jvx.geom
Class PwCurvature

java.lang.Object
  jv.object.PsObject
      jvx.geom.PwCurvature

All Implemented Interfaces:

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

public class PwCurvature

extends PsObject

Compute various discrete curvature terms of a polyhedral surface.

See Also:

PgElementSet, Serialized Form

Field Summary

Fields inherited from class jv.object.PsObject

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

Constructor Summary

PwCurvature()

Method Summary

static double	getGaussCurvature(PgElementSet geom, int aVertexInd) Get Gauss curvature at vertex with given index.
static double	getGaussCurvature(PgElementSet geom, PdVector gauss) Compute discrete Gauss curvature at all vertices, and return total interior Gauss curvature.
static boolean	getMeanCurvature(PgElementSet geom) Compute and assign vertex normals as mean curvature vectors.
static PdVector	getMeanCurvature(PgElementSet geom, PdVector mean) Compute the mean curvature at all vertices.
static PdVector[]	getMeanCurvature(PgElementSet geom, PdVector[] meanVec) Compute discrete mean curvature at all vertices.
static void	getPrincipalCurvatures(PgElementSet geom) Computes the principal curvatures and directions at each vertex of the surface and add two vector fields to the surface.
static void	getPrincipalCurvatures(PgElementSet geom, boolean divideByAreaOfStar) Computes the principal curvatures and directions at each vertex of the surface and add two vector fields to the surface.
static void	getPrincipalCurvatures(PgElementSet geom, PdMatrix[] shape, PdVector[] pcValues, PdVector[][] pcDirections) Computes the principal curvatures and directions at each vertex of the surface.
static void	getPrincipalCurvatures(PgElementSet geom, PdMatrix[] shape, PdVector[] pcValues, PdVector[][] pcDirections, boolean orderByAbsVal) Computes the principal curvatures and directions at each vertex of the surface.
static void	getPrincipalCurvatures(PgElementSet geom, PdVector[] pcValues, PdVector[][] pcDirections) Computes the principal curvatures and directions at each vertex of the surface.
static PdMatrix[]	getShapeOperator(PgElementSet geom, double d)
static PdMatrix[]	getShapeOperator(PgElementSet geom, PdMatrix[] shape) Computes the shape operator at each vertex of the surface, represented as a (d,d) matrix where d is the dimension of the ambient space.
static PdMatrix[]	getShapeOperator(PgElementSet geom, PdMatrix[] shape, boolean projectToTangentPlane) Computes the shape operator at each vertex of the surface, represented as a (d,d) matrix where d is the dimension of the ambient space.
static void	makeColorFromGaussCurvature(PgElementSet geom) Show discrete Gauss curvature at all vertices and elements.

Methods inherited from class jv.object.PsObject

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

Methods inherited from class java.lang.Object

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

Constructor Detail

PwCurvature

public PwCurvature()

Method Detail

makeColorFromGaussCurvature

public static void makeColorFromGaussCurvature(PgElementSet geom)

Show discrete Gauss curvature at all vertices and elements. Method calls getGaussCurvature(PgElementSet,PdVector).

getGaussCurvature

public static double getGaussCurvature(PgElementSet geom,
                                       int aVertexInd)

Get Gauss curvature at vertex with given index. HACK: Method is not implemented yet.

getGaussCurvature

public static double getGaussCurvature(PgElementSet geom,
                                       PdVector gauss)

Compute discrete Gauss curvature at all vertices, and return total interior Gauss curvature. If argument array is null or wrong size, it is created or its length is adjusted. Curvature is computed only for vertices which are referenced by elements. If a vertex is not reference, then its curvature value is 0. Curvature of boundary vertices is defined 0, therefore method requires a correct neighbour structure.

Note, polygonal faces with m>3 vertices are triangulated on the fly by cutting off the vertex with smallest vertex angle successively. This tries to ensure that the Gauss curvature is independent of the numbering of vertices inside an element, as it would depend on if we would use subtriangles {v[0],v[j],v[j+1]}.

If geometry has elements with more than three edges then we need the element normals for triangulating those elements. If the element normals do not exist in such a case, then we generate them using makeElementNormals().

