jvx.numeric

Class PnStraightestGeodesic

java.lang.Object

jvx.numeric.PnStraightestGeodesic

public class PnStraightestGeodesic
extends java.lang.Object

The exponential map on a PgElementSet. This class is intended to be used when the exponential map is evaluated very often. The basic idea is to speed up the calculations by computing and saving the linear transformations (3x3 matrices) that rotate around an edge from one element into another. These edge transformations can be computed all at once, when setGeometry is called, or only when needed.

Example:

    exp = new PnStraightestGeodesic(geom);
    exp.eval(inPoint, inDir, outPoint, outDir, outPoly);
    // turn around and go back
    outDir.multScalar(-1);
    exp.eval(outPoint, outDir, revOutPoint, revOutDir);
 

Now inPoint represents the same point as revOutPoint. Point being: If the geometry boundary is reached, outDir is scaled down to preserve this invariant. In this case, inDir and revOutDir may represent vectors of different length.

inPoint and revOutPoint are not necessarily on the same triangle (see below), but outPoly.getVertexBary(0) and revOutPoint are. Of course, outPoint is the last point of outPoly.

Barycentric coordinates are used to represent points and vectors. The geometry must be triangulated.

Author:

Andreas Haferburg

Version:

11.01.07, 1.10 revised (ah) Error check in computeTransformation.
01.03.06, 1.00 created (ah) Rewrite of PgPolygonOnElementSet.exp().

Field Summary

Fields

Modifier and Type	Field and Description
static double	BARYEPS Default accuracy used at checks for zero in barycentric coordinates (used e.g. in exp(...)).
double	m_eps This accuracy is actually used for zero-checks in barycentric coordinates (used e.g. in exp(...)).

Constructor Summary

Constructors

Constructor and Description
PnStraightestGeodesic(PgElementSet geometry) Creates a new instance of PnStraightestGeodesic.
PnStraightestGeodesic(PgElementSet geometry, boolean precompute) Creates a new instance of PnStraightestGeodesic.

Method Summary

Modifier and Type	Method and Description
int	eval(PdBary basePoint, PdBaryDir dir, PdBary outPoint) Evaluates the exponential map.
int	eval(PdBary basePoint, PdBaryDir dir, PdBary outPoint, PdBaryDir outDir) Evaluates the exponential map.
int	eval(PdBary base, PdBaryDir dir, PdBary outPoint, PdBaryDir outDir, PgPolygonOnElementSet outPoly) Evaluates the exponential map.
int	eval(PdBary basePoint, PdBaryDir dir, PgPolygonOnElementSet outPoly) Evaluates the exponential map.
int	eval(PdBary basePoint, PdBaryDir dir, PgPolygonOnElementSet outPoly, PdBaryDir outDir) Evaluates the exponential map.
double	getAccuracy() Returns the accuracy used when testing barycentric coordinates for zero.
PgElementSet	getGeometry() Returns the underlying geometry.
boolean	isSavingMatrices() Returns whether the linear transformations that rotate from one element into its neighbor are saved in an array.
void	setAccuracy(double accuracy) Sets the accuracy used when testing a barycentric coordinate for zero.
void	setGeometry(PgElementSet geom) Sets the underlying geometry.
void	setSavingMatrices(boolean bStoreMatrices) Sets if the edge transformations should be stored for later use.

Methods inherited from class java.lang.Object

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

Field Detail

BARYEPS

public static double BARYEPS

Default accuracy used at checks for zero in barycentric coordinates (used e.g. in exp(...)).

m_eps

public double m_eps

This accuracy is actually used for zero-checks in barycentric coordinates (used e.g. in exp(...)).

Constructor Detail

PnStraightestGeodesic

public PnStraightestGeodesic(PgElementSet geometry)

Creates a new instance of PnStraightestGeodesic. Calls setGeometry.

Parameters:

geometry - The underlying geometry.

PnStraightestGeodesic

public PnStraightestGeodesic(PgElementSet geometry,
                             boolean precompute)

Creates a new instance of PnStraightestGeodesic. Calls setGeometry.

