// Generate the control points, weights, and knots of a surface defined by 4 points
//
// **params**
// + first point in counter-clockwise form
// + second point in counter-clockwise form
// + third point in counter-clockwise form
// + forth point in counter-clockwise form
//
// **returns**
// + NurbsSurfaceData object
func FourPointSurface(p1, p2, p3, p4 *vec3.T, _degree *int) *verb.NurbsSurface {
var degree int
if _degree == nil {
degree = 3
} else {
degree = *_degree
}
degreeFloat := float64(degree)
pts := make([][]vec3.T, degree+1)
for i := range pts {
iFloat := float64(i)
row := make([]vec3.T, degree+1)
for j := range row {
l := 1 - iFloat/degreeFloat
p1p2 := vec3.Interpolate(p1, p2, l)
p4p3 := vec3.Interpolate(p4, p3, l)
row[j] = vec3.Interpolate(&p1p2, &p4p3, 1-float64(j)/degreeFloat)
}
pts[i] = row
}
// build uniform weights
weightRow := make([]float64, degree+1)
for i := range weightRow {
weightRow[i] = 1
}
weights := make([][]float64, degree+1)
for i := range weights {
weights[i] = weightRow
}
knots := make([]float64, 2*(degree+1))
for i := degree + 1; i < len(knots); i++ {
knots[i] = 1
}
return verb.NewNurbsSurfaceUnchecked(degree, degree, pts, weights, knots, knots)
}
func HomoInterpolated(hpt0, hpt1 *HomoPoint, t float64) HomoPoint {
return HomoPoint{
vec3.Interpolate(&hpt0.Vec3, &hpt1.Vec3, t),
(1-t)*hpt0.W + t*hpt1.W,
}
}
// Insert a collection of knots on a curve
//
// Corresponds to Algorithm A5.4 (Piegl & Tiller)
//
// **params**
// + NurbsCurveData object representing the curve
// + array of knots to insert
//
// **returns**
// + NurbsCurveData object representing the curve
//
func (this *NurbsCurve) knotRefine(knotsToInsert KnotVec) *NurbsCurve {
if len(knotsToInsert) == 0 {
return this.clone()
}
degree := this.degree
controlPoints := this.controlPoints
knots := this.knots
n := len(controlPoints) - 1
m := n + degree + 1
r := len(knotsToInsert) - 1
a := knots.Span(degree, knotsToInsert[0])
b := knots.Span(degree, knotsToInsert[r])
// TODO can we use slices instead of maps?
controlPointsPost := make(map[int]HomoPoint)
knotsPost := make(map[int]float64)
// new control pts
for i := 0; i <= a-degree; i++ {
controlPointsPost[i] = controlPoints[i]
}
for i := b - 1; i <= n; i++ {
controlPointsPost[i+r+1] = controlPoints[i]
}
// new knot vector
for i := 0; i <= a; i++ {
knotsPost[i] = knots[i]
}
for i := b + degree; i <= m; i++ {
knotsPost[i+r+1] = knots[i]
}
i := b + degree - 1
k := b + degree + r
j := r
for j >= 0 {
for knotsToInsert[j] <= knots[i] && i > a {
controlPointsPost[k-degree-1] = controlPoints[i-degree-1]
knotsPost[k] = knots[i]
k = k - 1
i = i - 1
}
controlPointsPost[k-degree-1] = controlPointsPost[k-degree]
for l := 1; l <= degree; l++ {
ind := k - degree + l
alfa := knotsPost[k+l] - knotsToInsert[j]
if math.Abs(alfa) < Epsilon {
controlPointsPost[ind-1] = controlPointsPost[ind]
} else {
alfa /= knotsPost[k+l] - knots[i-degree+l]
oldP, newP := controlPointsPost[ind], controlPointsPost[ind-1]
controlPointsPost[ind-1] = HomoPoint{
vec3.Interpolate(&oldP.Vec3, &newP.Vec3, alfa),
controlPointsPost[ind-1].W,
}
}
}
knotsPost[k] = knotsToInsert[j]
k = k - 1
j--
}
var maxCptsI int
for i := range controlPointsPost {
if i > maxCptsI {
maxCptsI = i
}
}
finalCpts := make([]HomoPoint, maxCptsI+1)
for i, cpt := range controlPointsPost {
finalCpts[i] = cpt
}
var maxKnotsI int
for i := range knotsPost {
if i > maxKnotsI {
maxKnotsI = i
}
}
finalKnots := make(KnotVec, maxKnotsI+1)
for i, knot := range knotsPost {
finalKnots[i] = knot
}
return &NurbsCurve{degree, finalCpts, finalKnots}
}