Constraint System Constructors

Class for Constructing a general constraint system.

Attributes

• vertices::Vector{Int}: Vertices describing the geometric constraint system. They are given as a list of integers.
• variables::Vector{Variable}: Coordinate variables representing the positions of the vertices.
• equations::Vector{Expression}: Equations corresponding to the constraint system.
• realization::Matrix{<:Real}: Realization of the geometric constraint system satisfying the equations.
• jacobian::Matrix{Expression}: Jacobian matrix for the equations and variables.
• dimension::Int: Dimension in which the geometric constraint system lives.
• xs::Union{Matrix{Variable}, Matrix{Expression}}: Matrix representing the possible realizations of a geometric constraint system.
• system::System: Polynomial system consisting of the equations and variables in the form of HomotopyContinuation.
• pinned_vertices::Vector{Int}: Pinned vertices of the system. These vertices remain unchanged and are added as constraints. Pinning can, for instance, be used to factor out rigid motions.

ConstraintSystem(vertices::Vector{Int}, variables::Vector{Variable}, equations::Vector{Expression}, realization::Matrix{<:Real}, xs)

Constructor of a ConstraintSystem object.

SpherePacking([vertices,] radii, realization[; pinned_vertices])

Class for sticky sphere packings.

SphericalDiskPacking([vertices,] contacts, [inversive_distances,] realization[; pinned_vertices])

Class for spherical disk packings in Minkowski space.

Polytope([vertices,] facets, realization[; pinned_vertices])

Class for 3-dimensional polytopes with edge-length and facet planarity constraints.

For the computation of the normals, we assume that the origin lies in the barycenter. Otherwise, we translate the polytope accordingly.

FacetPolytope([vertices,] facets, realization[; pinned_vertices])

Class for 3-dimensional polytopes with facet planarity constraints.

For the computation of the normals, we assume that the origin lies in the barycenter. Otherwise, we translate the polytope accordingly.

FrameworkOnSurface([vertices,] bars, realization, surface[; pinned_vertices])

Class for bar-joint frameworks constrained to a surface.

Framework([vertices,] bars, realization[; pinned_vertices])

Class for bar-joint frameworks.

VolumeHypergraph([vertices,] volumes, realization[; pinned_vertices])

Class for volume-constrained hypergraphs.

BodyHinge([vertices,] facets, realization[; pinned_vertices])

Class for body-hinge frameworks, which are essentially polytopes with rigid facets.

BodyBar([vertices,] facets, realization[; pinned_vertices])

Class for body-bar frameworks, which are essentially polytopes with rigid facets and connecting .

AngularFramework([vertices,] angles, realization[; pinned_vertices])

Class for angular bar-joint frameworks.

equations!(G, equations)

Set the equations of G to equations.

equations!(F, equations)

Set the equations of the geometric constraint system F.

add_equations!(G, equations)

Add the equations to those of G.

add_equations!(F, equations)

Add equations to the geometric constraint system F.

realization!(G, realization)

Set the realization of the constraint system G to realization.

realization!(F, realization)

Set the realization of the geometric constraint system F to realization.

realization!(F, realization)

Set the realization of the geometric constraint system F to realization.