protected static double[] getInitialBinormal(double[][] polygon, int metric) {
int n = polygon.length;
double[] B = new double[4];
for (int i = 1; i < n - 1; ++i) {
Pn.polarize(B, P3.planeFromPoints(null, polygon[i - 1], polygon[i], polygon[i + 1]), metric);
if (Rn.euclideanNormSquared(B) > 10E-16) return B;
}
B = new double[] {Math.random(), Math.random(), Math.random(), 1.0};
return Pn.polarizePlane(null, P3.planeFromPoints(null, B, polygon[1], polygon[2]), metric);
}
public static SceneGraphComponent tubeOneEdge(
SceneGraphComponent sgc,
double[] ip1,
double[] ip2,
double rad,
double[][] crossSection,
int metric) {
if (ip1.length < 3 || ip1.length > 4 || ip2.length < 3 || ip2.length > 4) {
throw new IllegalArgumentException("Invalid dimension");
}
double p1[] = new double[4];
double p2[] = new double[4];
if (ip1.length == 3) Pn.homogenize(p1, ip1);
else p1 = ip1;
if (ip2.length == 3) Pn.homogenize(p2, ip2);
else p2 = ip2;
boolean isValid1 = Pn.isValidCoordinate(p1, 3, metric);
boolean isValid2 = Pn.isValidCoordinate(p2, 3, metric);
if (!isValid1 && !isValid2) return new SceneGraphComponent();
if (!isValid1) Rn.linearCombination(p1, .99, p1, .01, p2); // (p1, p1, p2, .999, metric);
else if (!isValid2) Rn.linearCombination(p2, .99, p2, .01, p1); // (p2, p2, p1, .999, metric);
Pn.normalize(p1, p1, metric);
Pn.normalize(p2, p2, metric);
if ((debug & 2) != 0) theLogger.log(Level.FINE, "p1 is " + Rn.toString(p1));
if ((debug & 2) != 0) theLogger.log(Level.FINE, "p2 is " + Rn.toString(p2));
double[] polarPlane = Pn.polarizePoint(null, p1, metric);
if ((debug & 2) != 0) theLogger.log(Level.FINE, "Polar plane is " + Rn.toString(polarPlane));
double[] tangent = P3.lineIntersectPlane(null, p1, p2, polarPlane);
double[] diff = Rn.subtract(null, p2, p1);
if (Rn.innerProduct(diff, tangent) < 0.0) Rn.times(tangent, -1.0, tangent);
Pn.setToLength(tangent, tangent, 1.0, metric);
double[] normal = Pn.polarizePlane(null, P3.planeFromPoints(null, p1, tangent, e1), metric);
double[] binormal =
Pn.polarizePlane(null, P3.planeFromPoints(null, p1, tangent, normal), metric);
Pn.setToLength(normal, normal, 1.0, metric);
Pn.setToLength(binormal, binormal, 1.0, metric);
double[] frame = new double[16];
// for reasons unknown/murky, to get a RH.C.S. the vectors have to be assembled as follows in
// the matrix
System.arraycopy(binormal, 0, frame, 0, 4);
System.arraycopy(normal, 0, frame, 4, 4);
System.arraycopy(tangent, 0, frame, 8, 4);
System.arraycopy(p1, 0, frame, 12, 4);
// make sure the transformation is orientation-preserving
// NOTE: If there appear shading problems on tubes, un-comment this code
// if (Rn.determinant(frame) < 0) {
// System.arraycopy(normal, 0, frame, 0, 4);
// System.arraycopy(binormal, 0, frame, 4, 4);
//
// }
if ((debug & 16) != 0) {
theLogger.log(Level.FINE, "Frame is " + Rn.matrixToString(frame));
theLogger.log(Level.FINE, "Det is " + Rn.determinant(frame));
}
Rn.transpose(frame, frame);
double[] scaler = Rn.identityMatrix(4);
double dist = Pn.distanceBetween(p1, p2, metric);
double coord = dist / 2;
if (Double.isNaN(coord)) {
LoggingSystem.getLogger(TubeUtility.class).warning("bad coord");
return new SceneGraphComponent();
// throw new IllegalStateException("bad coord");
}
if (metric == Pn.HYPERBOLIC) coord = Pn.tanh(dist / 2.0);
else if (metric == Pn.ELLIPTIC) coord = Math.tan(dist / 2.0);
scaler[10] = 2 * coord;
double radcoord = rad;
if (metric == Pn.HYPERBOLIC) radcoord = Math.sqrt(1 - coord * coord) * Pn.tanh(rad);
else if (metric == Pn.ELLIPTIC) radcoord = Math.sqrt(1 + coord * coord) * Math.tan(rad);
scaler[0] = scaler[5] = radcoord;
if ((debug & 1) != 0) {
theLogger.log(
Level.FINE,
"distance is \t"
+ dist
+ " scaler is \t"
+ coord
+ " and radius factor is \t"
+ radcoord);
}
// LoggingSystem.getLogger().log(Level.FINE,"Frame is "+Rn.matrixToString(frames[0]));
// LoggingSystem.getLogger().log(Level.FINE,"Scaler is "+Rn.matrixToString(scaler));
double[] translate = {0, 0, coord, 1};
double[] translateM = P3.makeTranslationMatrix(null, translate, metric);
// the matrix net should be a transformation that takes the two input points
// to the (dehomogenized) points (0,0,+/-.5,1).
double[] net = Rn.times(null, frame, Rn.times(null, translateM, scaler));
if ((debug & 64) != 0) theLogger.log(Level.FINE, "net is \n" + Rn.matrixToString(net));
// double[] inet = Rn.inverse(null, net);
// double[] inp1 = Rn.matrixTimesVector(null, inet, p1);
// double[] inp2 = Rn.matrixTimesVector(null, inet, p2);
// if ((debug & 64) != 0) theLogger.log(Level.FINE,"Image of end points:
// "+Rn.toString(Pn.dehomogenize(null,inp1), 6)+" "+Rn.toString(Pn.dehomogenize(null,inp2),6));
if (sgc == null) sgc = new SceneGraphComponent();
sgc.setGeometry(urTube[metric + 1]);
if (sgc.getTransformation() == null) sgc.setTransformation(new Transformation());
sgc.getTransformation().setMatrix(net);
// LoggingSystem.getLogger().log(Level.FINE,"Matrix is
// "+Rn.matrixToString(sgc.getTransformation().getMatrix()));
return sgc;
}