2.pi.x).cos(2.2.pi.y)+cos(2.2.pi.y).cos(2.2.pi.z)+ cos(2.2.pi.x).cos(2.2.pi.z)+sin(2.2.pi.x).sin(2.2.pi.y).sin(2.2.pi.z)	2π	0.25