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| ### A Pluto.jl notebook ### | |
| # v0.12.18 | |
| using Markdown | |
| using InteractiveUtils | |
| # ╔═╡ b6cede50-fe79-11ea-10c2-13b9e4851b06 | |
| begin | |
| using LinearAlgebra | |
| using Plots | |
| using PlutoUI | |
| end | |
| # ╔═╡ 4e5ac200-fdff-11ea-3d80-d56549011cac | |
| md" | |
| ## Solving the TopologicalComputer N point interpolation problem in 3 dimensions | |
| The TopologicalComputer N point interpolation problem in 3 dimensions involves the generation of a continuous surface across a region defined by 4 points. This problem becomes more difficult in higher dimensions, as the number of permutations of {0, 1} for each dimension grows with the function 2^d, whereas the number of points required to make a linear function is equal to d. | |
| The solution I present is to use a similar method to the tracing above. Given 4 points, draw two lines between the points such that all 4 points have one line intersecting them. Then start from one end drawing traces between them such that a surface is drawn in the region bounded by the four points. Hello world | |
| " | |
| # ╔═╡ 63395150-fdff-11ea-317a-956ff6431475 | |
| P = [ | |
| 0 0 1 # A | |
| 1 0 1 # B | |
| 0 1 1 # C | |
| 1 1 -1 # D | |
| ] | |
| # ╔═╡ 0ff87db0-fe7a-11ea-3afb-ddca5f27acab | |
| begin | |
| A = P[1, :] | |
| B = P[2, :] | |
| C = P[3, :] | |
| D = P[4, :] | |
| end | |
| # ╔═╡ 7e3e4710-fe79-11ea-3d4b-4fc54cc58d07 | |
| vecMag(P1, P2) = √((P2 .- P1) ⋅ (P2 .- P1)) | |
| # ╔═╡ 00d26220-fe83-11ea-3cf6-492a6e1f3339 | |
| proj(u, v) = (u ⋅ v) / (v ⋅ v) * v | |
| # ╔═╡ b19ba752-3dc2-11eb-0b48-2bb17d047b06 | |
| md" | |
| $D_1(P)=||\overrightarrow{AP}-proj_{\overrightarrow{AB}}\overrightarrow{AP}||$ | |
| $D_2(P)=||\overrightarrow{CP}-proj_{\overrightarrow{CD}}\overrightarrow{CP}||$ | |
| " | |
| # ╔═╡ 74c51212-fe81-11ea-2b20-45511a32be82 | |
| D1(P) = vecMag((P .- A[1:2]) - proj((P .- A[1:2]), (B[1:2] .- A[1:2])), [0, 0]) | |
| # ╔═╡ 453a9720-fe83-11ea-2ef2-fb2f40fb9394 | |
| D2(P) = vecMag((P .- C[1:2]) - proj((P .- C[1:2]), (D[1:2] .- C[1:2])), [0, 0]) | |
| # ╔═╡ fd028552-3dc3-11eb-2538-31025cd4a16c | |
| md" | |
| $P_{ab}(P)=\frac{P\circ\overrightarrow{AB}}{||\overrightarrow{AB}||\frac{D_2(P)}{D_1(P) + D_2(P)}+||\overrightarrow{CD}||\frac{D_1(P)}{D_1(P)+D_2(P)}} + A_{xy}$ | |
