jvx.geom

Class PwShapeOperator

java.lang.Object

jv.object.PsObject

jvx.project.PjWorkshop

jvx.geom.PwShapeOperator

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, PsUpdateIf, PjWorkshopIf

public class PwShapeOperator
extends PjWorkshop

Provides methods for calculating the discrete shape operator for a PgElementSet.

See Also:

Serialized Form

Author:

Philip Hornig

Version:

20.02.2009, 1.32 revised (fk) Turn off convolution mask.
23.10.2008, 1.31 revised (fk) Display progress in the status bar.
22.10.2008, 1.30 revised (fk) Add possibility to use absolute curvature values.
10.09.2008, 1.20 revised (fk) Simplified a lot. Now 2x-3x faster.
09.05.2007, 1.10 revised (fk) Simplified orientation check. Add convolutionMask function.
06.12.2006, 1.00 created (ph)

Field Summary

Fields

Modifier and Type	Field and Description
static boolean	m_useConvolutionMask This flag specifies if all edges will be weighted equally or if edges that are closer to the center of the ball get higher weight.

Fields inherited from class jv.object.PsObject

HAS_BOUNDARY_PANEL, HAS_CONFIG_PANEL, HAS_INFO_PANEL, HAS_LABEL_PANEL, HAS_MATERIAL_PANEL, HAS_TEXTURE_PANEL, HAS_VECTOR_PANEL, INSPECTOR_INFO, INSPECTOR_INFO_EXT, IS_DELETED, IS_FIXED, IS_FOCUSSED, IS_PICKED, IS_SELECTED, IS_USED, NUM_TAGS

Fields inherited from interface jv.project.PjWorkshopIf

MODE_BUG, MODE_STANDARD, MODE_VALIDATE

Constructor Summary

Constructors

Constructor and Description
PwShapeOperator() Default constructor

Method Summary

Modifier and Type	Method and Description
static PdVector[]	calcEigensystem(PdMatrix matrix, PdVector normal, PdVector[] eigenVectors, PdVector eigenValues) Calculate the eigenvectors of the shape operator restricted to a given plane.
static void	enableAbsoluteValue(boolean useAbsoluteValue) Use absolute curvature values are used for curvature tensor calculation.
static void	enableConvolution(boolean useConvolution) Use a weighting mask.
static void	getPrincipalCurvatures(PgElementSet geom, PdMatrix[] shape, PdVector[] pcValues, PdVector[][] pcDirections, boolean projectToTangentPlane, boolean vertexBased) Computes the principal curvatures and directions at each vertex of the surface.
static PdMatrix[]	getShapeOperator(PgElementSet geom, double radius, boolean vertexBased, PdMatrix[] shape) Calculate the shape operator for the whole geometry geom.
static PdMatrix	getShapeOperator(PgElementSet geom, int elementInd, double radius, PdMatrix shape) Calculates the shape operator for the element with elementInd of the PgElementSet geom.
static PdMatrix	getShapeOperator(PgElementSet geom, int vertexInd, int elemInd, double radius, PdMatrix shape) Calculates the shape operator for the vertex with index vertexInd of the PgElementSet geom and stores it in the PdMatrix shape.
static PdMatrix	getShapeOperator(PgElementSet geom, PdBary bary, double radius, PdMatrix shape) Calculates the shape operator for the point on the PgElementSet geom within the element with index elementInd given by the barycentric coordinates baryCoords and stores it in the PdMatrix shape.
static boolean	isEnabledAbsoluteValue() Check if absolute curvature values are used for curvature tensor calculation.
static boolean	isEnabledConvolution() Check if convolution with a weighting mask is enabled.
static PgVectorField[]	makeElementBasedPrincipalCurvatures(PgElementSet geom, PdVector[] curvatureValues) Make element based principal curvature vector fields with an automatic calculated integration radius.
static PgVectorField[]	makeElementBasedPrincipalCurvatures(PgElementSet geom, PdVector[] curvatureValues, boolean bIntegrated) Make element based principal curvature vector fields.
static PgVectorField[]	makeElementBasedPrincipalCurvatures(PgElementSet geom, PdVector[] curvatureValues, double radius) Make element based principal curvature vector fields.
static PdVector	makeTrustFunction(PgVectorField vf, PdVector[] curvatures, boolean useSmoothProperty) Computes a scalar function indicating, how trusted the curvature information are in the actual point.
static PgVectorField[]	makeVertexBasedPrincipalCurvatures(PgElementSet geom, PdVector[] curvatures, boolean bIntegrated) Make vertex based principal curvature vector fields.
static PgVectorField[]	makeVertexBasedPrincipalCurvatures(PgElementSet geom, PdVector[] curvatures, double radius) Make vertex based principal curvature vector fields.
static void	normalizeFrame(PdVector v1, PdVector v2, PdVector baseX, PdVector baseY, PdVector normal) Normalizes a vector frame consisting of two vectors v1, v2.

