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BSplines: Add methods for Vector of Vectors #351

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BSplines: Add methods for Vector of Vectors #351

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430e87d
feat(BSplines): add methods for Vector{Vector}
ashutosh-b-b Oct 26, 2024
315dc9d
test(BSplines): add tests
ashutosh-b-b Oct 26, 2024
e71c552
test(BSplines): add tests
ashutosh-b-b Oct 26, 2024
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187 changes: 186 additions & 1 deletion src/interpolation_caches.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -738,6 +738,78 @@ function BSplineInterpolation(
u, t, d, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
end

function BSplineInterpolation(
u::AbstractVector{<:AbstractVector{T}}, t, d, pVecType, knotVecType; extrapolate = false,
assume_linear_t = 1e-2) where {T <: Number}
u, t = munge_data(u, t)
n = length(t)
n < d + 1 && error("BSplineInterpolation needs at least d + 1, i.e. $(d+1) points.")
s = zero(T)
p = zero(t)
k = zeros(eltype(t), n + d + 1)
l = zeros(T, n - 1)
p[1] = zero(eltype(t))
p[end] = one(eltype(t))

ax_u = axes(u)[1:(end - 1)]
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Is this line needed?


for i in 2:n
s += √((t[i] - t[i - 1])^2 + sum((u[i] - u[i - 1]) .^ 2))
l[i - 1] = s
end
if pVecType == :Uniform
for i in 2:(n - 1)
p[i] = p[1] + (i - 1) * (p[end] - p[1]) / (n - 1)
end
elseif pVecType == :ArcLen
for i in 2:(n - 1)
p[i] = p[1] + l[i - 1] / s * (p[end] - p[1])
end
end

lidx = 1
ridx = length(k)
while lidx <= (d + 1) && ridx >= (length(k) - d)
k[lidx] = p[1]
k[ridx] = p[end]
lidx += 1
ridx -= 1
end

ps = zeros(eltype(t), n - 2)
s = zero(eltype(t))
for i in 2:(n - 1)
s += p[i]
ps[i - 1] = s
end

if knotVecType == :Uniform
# uniformly spaced knot vector
# this method is not recommended because, if it is used with the chord length method for global interpolation,
# the system of linear equations would be singular.
for i in (d + 2):n
k[i] = k[1] + (i - d - 1) // (n - d) * (k[end] - k[1])
end
elseif knotVecType == :Average
# average spaced knot vector
idx = 1
if d + 2 <= n
k[d + 2] = 1 // d * ps[d]
end
for i in (d + 3):n
k[i] = 1 // d * (ps[idx + d] - ps[idx])
idx += 1
end
end
# control points
sc = zeros(eltype(t), n, n)
spline_coefficients!(sc, d, k, p)
c = (sc \ reduce(hcat, u)')'
c = collect(eachcol(c))
sc = zeros(eltype(t), n)
BSplineInterpolation(
u, t, d, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
end
"""
BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolate = false)

Expand Down Expand Up @@ -900,9 +972,106 @@ function BSplineApprox(
u, t, d, h, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
end

function BSplineApprox(
u::AbstractVector{<:AbstractVector{T}}, t, d, h, pVecType, knotVecType; extrapolate = false,
assume_linear_t = 1e-2) where {T}
u, t = munge_data(u, t)
n = length(t)
h < d + 1 && error("BSplineApprox needs at least d + 1, i.e. $(d+1) control points.")
s = zero(T)
p = zero(t)
k = zeros(eltype(t), h + d + 1)
l = zeros(T, n - 1)
p[1] = zero(eltype(t))
p[end] = one(eltype(t))

ax_u = axes(u)[1:(end - 1)]
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Is this line needed?


