shapes

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

  • 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 ‚ 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 €/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) ˆˆ 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 ˆˆ 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 ˆˆ 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

PLaSM is Free Software and may be distributed under GNU LGPL