| $P_{cd}(P)=\frac{P\circ\overrightarrow{CD}}{||\overrightarrow{AB}||\frac{D_2(P)}{D_1(P) + D_2(P)}+||\overrightarrow{CD}||\frac{D_1(P)}{D_1(P)+D_2(P)}} + C_{xy}$ | |
| " | |
| # ╔═╡ 246e2a50-fe80-11ea-1181-594649e2ce2e | |
| Pab(P) = (P .* (B[1:2] .- A[1:2])) / ((vecMag(A[1:2], B[1:2]) * (D2(P) / (D1(P) + D2(P)))) + (vecMag(C[1:2], D[1:2]) * (D1(P) / (D1(P) + D2(P))))) + A[1:2] | |
| # ╔═╡ 209fcaf0-fe85-11ea-0d9e-794a77c715a4 | |
| Pcd(P) = (P .* (D[1:2] .- C[1:2])) / ((vecMag(A[1:2], B[1:2]) * (D2(P) / (D1(P) + D2(P)))) + (vecMag(C[1:2], D[1:2]) * (D1(P) / (D1(P) + D2(P))))) + C[1:2] | |
| # ╔═╡ a015f1e0-3dc0-11eb-3cef-1ddcb8c1f656 | |
| md" | |
| $Z_{P_{ab}}(P)=(B_z-A_z)\frac{||\overrightarrow{AP_{ab}(P)}||}{||\overrightarrow{AB}||}+A_z$ | |
| $Z_{P_{cd}}(P)=(D_z-C_z)\frac{||\overrightarrow{CP_{ab}(P)}||}{||\overrightarrow{CD}||}+C_z$ | |
| " | |
| # ╔═╡ 252d9b00-fe86-11ea-269c-959635d8db35 | |
| ZPab(P) = ((B[3] - A[3]) / vecMag(A[1:2], B[1:2])) * vecMag(Pab(P), A[1:2]) + A[3] | |
| # ╔═╡ 7eb90970-fe86-11ea-346f-2b9cf9f8ea22 | |
| ZPcd(P) = ((D[3] - C[3]) / vecMag(C[1:2], D[1:2])) * vecMag(Pcd(P), C[1:2]) + C[3] | |
| # ╔═╡ 5bc2b230-3dc5-11eb-3dd7-a51cce70eebc | |
| md" | |
| $Z(P)=\left(Z_{P_{ab}}(P)-Z_{P_{cd}}(P)\right)\frac{||\overrightarrow{P_{cd}(P)P}||}{||\overrightarrow{P_{ab}(P)P_{cd}(P)}||}+Z_{P_{cd}}(P)$ | |
| " | |
| # ╔═╡ ba242d60-fe85-11ea-3397-8da61bd274ca | |
| Z(P) = ((ZPab(P) - ZPcd(P)) / vecMag(Pab(P), Pcd(P))) * vecMag(Pcd(P), P) + ZPcd(P) | |
| # ╔═╡ de52a1d0-3dbe-11eb-3860-3b72f74e299d | |
| Z(X, Y) = Z([X, Y]) | |
| # ╔═╡ b4b47ce0-3dbe-11eb-230a-a7eaa71cc91c | |
| x = min(P[:, 1]...):0.1:max(P[:, 1]...) | |
| # ╔═╡ b775bfc0-3dbe-11eb-3ec1-453899565e99 | |
| y = min(P[:, 2]...):0.1:max(P[:, 2]...) | |
| # ╔═╡ 015cae7e-fe88-11ea-353a-a9907ace0173 | |
| plot(x, y, Z, st=:surface) | |
| # ╔═╡ 601d1460-fe87-11ea-1066-0d86847a1ad9 | |
| begin | |
| p = plot(x, y, Z, st=:contour) | |
| plot!(p, P[:, 1], P[:, 2], st=:scatter) | |
| end | |
| # ╔═╡ 6562e540-3dbf-11eb-358e-ed02cee52f6d | |
| P[:, 1:2] | |
| # ╔═╡ Cell order: | |
| # ╟─4e5ac200-fdff-11ea-3d80-d56549011cac | |
| # ╠═b6cede50-fe79-11ea-10c2-13b9e4851b06 | |
| # ╠═63395150-fdff-11ea-317a-956ff6431475 | |
| # ╠═0ff87db0-fe7a-11ea-3afb-ddca5f27acab | |
| # ╠═7e3e4710-fe79-11ea-3d4b-4fc54cc58d07 | |
| # ╠═00d26220-fe83-11ea-3cf6-492a6e1f3339 | |
| # ╟─b19ba752-3dc2-11eb-0b48-2bb17d047b06 | |
| # ╠═74c51212-fe81-11ea-2b20-45511a32be82 | |