for i in 2:n
s += √((t[i] - t[i - 1])^2 + sum((u[i] - u[i - 1]) .^ 2))
l[i - 1] = s
end
if pVecType == :Uniform
for i in 2:(n - 1)
p[i] = p[1] + (i - 1) * (p[end] - p[1]) / (n - 1)
end
elseif pVecType == :ArcLen
for i in 2:(n - 1)
p[i] = p[1] + l[i - 1] / s * (p[end] - p[1])
end
end

lidx = 1
ridx = length(k)
while lidx <= (d + 1) && ridx >= (length(k) - d)
k[lidx] = p[1]
k[ridx] = p[end]
lidx += 1
ridx -= 1
end

ps = zeros(eltype(t), n - 2)
s = zero(eltype(t))
for i in 2:(n - 1)
s += p[i]
ps[i - 1] = s
end

if knotVecType == :Uniform
# uniformly spaced knot vector
# this method is not recommended because, if it is used with the chord length method for global interpolation,
# the system of linear equations would be singular.
for i in (d + 2):h
k[i] = k[1] + (i - d - 1) // (h - d) * (k[end] - k[1])
end
elseif knotVecType == :Average
# NOTE: verify that average method can be applied when size of k is less than size of p
# average spaced knot vector
idx = 1
if d + 2 <= h
k[d + 2] = 1 // d * ps[d]
end
for i in (d + 3):h
k[i] = 1 // d * (ps[idx + d] - ps[idx])
idx += 1
end
end
# control points
c = zeros(T, length(u[1]), h)
c[:, 1] = u[1]
c[:, end] = u[end]
q = zeros(T, length(u[1]), n)
sc = zeros(eltype(t), n, h)
for i in 1:n
spline_coefficients!(view(sc, i, :), d, k, p[i])
end
for k in 2:(n - 1)
q[:, k] = u[k] - sc[k, 1] * u[1] -
sc[k, h] * u[end]
end
Q = Matrix{T}(undef, length(u[1]), h - 2)
for i in 2:(h - 1)
s = zeros(eltype(sc), length(u[1]))
for k in 2:(n - 1)
s = s + sc[k, i] .* q[:, k]
end
Q[:, i - 1] = s
end
sc = sc[2:(end - 1), 2:(h - 1)]
M = transpose(sc) * sc
Q = reshape(Q, length(u[1]), :)

P = (M \ Q')'
P = reshape(P, length(u[1]), :)
c[:, 2:(end - 1)] = P
sc = zeros(eltype(t), h)
BSplineApprox(
u, t, d, h, p, k, eachcol(c), sc, pVecType, knotVecType, extrapolate, assume_linear_t)
end

function BSplineApprox(
u::AbstractArray{T, N}, t, d, h, pVecType, knotVecType; extrapolate = false,
assume_linear_t = 1e-2) where {T, N}
assume_linear_t = 1e-2) where {T <: Number, N}
u, t = munge_data(u, t)
n = length(t)
h < d + 1 && error("BSplineApprox needs at least d + 1, i.e. $(d+1) control points.")
Expand Down Expand Up @@ -945,6 +1114,22 @@ function BSplineApprox(
ps[i - 1] = s
end

lidx = 1
ridx = length(k)
while lidx <= (d + 1) && ridx >= (length(k) - d)
k[lidx] = p[1]
k[ridx] = p[end]
lidx += 1
ridx -= 1
end

ps = zeros(eltype(t), n - 2)
s = zero(eltype(t))
for i in 2:(n - 1)
s += p[i]
ps[i - 1] = s
end

Comment on lines +1117 to +1132
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Is this needed?

if knotVecType == :Uniform
# uniformly spaced knot vector
# this method is not recommended because, if it is used with the chord length method for global interpolation,
Expand Down
32 changes: 32 additions & 0 deletions src/interpolation_methods.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -216,6 +216,23 @@ function _interpolate(A::BSplineInterpolation{<:AbstractArray{T, N}},
ucum
end

