Bspline weights

I change weigts of my points, but nothing has changed. What should i do to solve this problem?

k = {{{16.24, 44.3486, 642}, {16.24, 44.3652, 625}, {16.24, 44.3818,
717}, {16.24, 44.3984, 940}, {16.24, 44.415, 955}, {16.24,
44.4316, 798}, {16.24, 44.4482, 764}, {16.24, 44.4648,
671}, {16.24, 44.4814, 606}, {16.24, 44.498, 1125}, {16.24,
44.5146, 1315}, {16.24, 44.5312, 1265}, {16.24, 44.5478,
1083}, {16.24, 44.5644, 639}, {16.24, 44.581, 625}, {16.24,
44.5976, 640}, {16.24, 44.6142, 591},
{16.24, 44.6308, 608},
{16.24, 44.6474, 591},
{16.24, 44.664, 596}},

{{16.2566, 44.3486, 664},
{16.2566, 44.3652, 820}, {16.2566, 44.3818, 1025}, {16.2566,
44.3984, 1020}, {16.2566, 44.415, 942}, {16.2566, 44.4316,
632}, {16.2566, 44.4482, 486}, {16.2566, 44.4648, 674}, {16.2566,
44.4814, 1005}, {16.2566, 44.498, 1395}, {16.2566, 44.5146,
1643}, {16.2566, 44.5312, 1289}, {16.2566, 44.5478,
769}, {16.2566, 44.5644, 605}, {16.2566, 44.581, 653}, {16.2566,
44.5976, 620}, {16.2566, 44.6142, 627},
{16.2566, 44.6308, 643},
{16.2566, 44.6474, 635}, {16.2566, 44.664, 643}},

{{16.2732, 44.3486, 848}, {16.2732, 44.3652, 1002}, {16.2732,
44.3818, 1023}, {16.2732, 44.3984, 969},
{16.2732, 44.415, 905}, {16.2732, 44.4316, 573},
{16.2732, 44.4482, 649}, {16.2732, 44.4648, 1092}, {16.2732,
44.4814, 1362}, {16.2732, 44.498, 1298}, {16.2732, 44.5146,
1219}, {16.2732, 44.5312, 968}, {16.2732, 44.5478,
720}, {16.2732, 44.5644, 599}, {16.2732, 44.581, 597}, {16.2732,
44.5976, 613}, {16.2732, 44.6142, 659},
{16.2732, 44.6308, 669},
{16.2732, 44.6474, 742}, {16.2732, 44.664, 824}},

{{16.2898, 44.3486, 1120}, {16.2898, 44.3652, 1008}, {16.2898,
44.3818, 1014},
{16.2898, 44.3984, 967}, {16.2898, 44.415, 758}, {16.2898,
44.4316, 447},
{16.2898, 44.4482, 821}, {16.2898, 44.4648, 1289}, {16.2898,
44.4814, 1495}, {16.2898, 44.498, 1393}, {16.2898, 44.5146,
1247}, {16.2898, 44.5312, 955}, {16.2898, 44.5478,
668}, {16.2898, 44.5644, 616}, {16.2898, 44.581, 615}, {16.2898,
44.5976, 635}, {16.2898, 44.6142, 659},
{16.2898, 44.6308, 753},
{16.2898, 44.6474, 764}, {16.2898, 44.664, 891}},

{{16.3064, 44.3486, 1062}, {16.3064, 44.3652, 889}, {16.3064,
44.3818, 771},
{16.3064, 44.3984, 742}, {16.3064, 44.415, 492}, {16.3064,
44.4316, 684}, {16.3064, 44.4482, 856}, {16.3064, 44.4648,
1326}, {16.3064, 44.4814, 1336}, {16.3064, 44.498,
1152}, {16.3064, 44.5146, 1206}, {16.3064, 44.5312,
772}, {16.3064, 44.5478, 681}, {16.3064, 44.5644, 622}, {16.3064,
44.581, 632}, {16.3064, 44.5976, 677}, {16.3064, 44.6142, 679},
{16.3064, 44.6308, 852},
{16.3064, 44.6474, 857}, {16.3064, 44.664, 879}}};

w = {{0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5}, {0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 1, 1, 1, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5}, {0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5}, {0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5}, {0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5}}

f = Graphics3D[{BSplineSurface[k, SplineDegree -> 3],
SplineWeights -> w}, BoxRatios -> 1];

Show[Graphics3D[{PointSize[Medium], Red, Map[Point, k]}],
Graphics3D[{Gray, Line[k], Gray, Line[Transpose[k]]}], f,
BoxRatios -> 1]

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1 Answer
1

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Comparing two SplineWeights, w and (w /. 1-> .5):

pos = Position[w, 1];
{fa, fb} = Graphics3D[{BSplineSurface[k, SplineDegree -> 3,
SplineWeights -> #]}, BoxRatios -> 1] & /@ {(w /. 1 -> .5), w};
{ga, gb} = Show[Graphics3D[{PointSize[Medium], Red, Map[Point, k], Blue,
PointSize[.03], Point@k[[##]] & @@@ pos, Gray, Line[k],
Line[Transpose[k]]}], #, BoxRatios -> 1, ImageSize -> 300] & /@ {fa, fb};
Row[{ga, gb}]

we get

Using Manipulate, you can see the effect of changing the weights more clearly:

ww = w /. {.5 -> wa, 1 -> wb};
pos = Position[w, 1];
Manipulate[f2 = Graphics3D[{BSplineSurface[k, SplineDegree -> 3,
SplineWeights -> (ww /. {wa -> a, wb -> b})]}, BoxRatios -> 1];
Show[Graphics3D[{PointSize[Medium], Red, Map[Point, k], Blue,
PointSize[.03], Point@k[[##]] & @@@ pos, Gray, Line[k],
Line[Transpose[k]]}], f2, BoxRatios -> 1],
{{a, .5}, 0.001, 1}, {{b, 1.}, 0, 1}]