| # ╠═453a9720-fe83-11ea-2ef2-fb2f40fb9394 | |
| # ╟─fd028552-3dc3-11eb-2538-31025cd4a16c | |
| # ╠═246e2a50-fe80-11ea-1181-594649e2ce2e | |
| # ╠═209fcaf0-fe85-11ea-0d9e-794a77c715a4 | |
| # ╟─a015f1e0-3dc0-11eb-3cef-1ddcb8c1f656 | |
| # ╠═252d9b00-fe86-11ea-269c-959635d8db35 | |
| # ╠═7eb90970-fe86-11ea-346f-2b9cf9f8ea22 | |
| # ╟─5bc2b230-3dc5-11eb-3dd7-a51cce70eebc | |
| # ╠═ba242d60-fe85-11ea-3397-8da61bd274ca | |
| # ╠═de52a1d0-3dbe-11eb-3860-3b72f74e299d | |
| # ╠═b4b47ce0-3dbe-11eb-230a-a7eaa71cc91c | |
| # ╠═b775bfc0-3dbe-11eb-3ec1-453899565e99 | |
| # ╠═015cae7e-fe88-11ea-353a-a9907ace0173 | |
| # ╠═601d1460-fe87-11ea-1066-0d86847a1ad9 | |
| # ╠═6562e540-3dbf-11eb-358e-ed02cee52f6d |
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| ### A Pluto.jl notebook ### | |
| # v0.12.17 | |
| using Markdown | |
| using InteractiveUtils | |
| # ╔═╡ b6cede50-fe79-11ea-10c2-13b9e4851b06 | |
| begin | |
| using LinearAlgebra | |
| using Plots | |
| using PlutoUI | |
| end | |
| # ╔═╡ 4e5ac200-fdff-11ea-3d80-d56549011cac | |
| md" | |
| ## Solving the TopologicalComputer N point interpolation problem in 3 dimensions | |
| The TopologicalComputer N point interpolation problem in 3 dimensions involves the generation of a continuous surface across a region defined by 4 points. This problem becomes more difficult in higher dimensions, as the number of permutations of {0, 1} for each dimension grows with the function 2^d, whereas the number of points required to make a linear function is equal to d. | |
| The solution I present is to use a similar method to the tracing above. Given 4 points, draw two lines between the points such that all 4 points have one line intersecting them. Then start from one end drawing traces between them such that a surface is drawn in the region bounded by the four points. Hello world | |
| " | |
| # ╔═╡ 63395150-fdff-11ea-317a-956ff6431475 | |
| P = [ | |
| 0 0 1 # A | |
| 1 0 1 # B | |
| 0 1 1 # C | |
| 1 1 -1 # D | |
| ] | |
| # ╔═╡ 0ff87db0-fe7a-11ea-3afb-ddca5f27acab | |
| begin | |
| A = P[1, :] | |
| B = P[2, :] | |
| C = P[3, :] | |
| D = P[4, :] | |
| end | |
| # ╔═╡ 7e3e4710-fe79-11ea-3d4b-4fc54cc58d07 | |
| vecMag(P1, P2) = √((P2 .- P1) ⋅ (P2 .- P1)) | |
| # ╔═╡ 00d26220-fe83-11ea-3cf6-492a6e1f3339 | |
| proj(u, v) = (u ⋅ v) / (v ⋅ v) * v | |
| # ╔═╡ b19ba752-3dc2-11eb-0b48-2bb17d047b06 | |
| md" | |