Parameters:

geometry - The underlying geometry.

precompute - Compute the 3x3-matrices that represent the rotations around edges of adjacent elements. For every edge, 2 matrices are computed.

Method Detail

eval

public int eval(PdBary basePoint,
                PdBaryDir dir,
                PdBary outPoint)

Evaluates the exponential map.

Parameters:

basePoint - The point defining the tangent space.

dir - The input vector in tangent space at which the exponential map is evaluated.

outPoint - The output point.

Returns:

1 if everything went normally, -1 if the base is invalid, 0 if the geometry boundary was reached.

eval

public int eval(PdBary basePoint,
                PdBaryDir dir,
                PdBary outPoint,
                PdBaryDir outDir)

Evaluates the exponential map.

Parameters:

basePoint - The point defining the tangent space.

dir - The input vector in tangent space at which the exponential map is evaluated.

outPoint - The output point.

outDir - Parallel translation of dir.

Returns:

1 if everything went normally, -1 if the base is invalid, 0 if the geometry boundary was reached.

eval

public int eval(PdBary basePoint,
                PdBaryDir dir,
                PgPolygonOnElementSet outPoly,
                PdBaryDir outDir)

Evaluates the exponential map.

Parameters:

basePoint - The point defining the tangent space.

dir - The input vector in tangent space at which the exponential map is evaluated.

outDir - Parallel translation of dir.

outPoly - Output geodesic.

Returns:

1 if everything went normally, -1 if the base is invalid, 0 if the geometry boundary was reached.

eval

public int eval(PdBary basePoint,
                PdBaryDir dir,
                PgPolygonOnElementSet outPoly)

Evaluates the exponential map.

Parameters:

basePoint - The point defining the tangent space.

dir - The input vector in tangent space at which the exponential map is evaluated.

outPoly - Output geodesic.

Returns:

1 if everything went normally, -1 if the base is invalid, 0 if the geometry boundary was reached.

eval

public int eval(PdBary base,
                PdBaryDir dir,
                PdBary outPoint,
                PdBaryDir outDir,
                PgPolygonOnElementSet outPoly)

Evaluates the exponential map. The last two points of outPoly are guaranteed to be on the same element, and two consecutive points will be on elements that are neighbors.
Normally, base is the first point of the outPoly. However, in the special case where base is on an edge or a vertex, and dir doesn't point at base's element, base won't be included in the output, but only the representation in a triangle dir points at.

Parameters:

base - The point defining the tangent space.

dir - The input vector in tangent space at which the exponential map is evaluated.

outPoint - The output point, may be null.

outDir - Parallel translation of dir, may be null.

outPoly - Output geodesic, may be null.

Returns:

1 if everything went normally, -1 if the base is invalid, 0 if the geometry boundary was reached.

Version:

01.03.06, 1.01 (ah) Modify poly vertices directly to avoid copying.

setGeometry

public void setGeometry(PgElementSet geom)

Sets the underlying geometry. Computes the edge transformations if it was specified in the constructor.

Parameters:

geom - New underlying geometry, must be triangulated.

getGeometry

public PgElementSet getGeometry()

Returns the underlying geometry.

Returns:

The underlying geometry.

getAccuracy

public double getAccuracy()

Returns the accuracy used when testing barycentric coordinates for zero.

Returns:

the accuracy

setAccuracy

public void setAccuracy(double accuracy)

Sets the accuracy used when testing a barycentric coordinate for zero. In all methods of this class, a barycentric coordinate b is treated as zero, iff Math.abs(b)<m_accuracy

Parameters:

accuracy - Accuracy to be used.

isSavingMatrices

public boolean isSavingMatrices()

Returns whether the linear transformations that rotate from one element into its neighbor are saved in an array.

Returns:

Edge transformations are saved.

setSavingMatrices

public void setSavingMatrices(boolean bStoreMatrices)

Sets if the edge transformations should be stored for later use.

Parameters:

bStoreMatrices - matrices are stored.