jvx.geom
Class PwBary

java.lang.Object
  |
  +--jvx.geom.PwBary

public class PwBary

extends java.lang.Object

Static methods that handle barycentric coordinates on triangulated element sets.

Version:

26.01.00, 1.04 revised (ep) corrected and changed getTransRepr(-Values).
09.01.00, 1.03 revised (ep) get...Repr-methods extended.
04.01.00, 1.02 revised (ep) getGeodTransRepr corrected.
21.11.99, 1.00 created (ep)

Author:

Eike Preuß

Constructor Summary

PwBary()

Method Summary

static PdBaryDir[]	getGeodRepresentation(PgElementSet geom, int origElem, PdBaryDir origDir, int localvertexindex, PiVector elements, PiVector localind) Calculates the representations of a given vector in all elements of a vertex star by completion to a unnormalized angle of theta/2.
static double	getOrientedAngle(PgElementSet geom, int elemInd, PdBaryDir a, PdBaryDir b, boolean recalc) Oriented angle between two barycentric vectors.
static PdBaryDir[]	getProjRepresentation(PgElementSet geom, int origElem, PdBaryDir origDir, int localvertexindex, PiVector elements, PiVector locind) Calculates the representations of a given vector in all elements of a vertex star by projection onto the plane the element lays in.
static PdBaryDir[]	getTransRepresentation(PgElementSet geom, int origElem, PdBaryDir origDir, int localvertexindex, PiVector elements, PiVector locind) Calculates the representations of a given vector in all elements of a vertex star by parallel translation along a straightest geodesic (half angles).
static double	getTransRepresentationValues(PgElementSet geom, int origElem, PdBaryDir origDir, int localvertexindex, PiVector elements, PiVector locind, PdVector betas) Calculates the values (beta,theta) of a given vector in all elements of a vertex star by parallel translation along a straightest geodesic.
static double	getVertexAngles(PgVertexStar star, PgElementSet geom, PdVector angles) Calculates inner angles of the elements of a vertexstar.
static int	liesOnVertex(PdBary pos) Checks if given barycentric position lies on any vertex
static double	norm(PgElementSet geom, int elemInd, PdBaryDir x, boolean forceRecalc) Euklidian norm of two intrinsic (barycentric) vectors.
static void	projectOntoElement(PgElementSet geom, int elemInd, PdVector dir, PdBaryDir outdir) Projects given vector onto elements plane.
static int	rotateAtVertex(PgElementSet geom, int elemind, int localvertexind, PdBaryDir dir, PdBaryDir outdir, PdBary bary, double angle) Rotates direction at vertex in same orientation as the star.
static void	rotateInElement(PgElementSet geom, int elemInd, PdBaryDir dir, double angle, PdBaryDir outdir, boolean recalc) Rotates direction in same orientation as the element's.
static double	scalar(PgElementSet geom, int elemInd, PdBaryDir x, PdBaryDir y, boolean forceRecalc) Computes scalar product of barycentric directions in world coordinates, that means the scalar product of the vectors in euklidian space.
static boolean	showsIntoElement(PdBaryDir dir, int vertexindex) Checks if given barycentric vector shows into it's element.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PwBary

public PwBary()

Method Detail

scalar

public static double scalar(PgElementSet geom,
                            int elemInd,
                            PdBaryDir x,
                            PdBaryDir y,
                            boolean forceRecalc)

Computes scalar product of barycentric directions in world coordinates, that means the scalar product of the vectors in euklidian space. The directions have to live on the same element. If geometry and element index are the same as they were at previous call of scalar and parameter forceRecalc == false then some calculations are skipped.

Parameters:

geom - geometry the barycentric directions live on

elemInd - element the barycentric directions live on

x - one direction

y - other direction

forceRecalc - if true all variables are forced two be recalculated; should only be used if the geometry may not be the same (in world coordinates) as in previous calls

Returns:

scalar product

norm

public static double norm(PgElementSet geom,
                          int elemInd,
                          PdBaryDir x,
                          boolean forceRecalc)

Euklidian norm of two intrinsic (barycentric) vectors.

Parameters:

geom - the geometry the barycentric direction lives on

elemInd - the element the barycentric direction lives on

x - barycentric vector

recalc - used for scalar product

Returns:

sqrt()

See Also:

scalar(jv.geom.PgElementSet, int, jv.vecmath.PdBaryDir, jv.vecmath.PdBaryDir, boolean)

getVertexAngles

public static double getVertexAngles(PgVertexStar star,
                                     PgElementSet geom,
                                     PdVector angles)

Calculates inner angles of the elements of a vertexstar. Only for triangulations.

Parameters:

star - the star

geom - the geometry

angles - output: vertex angles of star. if necessary it is resized.

Returns:

sum of the angles

getGeodRepresentation

public static PdBaryDir[] getGeodRepresentation(PgElementSet geom,
                                                int origElem,
                                                PdBaryDir origDir,
                                                int localvertexindex,
                                                PiVector elements,
                                                PiVector localind)

Calculates the representations of a given vector in all elements of a vertex star by completion to a unnormalized angle of theta/2. Element set must be triangulated.