| $D_1(P)=||\overrightarrow{AP}-proj_{\overrightarrow{AB}}\overrightarrow{AP}||$ | |
| $D_2(P)=||\overrightarrow{CP}-proj_{\overrightarrow{CD}}\overrightarrow{CP}||$ | |
| " | |
| # ╔═╡ 74c51212-fe81-11ea-2b20-45511a32be82 | |
| D1(P) = vecMag((P .- A[1:2]) - proj((P .- A[1:2]), (B[1:2] .- A[1:2])), [0, 0]) | |
| # ╔═╡ 453a9720-fe83-11ea-2ef2-fb2f40fb9394 | |
| D2(P) = vecMag((P .- C[1:2]) - proj((P .- C[1:2]), (D[1:2] .- C[1:2])), [0, 0]) | |
| # ╔═╡ fd028552-3dc3-11eb-2538-31025cd4a16c | |
| md" | |
| $P_{ab}(P)=\frac{P\circ\overrightarrow{AB}}{||\overrightarrow{AB}||\frac{D_2(P)}{D_1(P) + D_2(P)}+||\overrightarrow{CD}||\frac{D_1(P)}{D_1(P)+D_2(P)}} + A_{xy}$ | |
| $P_{cd}(P)=\frac{P\circ\overrightarrow{CD}}{||\overrightarrow{AB}||\frac{D_2(P)}{D_1(P) + D_2(P)}+||\overrightarrow{CD}||\frac{D_1(P)}{D_1(P)+D_2(P)}} + C_{xy}$ | |
| " | |
| # ╔═╡ 246e2a50-fe80-11ea-1181-594649e2ce2e | |
| Pab(P) = (P .* (B[1:2] .- A[1:2])) / ((vecMag(A[1:2], B[1:2]) * (D2(P) / (D1(P) + D2(P)))) + (vecMag(C[1:2], D[1:2]) * (D1(P) / (D1(P) + D2(P))))) + A[1:2] | |
| # ╔═╡ 209fcaf0-fe85-11ea-0d9e-794a77c715a4 | |
| Pcd(P) = (P .* (D[1:2] .- C[1:2])) / ((vecMag(A[1:2], B[1:2]) * (D2(P) / (D1(P) + D2(P)))) + (vecMag(C[1:2], D[1:2]) * (D1(P) / (D1(P) + D2(P))))) + C[1:2] | |
| # ╔═╡ a015f1e0-3dc0-11eb-3cef-1ddcb8c1f656 | |
| md" | |
| $Z_{P_{ab}}(P)=(B_z-A_z)\frac{||\overrightarrow{AP_{ab}(P)}||}{||\overrightarrow{AB}||}+A_z$ | |
| $Z_{P_{cd}}(P)=(D_z-C_z)\frac{||\overrightarrow{CP_{ab}(P)}||}{||\overrightarrow{CD}||}+C_z$ | |
| " | |
| # ╔═╡ 252d9b00-fe86-11ea-269c-959635d8db35 | |
| ZPab(P) = ((B[3] - A[3]) / vecMag(A[1:2], B[1:2])) * vecMag(Pab(P), A[1:2]) + A[3] | |
| # ╔═╡ 7eb90970-fe86-11ea-346f-2b9cf9f8ea22 | |
| ZPcd(P) = ((D[3] - C[3]) / vecMag(C[1:2], D[1:2])) * vecMag(Pcd(P), C[1:2]) + C[3] | |
| # ╔═╡ 5bc2b230-3dc5-11eb-3dd7-a51cce70eebc | |
| md" | |
| $Z(P)=\left(Z_{P_{ab}}(P)-Z_{P_{cd}}(P)\right)\frac{||\overrightarrow{P_{cd}(P)P}||}{||\overrightarrow{P_{ab}(P)P_{cd}(P)}||}+Z_{P_{cd}}(P)$ | |
| " | |
| # ╔═╡ ba242d60-fe85-11ea-3397-8da61bd274ca | |
| Z(P) = ((ZPab(P) - ZPcd(P)) / vecMag(Pab(P), Pcd(P))) * vecMag(Pcd(P), P) + ZPcd(P) | |
| # ╔═╡ de52a1d0-3dbe-11eb-3860-3b72f74e299d | |
| Z(X, Y) = Z([X, Y]) | |
| # ╔═╡ b4b47ce0-3dbe-11eb-230a-a7eaa71cc91c | |
| x = min(P[:, 1]...):0.1:max(P[:, 1]...) | |
| # ╔═╡ b775bfc0-3dbe-11eb-3ec1-453899565e99 | |
| y = min(P[:, 2]...):0.1:max(P[:, 2]...) | |
