// Generate the control points, weights, and knots of an elliptical arc
//
// **params**
// + the center
// + the scaled x axis
// + the scaled y axis
// + start angle of the ellipse arc, between 0 and 2pi, where 0 points at the xaxis
// + end angle of the arc, between 0 and 2pi, greater than the start angle
//
// **returns**
// + a NurbsCurveData object representing a NURBS curve
func EllipseArc(center *vec3.T, xaxis, yaxis *vec3.T, startAngle, endAngle float64) *verb.NurbsCurve {
xradius, yradius := xaxis.Length(), yaxis.Length()
xaxisNorm, yaxisNorm := xaxis.Normalized(), yaxis.Normalized()
// if the end angle is less than the start angle, do a circle
if endAngle < startAngle {
endAngle = 2.0*math.Pi + startAngle
}
theta := endAngle - startAngle
// how many arcs?
var numArcs int
if theta <= math.Pi/2 {
numArcs = 1
} else {
if theta <= math.Pi {
numArcs = 2
} else if theta <= 3*math.Pi/2 {
numArcs = 3
} else {
numArcs = 4
}
}
dtheta := theta / float64(numArcs)
w1 := math.Cos(dtheta / 2)
xCompon := xaxisNorm.Scaled(xradius * math.Cos(startAngle))
yCompon := yaxisNorm.Scaled(yradius * math.Sin(startAngle))
P0 := vec3.Add(&xCompon, &yCompon)
temp0 := yaxisNorm.Scaled(math.Cos(startAngle))
temp1 := xaxisNorm.Scaled(math.Sin(startAngle))
T0 := vec3.Sub(&temp0, &temp1)
controlPoints := make([]vec3.T, 2*numArcs+1)
knots := make([]float64, 2*numArcs+3)
index := 0
angle := startAngle
weights := make([]float64, numArcs*2)
controlPoints[0] = P0
weights[0] = 1.0
for i := 1; i <= numArcs; i++ {
angle += dtheta
xCompon = xaxisNorm.Scaled(xradius * math.Cos(angle))
yCompon = yaxisNorm.Scaled(yradius * math.Sin(angle))
offset := vec3.Add(&xCompon, &yCompon)
P2 := vec3.Add(center, &offset)
weights[index+2] = 1
controlPoints[index+2] = P2
temp0 := yaxisNorm.Scaled(math.Cos(angle))
temp1 := xaxisNorm.Scaled(math.Sin(angle))
T2 := vec3.Sub(&temp0, &temp1)
T0Norm := T0.Normalized()
T2Norm := T2.Normalized()
inters := intersect.Rays(&P0, &T0Norm, &P2, &T2Norm)
T0Scaled := T0.Scaled(inters.U0)
P1 := vec3.Add(&P0, &T0Scaled)
weights[index+1] = w1
controlPoints[index+1] = P1
index += 2
if i < numArcs {
P0 = P2
T0 = T2
}
}
j := 2*numArcs + 1
for i := 0; i < 3; i++ {
knots[i] = 0.0
knots[i+j] = 1.0
}
switch numArcs {
case 2:
knots[3] = 0.5
knots[4] = 0.5
case 3:
knots[3] = 1 / 3
knots[4] = 1 / 3
knots[5] = 2 / 3
knots[6] = 2 / 3
case 4:
knots[3] = 0.25
knots[4] = 0.25
knots[5] = 0.5
knots[6] = 0.5
knots[7] = 0.75
knots[8] = 0.75
}
return verb.NewNurbsCurveUnchecked(2, controlPoints, weights, knots)
}
