HalfEdge (Artisynth API documentation)

java.lang.Object
- maspack.geometry.Feature
- - maspack.geometry.HalfEdge

All Implemented Interfaces:

Boundable
```
public class HalfEdge
extends Feature
implements Boundable
```
Half-edge for 3D dimensional polyhedral objects. A half-edge is a directed edge between two counter-clockwise adjacent vertices of a face. Two adjacent half-edges together define a single edge.

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`ELEM_EDGE` Flag indicating that a HalfEdge corresponds to the edge of an underlying ``element''.
`Vertex3d`	`head`
`HalfEdge`	`opposite`
`Vertex3d`	`tail`

Fields inherited from class maspack.geometry.Feature
CELL, EDGE, FACE, FACET, HALF_EDGE, LINE_SEGMENT, TYPE_MASK, UNKNOWN, VERTEX_3D, VISITED

Constructor Summary

Constructors
Constructor and Description
`HalfEdge()`
`HalfEdge(Vertex3d head, HalfEdge opp, Face face)` Creates a new half-edge with a specified head vertex, opposite half-edge, and face.
`HalfEdge(Vertex3d head, Vertex3d tail, Face face)` Creates a new half-edge with a specified head vertex, tail vertex, and face.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`addAngleWeightedNormal(Vector3d res, HalfEdge he)`
`void`	`computeCentroid(Vector3d p)` Computed the centroid of this element.
`double`	`computeCovariance(Matrix3d C)` Computes covariance of this half edge and returns its length.
`double`	`computeEdgeUnitVec(Vector3d u)` Computes a unit vector for the edge associated with this half-edge, and returns the edge's length.
`void`	`computeUnitVec(Vector3d u)` Computes a unit vector in the direction of this edge, and returns the edge's length.
`void`	`computeVertexNormal(Vector3d nrm, boolean useRenderNormals)` Computes a normal for the head vertex of this half-edge, by averaging all the surrounding face normals starting with the face corresponding to this half edge, and ending when either a hard edge is encountered, or when all faces have been traversed.
`boolean`	`connectsFaces(Face f0, Face f1)` Returns `true` if this HalfEdge and its opposite connects faces `f0` and `f1`.
`static HalfEdge`	`createLineSegment(Vertex3d v1, Vertex3d v2)` Creates a pair of adjacent half-edges that together define a line segment connecting two vertices.
`double`	`dotDirection(Vector3d v1)` Computes the dot product between a vector v1 and a non-normalized vector in the direction of this half-edge.
`java.lang.String`	`faceStr()` Returns a string identifying this HalfEdge using the indices of its primary and opposite faces.
`Face`	`getFace()` Returns the face associated with this half-edge.
`Vertex3d`	`getHead()`
`int`	`getIndex()` Returns an index for this half-edge, computed as
`HalfEdge`	`getNext()`
`Face`	`getOppositeFace()` Returns the face opposite to this half-edge, if any
`Point3d`	`getPoint(int idx)` Returns the `idx`-th point associated with this element.
`HalfEdge`	`getPrimary()`
`double`	`getProjectionParameter(Point3d pnt)`
`Vertex3d`	`getTail()`
`boolean`	`isHard()`
`boolean`	`isPrimary()`
`HalfEdge`	`lastHardEdge()` Returns the last hard edge (if any) incident on this half-edge's head vertex, relative to this half-edge in a counter-clockwise direction about the vertex.
`double`	`length()` Returns the length of this half-edge.
`double`	`lengthSquared()` Returns the length squared of this half-edge.
`void`	`nearestPoint(Point3d nearest, Point3d pnt)` Determine nearest point to this feature
`int`	`numPoints()` Returns the number of points associated with this element, if any, or zero otherwise.
`java.lang.String`	`pointList()`
`static double`	`projectionParameter(Point3d p0, Point3d p1, Point3d px)` Computes the projection parameter of a point `px` with respect to a line defined by points `p0` and `p1`.
`void`	`setHard(boolean hard)`
`void`	`setNext(HalfEdge heNext)` Sets the next half-edge adjacent to this one (in a counter-clockwise sense).
`void`	`setPrimary(boolean primary)`
`double`	`sideProductDirection(Vector3d v1, Vector3d v2)` Computes the dot product of (v1 X dir) and v2, where dir is the vector from the head to the tail of this half-edge.
`void`	`updateBounds(Vector3d min, Vector3d max)` Updates the axis-aligned bounds of this element.
`java.lang.String`	`vertexStr()` Returns a string identifying this HalfEdge using the indices of its tail and head vertices.

Methods inherited from class maspack.geometry.Feature
checkFlag, clearFlag, clearVisited, getType, getTypeName, isVisited, setFlag, setVisited

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - ELEM_EDGE
```
public static final int ELEM_EDGE
```
    Flag indicating that a HalfEdge corresponds to the edge of an underlying ``element''. Used in FEM applications.
    