Methods inherited from class jvx.project.PjWorkshop

cancel, close, getDisplay, getDisplays, getGeometry, getMode, getSavedGeometry, getViewer, init, isModal, isStandalone, ok, removeGeometry, reset, setDisplay, setDisplays, setGeometry, setModal, setMode, setStandalone, setViewer, update

Methods inherited from class jv.object.PsObject

addInspector, addUpdateListener, assureInspector, clearTag, clone, clone, clone, copy, getFather, getInfoPanel, getInspector, getName, getNumObjects, getSymbol, hasInspector, hasTag, hasUpdateListener, instanceOf, instanceOf, newInspector, newInspector, removeInspector, removeInspector, removeUpdateListener, setName, setParent, setSymbol, setTag, toString, updatePanels

Methods inherited from class java.lang.Object

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

Methods inherited from interface jv.object.PsUpdateIf

getFather, getName, setParent

Field Detail

m_useConvolutionMask

public static boolean m_useConvolutionMask

This flag specifies if all edges will be weighted equally or if edges that are closer to the center of the ball get higher weight. At least on tubular surfaces the convolution mask yield much worse results, so I turned the mask off again (which is also in line with Morvan et al.). A stencil which assigns smaller weights to outer edges also has to visit more edges to have the same "average distance of an edge" than an unweighted scheme. Therefore, the radius can be chosen smaller when the convolution mask is off, which is much faster. (fk)

Constructor Detail

PwShapeOperator

public PwShapeOperator()

Default constructor

Method Detail

isEnabledConvolution

public static boolean isEnabledConvolution()

Check if convolution with a weighting mask is enabled.

Author:

Felix Kaelberer

Version:

23.10.2008, 1.00 created (fk)

enableConvolution

public static void enableConvolution(boolean useConvolution)

Use a weighting mask.

Author:

Felix Kaelberer

Version:

23.10.2008, 1.00 created (fk)

isEnabledAbsoluteValue

public static boolean isEnabledAbsoluteValue()

Check if absolute curvature values are used for curvature tensor calculation.

Author:

Felix Kaelberer

Version:

23.10.2008, 1.00 created (fk)

enableAbsoluteValue

public static void enableAbsoluteValue(boolean useAbsoluteValue)

Use absolute curvature values are used for curvature tensor calculation. This is useful if only directions of curvatures are needed.

Author:

Felix Kaelberer

Version:

23.10.2008, 1.00 created (fk)

getShapeOperator

public static PdMatrix[] getShapeOperator(PgElementSet geom,
                                          double radius,
                                          boolean vertexBased,
                                          PdMatrix[] shape)

Calculate the shape operator for the whole geometry geom. The shape operator is being calculated for every vertex or every element depending on vertexBased. The shape operator is calculated over every edge within a Euclidean ball of radius radius by adding the curvature (the signed angle between face normals) weighted by the length of the edge within the ball, divided by the total area of the surface enclosed by the ball.

Parameters:

geom - A PgElementSet to work on.

radius - The radius of the ball determining the edges to be included in the calculation of the shape operator.

vertexBased - If true, calculates shape operator for every vertex, if false, calculate shape operator for every element

shape - An PdMatrix array of length equal to the number of vertices or elements, depending on vertexBased, may be null.

