TPMS - Galerie 4

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

TPMS mit ϕ (x,y,z) = 0 als 360°-Animation
Sheet mit | ϕ (x,y,z) | ≤ d, d ∈ |R⁺
Solid A mit ϕ (x,y,z) > 0
Solid B mit ϕ (x,y,z) < 0
TPMS mit ϕ (x,y,z) = c_pinch (360°-Animation)

und ggf. weitere Grafiken. Bezüglich Nomenklatur siehe TPMS – Einführung.

Die TPMS-Flächen wurden mit dem Graphing Calculator 3D erzeugt (Funktion und Werte für d und c_pinch s. Tabelle am Seitenende), für die "physikalischen" Modelle Sheet, Solid A und
Solid B wurde die Software MSLattice verwendet.

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
Tub. IWP

D'

ϕ (x,y,z) = ½ (C_xC_yC_z + C_xS_yS_z + S_xC_yS_z + S_xS_yC_z) - ½ (S_2xS_2y + S_2yS_2z + S_2zS_2x) - 0.2

D' - TPMS, p=π

D' - Sheet, p=π

D' - Solid A, p=π

D' - Solid B, p=π

D'₂ - TPMS

D' - TPMS, c = c_pinch.a

D' - TPMS, c = c_pinch.b

D' - TPMS, c = c_pinch.c

D' - Sheet, p=2π

D' - Solid A, p=2π

D' - Solid B, p=2π

Variante: ϕ (x,y,z) = ½ (S_xS_yS_z + C_xC_yC_z) – ½ (C_2xC_2y + C_2yC_2z + C_2zC_2x) – 0.2

D'₂ - TPMS

D'₂ - TPMS, c = c_pinch.a

D'₂ - TPMS, c = c_pinch.b

D'₂ - TPMS, c = c_pinch.c

D'₂ - Sheet

D'₂ - Solid A

D'₂ - Solid B

G' Surface

ϕ (x,y,z) = S_2xC_yS_z + S_xS_2yC_z + C_xS_yS_2z + 0.32

G' - TPMS

G' - TPMS, c = c_pinch.a

G' - TPMS, c = c_pinch.b

G' - TPMS, c = c_pinch.c

G' - Sheet

G' - Solid A

G' - Solid B

Variante: ϕ (x,y,z) = 5 (S_2xC_yS_z + S_xS_2yC_z + C_xS_yS_2z) + (C_2xC_2y + C_2yC_2z + C_2zC_2x)

G'₂ - TPMS

G'₂ - TPMS, c = c_pinch.a

G'₂ - TPMS, c = c_pinch.b

G'₂ - TPMS, c = c_pinch.c

G'₂ - Sheet

G'₂ - Solid A

G'₂ - Solid B

K Surface • Karcher K, KP

ϕ (x,y,z) = 0.3 (C_x + C_y + C_z) + 0.3 (C_xC_y + C_yC_z + C_zC_x) − 0.4 (C_2x + C_2y + C_2z) + 0.2

K - TPMS

K - TPMS, c = c_pinch.a

K - TPMS, c = c_pinch.b

K - Sheet

K - Solid A

K - Solid B

Lidinoid • HG, L

ϕ (x,y,z) = S_2xC_yS_z + S_2yC_zS_x + S_2zC_xS_y − (C_2xC_2y + C_2yC_2z + C_2zC_2x) + 0.3

Lidinoid - TPMS

Lidinoid - TPMS, c = c_pinch.a

Lidinoid - TPMS, c = c_pinch.b

Lidinoid - TPMS, c = c_pinch.c

Lidinoid - Sheet

Lidinoid - Solid A

Lidinoid - Solid B

P+C(P) • PN

ϕ (x,y,z) = 0.3 (C_xC_yC_z) + 0.2 (C_x + C_y + C_z) + 0.1 C_2xC_2yC_2z + 0.1 (C_2x +C_2y +C_2z) +
0.05 (C_3x + C_3y + C_3z) + 0.1 (C_xC_y +C_yC_z +C_zC_x)

P+C(P) - TPMS

P+C(P) - TPMS, c = c_pinch.a

P+C(P) - TPMS, c = c_pinch.b

P+C(P) - Sheet

P+C(P) - Solid A

P+C(P) - Solid B

Die folgende Tabelle enthält die Funktionen und Parameter mit denen die Flächen und Festkörper auf dieser Seite erstellt wurden. Die für eine Fläche jeweils angegebene zweite Funktion enthält die Zeichenfolge ".*" für die multiplikative Verknüpfung und kann so direkt in MSLattice eingefügt werden. Falls nicht anders angegeben, ist jeweils p = 2π.

