PLaSM

operators to generate some important classes of surfaces, including the profile product surfaces, the rotational surfaces, the ruled surfaces, and the tensor product surfaces

• Beziermanifold generator of B´ezier d-manifolds in IEn, for any dimensions/degrees
  Pre/Post conds (degrees::isseqof:isnat)(controlpoints::isseq)
  => (isseqof:isfun)
  Example see Script 12.4.1

• Beziersurface generator of B´ezier surfaces of arbitrary degree
  Pre/Post conds (controlpoints::ismatof:ispoint) => (isseqof:isfun)
  Example MAP:(BezierSurface:pointArray):((sqr ~ intervals:1):10)

• Bilinearsurface generator of coord functions of a bilinear surface in IEn
  Pre/Post conds (controlpoints::ismatof:ispoint) => (isseqof:isfun)
  Example def mapping = bilinearsurface:
  < < < 0,0,0>,< 2,-4,2>>,< < 0,3,1>,< 4,0,0>>>;

• map:mapping:((sqr~intervals:1):10)
  Biquadraticsurface generator of coord functions of a biquadratic surface in IEn
  Pre/Post conds (controlpoints::ismatof:ispoint) => (isseqof:isfun)
  Example biquadraticSurface:< < < 0,0,0>, < 2,0,1>,< 3,1,1>>,
  < < 1,3,-1>,< 3,2,0>,< 4,2,0>>, < < 0,9,0>, < 2,5,1>,< 3,3,2>> >;

• map:mapping:((sqr~intervals:1):10)
  Conicalsurface generalized cone, with apex a and curve beta crossing all the rules
  Pre/Post conds (a::isseqof:isreal; beta::isseqof:isfun) => (isseqof:isfun)
  Example map:(conicalsurface:< < 0,0,1>,beta>):((sqr~intervals:1):10)

• Cylindricalsurface generalized cylinder, with direction a and curve beta
  crossing all the rules
  Pre/Post conds (a::isseqof:isreal; beta::isseqof:isfun) => (isseqof:isfun)
  Example map:(cylindricalsurface:< < 0,0,1>,beta>):((sqr~intervals:1):10)

• Hermitesurface generator of coord functions of the bicubic Hermite surface
  Pre/Post conds (controlpoints::ismatof:ispoint) => (isseqof:isfun)
  Example map:(hermitesurface:< 4 × 4 matrix of points >):domain2d

• Profileprodsurface returns the coord functions of a profile product surface
  Pre/Post conds (profile, section::isseqof:isfun) => (isseqof:isfun)
  Example map:(profileprodsurface:< alpha, beta >):domain2d

• Rotationalsurface generates a surface by rotation of profilecurve.The opening
  angle of the rotational patch depends on the 2nd domain parameter
  Pre/Post conds (profilecurve::isseqof:isfun) => (isseqof:isfun)
  Example map:(rotationalsurface:(bezier:s1:< < 0,0>,< 8,5>,< 0,10>>)):
  (intervals:1:12 * intervals:(2*pi):24)

• Ruledsurface surface from profile alpha(u) and tangent vectors beta(u)
  Pre/Post conds (alpha,beta::isseqof:isfun) => (isseqof:isfun)
  Example map:(ruledsurface:< c1, c2 vectdiff c1 >):domain2d

• Tensorprodsurface tensor product surface generator
  Pre/Post conds (ubasis,vbasis::isseqof:isfun)(points::ismatof:ispoint)
  => (isseqof:isfun)
  Example (tensorprodsurface:< bernsteinbasis:s1:3, bernsteinbasis:s1:3>:controlpoints)

• Thinsolid thin solid generated by a surface
  Pre/Post conds (surface::isseqof:isfun) => (isseqof:isfun)
  Example def solidmapping = (thinsolid ~ coonspatch):< su0,su1,s0v,s1v>