Constrained Triangulation

Disjoint Domains

Now we consider an example where we are triangulating disjoint domains. The way to setup these domains is similar to the previous tutorials, with the outer boundaries being counter-clockwise, and all the interior boundaries clockwise (and other interiors inside interiors counter-clockwise, etc., if you please). Here is a simple example.

using DelaunayTriangulation
using CairoMakie

θ = LinRange(0, 2π, 20) |> collect
θ[end] = 0 # need to make sure that 2π gives the exact same coordinates as 0
xy = Vector{Vector{Vector{NTuple{2, Float64}}}}()
cx = 0.0
for i in 1:2
    global cx
    # Make the exterior circle
    push!(xy, [[(cx + cos(θ), sin(θ)) for θ in θ]])
    # Now the interior circle - clockwise
    push!(xy, [[(cx + 0.5cos(θ), 0.5sin(θ)) for θ in reverse(θ)]])
    cx += 3.0
end
boundary_nodes, points = convert_boundary_points_to_indices(xy)
tri = triangulate(points; boundary_nodes = boundary_nodes)
fig, ax, sc = triplot(tri)
fig

Here is another example.

C = (15.7109521325776, 33.244486807457)
D = (14.2705719699703, 32.8530791545746)
E = (14.3, 27.2)
F = (14.1, 27.0)
G = (13.7, 27.2)
H = (13.4, 27.5)
I = (13.1, 27.6)
J = (12.7, 27.4)
K = (12.5, 27.1)
L = (12.7, 26.7)
M = (13.1, 26.5)
N = (13.6, 26.4)
O = (14.0, 26.4)
P = (14.6, 26.5)
Q = (15.1983491346581, 26.8128534095401)
R = (15.6, 27.6)
S = (15.6952958264624, 28.2344688505621)
T = (17.8088971520274, 33.1192363585346)
U = (16.3058917649589, 33.0722674401887)
V = (16.3215480710742, 29.7374742376305)
W = (16.3841732955354, 29.393035503094)
Z = (16.6190178872649, 28.9233463196351)
A1 = (17.0417381523779, 28.5319386667527)
B1 = (17.5114273358368, 28.3753756055997)
C1 = (18.1376795804487, 28.3597192994844)
D1 = (18.7169629067146, 28.5632512789833)
E1 = (19.2805899268653, 28.8920337074045)
F1 = (19.26493362075, 28.4536571361762)
G1 = (20.6426885588962, 28.4223445239456)
H1 = (20.689657477242, 33.1035800524193)
I1 = (19.2805899268653, 33.0722674401887)
J1 = (19.2962462329806, 29.7531305437458)
K1 = (19.0614016412512, 29.393035503094)
L1 = (18.7482755189452, 29.236472441941)
M1 = (18.4508057027546, 29.1425346052493)
N1 = (18.1689921926793, 29.3147539725175)
O1 = (17.7932408459121, 29.6278800948235)
P1 = (22.6466957416542, 35.4207133574833)
Q1 = (21.2219718851621, 34.9979930923702)
R1 = (21.2376281912774, 28.4693134422915)
S1 = (22.6780083538847, 28.4380008300609)
T1 = (24.5724213938357, 33.1975178891111)
U1 = (23.3512295168425, 32.8530791545746)