| # ╔═╡ 015cae7e-fe88-11ea-353a-a9907ace0173 | |
| plot(x, y, Z, st=:surface) | |
| # ╔═╡ 601d1460-fe87-11ea-1066-0d86847a1ad9 | |
| begin | |
| p = plot(x, y, Z, st=:contour) | |
| plot!(p, P[:, 1], P[:, 2], st=:scatter) | |
| end | |
| # ╔═╡ 6562e540-3dbf-11eb-358e-ed02cee52f6d | |
| P[:, 1:2] | |
| # ╔═╡ Cell order: | |
| # ╟─4e5ac200-fdff-11ea-3d80-d56549011cac | |
| # ╠═b6cede50-fe79-11ea-10c2-13b9e4851b06 | |
| # ╠═63395150-fdff-11ea-317a-956ff6431475 | |
| # ╠═0ff87db0-fe7a-11ea-3afb-ddca5f27acab | |
| # ╠═7e3e4710-fe79-11ea-3d4b-4fc54cc58d07 | |
| # ╠═00d26220-fe83-11ea-3cf6-492a6e1f3339 | |
| # ╟─b19ba752-3dc2-11eb-0b48-2bb17d047b06 | |
| # ╠═74c51212-fe81-11ea-2b20-45511a32be82 | |
| # ╠═453a9720-fe83-11ea-2ef2-fb2f40fb9394 | |
| # ╟─fd028552-3dc3-11eb-2538-31025cd4a16c | |
| # ╠═246e2a50-fe80-11ea-1181-594649e2ce2e | |
| # ╠═209fcaf0-fe85-11ea-0d9e-794a77c715a4 | |
| # ╟─a015f1e0-3dc0-11eb-3cef-1ddcb8c1f656 | |
| # ╠═252d9b00-fe86-11ea-269c-959635d8db35 | |
| # ╠═7eb90970-fe86-11ea-346f-2b9cf9f8ea22 | |
| # ╟─5bc2b230-3dc5-11eb-3dd7-a51cce70eebc | |
| # ╠═ba242d60-fe85-11ea-3397-8da61bd274ca | |
| # ╠═de52a1d0-3dbe-11eb-3860-3b72f74e299d | |
| # ╠═b4b47ce0-3dbe-11eb-230a-a7eaa71cc91c | |
| # ╠═b775bfc0-3dbe-11eb-3ec1-453899565e99 | |
| # ╠═015cae7e-fe88-11ea-353a-a9907ace0173 | |
| # ╠═601d1460-fe87-11ea-1066-0d86847a1ad9 | |
| # ╠═6562e540-3dbf-11eb-358e-ed02cee52f6d |
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| ### A Pluto.jl notebook ### | |
| # v0.12.17 | |
| using Markdown | |
| using InteractiveUtils | |
| # ╔═╡ b6cede50-fe79-11ea-10c2-13b9e4851b06 | |
| begin | |
| using LinearAlgebra | |
| using Plots | |
| using PlutoUI | |
| end | |
| # ╔═╡ 4e5ac200-fdff-11ea-3d80-d56549011cac | |
| md" | |
| ## Solving the TopologicalComputer N point interpolation problem in 3 dimensions | |
| The TopologicalComputer N point interpolation problem in 3 dimensions involves the generation of a continuous surface across a region defined by 4 points. This problem becomes more difficult in higher dimensions, as the number of permutations of {0, 1} for each dimension grows with the function 2^d, whereas the number of points required to make a linear function is equal to d. | |
| The solution I present is to use a similar method to the tracing above. Given 4 points, draw two lines between the points such that all 4 points have one line intersecting them. Then start from one end drawing traces between them such that a surface is drawn in the region bounded by the four points. Hello world | |
