public Rational_BSpline_Surface(double[] Parameters, TransformationMatrix _R = null, int _ParameterId = -1)
{
R = _R;
ParameterId = _ParameterId;
K1 = (int)Parameters[1];
K2 = (int)Parameters[2];
M1 = (int)Parameters[3];
M2 = (int)Parameters[4];
PROP1 = (int)Parameters[5];
PROP2 = (int)Parameters[6];
PROP3 = (int)Parameters[7];
PROP4 = (int)Parameters[8];
PROP5 = (int)Parameters[9];
int N1 = 1 + K1 - M1;
int N2 = 1 + K2 - M2;
int A = N1 + 2 * M1;
int B = N2 + 2 * M2;
int C = (1 + K1) * (1 + K2);
S = new double[N1 + 2 * M1 + 1];
Array.Copy(Parameters, 10, S, 0, S.Length);
T = new double[N2 + 2 * M2 + 1];
Array.Copy(Parameters, 11 + A, T, 0, T.Length);
W = new double[(K1 + 1) * (K2 + 1)];
X = new double[W.Length];
Y = new double[X.Length];
Z = new double[Y.Length];
Array.Copy(Parameters, 12 + A + B, W, 0, W.Length);
var PTS = new double[3 * X.Length];
Array.Copy(Parameters, 12 + A + B + C, PTS, 0, PTS.Length);
for (int i = 0; i < X.Length; i++)
{
X[i] = PTS[3 * i];
Y[i] = PTS[3 * i + 1];
Z[i] = PTS[3 * i + 2];
}
U0 = Parameters[12 + A + B + 4 * C];
U1 = Parameters[13 + A + B + 4 * C];
V0 = Parameters[14 + A + B + 4 * C];
V1 = Parameters[15 + A + B + 4 * C];
Bi = new BSpline_Basis_Function(S, M1 + 1);
Bj = new BSpline_Basis_Function(T, M2 + 1);
}
static private void TestBasisFunction()
{
// Unit Test Case Taken from Example 3.3 pp 58 An Introduction to NURBS by Rogers
// Calculate the five third order basis functions for the following knot vector
// [X] = [0 0 0 1 1 3 3 3]
var KnotVector1 = new double[] { 0, 0, 0, 1, 1, 3, 3, 3 };
var N = new BSpline_Basis_Function(KnotVector1, 3);
var TestVals = new double[] { 0, 0.5, 1, 2, 2.9 };
for (int i = 0; i < TestVals.Length; i++)
{
if (TestVals[i] >= 0 && TestVals[i] < 1)
{
Approx_Assert(N.Polys[0].Evaluate(TestVals[i]), Math.Pow(1.0 - TestVals[i], 2));
Approx_Assert(N.Polys[1].Evaluate(TestVals[i]), 2.0 * TestVals[i] * (1.0 - TestVals[i]));
Approx_Assert(N.Polys[2].Evaluate(TestVals[i]), TestVals[i] * TestVals[i]);
Approx_Assert(N.Polys[3].Evaluate(TestVals[i]), 0);
Approx_Assert(N.Polys[4].Evaluate(TestVals[i]), 0);
}
else if (TestVals[i] >= 1 && TestVals[i] < 3)
{
Approx_Assert(N.Polys[0].Evaluate(TestVals[i]), 0);
Approx_Assert(N.Polys[1].Evaluate(TestVals[i]), 0);
Approx_Assert(N.Polys[2].Evaluate(TestVals[i]), (Math.Pow(3.0 - TestVals[i], 2) / 4.0));
Approx_Assert(N.Polys[3].Evaluate(TestVals[i]), ((3 - TestVals[i]) * (TestVals[i] - 1.0) / 2.0));
Approx_Assert(N.Polys[4].Evaluate(TestVals[i]), (Math.Pow(TestVals[i] - 1.0, 2) / 4.0));
}
}
// we must also do checksums to see that they add up to 1
for (int i = 0; i < TestVals.Length; i++)
{
double CheckSum = 0;
for (int j = 0; j < 5; j++)
{
CheckSum += N.Polys[j].Evaluate(TestVals[i]);
}
Approx_Assert(CheckSum, 1.0);
}
}
public Rational_BSpline_Curve(double[] Parameters, TransformationMatrix _R = null, int _ParameterId = -1)
{
R = _R;
ParameterId = _ParameterId;
K = (int)Parameters[1];
M = (int)Parameters[2];
PROP1 = (int)Parameters[3];
PROP2 = (int)Parameters[4];
PROP3 = (int)Parameters[5];
PROP4 = (int)Parameters[6];
int N = 1 + K - M;
int A = N + 2 * M;
T = new double[A + 1];
Array.Copy(Parameters, 7, T, 0, T.Length);
W = new double[K + 1];
Array.Copy(Parameters, 8 + A, W, 0, W.Length);
var PTS = new double[(K + 1) * 3];
Array.Copy(Parameters, 8 + A + K, PTS, 0, PTS.Length);
X = new double[K + 1];
Y = new double[K + 1];
Z = new double[K + 1];
int id = 0;
for (int i = 0; i < PTS.Length; i += 3)
{
X[id] = PTS[i];
Y[id] = PTS[i + 1];
Z[id] = PTS[i + 2];
id++;
}
V0 = Parameters[12 + A + 4 * K];
V1 = Parameters[13 + A + 4 * K];
XNORM = Parameters[14 + A + 4 * K];
YNORM = Parameters[15 + A + 4 * K];
ZNORM = Parameters[16 + A + 4 * K];
// using the Cox-de Boor formula to calculate the basis functions
B = new BSpline_Basis_Function(T, M + 1);
}