V1 = (23.3199169046119, 28.4380008300609)
W1 = (24.6663592305274, 28.3753756055997)
Z1 = (15.1942940307729, 35.4363696635986)
A2 = (14.7246048473139, 35.3737444391374)
B2 = (14.3645098066621, 35.1858687657538)
C2 = (14.1766341332786, 34.8570863373326)
D2 = (14.1140089088174, 34.3247719294125)
E2 = (14.2705719699703, 33.8394264398383)
F2 = (14.7246048473139, 33.6202381542241)
G2 = (15.4604512347329, 33.6045818481088)
H2 = (16.0, 34.0)
I2 = (15.9771093365377, 34.6848669700643)
J2 = (15.6170142958859, 35.2328376840997)
K2 = (24.1653574348379, 35.4520259697138)
L2 = (23.7739497819555, 35.4363696635986)
M2 = (23.4608236596496, 35.2641502963303)
N2 = (23.272947986266, 34.9040552556785)
O2 = (23.1320412312284, 34.5909291333725)
P2 = (23.1163849251131, 34.2151777866054)
Q2 = (23.2886042923813, 33.8081138276077)
R2 = (23.8209187003014, 33.6045818481088)
S2 = (24.3062641898756, 33.5576129297629)
T2 = (24.7602970672192, 33.8550827459536)
U2 = (25.010797965064, 34.4656786844502)
V2 = (24.8385785977957, 34.9666804801397)
W2 = (24.5254524754898, 35.2641502963303)
Z2 = (25.3708930057158, 37.4716894585871)
A3 = (24.7916096794498, 37.3464390096648)
B3 = (24.4471709449133, 36.9550313567823)
C3 = (24.3062641898756, 36.5636237038999)
D3 = (24.4941398632592, 35.9999966837492)
E3 = (25.0264542711793, 35.5929327247515)
F3 = (25.5587686790994, 35.5929327247515)
F3 = (25.5587686790994, 35.5929327247515)
G3 = (26.0, 36.0)
H3 = (26.1380520053653, 36.5792800100152)
I3 = (26.0, 37.0)
J3 = (25.7466443524829, 37.2838137852036)
K3 = (26.3885529032101, 35.4676822758291)
L3 = (25.9814889442124, 35.3580881330221)
M3 = (25.6840191280217, 35.1858687657538)
N3 = (25.5274560668688, 34.9040552556785)
O3 = (25.4961434546382, 34.5596165211419)
P3 = (25.5274560668688, 34.246490398836)
Q3 = (25.6683628219064, 33.8394264398383)
R3 = (26.0284578625583, 33.6358944603394)
S3 = (26.5451159643631, 33.6202381542241)
T3 = (27.0, 34.0)
U3 = (27.280962351782, 34.5596165211419)
V3 = (27.0304614539373, 35.2171813779844)
W3 = (26.1693646175959, 33.087923746304)
Z3 = (26.0, 33.0)
A4 = (25.5274560668688, 32.7278287056522)
B4 = (25.2612988629087, 32.4147025833463)
C4 = (25.1830173323322, 32.0702638488098)
D4 = (25.2299862506781, 31.7727940326191)
E4 = (25.6527065157911, 31.5222931347744)
F4 = (26.2946150665183, 31.7258251142732)
G4 = (26.5607722704784, 32.5086404200381)
H4 = (27.1557119028596, 32.7434850117675)
I4 = (27.6097447802033, 32.4929841139228)
J4 = (27.6410573924338, 32.1015764610403)