Returns:

total Gauss curvature

getMeanCurvature

public static PdVector[] getMeanCurvature(PgElementSet geom,
                                          PdVector[] meanVec)

Compute discrete mean curvature at all vertices. If argument array is null or wrong size, it is created or its length is adjusted. Curvature is computed only for vertices which are referenced by elements. If a vertex is not reference, then its curvature value is 0. Curvature of boundary vertices is defined 0, therefore method requires correct neighbour structure.

Returns:

array of mean curvature vectors, one vector per vertex

getMeanCurvature

public static boolean getMeanCurvature(PgElementSet geom)

Compute and assign vertex normals as mean curvature vectors. Showing of vertex normals must be enabled elsewhere.

Returns:

true on success.

getMeanCurvature

public static PdVector getMeanCurvature(PgElementSet geom,
                                        PdVector mean)

Compute the mean curvature at all vertices.

Careful: If array 'mean' is too small then a new array with correct size is created, i.e. the array is not expanded.

Method requires existence of correct vertex normals to compute the sign. Mean curvature is negative of mean curvature vector has negative scalar product with vertex normal.

Returns:

vector with a scalar mean curvature value per vertex

getShapeOperator

public static PdMatrix[] getShapeOperator(PgElementSet geom,
                                          PdMatrix[] shape)

Computes the shape operator at each vertex of the surface, represented as a (d,d) matrix where d is the dimension of the ambient space. The operator is an integrated quatity, the matrix at each vertex represents an integral of the shape operator over the star of the vertex. To get a piecewise linear shape operator use PnMassMatrix.multInvMassMatrix(PgElementSet, PdMatrix[], boolean).

getShapeOperator

public static PdMatrix[] getShapeOperator(PgElementSet geom,
                                          PdMatrix[] shape,
                                          boolean projectToTangentPlane)

Computes the shape operator at each vertex of the surface, represented as a (d,d) matrix where d is the dimension of the ambient space. The operator is an integrated quatity, the matrix at each vertex represents an integral of the shape operator over the star of the vertex. To get a piecewise linear shape operator use PnMassMatrix.multInvMassMatrix(PgElementSet, PdMatrix[], boolean). If the projection is enabled each matrix is transformed such that the trace of the matrix is preserved and = 0 is valid, where n is the vertex normal.

getShapeOperator

public static PdMatrix[] getShapeOperator(PgElementSet geom,
                                          double d)

getPrincipalCurvatures

public static void getPrincipalCurvatures(PgElementSet geom,
                                          PdVector[] pcValues,
                                          PdVector[][] pcDirections)

Computes the principal curvatures and directions at each vertex of the surface. The curvatures are integrated quatities. 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.

getPrincipalCurvatures

public static void getPrincipalCurvatures(PgElementSet geom)

Computes the principal curvatures and directions at each vertex of the surface and add two vector fields to the surface. Each vector has the points into a principal curvature direction and has length according to the absolute of the principal curvature value. The principal curvatures at a vertex represents an integral over the star of a vertex. This means the value at the vertex depends on the size of the star of the vertex. To get principal curvatures that independent of the size of the star use getPrincipalCurvatures(PgElementSet, boolean). }.

getPrincipalCurvatures

public static void getPrincipalCurvatures(PgElementSet geom,
                                          boolean divideByAreaOfStar)

Computes the principal curvatures and directions at each vertex of the surface and add two vector fields to the surface. Each vector has the points into a principal curvature direction and has length according to the absolute of the principal curvature value. The principal curvatures at a vertex represents an integral over the star of a vertex. This means the value at the vertex depends on the size of the star of the vertex. To get principal curvatures that independent of the size of the star set the argument divideByAreaOfStar = true.

getPrincipalCurvatures

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

Computes the principal curvatures and directions at each vertex of the surface. The curvatures are integrated quatities. 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. This argument can optionally be null.

getPrincipalCurvatures

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

Computes the principal curvatures and directions at each vertex of the surface. The curvatures are integrated quatities. 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. This argument can optionally be null.

orderByAbsVal - true - principal curvature are ordered by their absolute value.