function _interpolate(A::BSplineInterpolation{<:AbstractVector{<:AbstractVector{T}}},
t::Number,
iguess) where {T <: Number}
t < A.t[1] && return A.u[1]
t > A.t[end] && return A.u[end]
# change t into param [0 1]
idx = get_idx(A, t, iguess)
t = A.p[idx] + (t - A.t[idx]) / (A.t[idx + 1] - A.t[idx]) * (A.p[idx + 1] - A.p[idx])
n = length(A.t)
sc = t isa ForwardDiff.Dual ? zeros(eltype(t), n) : A.sc
nonzero_coefficient_idxs = spline_coefficients!(sc, A.d, A.k, t)
ucum = zeros(T, size(A.u[1]))
for i in nonzero_coefficient_idxs
ucum += sc[i] * A.c[i]
end
ucum
end
# BSpline Curve Approx
function _interpolate(A::BSplineApprox{<:AbstractVector{<:Number}}, t::Number, iguess)
t < A.t[1] && return A.u[1]
Expand Down Expand Up @@ -249,6 +266,21 @@ function _interpolate(
ucum
end

function _interpolate(A::BSplineApprox{<:AbstractVector{<:AbstractVector{T}}},
t::Number, iguess) where {T <: Number}
t < A.t[1] && return A.u[1]
t > A.t[end] && return A.u[end]
# change t into param [0 1]
idx = get_idx(A, t, iguess)
t = A.p[idx] + (t - A.t[idx]) / (A.t[idx + 1] - A.t[idx]) * (A.p[idx + 1] - A.p[idx])
sc = t isa ForwardDiff.Dual ? zeros(eltype(t), A.h) : A.sc
nonzero_coefficient_idxs = spline_coefficients!(sc, A.d, A.k, t)
ucum = zeros(T, size(A.u[1]))
for i in nonzero_coefficient_idxs
ucum += sc[i] * A.c[i]
end
ucum
end
# Cubic Hermite Spline
function _interpolate(
A::CubicHermiteSpline{<:AbstractVector{<:Number}}, t::Number, iguess)
Expand Down
30 changes: 30 additions & 0 deletions test/interpolation_tests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -664,6 +664,21 @@ end
@test_throws DataInterpolations.ExtrapolationError A(-1.0)
@test_throws DataInterpolations.ExtrapolationError A(300.0)

@testset "Vector{Vector}" begin
t = 0.1:0.1:1.0
u_vec = [[sin.(t_), cos.(t_)] for t_ in t]
A = BSplineInterpolation(u_vec, t, 2, :Uniform, :Uniform)
t_test = 0.1:0.05:1.0
u_test = reduce(hcat, A.(t_test))
@test isapprox(u_test[1, :], sin.(t_test), atol = 1e-3)
@test isapprox(u_test[2, :], cos.(t_test), atol = 1e-3)

A = BSplineInterpolation(u_vec, t, 2, :ArcLen, :Average)
u_test = reduce(hcat, A.(t_test))
@test isapprox(u_test[1, :], sin.(t_test), atol = 1e-2)
@test isapprox(u_test[2, :], cos.(t_test), atol = 1e-2)
end

@testset "AbstractMatrix" begin
t = 0.1:0.1:1.0
u2d = [sin.(t) cos.(t)]' |> collect
Expand Down Expand Up @@ -721,6 +736,21 @@ end
@test_throws DataInterpolations.ExtrapolationError A(-1.0)
@test_throws DataInterpolations.ExtrapolationError A(300.0)

@testset "Vector{Vector}" begin
t = 0.1:0.1:1.0
u_vec = [[sin.(t_), cos.(t_)] for t_ in t]
A = BSplineApprox(u_vec, t, 2, 5, :Uniform, :Uniform)
t_test = 0.1:0.05:1.0
u_test = reduce(hcat, A.(t_test))
@test isapprox(u_test[1, :], sin.(t_test), atol = 1e-3)
@test isapprox(u_test[2, :], cos.(t_test), atol = 1e-3)

A = BSplineApprox(u_vec, t, 2, 5, :ArcLen, :Average)
u_test = reduce(hcat, A.(t_test))
@test isapprox(u_test[1, :], sin.(t_test), atol = 1e-2)
@test isapprox(u_test[2, :], cos.(t_test), atol = 1e-2)
end

@testset "AbstractMatrix" begin
t = 0.1:0.1:1.0
u2d = [sin.(t) cos.(t)]' |> collect
Expand Down
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