K4 = (27.7193389230103, 31.6005746653509)
L4 = (27.437525412935, 31.4283552980826)
M4 = (26.9834925355914, 31.2561359308143)
N4 = (26.5764285765937, 31.0995728696614)
O4 = (26.0441141686736, 30.7864467473554)
P4 = (25.6527065157911, 30.5672584617413)
Q4 = (25.3239240873699, 30.1915071149741)
R4 = (25.1673610262169, 29.8783809926682)
S4 = (25.1047358017558, 29.6122237887082)
T4 = (25.0890794956405, 29.1895035235952)
U4 = (25.2926114751393, 28.8294084829433)
V4 = (25.6840191280217, 28.5632512789833)
W4 = (26.1537083114806, 28.3753756055997)
Z4 = (26.8269294744384, 28.391031911715)
A5 = (27.4844943312809, 28.6102201973292)
B5 = (27.7342002330051, 28.7239579596219)
C5 = (27.7264126450755, 28.4202565942047)
D5 = (29.1825559185446, 28.3922538389457)
E5 = (29.1545531632856, 32.2146299318021)
F5 = (29.000538009361, 32.5786657501693)
G5 = (28.6785063238822, 32.9006974356481)
H5 = (28.3144705055149, 33.0827153448317)
I5 = (27.9084305542591, 33.2367304987563)
J5 = (27.3343740714492, 33.3207387645334)
K5 = (26.8303244767868, 33.2367304987563)
L5 = (27.6564057569279, 30.786489413592)
M5 = (27.6984098898165, 30.3944508399657)
N5 = (27.6984098898165, 29.7363860913787)
O5 = (27.5863988687804, 29.4143544059)
P5 = (27.2643671833016, 29.2043337414573)
Q5 = (26.9843396307114, 29.1763309861983)
R5 = (26.6903107004917, 29.3163447624934)
S5 = (26.5782996794556, 29.7503874690082)
T5 = (26.7603175886393, 30.3384453294476)
U5 = (27.3203726938197, 30.7024811478149)
J_curve = [[C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, C]]
U_curve = [[T, U, V, W, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, T]]
L_curve = [[P1, Q1, R1, S1, P1]]
I_curve = [[T1, U1, V1, W1, T1]]
A_curve_outline = [
    [
        K5, W3, Z3, A4, B4, C4, D4, E4, F4, G4, H4, I4, J4, K4, L4, M4, N4,
        O4, P4, Q4, R4, S4, T4, U4, V4, W4, Z4, A5, B5, C5, D5, E5, F5, G5,
        H5, I5, J5, K5,
    ],
]
A_curve_hole = [[L5, M5, N5, O5, P5, Q5, R5, S5, T5, U5, L5]]
dot_1 = [[Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, Z1]]
dot_2 = [[Z2, A3, B3, C3, D3, E3, F3, G3, H3, I3, J3, Z2]]
dot_3 = [[K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2, K2]]
dot_4 = [[K3, L3, M3, N3, O3, P3, Q3, R3, S3, T3, U3, V3, K3]]
curves = [J_curve, U_curve, L_curve, I_curve, A_curve_outline, A_curve_hole, dot_1, dot_2, dot_3, dot_4]
nodes, points = convert_boundary_points_to_indices(curves)
tri = triangulate(points; boundary_nodes = nodes)
fig, ax, sc = triplot(tri)
fig

