Java Vector3d.cross方法代碼示例

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static double getTorsionAngleRadians(double[] a, double[] b, double[] c, double[] d,
                                            Vector3d r1, Vector3d r2, Vector3d r3) {
  //   a --r1--> b --r2--> c --r3--> d

  // get r1 x r2 ==> r1 
  // and r2 x r3 ==> r3
  // then
  // sinTheta/cosTheta = r2.(r1 x r3)/(r1 . r3)
  
  sub(b, a, r1); 
  sub(c, b, r2);
  r2.normalize();
  r1.cross(r1, r2); //p1
  sub(d, c, r3); 
  r3.cross(r2, r3); //p2
  double p1dotp2 = r1.dot(r3);
  r1.cross(r3, r1);
  double theta = Math.atan2(
      -r2.dot(r1), // sin theta ~ r2.(p2 x p1) / |r2|
      p1dotp2);   // cos theta ~ p1.p2  
  return theta;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static double pointPlaneAngleRadians(Vector3d a, Vector3d b,
                                            Vector3d c, Vector3d d,
                                            Vector3d v1,Vector3d v2, 
                                            Vector3d norm) {
  v1.sub(b, c);
  v2.sub(b, d);
  norm.cross(v1, v2);
  v2.add(v1);
  v1.sub(b, a);
  double angleA_CD = vectorAngleRadians(v2, v1);
  double angleNorm = vectorAngleRadians(norm, v1);
  if (angleNorm > Math.PI / 2)
    angleNorm = Math.PI - angleNorm;
  return Math.PI / 2.0 + (angleA_CD > Math.PI / 2.0 ? -angleNorm : angleNorm) ;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public boolean hasPoint(Point3d p){
      Vector3d u =GeometryUtils.vectorSubtract(this.p1.asPoint3d(), this.p0.asPoint3d());
      Vector3d v =GeometryUtils.vectorSubtract(this.p2.asPoint3d(), this.p0.asPoint3d());
      Vector3d n=new Vector3d();
      n.cross(u, v);
      Vector3d w=GeometryUtils.vectorSubtract(p, this.p0.asPoint3d());
      double r=Math.abs(GeometryUtils.vectorCross(u,w).dot(n))/n.lengthSquared();
      double b=Math.abs(GeometryUtils.vectorCross(w,v).dot(n))/n.lengthSquared();
      double a=1-r-b;
      if(a>=0&&a<=1&&b>=0&&b<=1&&r>=0&&r<=1){
    	  return true;
      }
      return false;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
static double distancePointSegment3D(Point3d pt, Segment seg) throws GeometryException {
	Vector3d diff = GeometryUtils.vectorSubtract(pt, seg.p0.asPoint3d());
	Vector3d segvec = GeometryUtils.vectorSubtract(seg.p1.asPoint3d(), seg.p0.asPoint3d());
	double d = diff.dot(segvec);
	if (d <= 0)
		return (diff.length());
	if ((d * diff.length()) > (segvec.length()))
		return distancePointPoint3D(pt, seg.p1.asPoint3d());

	Vector3d cr = new Vector3d();
			cr.cross(segvec,diff);
	return cr.length() / (segvec.length());
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static double area( Triangle g )
{
    Vector3d v1=GeometryUtils.vectorSubtract(g.p1.asPoint3d(),g.p0.asPoint3d());
    Vector3d v2=GeometryUtils.vectorSubtract(g.p2.asPoint3d(),g.p0.asPoint3d());
    Vector3d cross=new Vector3d();
    cross.cross(v1, v2);
    return cross.length()/2;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public Vector3d getNormal(){
	if(this.normal!=null){
		return normal;
	}
	Vector3d v1=GeometryUtils.vectorSubtract(p1, p0);
	Vector3d v2=GeometryUtils.vectorSubtract(p2, p1);
	Vector3d u=new Vector3d();
	u.cross(v1, v2);
	u.normalize();
	this.normal=u;
	return normal;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static void tube (MeshBuilder out, 
			Collection<LinearForm3D> before, Collection<LinearForm3D> after, 
			Line3d line, LinearForm3D left, LinearForm3D right, CrossGen gen ) {
		
		if (angle ( before, line) < 0.1 || angle ( after, line ) < 0.1 )
			return; // too pointy to touch
		
		Point3d middle = line.fromPPram( 0.5 );
		
		Vector3d along = line.dir();
		along.normalize();
		Vector3d nAlong = new Vector3d (along);
		nAlong.negate();
		
		Vector3d o1 = left.normal(), u1 = new Vector3d();
		u1.cross( along, o1 );
		
		Frame frame = Mathz.buildFrame ( o1, u1, along, middle);
		
		Vector3d u2 = right.normal();
		u2.cross( u2, along );
//		u2.add( middle );
		
		Vector2d leftDir = Mathz.toXY ( frame, u1 );
		Vector2d rightDir = Mathz.toXY ( frame, u2 );
		