Version:

23.10.2008, 1.10 revised (fk) Display progress in the status bar.

getShapeOperator

public static PdMatrix getShapeOperator(PgElementSet geom,
                                        int vertexInd,
                                        int elemInd,
                                        double radius,
                                        PdMatrix shape)

Calculates the shape operator for the vertex with index vertexInd of the PgElementSet geom and stores it in the PdMatrix shape. Normals of the geometry must exist.

Parameters:

geom - A PgElementSet of which the shape operator is to be calculated.

vertexInd - The index of the vertex which shape operator shall be calculated.

elemInd - Index of one element containing the vertex with index vertexInd, maybe -1, but then a linear search is required to find one.

radius - The radius of the ball determining the edges to be included in the calculation of the shape operator of the vertex.

shape - A possibly null reference to a PdMatrix object in which the shape operator for the vertex will be stored.

Author:

Philip Hornig, Felix Kaelberer

Version:

06.05.2008, 1.00 revised (fk) simplified, moved code to makeShapeOperator. 00.12.2006, 1.00 created (ph)

getShapeOperator

public static PdMatrix getShapeOperator(PgElementSet geom,
                                        PdBary bary,
                                        double radius,
                                        PdMatrix shape)

Calculates the shape operator for the point on the PgElementSet geom within the element with index elementInd given by the barycentric coordinates baryCoords and stores it in the PdMatrix shape.

Parameters:

geom - A PgElementSet of which the shape operator is to be calculated.

bary - PdBary containing the relevant element index and barycentric coordinates of the center vertex

radius - The radius of the ball determining the edges to be included in the calculation of the shape operator of any given vertex.

shape - A possibly null reference to a PdMatrix object in which the shape operator for the point will be stored.

Author:

Philip Hornig, Felix Kaelberer

Version:

06.05.2008, 1.00 revised (fk) simplified, moved code to makeShapeOperator. 00.12.2006, 1.00 created (ph)

getShapeOperator

public static PdMatrix getShapeOperator(PgElementSet geom,
                                        int elementInd,
                                        double radius,
                                        PdMatrix shape)

Calculates the shape operator for the element with elementInd of the PgElementSet geom. The result will be the shape operator of the barycentric center of the element.

Parameters:

geom - A PgElementSet of which the shape operator is to be calculated.

elementInd - The element containing the point of which the shape operator shall be calculated.

radius - The radius of the ball determining the edges to be included in the calculation of the shape operator of any given vertex.

shape - A possibly null reference to a PdMatrix object in which the shape operator for the point will be stored.

getPrincipalCurvatures

public static void getPrincipalCurvatures(PgElementSet geom,
                                          PdMatrix[] shape,
                                          PdVector[] pcValues,
                                          PdVector[][] pcDirections,
                                          boolean projectToTangentPlane,
                                          boolean vertexBased)

Computes the principal curvatures and directions at each vertex of the surface. The curvatures are integrated quantities. To get a piecewise linear shape operator use PnMassMatrix.multInvMassMatrix(PgElementSet, PdMatrix[], boolean). If only the only the direction or the values are needed, the other argument can be null.

Parameters:

geom - geometry to operate on.

pcValues - array with length 2 and vector length equal to the number of vertices.

pcDirections - array with length [2][nov] where nov is the number of vertices. Each vector must have dimension equal to the dimension of the ambient space.

shape - array of length equal to the number of vertices of the geometry.

makeElementBasedPrincipalCurvatures

public static PgVectorField[] makeElementBasedPrincipalCurvatures(PgElementSet geom,
                                                                  PdVector[] curvatureValues,
                                                                  boolean bIntegrated)

Make element based principal curvature vector fields.

Parameters:

geom - Given geometry.

curvatureValues - Output vector for curvature values. Dimension [numElements] or null.

bIntegrated - If true, computes the curvatures integrated over the actual element.