Just the code

An uncommented version of this example is given below. You can view the source code for this file here.

using DelaunayTriangulation
using CairoMakie

θ = LinRange(0, 2π, 20) |> collect
θ[end] = 0 # need to make sure that 2π gives the exact same coordinates as 0
xy = Vector{Vector{Vector{NTuple{2, Float64}}}}()
cx = 0.0
for i in 1:2
    global cx
    # Make the exterior circle
    push!(xy, [[(cx + cos(θ), sin(θ)) for θ in θ]])
    # Now the interior circle - clockwise
    push!(xy, [[(cx + 0.5cos(θ), 0.5sin(θ)) for θ in reverse(θ)]])
    cx += 3.0
end
boundary_nodes, points = convert_boundary_points_to_indices(xy)
tri = triangulate(points; boundary_nodes = boundary_nodes)
fig, ax, sc = triplot(tri)
fig

C = (15.7109521325776, 33.244486807457)
D = (14.2705719699703, 32.8530791545746)
E = (14.3, 27.2)
F = (14.1, 27.0)
G = (13.7, 27.2)
H = (13.4, 27.5)
I = (13.1, 27.6)
J = (12.7, 27.4)
K = (12.5, 27.1)
L = (12.7, 26.7)
M = (13.1, 26.5)
N = (13.6, 26.4)
O = (14.0, 26.4)
P = (14.6, 26.5)
Q = (15.1983491346581, 26.8128534095401)
R = (15.6, 27.6)
S = (15.6952958264624, 28.2344688505621)
T = (17.8088971520274, 33.1192363585346)
U = (16.3058917649589, 33.0722674401887)
V = (16.3215480710742, 29.7374742376305)
W = (16.3841732955354, 29.393035503094)
Z = (16.6190178872649, 28.9233463196351)
A1 = (17.0417381523779, 28.5319386667527)
B1 = (17.5114273358368, 28.3753756055997)
C1 = (18.1376795804487, 28.3597192994844)
D1 = (18.7169629067146, 28.5632512789833)
E1 = (19.2805899268653, 28.8920337074045)
F1 = (19.26493362075, 28.4536571361762)
G1 = (20.6426885588962, 28.4223445239456)
H1 = (20.689657477242, 33.1035800524193)
I1 = (19.2805899268653, 33.0722674401887)
J1 = (19.2962462329806, 29.7531305437458)
K1 = (19.0614016412512, 29.393035503094)
L1 = (18.7482755189452, 29.236472441941)
M1 = (18.4508057027546, 29.1425346052493)
N1 = (18.1689921926793, 29.3147539725175)
O1 = (17.7932408459121, 29.6278800948235)
P1 = (22.6466957416542, 35.4207133574833)
Q1 = (21.2219718851621, 34.9979930923702)
R1 = (21.2376281912774, 28.4693134422915)
S1 = (22.6780083538847, 28.4380008300609)
T1 = (24.5724213938357, 33.1975178891111)
U1 = (23.3512295168425, 32.8530791545746)
V1 = (23.3199169046119, 28.4380008300609)
W1 = (24.6663592305274, 28.3753756055997)
Z1 = (15.1942940307729, 35.4363696635986)
A2 = (14.7246048473139, 35.3737444391374)
B2 = (14.3645098066621, 35.1858687657538)
C2 = (14.1766341332786, 34.8570863373326)
D2 = (14.1140089088174, 34.3247719294125)
E2 = (14.2705719699703, 33.8394264398383)
F2 = (14.7246048473139, 33.6202381542241)
G2 = (15.4604512347329, 33.6045818481088)
H2 = (16.0, 34.0)
I2 = (15.9771093365377, 34.6848669700643)
J2 = (15.6170142958859, 35.2328376840997)
K2 = (24.1653574348379, 35.4520259697138)
L2 = (23.7739497819555, 35.4363696635986)
M2 = (23.4608236596496, 35.2641502963303)
N2 = (23.272947986266, 34.9040552556785)
O2 = (23.1320412312284, 34.5909291333725)
P2 = (23.1163849251131, 34.2151777866054)
Q2 = (23.2886042923813, 33.8081138276077)
R2 = (23.8209187003014, 33.6045818481088)
S2 = (24.3062641898756, 33.5576129297629)
T2 = (24.7602970672192, 33.8550827459536)
U2 = (25.010797965064, 34.4656786844502)
V2 = (24.8385785977957, 34.9666804801397)
W2 = (24.5254524754898, 35.2641502963303)
Z2 = (25.3708930057158, 37.4716894585871)
A3 = (24.7916096794498, 37.3464390096648)
B3 = (24.4471709449133, 36.9550313567823)
C3 = (24.3062641898756, 36.5636237038999)
D3 = (24.4941398632592, 35.9999966837492)
E3 = (25.0264542711793, 35.5929327247515)
F3 = (25.5587686790994, 35.5929327247515)
F3 = (25.5587686790994, 35.5929327247515)