Parameters:

geom - triangulation

origElem - element in which the vector is given

origDir - vector that will be translated to the other elements

localvertexindex - local index in origElem of the vertex at which the vector is given

elements - output: global element indices of the vertex star

localind - output: local vertex indices of common vertex in elements at vertex star

Returns:

array of the calculated directions at success, null else

getTransRepresentation

public static PdBaryDir[] getTransRepresentation(PgElementSet geom,
                                                 int origElem,
                                                 PdBaryDir origDir,
                                                 int localvertexindex,
                                                 PiVector elements,
                                                 PiVector locind)

Calculates the representations of a given vector in all elements of a vertex star by parallel translation along a straightest geodesic (half angles). Element set must be triangulated.

Parameters:

geom - triangulation

origElem - element in which the vector is given

origDir - vector that will be translated to the other elements

localvertexindex - the local index in origElem of the vertex in which the vector is given

elements - output: global element indices of the vertex star

locind - output: local vertex indices of the vertex star

Returns:

array of the calculated directions at success, null else

getTransRepresentationValues

public static double getTransRepresentationValues(PgElementSet geom,
                                                  int origElem,
                                                  PdBaryDir origDir,
                                                  int localvertexindex,
                                                  PiVector elements,
                                                  PiVector locind,
                                                  PdVector betas)

Calculates the values (beta,theta) of a given vector in all elements of a vertex star by parallel translation along a straightest geodesic. Rotate counter-clockwise next edge by angleOfEvaluationPointToEdge - 2*PI/theta*(beta+angle), where angle is the angle between evaluation position and edge. Element set must be triangulated.

Parameters:

geom - set of elements

origElem - element in which the vector is given

origDir - vector that will be translated to the other elements

localvertexindex - the local index in origElem of the vertex in which the vector is given

elements - output: global element indices of the vertex star, beginning with origElem

locind - output: local indices of common vertex of star, beginning with localvertexindex

betas - output: beta values

Returns:

theta

getProjRepresentation

public static PdBaryDir[] getProjRepresentation(PgElementSet geom,
                                                int origElem,
                                                PdBaryDir origDir,
                                                int localvertexindex,
                                                PiVector elements,
                                                PiVector locind)

Calculates the representations of a given vector in all elements of a vertex star by projection onto the plane the element lays in. Element set must be triangulated.

Parameters:

geom - set of elements

origElem - element on which the vector is given

origDir - vector that will be translated to the other elements

localvertexindex - the local index in origElem of the vertex in which the vector is given

elements - output: global element indicee of the vertex star

locind - output: local vertex indices of the vertex star

Returns:

array of the calculated directions at success, null else

projectOntoElement

public static void projectOntoElement(PgElementSet geom,
                                      int elemInd,
                                      PdVector dir,
                                      PdBaryDir outdir)

Projects given vector onto elements plane.

Parameters:

geom - underlying geometry

elemInd - global element index

dir - in world coordinates

outdir - output: barycentric coordinates of the projected vector

getOrientedAngle

public static double getOrientedAngle(PgElementSet geom,
                                      int elemInd,
                                      PdBaryDir a,
                                      PdBaryDir b,
                                      boolean recalc)

Oriented angle between two barycentric vectors.

Parameters:

geom - underlying geometry

elemInd - global element index

a - first vector

b - second vector

recalc - used for scalar product

Returns:

oriented angle out of [-PI, PI]; negative if a must be rotated against the orientation of the triangle; -3*PI if an error occurred

See Also:

scalar(jv.geom.PgElementSet, int, jv.vecmath.PdBaryDir, jv.vecmath.PdBaryDir, boolean)

rotateInElement

public static void rotateInElement(PgElementSet geom,
                                   int elemInd,
                                   PdBaryDir dir,
                                   double angle,
                                   PdBaryDir outdir,
                                   boolean recalc)

Rotates direction in same orientation as the element's.

Parameters:

geom - underlying geometry

elemInd - element on that vector lies

dir - barycentric direction

angle - rad

outdir - output: result of rotation

recalc - used for scalar product

See Also:

scalar(jv.geom.PgElementSet, int, jv.vecmath.PdBaryDir, jv.vecmath.PdBaryDir, boolean)

rotateAtVertex

public static int rotateAtVertex(PgElementSet geom,
                                 int elemind,
                                 int localvertexind,
                                 PdBaryDir dir,
                                 PdBaryDir outdir,
                                 PdBary bary,
                                 double angle)

Rotates direction at vertex in same orientation as the star. An angle of 2*Pi means a complete turn around the star.

Parameters:

geom - underlying geometry

elemind - global element index

localvertexind - local index of vertex that is base of the rotation

dir - original vector

outdir - output: result of rotation

bary - output: barycentric coordinates of the base point of the result

angle - normalized angle [0;2*PI] ^= 360°

Returns:

global element index where outdir lies on

showsIntoElement

public static boolean showsIntoElement(PdBaryDir dir,
                                       int vertexindex)

Checks if given barycentric vector shows into it's element.

Parameters:

dir - barycentric vector that shall be checked

vertexindex - local vertex index that is the base of the direction

Returns:

true if barycentric vector shows into it's element

liesOnVertex

public static int liesOnVertex(PdBary pos)

Checks if given barycentric position lies on any vertex

Parameters:

pos - barycentric point

Returns:

localvertexindex if pos lays in jv.vecmath.PuMath.EPS-sphere around any vertex;
-1 else