func get_nurbs_xmat(nurbs *gm.Nurbs, ibasis []int) (xmat [][]float64) {
nd := nurbs.Gnd()
xmat = utl.DblsAlloc(nd, len(ibasis))
for k, l := range ibasis {
q := nurbs.GetQl(l)
for j := 0; j < nd; j++ {
xmat[j][k] = q[j]
}
}
return
}
func get_nurbs_B() *gm.Nurbs {
verts := [][]float64{
{5.0, 10, 0, 1}, // global 0
{8.0, 10, 0, 1}, // global 1
{8.0, 13, 0, 1}, // global 2
{5.0, 13, 0, 1}, // global 3
{6.0, 11, 0, 1}, // global 4
{6.0, 12, 0, 1}, // global 5
{7.0, 11, 0, 1}, // global 6
{7.0, 12, 0, 1}, // global 7
}
knots := [][]float64{
{0, 0, 0, 0.5, 1, 1, 1},
{0, 0, 1, 1},
}
ctrls := []int{
0, 4, 6, 1, // first level along x
3, 5, 7, 2, // second level along x
}
var nurbs gm.Nurbs
nurbs.Init(2, []int{2, 1}, knots)
nurbs.SetControl(verts, ctrls)
return &nurbs
}
// GetShapeNurbs returns a shape structure based on NURBS
// Note: span are the local ids of control points in NURBS defining elements
// Note: FaceLocalVerts does not work for internal surfaces; only those @ boundaries
func GetShapeNurbs(nurbs *gm.Nurbs, nrbfaces []*gm.Nurbs, span []int) (o *Shape) {
// basic data
o = new(Shape)
o.Type = "nurbs"
o.FaceType = "nurbs"
o.Gndim = nurbs.Gnd()
switch o.Gndim {
case 1:
o.BasicType = "lin2"
case 2:
o.BasicType = "qua4"
case 3:
o.BasicType = "hex8"
}
o.Nverts = nurbs.GetElemNumBasis()
o.VtkCode = VTK_POLY_VERTEX
o.Func = o.NurbsFunc
o.FaceFunc = o.NurbsFaceFunc
o.Nurbs = nurbs
o.Span = span
o.Ibasis = o.Nurbs.IndBasis(o.Span)
o.U = make([]float64, o.Gndim)
// faces basic data
nfaces := 2 * o.Gndim
o.FaceLocalVerts = nurbs.ElemBryLocalInds()
if o.Gndim == 3 {
o.NurbsFaces = nrbfaces
o.SpanFace = [][]int{
span[0:2], span[0:2],
span[2:4], span[2:4],
span[4:6], span[4:6],
}
o.FaceFlip = []bool{false, true, false, true, false, true} // => point to the inside
} else {
o.NurbsFaces = []*gm.Nurbs{nrbfaces[2], nrbfaces[1], nrbfaces[3], nrbfaces[0]}
o.SpanFace = [][]int{span[0:2], span[2:4], span[0:2], span[2:4]}
o.FaceFlip = []bool{false, false, true, true} // => point to the inside
}
o.IbasisFace = make([][]int, nfaces)
for idxface, face := range o.NurbsFaces {
o.IbasisFace[idxface] = face.IndBasis(o.SpanFace[idxface])
if idxface == 0 {
o.FaceNvertsMax = len(o.IbasisFace[idxface])
} else {
o.FaceNvertsMax = utl.Imax(o.FaceNvertsMax, len(o.IbasisFace[idxface]))
}
}
// allocate stracthpad variables
o.init_scratchpad()
return
}
// nurbs_func implements shape/deriv functions for NURBS
func nurbs_func(u, S []float64, dSdR [][]float64, r []float64, derivs bool, nurbs *gm.Nurbs, ibasis, span []int) {
// compute mapping to knots space
nd := nurbs.Gnd()
var umin, umax float64
for i := 0; i < nd; i++ {
umin = nurbs.U(i, span[i*2])
umax = nurbs.U(i, span[i*2+1])
u[i] = ((umax-umin)*r[i] + (umax + umin)) / 2.0
if u[i] < umin || u[i] > umax {
chk.Panic("cannot compute NURBS shape function outide cell range:\nr[%d]=%v, u[%d]=%v, urange=[%v,%v]", i, r[i], i, u[i], umin, umax)
}
}
// shape and/or derivatives in knots space
if derivs {
nurbs.CalcBasisAndDerivs(u)
} else {
nurbs.CalcBasis(u)
}
for k, l := range ibasis {
S[k] = nurbs.GetBasisL(l)
}
// derivatives in natural space
if derivs {
for k, l := range ibasis {
nurbs.GetDerivL(dSdR[k], l) // dSdR := dSdU
for i := 0; i < nd; i++ {
umin = nurbs.U(i, span[i*2])
umax = nurbs.U(i, span[i*2+1])
dSdR[k][i] *= (umax - umin) / 2.0 // dSdR[i] := dSdU[i] * du[i]/dr[i] (no sum on i)
}
}
}
return
}