		List<Point3d> profilePts = gen.gen( leftDir, rightDir ).stream().
				map( p -> Mathz.fromXY( frame, p ) ).collect( Collectors.toList() );
		
		List<LinearForm3D> dummy = new ArrayList<>();
		
		for (Pair <Point3d, Point3d> pair : new ConsecutivePairs<Point3d>( profilePts, true ) ) {
			
			Point3d 
					f1 = clip ( pair.first (), along , after , dummy ),
					f2 = clip ( pair.second(), along , after , dummy ),
					b1 = clip ( pair.first (), nAlong, before, dummy ),
					b2 = clip ( pair.second(), nAlong, before, dummy );

			out.add (f2, f1, b1, b2);
		}
		
//		cap( out, after ,  along, profilePts, true  );
//		cap( out, before, nAlong, profilePts, false );
	}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
protected void createWindow( DRectangle winPanel, Matrix4d to3d, 
		MeshBuilder wall, 
		MeshBuilder window, 
		MeshBuilder glass, 
		double depth,
		float sillDepth, float sillHeight,
		float corniceHeight,
		double panelWidth, double panelHeight ) {
	
	Point2d[] pts = winPanel.points();
	
	Point3d[] ptt = new Point3d[4];
	
	for (int i = 0; i < 4; i++) {
		ptt[i] = Pointz.to3( pts[i] );
		to3d.transform( ptt[i] ); 
	}
	
	Vector3d along = new Vector3d(ptt[3]);
	along.sub(ptt[0]);
	along.normalize();
	
	Vector3d up = new Vector3d(ptt[1]);
	up.sub(ptt[0]);
	up.normalize();

	Vector3d out = new Vector3d();
	out.cross( along, up );
	out.scale(-1/out.length());
	
	Vector3d loc = new Vector3d();
	loc.cross( along, up );
	loc.scale ( -depth / loc.length() );
	loc.add(ptt[0]);
	
	WindowGen.createWindow( window, glass, new Window( Jme3z.to ( loc ), Jme3z.to(along), Jme3z.to(up), 
			winPanel.width, winPanel.height, 0.3, panelWidth, panelHeight ) ); 
	
	Vector3f u = Jme3z.to(up), o = Jme3z.to( out );
	
	wall.addInsideRect( Jme3z.to ( ptt[0] ), o, Jme3z.to(along), u,  
			 (float)depth, (float)winPanel.width,(float) winPanel.height  );
	
	if (sillDepth > 0 && sillHeight > 0)
		window.addCube( Jme3z.to ( ptt[0] ).add( u.mult( -sillHeight + 0.01f ) ).add( o.mult( -sillDepth) ),
			Jme3z.to(out), Jme3z.to(along), Jme3z.to(up),
			(float)depth + sillDepth, (float)winPanel.width,(float) sillHeight  );
	
	if (corniceHeight > 0) 
		moulding( to3d, new DRectangle(winPanel.x, winPanel.getMaxY(), winPanel.width, corniceHeight), wall );
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static double restorativeForceAndTorsionAngleRadians(Vector3d i, Vector3d j,
                                                    Vector3d k, Vector3d l) {
  // This is adapted from http://scidok.sulb.uni-saarland.de/volltexte/2007/1325/pdf/Dissertation_1544_Moll_Andr_2007.pdf
  // Many thanks to Andreas Moll and the BALLView developers for this

  // Bond vectors of the three atoms

  i.sub(j, i);
  j.sub(k, j);
  k.sub(l, k);

  double len_ij = i.length();
  double len_jk = j.length();
  double len_kl = k.length();

  if (isNearZero(len_ij) || isNearZero(len_jk) || isNearZero(len_kl)) {
    i.set(0, 0, 0);
    j.set(0, 0, 0);
    k.set(0, 0, 0);
    l.set(0, 0, 0);
    return 0.0;
  }

  double ang = vectorAngleRadians(i, j);
  double sin_j = Math.sin(ang);
  double cos_j = Math.cos(ang);
  
  ang = vectorAngleRadians(j, k);
  double sin_k = Math.sin(ang);
  double cos_k = Math.cos(ang);

  // normalize the bond vectors:

  i.normalize();
  j.normalize();
  k.normalize();

  // use i, k, and l for temporary variables as well
  i.cross(i, j);  //a
  l.cross(j, k);  //b
  k.cross(i, l);  //c

  double theta = -Math.atan2(
      k.dot(j),  // ((ij x jk) x (jk x kl)) . jk 
      i.dot(l)); //  (ij x jk) . (jk x kl)
      
  i.scale(1. / len_ij / sin_j / sin_j);
 
  l.scale(-1. / len_kl / sin_k / sin_k);

  j.set(i);
  j.scale(-len_ij / len_jk * cos_j - 1.);
  k.set(l);
  k.scale(-len_kl / len_jk * cos_k);
  j.sub(k);
  
  k.set(i);
  k.add(j);
  k.add(l);
  k.scale(-1);

  return theta;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static Line3d intersect3D_2Planes(Plane pn1, Plane pn2) {
	Vector3d u = new Vector3d();
	u.cross(pn1.getNormal(), pn2.getNormal()); // cross product
	double ax = (u.x >= 0 ? u.x : -u.x);
	double ay = (u.y >= 0 ? u.y : -u.y);
	double az = (u.z >= 0 ? u.z : -u.z);

