the library collects the generators of 1D, 2D, 3D geometric objects, as well the generators of poluhedral objects of higher dimensions, including the Sierpinski simplex of any dimension, the n-dimensioonal sphere, the n-dimensional permutahedron, and so on
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Circle returns on approx. with m×n quads/triangles of the 2D circle of r radius
Pre/Post conds (r::isreal)(m,n::isintpos) => (ispol)
Example circle:1:< 24,1> -
Circumference approx. with m segments of the 2D circle boundary of unit radius
Pre/Post conds (m::isintpos) => (ispol)
Example circumference:36 -
Cone approx. with m facets of the 3D cone with r radius and h height
Pre/Post conds (r, h::isreal)(n::isint) => (ispol)
Example Cone:< 1,2>:24 -
Convexhull multidimensional operator returning the convex hull of points â‚ IEd
Pre/Post conds (points::ismat) => (ispol)
Example convexhull:< < 0,0,0,0>,< 1,0,0,0>,< 0,1,0,0>,< 0,0,1,0>,< 0,0,0,1>> -
Crosspolytope returns the d-dimensional crossPolytope
Pre/Post conds (d::isintpos) => (ispol)
Example crossPolytope:3 -
Cube generator of the 3D hexahedron of given side, with a vertex on the origin
Pre/Post conds (side::isrealpos) => (ispol)
Example mxmy:(cube:2) -
Dsphere generator of d-sphere of unit radius, with boundary facets of π/m resolution
Pre/Post conds (d::isnat)(m::isintpos) => (ispol)
Example dsphere:3:24 material transparentmaterial:< red,0.7> -
Dodecahedron constant value inscribed in the unit sphere
Pre/Post conds => (ispol)
Example VRML:dodecahedron: path/out.wrl -
Ellipse approx. with 4 × m segments of the ellipse boundary of a,b radiuses
Pre/Post conds (a,b::isreal)(m::isintpos) => (ispol)
Example ellipse:< 1/2,1>:8 * quote:< 1/2> -
Finitecone d-dimensional cone with given basis and apex in (0, . . . , 0) ∈ IEd
Pre/Post conds (basis::ispol) => (ispol)
Example finitecone:((t:< 1,2,3>:< 1,2,3> ~ cuboid):< 1,1,1>) -
Fractalsimplex generator of recursive d-simplex with n levels
Pre/Post conds (d::isintpos)(n::isintpos) => (ispol)
Example fractalsimplex:3:5 -
Hexahedron constant value. 3D cube inscribed in the standard unit sphere
Pre/Post conds => (ispol)
Example VRML:hexahedron: path/out.wrl -
Icosahedron constant value. 3D icosahedron inscribed in the standard unit sphere
Pre/Post conds => (ispol)
Example VRML:icosahedron: path/out.wrl -
Intervals constructor of a uniform partition of 1D interval [0, a] with m segments
Pre/Post conds (a::isrealpos)(m::isintpos)
=> (and ~ [ispol,c:eq:< 1,1> ~ [dim,rn]])
Example intervals:(2*pi):24 -
Ispolytope predicate testing if arg is a polytope (bounded polyhedron) or not
Pre/Post conds (arg::ispol) => (isbool)
Example ispolytope:(cuboid:< 1,1,1,1>) == true -
Issimplex predicate testing if arg is either a simplex or not
Pre/Post conds (arg::ispol) => (isbool)
Example issimplex:(simplex:3) == true -
Mkframe constant geometric value, returning a model of the 3D reference frame
Pre/Post conds => (ispol)
Example struct:< mkframe, cuboid:< 1,1,1>> -
Mkvector constructor of a 3D model of vector p2 - p1, with p1,p2 ∈ IE3
Pre/Post conds (p1::ispoint)(p2::ispoint) => (ispol)
Example mkvector:< 1,0,0>:< 1,1,1> -
Mkversork constant geometric value. Returns a 3D model of unit vector e3 ∈ IE3
Pre/Post conds => (ispol)
Example struct:< mkversork, cuboid:< 1,1,1>> -
Ngon constructor of 2D regular polygons with n sides
Pre/Post conds (n::and ~ [isintpos, ge:3]) => (ispol)
Example (struct ~ cat):(aa:ngon:(3..8) distr t:1:2.5) -
Octahedron constant value. 3D Octahedron inscribed in the standard unit sphere
Pre/Post conds => (ispol)
Example VRML:octahedron: path/out.wrl -
Permutahedron generator of the d-dimensional permutahedron
Pre/Post conds (d::isintpos) => (ispol)
Example permutahedron:3 -
Plane generator of the 2-flat passing through 3 points in IE3
Pre/Post conds (point0, point1, point2::ispoint) => (ispol)
Example (s3 ~ plane):< < 0,0,0>,< 1,0,0>,< 1,1,1>> -
Prism generator of the (d + 1)-prism with given height and d-dimensional basis
Pre/Post conds (height::isrealpos)(basis::ispol) => (ispol)
Example prism:1:(crosspolytope:2) -
Pyramid complex of (d+1)-pyramids of h height, associated with the basis d-cells
Pre/Post conds (h::isreal)(basis::ispol) => (ispol)
Example (struct ~ aa:(pyramid:1) ~ splitcells): (q:< 3,3,3>*q:< 3,3,3>) -
Ring difference of 2D circles with radiuses r1, r2, approximated with m×n steps
Pre/Post conds (r1,r2::isrealpos)(m,n::isintpos) => (ispol)
Example (@1 ~ Ring:< 0.5,1>):< 24,2> -
Segment scaled segment through two d-points a and b, with coeffi cient sx
Pre/Post conds (sx::isreal)(a,b::ispoint) => (ispol)
Example segment:2:< < 0,0,0>,< 1,1,1>> -
Simplexpile extrusion operator for the d-simplex
Pre/Post conds (cell::issimplex) => (ispol)
Example (struct ~ [@1 ~ simplexpile, id] ~ simplex):2 -
Sphere generator of 3D sphere of r radius, approximated with m×n facets
Pre/Post conds (r::isrealpos)(m,n::isintpos) => (ispol)
Example Sphere:1:< 12,24> -
Tetrahedron constant value. 3D regular tetrahedron, inscribed in the unit sphere
Pre/Post conds => (ispol)
Example VRML:tetrahedron: path/out.wrl -
Torus generator of 3D torus with radiuses r1,r2, approximated with m×n facets
Pre/Post conds (r1,r2::isreal) (n,m::isintpos) => (ispol)
Example torus:< 1,3>:< 12,24> == PolComplex< 2,3> -
Truncone 3D truncated cone, with h height, r1,r2 radiuses and n lateral facets
Pre/Post conds (r1,r2,h::isrealpos)(n::isintpos) => (ispol)
Example truncone:< 2,1,2>:24 -
Tube 3D empty tube with h height, r1,r2 radiuses and 2 × n lateral facets
Pre/Post conds (r1,r2,h::isreal)(n::isint) => (ispol)
Example tube:< 0.8,1,2>:24