Author:

Matthias Nieser

Version:

04.10.06, 1.30 revised (fk) Moved to PnUtil.
04.10.06, 1.20 revised (fk) Return PgVectorField[] instead of PgFrameField.
20.07.06, 1.10 revised (mn) Moved to PnFrameField and extract content to submethods.
00.00.06, 1.00 created (mn)

makeVertexBasedPrincipalCurvatures

public static PgVectorField[] makeVertexBasedPrincipalCurvatures(PgElementSet geom,
                                                                 PdVector[] curvatures,
                                                                 boolean bIntegrated)

Make vertex based principal curvature vector fields. They are assembled in a frame field defined on the surface.

The field is returned as PgVectorField[] because PgFrameField does not support vertex based vectors yet.

Parameters:

geom - Given geometry.

bIntegrated - If true, computes the curvatures integrated over the actual element.

Author:

Matthias Nieser

Version:

10.08.06, 1.00 created (mn)

makeElementBasedPrincipalCurvatures

public static PgVectorField[] makeElementBasedPrincipalCurvatures(PgElementSet geom,
                                                                  PdVector[] curvatureValues)

Make element based principal curvature vector fields with an automatic calculated integration radius. It is r = 5*average edge length of the mesh.

Parameters:

geom - Given geometry.

Author:

Matthias Nieser

Version:

22.01.07, 1.00 created (mn)

makeElementBasedPrincipalCurvatures

public static PgVectorField[] makeElementBasedPrincipalCurvatures(PgElementSet geom,
                                                                  PdVector[] curvatureValues,
                                                                  double radius)

Make element based principal curvature vector fields.

Parameters:

geom - Given geometry.

Author:

Matthias Nieser

Version:

24.10.06, 1.00 created (mn)

makeVertexBasedPrincipalCurvatures

public static PgVectorField[] makeVertexBasedPrincipalCurvatures(PgElementSet geom,
                                                                 PdVector[] curvatures,
                                                                 double radius)

Make vertex based principal curvature vector fields.

Parameters:

geom - Given geometry.

Author:

Matthias Nieser

Version:

24.10.06, 1.00 created (mn)

calcEigensystem

public static PdVector[] calcEigensystem(PdMatrix matrix,
                                         PdVector normal,
                                         PdVector[] eigenVectors,
                                         PdVector eigenValues)

Calculate the eigenvectors of the shape operator restricted to a given plane. The element [0] will contain the eigenvector of the absolute bigger eigenvalue.

Parameters:

matrix - 3x3 matrix representing the shape operator.

normal - Normal vector to the plane.

eigenVectors - Preallocated memory for eigenvectors. May be null.

Author:

Matthias Nieser

makeTrustFunction

public static PdVector makeTrustFunction(PgVectorField vf,
                                         PdVector[] curvatures,
                                         boolean useSmoothProperty)

Computes a scalar function indicating, how trusted the curvature information are in the actual point. Curvatures are treated as "trusted" if the curvature values k_1 and k_2 are not equal. Additionally, if the "smoothProperty" is used, curvatures are treated as less trusted at point where they are less smooth.

Parameters:

vf - TODO

curvatures - minimal and maximal curvature value of field.

Returns:

A boolean array whether the elements are trusted.

Author:

Felix Kaelberer

Version:

08.02.10, 2.10 revised (fk) fixed: least trusted angle is 90 degrees, as principal curv dirs are unsigned.
16.09.09, 2.00 revised (mn) Moved function smoothing to external method and moved method to dev.
17.06.09, 1.10 revised (mn) Add parameter for smoothProperty and smoothFunction.
17.06.09, 1.00 created (fk)

normalizeFrame

public static void normalizeFrame(PdVector v1,
                                  PdVector v2,
                                  PdVector baseX,
                                  PdVector baseY,
                                  PdVector normal)

Normalizes a vector frame consisting of two vectors v1, v2. The vectors will be normalized to a length of 1. If one vector is (nearly) 0, it will be set to the 90 degrees rotated other vector. If both are 0, an arbitrary orthonormal frame will be returned. The input vectors (baseX, baseY) must be an orthonormal frame of TM, normal the normal vector.

Author:

Matthias Nieser

Version:

09.03.15, 2.00 revised (kp) Moved to PwShapeOperator from devCovering.PnFrameField.
08.08.06, 1.00 created (mn)