	// Pn1 and Pn2 intersect in a line
	// first determine max abs coordinate of cross product
	int maxc; // max coordinate
	if (ax > ay) {
		if (ax > az)
			maxc = 1;
		else
			maxc = 3;
	} else {
		if (ay > az)
			maxc = 2;
		else
			maxc = 3;
	}

	// next, to get a point on the intersect line
	// zero the max coord, and solve for the other two
	Point3d iP = new Point3d(); // intersect point
	double d1, d2; // the constants in the 2 plane equations
	d1 = -pn1.normal.dot(new Vector3d(pn1.p0.x, pn1.p0.y, pn1.p0.z)); // note:
																		// could
																		// be
																		// pre-stored
																		// with
																		// plane
	d2 = -pn2.normal.dot(new Vector3d(pn2.p0.x, pn2.p0.y, pn2.p0.z)); // ditto

	switch (maxc) { // select max coordinate
	case 1: // intersect with x=0
		iP.x = 0;
		iP.y = (d2 * pn1.normal.z - d1 * pn2.normal.z) / u.x;
		iP.z = (d1 * pn2.normal.y - d2 * pn1.normal.y) / u.x;
		break;
	case 2: // intersect with y=0
		iP.x = (d1 * pn2.normal.z - d2 * pn1.normal.z) / u.y;
		iP.y = 0;
		iP.z = (d2 * pn1.normal.x - d1 * pn2.normal.x) / u.y;
		break;
	case 3: // intersect with z=0
		iP.x = (d2 * pn1.normal.y - d1 * pn2.normal.y) / u.z;
		iP.y = (d1 * pn2.normal.x - d2 * pn1.normal.x) / u.z;
		iP.z = 0;
	}
	Line3d l = new Line3d(iP, new Point3d(iP.x + u.x, iP.y + u.y, iP.z + u.z));
	return l;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static Line3d intersect3D_2Planes(Plane pn1, Plane pn2)
{
    Vector3d   u= new Vector3d();
    u.cross(pn1.getNormal(), pn2.getNormal());          // cross product
    double    ax = (u.x >= 0 ? u.x : -u.x);
    double    ay = (u.y >= 0 ? u.y : -u.y);
    double    az = (u.z >= 0 ? u.z : -u.z);

    // Pn1 and Pn2 intersect in a line
    // first determine max abs coordinate of cross product
    int      maxc;                       // max coordinate
    if (ax > ay) {
        if (ax > az)
             maxc =  1;
        else maxc = 3;
    }
    else {
        if (ay > az)
             maxc =  2;
        else maxc = 3;
    }

    // next, to get a point on the intersect line
    // zero the max coord, and solve for the other two
    Point3d    iP=new Point3d();                // intersect point
    double    d1, d2;            // the constants in the 2 plane equations
    d1 = -pn1.normal.dot(new Vector3d(pn1.p0.x,pn1.p0.y,pn1.p0.z));  // note: could be pre-stored  with plane
    d2 = -pn2.normal.dot(new Vector3d(pn2.p0.x,pn2.p0.y,pn2.p0.z));  // ditto

    switch (maxc) {             // select max coordinate
    case 1:                     // intersect with x=0
        iP.x = 0;
        iP.y = (d2*pn1.normal.z - d1*pn2.normal.z) /  u.x;
        iP.z = (d1*pn2.normal.y - d2*pn1.normal.y) /  u.x;
        break;
    case 2:                     // intersect with y=0
        iP.x = (d1*pn2.normal.z - d2*pn1.normal.z) /  u.y;
        iP.y = 0;
        iP.z = (d2*pn1.normal.x - d1*pn2.normal.x) /  u.y;
        break;
    case 3:                     // intersect with z=0
        iP.x = (d2*pn1.normal.y - d1*pn2.normal.y) /  u.z;
        iP.y = (d1*pn2.normal.x - d2*pn1.normal.x) /  u.z;
        iP.z = 0;
    }
    Line3d l=new Line3d(iP,new Point3d(iP.x+u.x,iP.y+u.y,iP.z+u.z));
    return l;
}
 

import javax.vecmath.Vector3d; //導入方法依賴的package包/類
public static Vector3d vectorCross(Vector3d u, Vector3d w) {
	Vector3d v=new Vector3d();
	v.cross(u, w);
	return v;
}