    See Also:
    
    Constant Field Values
  - head
```
public Vertex3d head
```
  - tail
```
public Vertex3d tail
```
  - opposite
```
public HalfEdge opposite
```
- Constructor Detail
  - HalfEdge
```
public HalfEdge()
```
  - HalfEdge
```
public HalfEdge(Vertex3d head,
                Vertex3d tail,
                Face face)
```
    Creates a new half-edge with a specified head vertex, tail vertex, and face.
    
    Parameters:
    
    head - head vertex
    
    tail - head vertex
    
    face - associated face
  - HalfEdge
```
public HalfEdge(Vertex3d head,
                HalfEdge opp,
                Face face)
```
    Creates a new half-edge with a specified head vertex, opposite half-edge, and face. The head vertex is assumed to correspond to the tail of the opposite half-edge. Both half-edges are set to be each other's opposites.
    
    Parameters:
    
    head - head vertex
    
    opp - opposite half-edge
    
    face - associated face
- Method Detail
  - isHard
```
public boolean isHard()
```
  - setHard
```
public void setHard(boolean hard)
```
  - setNext
```
public void setNext(HalfEdge heNext)
```
    Sets the next half-edge adjacent to this one (in a counter-clockwise sense).
    
    Parameters:
    
    heNext - next half-edge
  - createLineSegment
```
public static HalfEdge createLineSegment(Vertex3d v1,
                                         Vertex3d v2)
```
    Creates a pair of adjacent half-edges that together define a line segment connecting two vertices.
    
    Parameters:
    
    v1 - first vertex on the line segment
    
    v2 - second vertex on the line segment
    
    Returns:
    
    the half edge whose head is the first vertex
  - computeEdgeUnitVec
```
public double computeEdgeUnitVec(Vector3d u)
```
    Computes a unit vector for the edge associated with this half-edge, and returns the edge's length. The direction runs from the tail to the head if the half-edge is primary (i.e., isPrimary() returns true), and from the head to the tail otherwise. If the length of the edge is 0, all elements of the vector are set to 0.
    
    Parameters:
    
    u - returns the edge unit vector
  - computeUnitVec
```
public void computeUnitVec(Vector3d u)
```
    Computes a unit vector in the direction of this edge, and returns the edge's length. The direction is defined as running from the tail to the head. If the length of the edge is 0, all elements of the vector are set to 0.
    
    Parameters:
    
    u - returns the normalized direction vector
  - getFace
```
public Face getFace()
```
    Returns the face associated with this half-edge.
    
    Returns:
    
    associated face
  - getIndex
```
public int getIndex()
```
    Returns an index for this half-edge, computed as
```
 3 * faceIdx + edgeNum
 
```
    where faceIdx is the index of its face, and edgeNum is the edge number with respect to the face (with face.firstHalfEdge() corresponding to 0).
  - getOppositeFace
```
public Face getOppositeFace()
```
    Returns the face opposite to this half-edge, if any
    
    Returns:
    
    opposite face, or null.
  - lastHardEdge
```
public HalfEdge lastHardEdge()
```
    Returns the last hard edge (if any) incident on this half-edge's head vertex, relative to this half-edge in a counter-clockwise direction about the vertex. If there is no hard-edge incident on the vertex, null is returned.
  - computeVertexNormal
```
public void computeVertexNormal(Vector3d nrm,
                                boolean useRenderNormals)
```
    Computes a normal for the head vertex of this half-edge, by averaging all the surrounding face normals starting with the face corresponding to this half edge, and ending when either a hard edge is encountered, or when all faces have been traversed. Face traversal proceeds in a clockwise direction about the vertex.
  - dotDirection
```
public double dotDirection(Vector3d v1)
```
    Computes the dot product between a vector v1 and a non-normalized vector in the direction of this half-edge.
    
    Parameters:
    
    v1 - vector to dot with direction vector
    
    Returns:
    
    dot product
  - addAngleWeightedNormal
```
public void addAngleWeightedNormal(Vector3d res,
                                   HalfEdge he)
```
  - length
```
public double length()
```
    Returns the length of this half-edge.
    
    Returns:
    
    half-edge length
  - lengthSquared
```
public double lengthSquared()
```
    Returns the length squared of this half-edge.
    