TPMS	ϕ_TPMS \| F(x,y,z) für MSLattice	d
D'	0.5(cos(px)cos(py)cos(pz)+cos(px)sin(py)sin(pz)+sin(px)cos(py)sin(pz)+ sin(px)sin(py)cos(pz))-0.5(sin(2px)sin(2py)+sin(2py)sin(2pz)+sin(2pz)sin(2px))−0.2 c_pinch.a = 0.362 c_pinch.b = -0.106 c_pinch.c = -0.699 0.5.(cos(2.pi.x).cos(2.pi.y).cos(2.pi.z)+cos(2.pi.x).sin(2.pi.y).sin(2.pi.z)+ sin(2.pi.x).cos(2.pi.y).sin(2.pi.z)+sin(2.pi.x).sin(2.pi.y).cos(2.pi.z))- 0.5.(sin(2.pi.2.x).sin(2.pi.2.y)+sin(2.pi.2.y).sin(2.pi.2.z)+ sin(2.pi.2.z).sin(2.pi.2.x))-0.2 Variante: 0.5(sin(px)sin(py)sin(pz)+cos(px)cos(py)cos(pz))–0.5(cos(2px)cos(2py)+cos(2py)cos(2pz)+cos(2pz)cos(2px))–0.2 c_pinch.a = 0.331 c_pinch.b = -0.153 c_pinch.c = -0.551 0.5.(sin(2.pi.x).sin(2.pi.y).sin(2.pi.z)+cos(2.pi.x).cos(2.pi.y).cos(2.pi.z))- 0.5.(cos(2.pi.2.x).cos(2.pi.2.y)+cos(2.pi.2.y).cos(2.pi.2.z)+ cos(2.pi.2.z).cos(2.pi.2.x))-0.2	0.1 0.15
G'	sin(2px)cos(py)sin(pz)+sin(px)sin(2py)cos(pz)+cos(px)sin(py)sin(2pz)+0.32 c_pinch.a = 0.319 c_pinch.b = 1.319 c_pinch.c = -0.494 sin(pi.2.x).cos(pi.y).sin(pi.z)+sin(pi.x).sin(pi.2.y).cos(pi.z)+ cos(pi.x).sin(pi.y).sin(pi.2.z)+0.32 Variante: 5(sin(2px)cos(py)sin(pz)+sin(px)sin(2py)cos(pz)+cos(px)sin(py)sin(2pz))+ (cos(2px)cos(2py)+cos(2py)cos(2pz)+cos(2pz)cos(2px)) c_pinch.a = 2.999 c_pinch.b = 3.999 c_pinch.c = -4.429 5.(sin(pi.2.x).cos(pi.y).sin(pi.z)+ sin(pi.x).sin(pi.2.y).cos(pi.z)+cos(pi.x).sin(pi.y).sin(pi.2.z))+ (cos(pi.2.x).cos(pi.2.y)+cos(pi.2.y).cos(pi.2.z)+ cos(pi.2.z).cos(pi.2.x))	0.1
K	0.3(cos(px)+cos(py)+cos(pz))+0.3(cos(px)cos(py)+cos(py)cos(pz)+cos(pz)cos(px))− 0.4(cos(2px)+cos(2py)+cos(2pz))+0.2 c_pinch.a = 0.299 c_pinch.b = -0.471 0.3.(cos(2.pi.x)+cos(2.pi.y)+cos(2.pi.z))+0.3.(cos(2.pi.x).cos(2.pi.y)+ cos(2.pi.y).cos(2.pi.z)+cos(2.pi.z).cos(2.pi.x))-0.4.(cos(2.2.pi.x)+ cos(2.2.pi.y)+cos(2.2.pi.*z))+0.2	0.1
Lidinoid	(sin(2x)cos(y)sin(z)+sin(2y)cos(z)sin(x)+sin(2z)cos(x)sin(y))− (cos(2x)cos(2y)+cos(2y)cos(2z)+cos(2z)cos(2x))+0.3 c_pinch.a = 0.299 c_pinch.b = 1.873 c_pinch.c = -0.347 sin(2.pi.2.x).cos(2.pi.y).sin(2.pi.z)+sin(2.pi.2.y).cos(2.pi.z).sin(2.pi.x)+ sin(2.pi.2.z).cos(2.pi.x).sin(2.pi.y)-(cos(2.pi.2.x).cos(2.pi.2.y)+ cos(2.pi.2.y).cos(2.pi.2.z)+cos(2.pi.2.z).cos(2.pi.2.x))+0.3	0.25
P+C(P)	0.3(cos(px)cos(py)cos(pz))+0.2(cos(px)+cos(py)+cos(pz))+ 0.1(cos(2px)cos(2py)cos(2pz))+0.1(cos(2px)+cos(2py)+cos(2pz))+ 0.05(cos(3px)+cos(3py)+cos(3pz))+0.1(cos(px)cos(py)+ cos(py)cos(pz)+cos(pz)cos(px)) c_pinch.a = 0.174 c_pinch.b = -0.134 0.3.(cos(2.pi.x).cos(2.pi.y).cos(2.pi.z))+0.2.(cos(2.pi.x)+cos(2.pi.y)+ cos(2.pi.z))+0.1.(cos(2.pi.2.x).cos(2.pi.2.y).cos(2.pi.2.z))+ 0.1.(cos(2.pi.2.x)+cos(2.pi.2.y)+cos(2.pi.2.z))+0.05.(cos(2.pi.3.x)+ cos(2.pi.3.y)+cos(2.pi.3.z))+0.1.(cos(2.pi.x).cos(2.pi.y)+ cos(2.pi.y).cos(2.pi.z)+cos(2.pi.z).cos(2.pi.x))	0.5