| " | |
| # ╔═╡ 63395150-fdff-11ea-317a-956ff6431475 | |
| P = [ | |
| 0 0 1 # A | |
| 1 0 1 # B | |
| 0 1 1 # C | |
| 1 1 -1 # D | |
| ] | |
| # ╔═╡ 0ff87db0-fe7a-11ea-3afb-ddca5f27acab | |
| begin | |
| A = P[1, :] | |
| B = P[2, :] | |
| C = P[3, :] | |
| D = P[4, :] | |
| end | |
| # ╔═╡ 7e3e4710-fe79-11ea-3d4b-4fc54cc58d07 | |
| vecMag(P1, P2) = √((P2 .- P1) ⋅ (P2 .- P1)) | |
| # ╔═╡ 00d26220-fe83-11ea-3cf6-492a6e1f3339 | |
| proj(u, v) = (u ⋅ v) / (v ⋅ v) * v | |
| # ╔═╡ b19ba752-3dc2-11eb-0b48-2bb17d047b06 | |
| md" | |
| $D_1(P)=||\overrightarrow{AP}-proj_{\overrightarrow{AB}}\overrightarrow{AP}||$ | |
| $D_2(P)=||\overrightarrow{CP}-proj_{\overrightarrow{CD}}\overrightarrow{CP}||$ | |
| " | |
| # ╔═╡ 74c51212-fe81-11ea-2b20-45511a32be82 | |
| D1(P) = vecMag((P .- A[1:2]) - proj((P .- A[1:2]), (B[1:2] .- A[1:2])), [0, 0]) | |
| # ╔═╡ 453a9720-fe83-11ea-2ef2-fb2f40fb9394 | |
| D2(P) = vecMag((P .- C[1:2]) - proj((P .- C[1:2]), (D[1:2] .- C[1:2])), [0, 0]) | |
| # ╔═╡ fd028552-3dc3-11eb-2538-31025cd4a16c | |
| md" | |
| $P_{ab}(P)=\frac{P\circ\overrightarrow{AB}}{||\overrightarrow{AB}||\frac{D_2(P)}{D_1(P) + D_2(P)}+||\overrightarrow{CD}||\frac{D_1(P)}{D_1(P)+D_2(P)}} + A_{xy}$ | |
| $P_{cd}(P)=\frac{P\circ\overrightarrow{CD}}{||\overrightarrow{AB}||\frac{D_2(P)}{D_1(P) + D_2(P)}+||\overrightarrow{CD}||\frac{D_1(P)}{D_1(P)+D_2(P)}} + C_{xy}$ | |
| " | |
| # ╔═╡ 246e2a50-fe80-11ea-1181-594649e2ce2e | |
| Pab(P) = (P .* (B[1:2] .- A[1:2])) / ((vecMag(A[1:2], B[1:2]) * (D2(P) / (D1(P) + D2(P)))) + (vecMag(C[1:2], D[1:2]) * (D1(P) / (D1(P) + D2(P))))) + A[1:2] | |
| # ╔═╡ 209fcaf0-fe85-11ea-0d9e-794a77c715a4 | |
| Pcd(P) = (P .* (D[1:2] .- C[1:2])) / ((vecMag(A[1:2], B[1:2]) * (D2(P) / (D1(P) + D2(P)))) + (vecMag(C[1:2], D[1:2]) * (D1(P) / (D1(P) + D2(P))))) + C[1:2] | |
| # ╔═╡ a015f1e0-3dc0-11eb-3cef-1ddcb8c1f656 | |
| md" | |
| $Z_{P_{ab}}(P)=(B_z-A_z)\frac{||\overrightarrow{AP_{ab}(P)}||}{||\overrightarrow{AB}||}+A_z$ | |
| $Z_{P_{cd}}(P)=(D_z-C_z)\frac{||\overrightarrow{CP_{ab}(P)}||}{||\overrightarrow{CD}||}+C_z$ | |
| " | |
| # ╔═╡ 252d9b00-fe86-11ea-269c-959635d8db35 | |
| ZPab(P) = ((B[3] - A[3]) / vecMag(A[1:2], B[1:2])) * vecMag(Pab(P), A[1:2]) + A[3] | |
| # ╔═╡ 7eb90970-fe86-11ea-346f-2b9cf9f8ea22 | |
