glen/dyna3
1
0
Fork 0
Code Issues 11 Pull Requests Actions Projects Releases 2 Wiki Activity

Find real solutions for three mutually tangent spheres

Browse Source 
I'm not sure why the solver wasn't working before. It might've been just
an unlucky random number draw.
This commit is contained in:
Aaron Fenyes 2024-02-15 16:16:06 -08:00
parent ae5db0f9ea
commit ba365174d3
2 changed files with 19 additions and 19 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

20
engine-proto/Engine.Algebraic.jl
View File

@ -186,16 +186,16 @@ function realize(ctx::Construction{T}) where T
# add relations to center, orient, and scale the construction # add relations to center, orient, and scale the construction
# [to do] the scaling constraint, as written, can be impossible to satisfy # [to do] the scaling constraint, as written, can be impossible to satisfy
# when all of the spheres have to go through the origin # when all of the spheres have to go through the origin
##if !isempty(ctx.points) if !isempty(ctx.points)
## append!(eqns, [sum(pt.coords[k] for pt in ctx.points) for k in 1:3]) append!(eqns, [sum(pt.coords[k] for pt in ctx.points) for k in 1:3])
##end end
##if !isempty(ctx.spheres) if !isempty(ctx.spheres)
## append!(eqns, [sum(sph.coords[k] for sph in ctx.spheres) for k in 3:4]) append!(eqns, [sum(sph.coords[k] for sph in ctx.spheres) for k in 3:4])
##end end
##n_elts = length(ctx.points) + length(ctx.spheres) n_elts = length(ctx.points) + length(ctx.spheres)
##if n_elts > 0 if n_elts > 0
## push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts) push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts)
##end end
(Generic.Ideal(coordring, eqns), eqns) (Generic.Ideal(coordring, eqns), eqns)
## [test] (nothing, eqns) ## [test] (nothing, eqns)

18
engine-proto/Engine.jl
View File

@ -59,13 +59,13 @@ tangencies = [
ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies) ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies)
ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph) ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
##small_eqns_tan_sph = eqns_tan_sph ##small_eqns_tan_sph = eqns_tan_sph
small_eqns_tan_sph = [ ##small_eqns_tan_sph = [
eqns_tan_sph; ## eqns_tan_sph;
spheres[2].coords - [1, 0, 0, 0, 1]; ## spheres[2].coords - [1, 0, 0, 0, 1];
spheres[3].coords - [1, 0, 0, 0, -1]; ## spheres[3].coords - [1, 0, 0, 0, -1];
] ##]
small_ideal_tan_sph = Generic.Ideal(base_ring(ideal_tan_sph), small_eqns_tan_sph) ##small_ideal_tan_sph = Generic.Ideal(base_ring(ideal_tan_sph), small_eqns_tan_sph)
freedom = Engine.dimension(small_ideal_tan_sph) freedom = Engine.dimension(ideal_tan_sph)
println("Three mutually tangent spheres, with two fixed: $freedom degrees of freedom") println("Three mutually tangent spheres, with two fixed: $freedom degrees of freedom")
##points = [Engine.Point{CoeffType}() for _ in 1:3] ##points = [Engine.Point{CoeffType}() for _ in 1:3]
@ -83,11 +83,11 @@ println("Three mutually tangent spheres, with two fixed: $freedom degrees of fre
# --- test rational cut --- # --- test rational cut ---
coordring = base_ring(small_ideal_tan_sph) coordring = base_ring(ideal_tan_sph)
vbls = Variable.(symbols(coordring)) vbls = Variable.(symbols(coordring))
# test a random witness set # test a random witness set
system = CompiledSystem(System(small_eqns_tan_sph, variables = vbls)) system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
norm2 = vec -> real(dot(conj.(vec), vec)) norm2 = vec -> real(dot(conj.(vec), vec))
rng = MersenneTwister(6071) rng = MersenneTwister(6071)
n_planes = 3 n_planes = 3