Create Surface From Points and Knots

Demonstrates how to create a surface from scratch from points and knots.

partial class Examples
{
public static Result CreateSurfaceFromPointsAndKnots(RhinoDoc doc)
{
const bool is_rational = false;
const int number_of_dimensions = 3;
const int u_degree = 2;
const int v_degree = 3;
const int u_control_point_count = 3;
const int v_control_point_count = 5;

// The knot vectors do NOT have the 2 superfluous knots
// at the start and end of the knot vector.  If you are
// coming from a system that has the 2 superfluous knots,
// just ignore them when creating NURBS surfaces.
var u_knots = new double[u_control_point_count + u_degree - 1];
var v_knots = new double[v_control_point_count + v_degree - 1];

// make up a quadratic knot vector with no interior knots
u_knots[0] = u_knots[1] = 0.0;
u_knots[2] = u_knots[3] = 1.0;

// make up a cubic knot vector with one simple interior knot
v_knots[0] = v_knots[1] = v_knots[2] = 0.0;
v_knots[3] = 1.5;
v_knots[4] = v_knots[5] = v_knots[6] = 2.0;

// Rational control points can be in either homogeneous
// or euclidean form. Non-rational control points do not
// need to specify a weight.
var control_points = new Point3d[u_control_point_count, v_control_point_count];

for (int u = 0; u < u_control_point_count; u++)
{
for (int v = 0; v < v_control_point_count; v++)
{
control_points[u,v] = new Point3d(u, v, u-v);
}
}

// creates internal uninitialized arrays for
// control points and knots
var nurbs_surface = NurbsSurface.Create(
number_of_dimensions,
is_rational,
u_degree + 1,
v_degree + 1,
u_control_point_count,
v_control_point_count
);

for (int u = 0;  u < nurbs_surface.KnotsU.Count; u++)
nurbs_surface.KnotsU[u] = u_knots[u];
for (int v = 0; v < nurbs_surface.KnotsV.Count; v++)
nurbs_surface.KnotsV[v] = v_knots[v];

for (int u = 0; u < nurbs_surface.Points.CountU; u++)
{
for (int v = 0; v < nurbs_surface.Points.CountV; v++)
{
nurbs_surface.Points.SetControlPoint(u, v, control_points[u, v]);
}
}

if (nurbs_surface.IsValid)
{
doc.Views.Redraw();
return Result.Success;
}
return Result.Failure;
}
}

Partial Friend Class Examples
Public Shared Function CreateSurfaceFromPointsAndKnots(ByVal doc As RhinoDoc) As Result
Const is_rational As Boolean = False
Const number_of_dimensions As Integer = 3
Const u_degree As Integer = 2
Const v_degree As Integer = 3
Const u_control_point_count As Integer = 3
Const v_control_point_count As Integer = 5

' The knot vectors do NOT have the 2 superfluous knots
' at the start and end of the knot vector.  If you are
' coming from a system that has the 2 superfluous knots,
' just ignore them when creating NURBS surfaces.
Dim u_knots = New Double(u_control_point_count + u_degree - 2){}
Dim v_knots = New Double(v_control_point_count + v_degree - 2){}

' make up a quadratic knot vector with no interior knots
u_knots(1) = 0.0
u_knots(0) = u_knots(1)
u_knots(3) = 1.0
u_knots(2) = u_knots(3)

' make up a cubic knot vector with one simple interior knot
v_knots(2) = 0.0
v_knots(1) = v_knots(2)
v_knots(0) = v_knots(1)
v_knots(3) = 1.5
v_knots(6) = 2.0
v_knots(5) = v_knots(6)
v_knots(4) = v_knots(5)

' Rational control points can be in either homogeneous
' or euclidean form. Non-rational control points do not
' need to specify a weight.
Dim control_points = New Point3d(u_control_point_count - 1, v_control_point_count - 1){}

For u As Integer = 0 To u_control_point_count - 1
For v As Integer = 0 To v_control_point_count - 1
control_points(u,v) = New Point3d(u, v, u-v)
Next v
Next u

' creates internal uninitialized arrays for
' control points and knots
Dim nurbs_surface = NurbsSurface.Create(number_of_dimensions, is_rational, u_degree + 1, v_degree + 1, u_control_point_count, v_control_point_count)

For u As Integer = 0 To nurbs_surface.KnotsU.Count - 1
nurbs_surface.KnotsU(u) = u_knots(u)
Next u
For v As Integer = 0 To nurbs_surface.KnotsV.Count - 1
nurbs_surface.KnotsV(v) = v_knots(v)
Next v

For u As Integer = 0 To nurbs_surface.Points.CountU - 1
For v As Integer = 0 To nurbs_surface.Points.CountV - 1
nurbs_surface.Points.SetControlPoint(u, v, control_points(u, v))
Next v
Next u

If nurbs_surface.IsValid Then
doc.Views.Redraw()
Return Result.Success
End If
Return Result.Failure
End Function
End Class

from Rhino.Geometry import Point3d, NurbsSurface, ControlPoint
from scriptcontext import doc

def RunCommand():
bIsRational = False
dim = 3
u_degree = 2
v_degree = 3
u_cv_count = 3
v_cv_count = 5

# make up a quadratic knot vector with no interior knots
u_knot = [0.0, 0.0, 1.0, 1.0]

# make up a cubic knot vector with one simple interior knot
v_knot = [0.0, 0.0, 0.0, 1.5, 2.0, 2.0, 2.0]

# Rational control points can be in either homogeneous
# or euclidean form. Non-rational control points do not
# need to specify a weight.
CV = dict( ((i,j),None) for i in range(2) for j in range(3) )
for i in range(0, u_cv_count):
for j in range(0, v_cv_count):
CV[i,j] = Point3d(i, j, i-j)

# creates internal uninitialized arrays for
# control points and knots
nurbs_surface = NurbsSurface.Create(dim, bIsRational, u_degree + 1, v_degree + 1, u_cv_count, v_cv_count)

for i in range(0, nurbs_surface.KnotsU.Count):
nurbs_surface.KnotsU[i] = u_knot[i]
for j in range(0, nurbs_surface.KnotsV.Count):
nurbs_surface.KnotsV[j] = v_knot[j]