TPMS - Galerie 3

In dieser Galerie sind für diverse TPMS (s. rechts) folgende Objekte dargestellt:

TPMS mit ϕ (x,y,z) = 0
Sheet mit | ϕ (x,y,z) | ≤ c, c ∈ |R⁺
Solid A mit ϕ (x,y,z) > 0
Solid B mit ϕ (x,y,z) < 0

(s. dazu auch TPMS – Grundlagen) und ggf. weitere Grafiken.

Die TPMS wurde mit dem Graphing Calculator 3D, die anderen Objekte wurden mit MSLattice erzeugt, wobei dessen Feature, eigene Funktionen definieren zu können, verwendet wurde.

Galerie 1

D
P
Neovius
IWP
FRD
OCTO
C(D)
Gyroid
C(G)
S
C(S)

Galerie 2

Y
C(Y)
±Y
C(±Y)
I2-Y**
C(I2-Y**)
D'
G'
K
Lidinoid
P+C(P)

Galerie 3

Slotted-P
Split-P
Q*
W
F
Double D
Double G
Double P
Tubular D
Tubular G
Tubular P

Anstatt zu scrollen kann man durch Anklicken eines TPMS-Namens in den Spalten oben rechts direkt zur gewünschten TPMS (oder auch direkt in die Galerie 1 oder Galerie 3) springen.

Für eigene Experimente findet die interessierte Leserschaft am Ende der Seite die TPMS-Funktionen in gewohnter Syntax und spezieller MSLattice-Syntax für Copy & Paste.

Slotted−P

−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) = t

Slotted-P - Sheet

Slotted-P - Solid A

Slotted-P - Solid B

Split−P

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) = t

Split-P - Sheet

Split-P - Solid A

Split-P - Solid B

Q*

(C_x – 2 C_y) C_z − √3 S_z (C_x−y − C_x) + C_x−yC_z = t

Q* - Sheet

Q* - Solid A

Q* - Solid B

W • W*

(C_2xC_y + C_2yC_z +C_xC_2z) − (C_xC_2y + C_yC_2z + C_2xCz) = t

W - Sheet

W - Solid A

W - Solid B

F • F*, Tripleplane 1

C_x C_y C_z= t

P - Isosurface

F - Sheet

F - Solid A

F - Solid B

Double D

(S_2xS_2y + S_2yS_2z +S_2zS_2x) + C_2xC_2yC_2z = t

Double D - Sheet

Double D - Solid A

Double D - Solid B

Variante: C_2xC_2y + C_2yC_2z + C_2xC_2z + S_2xS_2yS_2z = t

Double D₂ - Sheet

Double D₂ - Solid A

Double D₂ - Solid B

Double G

2.75 (S_2xC_yS_z + S_2yC_xS_z + S_2zS_yC_x) − (C_2xC_2y + C_2yC_2z + C_2zC_2x) = t

Double G - Sheet

Double G - Solid A

Double G - Solid B

Double P

½ (C_xC_y + C_yC_z + C_zC_x) + 0.2 (C_2x + C_2y + C_2z) = t

Double P - Sheet

Double P - Solid A

Double P - Solid B

Tubular D

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 = t

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

Tubular D - Sheet

Tubular D -Sheet, -1 ≤ z ≤ 1

Tubular G

10 (C_xS_y + C_yS_z + C_zS_x) − 0.5 (C_2xC_2y + C_2yC_2z + C_2zC_2x) – 14 = t

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 = 0

Tubular P - Sheet

Tubular P - Sheet, -1 ≤ z ≤ 1

TPMS	ϕ_TPMS \| F(x,y,z) für MSLattice	p	c
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=0 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=0 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	2π	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=0 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))=0 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))	2π	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=t 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	2π	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=t 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=t	2π	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))=t 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))	2π	.05
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))=t -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))=t 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)=t (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))=t (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) = 0 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)=t (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)=t 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
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))=t 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))=t 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
Bionic Bone