G3 = (26.0, 36.0)
H3 = (26.1380520053653, 36.5792800100152)
I3 = (26.0, 37.0)
J3 = (25.7466443524829, 37.2838137852036)
K3 = (26.3885529032101, 35.4676822758291)
L3 = (25.9814889442124, 35.3580881330221)
M3 = (25.6840191280217, 35.1858687657538)
N3 = (25.5274560668688, 34.9040552556785)
O3 = (25.4961434546382, 34.5596165211419)
P3 = (25.5274560668688, 34.246490398836)
Q3 = (25.6683628219064, 33.8394264398383)
R3 = (26.0284578625583, 33.6358944603394)
S3 = (26.5451159643631, 33.6202381542241)
T3 = (27.0, 34.0)
U3 = (27.280962351782, 34.5596165211419)
V3 = (27.0304614539373, 35.2171813779844)
W3 = (26.1693646175959, 33.087923746304)
Z3 = (26.0, 33.0)
A4 = (25.5274560668688, 32.7278287056522)
B4 = (25.2612988629087, 32.4147025833463)
C4 = (25.1830173323322, 32.0702638488098)
D4 = (25.2299862506781, 31.7727940326191)
E4 = (25.6527065157911, 31.5222931347744)
F4 = (26.2946150665183, 31.7258251142732)
G4 = (26.5607722704784, 32.5086404200381)
H4 = (27.1557119028596, 32.7434850117675)
I4 = (27.6097447802033, 32.4929841139228)
J4 = (27.6410573924338, 32.1015764610403)
K4 = (27.7193389230103, 31.6005746653509)
L4 = (27.437525412935, 31.4283552980826)
M4 = (26.9834925355914, 31.2561359308143)
N4 = (26.5764285765937, 31.0995728696614)
O4 = (26.0441141686736, 30.7864467473554)
P4 = (25.6527065157911, 30.5672584617413)
Q4 = (25.3239240873699, 30.1915071149741)
R4 = (25.1673610262169, 29.8783809926682)
S4 = (25.1047358017558, 29.6122237887082)
T4 = (25.0890794956405, 29.1895035235952)
U4 = (25.2926114751393, 28.8294084829433)
V4 = (25.6840191280217, 28.5632512789833)
W4 = (26.1537083114806, 28.3753756055997)
Z4 = (26.8269294744384, 28.391031911715)
A5 = (27.4844943312809, 28.6102201973292)
B5 = (27.7342002330051, 28.7239579596219)
C5 = (27.7264126450755, 28.4202565942047)
D5 = (29.1825559185446, 28.3922538389457)
E5 = (29.1545531632856, 32.2146299318021)
F5 = (29.000538009361, 32.5786657501693)
G5 = (28.6785063238822, 32.9006974356481)
H5 = (28.3144705055149, 33.0827153448317)
I5 = (27.9084305542591, 33.2367304987563)
J5 = (27.3343740714492, 33.3207387645334)
K5 = (26.8303244767868, 33.2367304987563)
L5 = (27.6564057569279, 30.786489413592)
M5 = (27.6984098898165, 30.3944508399657)
N5 = (27.6984098898165, 29.7363860913787)
O5 = (27.5863988687804, 29.4143544059)
P5 = (27.2643671833016, 29.2043337414573)
Q5 = (26.9843396307114, 29.1763309861983)
R5 = (26.6903107004917, 29.3163447624934)
S5 = (26.5782996794556, 29.7503874690082)
T5 = (26.7603175886393, 30.3384453294476)
U5 = (27.3203726938197, 30.7024811478149)
J_curve = [[C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, C]]
U_curve = [[T, U, V, W, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, T]]
L_curve = [[P1, Q1, R1, S1, P1]]
I_curve = [[T1, U1, V1, W1, T1]]
A_curve_outline = [
    [
        K5, W3, Z3, A4, B4, C4, D4, E4, F4, G4, H4, I4, J4, K4, L4, M4, N4,
        O4, P4, Q4, R4, S4, T4, U4, V4, W4, Z4, A5, B5, C5, D5, E5, F5, G5,
        H5, I5, J5, K5,
    ],
]
A_curve_hole = [[L5, M5, N5, O5, P5, Q5, R5, S5, T5, U5, L5]]
dot_1 = [[Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, Z1]]
dot_2 = [[Z2, A3, B3, C3, D3, E3, F3, G3, H3, I3, J3, Z2]]
dot_3 = [[K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2, K2]]
dot_4 = [[K3, L3, M3, N3, O3, P3, Q3, R3, S3, T3, U3, V3, K3]]
curves = [J_curve, U_curve, L_curve, I_curve, A_curve_outline, A_curve_hole, dot_1, dot_2, dot_3, dot_4]
nodes, points = convert_boundary_points_to_indices(curves)
tri = triangulate(points; boundary_nodes = nodes)
fig, ax, sc = triplot(tri)
fig

This page was generated using Literate.jl.