func TestLeastSquares(t *testing.T) {
matA := mat64.NewDense(5, 3, []float64{
1, -2, 4,
1, -1, 1,
1, 0, 0,
1, 1, 1,
1, 2, 4,
})
vecb := mat64.NewVector(5, []float64{
0,
0,
1,
0,
0,
})
x := vec3(linalg.LeastSquares(matA, vecb))
expected := Vec3{34.0 / 70.0, 0.0, -10.0 / 70.0}
if x != expected {
t.Errorf("expected %v, got %v", expected, x)
}
}
func Dual(f F, df DF, size int) (vertices []Vec3, faces [][3]int) {
hdata := make([][2]Vec3, 0, 8)
a := make([]float64, 0, 8*3)
b := make([]float64, 0, 8)
vindex := make(map[Vec3]int)
it := cartesian(size, size, size)
for x, y, z, next := it(); next; x, y, z, next = it() {
o := Vec3{float64(x), float64(y), float64(z)}
var signs [8]bool
for i, v := range cube {
signs[i] = f(o.Add(v)) > 0
}
hdata = hdata[0:0]
for _, e := range edges {
if signs[e[0]] == signs[e[1]] {
continue
}
h := hermite(f, df, o.Add(cube[e[0]]), o.Add(cube[e[1]]))
hdata = append(hdata, h)
}
a = a[0:0]
for _, h := range hdata {
a = append(a, h[1][:]...)
}
b = b[0:0]
for _, h := range hdata {
b = append(b, h[0].Dot(h[1]))
}
mata := mat64.NewDense(len(b), 3, a)
vecb := mat64.NewVector(len(b), b)
v := vec3(linalg.LeastSquares(mata, vecb))
if v.Sub(o).Len() > 1.5 {
continue
}
vindex[o] = len(vertices)
vertices = append(vertices, v)
}
it = cartesian(size, size, size)
for x, y, z, next := it(); next; x, y, z, next = it() {
o := Vec3{float64(x), float64(y), float64(z)}
var ok bool
var o0 int
if o0, ok = vindex[o]; !ok {
continue
}
for i := 0; i < 3; i++ {
for j := 0; j < i; j++ {
var oi, oj, oij int
if oi, ok = vindex[o.Add(base[i])]; !ok {
continue
}
if oj, ok = vindex[o.Add(base[j])]; !ok {
continue
}
if oij, ok = vindex[o.Add(base[i].Add(base[j]))]; !ok {
continue
}
faces = append(faces, [3]int{o0, oi, oj}, [3]int{oij, oj, oi})
}
}
}
return vertices, faces
}