| ZPcd(P) = ((D[3] - C[3]) / vecMag(C[1:2], D[1:2])) * vecMag(Pcd(P), C[1:2]) + C[3] | |
| # ╔═╡ 5bc2b230-3dc5-11eb-3dd7-a51cce70eebc | |
| md" | |
| $Z(P)=\left(Z_{P_{ab}}(P)-Z_{P_{cd}}(P)\right)\frac{||\overrightarrow{P_{cd}(P)P}||}{||\overrightarrow{P_{ab}(P)P_{cd}(P)}||}+Z_{P_{cd}}(P)$ | |
| " | |
| # ╔═╡ ba242d60-fe85-11ea-3397-8da61bd274ca | |
| Z(P) = ((ZPab(P) - ZPcd(P)) / vecMag(Pab(P), Pcd(P))) * vecMag(Pcd(P), P) + ZPcd(P) | |
| # ╔═╡ de52a1d0-3dbe-11eb-3860-3b72f74e299d | |
| Z(X, Y) = Z([X, Y]) | |
| # ╔═╡ b4b47ce0-3dbe-11eb-230a-a7eaa71cc91c | |
| x = min(P[:, 1]...):0.1:max(P[:, 1]...) | |
| # ╔═╡ b775bfc0-3dbe-11eb-3ec1-453899565e99 | |
| y = min(P[:, 2]...):0.1:max(P[:, 2]...) | |
| # ╔═╡ 015cae7e-fe88-11ea-353a-a9907ace0173 | |
| plot(x, y, Z, st=:surface) | |
| # ╔═╡ 601d1460-fe87-11ea-1066-0d86847a1ad9 | |
| begin | |
| p = plot(x, y, Z, st=:contour) | |
| plot!(p, P[:, 1], P[:, 2], st=:scatter) | |
| end | |
| # ╔═╡ 6562e540-3dbf-11eb-358e-ed02cee52f6d | |
| P[:, 1:2] | |
| # ╔═╡ a6357100-424c-11eb-3910-010a00239136 | |
| test = "true" | |
| # ╔═╡ f33d9860-424c-11eb-1ab1-c7d54e959dce | |
| println("hello world") | |
| # ╔═╡ Cell order: | |
| # ╟─4e5ac200-fdff-11ea-3d80-d56549011cac | |
| # ╠═b6cede50-fe79-11ea-10c2-13b9e4851b06 | |
| # ╠═63395150-fdff-11ea-317a-956ff6431475 | |
| # ╠═0ff87db0-fe7a-11ea-3afb-ddca5f27acab | |
| # ╠═7e3e4710-fe79-11ea-3d4b-4fc54cc58d07 | |
| # ╠═00d26220-fe83-11ea-3cf6-492a6e1f3339 | |
| # ╟─b19ba752-3dc2-11eb-0b48-2bb17d047b06 | |
| # ╠═74c51212-fe81-11ea-2b20-45511a32be82 | |
| # ╠═453a9720-fe83-11ea-2ef2-fb2f40fb9394 | |
| # ╟─fd028552-3dc3-11eb-2538-31025cd4a16c | |
| # ╠═246e2a50-fe80-11ea-1181-594649e2ce2e | |
| # ╠═209fcaf0-fe85-11ea-0d9e-794a77c715a4 | |
| # ╟─a015f1e0-3dc0-11eb-3cef-1ddcb8c1f656 | |
| # ╠═252d9b00-fe86-11ea-269c-959635d8db35 | |
| # ╠═7eb90970-fe86-11ea-346f-2b9cf9f8ea22 | |
| # ╟─5bc2b230-3dc5-11eb-3dd7-a51cce70eebc | |
| # ╠═ba242d60-fe85-11ea-3397-8da61bd274ca | |
| # ╠═de52a1d0-3dbe-11eb-3860-3b72f74e299d | |
| # ╠═b4b47ce0-3dbe-11eb-230a-a7eaa71cc91c | |
| # ╠═b775bfc0-3dbe-11eb-3ec1-453899565e99 | |
| # ╠═015cae7e-fe88-11ea-353a-a9907ace0173 | |
| # ╠═601d1460-fe87-11ea-1066-0d86847a1ad9 | |
| # ╠═6562e540-3dbf-11eb-358e-ed02cee52f6d | |
| # ╠═a6357100-424c-11eb-3910-010a00239136 | |
| # ╠═f33d9860-424c-11eb-1ab1-c7d54e959dce |
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