    Returns:
    
    length squared
  - sideProductDirection
```
public double sideProductDirection(Vector3d v1,
                                   Vector3d v2)
```
    Computes the dot product of (v1 X dir) and v2, where dir is the vector from the head to the tail of this half-edge.
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    dot product
  - getHead
```
public final Vertex3d getHead()
```
  - getNext
```
public final HalfEdge getNext()
```
  - getTail
```
public final Vertex3d getTail()
```
  - pointList
```
public java.lang.String pointList()
```
  - isPrimary
```
public boolean isPrimary()
```
  - getPrimary
```
public HalfEdge getPrimary()
```
  - setPrimary
```
public void setPrimary(boolean primary)
```
  - updateBounds
```
public void updateBounds(Vector3d min,
                         Vector3d max)
```
    Description copied from interface: Boundable
    
    Updates the axis-aligned bounds of this element. The value in min and max should be decreased or increased, respectively, so that all spatial points associated with this element lie within the axis-aligned box defined by min and max.
    
    Specified by:
    
    updateBounds in interface Boundable
    
    Parameters:
    
    min - minimum values to be updated
    
    max - maximum values to be updated
  - computeCentroid
```
public void computeCentroid(Vector3d p)
```
    Description copied from interface: Boundable
    
    Computed the centroid of this element.
    
    Specified by:
    
    computeCentroid in interface Boundable
    
    Parameters:
    
    p - returns the computed centroid value.
  - computeCovariance
```
public double computeCovariance(Matrix3d C)
```
    Computes covariance of this half edge and returns its length.
    The formula was determined by substituting the the parametric form for x
```
 x = (1-s) p0 + s p1
 
```
    into the general formula for C
```
 C = \int_V \rho x x^T dV
 
```
    and evaluating the integral over the s interval [0,1].
    Specified by:
    
    computeCovariance in interface Boundable
    
    Parameters:
    
    C - returns the covariance
    
    Returns:
    
    length of the half edge
  - numPoints
```
public int numPoints()
```
    Description copied from interface: Boundable
    
    Returns the number of points associated with this element, if any, or zero otherwise. If the element has points, then it's spatial extent is assumed to be enclosed within their convex hull. At present, elements that do not have points cannot be enclosed within oriented bounding box (OBB) trees.
    
    Specified by:
    
    numPoints in interface Boundable
    
    Returns:
    
    number of points associated with this element
  - getPoint
```
public Point3d getPoint(int idx)
```
    Description copied from interface: Boundable
    
    Returns the idx-th point associated with this element.
    
    Specified by:
    
    getPoint in interface Boundable
    
    Parameters:
    
    idx - index of the point (must be on the range 0 to Boundable.numPoints()).
    
    Returns:
    
    idx-th point associated with this element. Must not be modified.
  - vertexStr
```
public java.lang.String vertexStr()
```
    Returns a string identifying this HalfEdge using the indices of its tail and head vertices.
    
    Returns:
    
    vertex-based identifying string
  - faceStr
```
public java.lang.String faceStr()
```
    Returns a string identifying this HalfEdge using the indices of its primary and opposite faces.
    
    Returns:
    
    face-based identifying string
  - connectsFaces
```
public boolean connectsFaces(Face f0,
                             Face f1)
```
    Returns true if this HalfEdge and its opposite connects faces f0 and f1.
  - projectionParameter
```
public static double projectionParameter(Point3d p0,
                                         Point3d p1,
                                         Point3d px)
```
    Computes the projection parameter of a point px with respect to a line defined by points p0 and p1. This is the value s such that
```
 pp = (1-s) p0 + s p1
 
```
    gives the projection of px-p0 onto the line. If p0 and p1 are identical, the method returns positive infinity.
    Parameters:
    
    p0 - first point defining the line
    
    p1 - second point defining the libe
    
    px - point for which the project parameter should be computed
    
    Returns:
    
    parameter s which projects px onto the line
  - getProjectionParameter
```
public double getProjectionParameter(Point3d pnt)
```
  - nearestPoint
```
public void nearestPoint(Point3d nearest,
                         Point3d pnt)
```
    Description copied from class: Feature
    
    Determine nearest point to this feature
    
    Specified by:
    
    nearestPoint in class Feature
    
    Parameters:
    
    nearest - populated nearest point
    
    pnt - point to check distance to

Class HalfEdge

Field Summary

Fields inherited from class maspack.geometry.Feature

Constructor Summary

Method Summary

Methods inherited from class maspack.geometry.Feature

Methods inherited from class java.lang.Object

Field Detail

ELEM_EDGE

head

tail

opposite

Constructor Detail

HalfEdge

HalfEdge

HalfEdge

Method Detail

isHard

setHard

setNext

createLineSegment

computeEdgeUnitVec

computeUnitVec

getFace

getIndex

getOppositeFace

lastHardEdge

computeVertexNormal

dotDirection

addAngleWeightedNormal

length

lengthSquared

sideProductDirection

getHead

getNext

getTail

pointList

isPrimary

getPrimary

setPrimary

updateBounds

computeCentroid

computeCovariance

numPoints

getPoint

vertexStr

faceStr

connectsFaces

projectionParameter

getProjectionParameter

nearestPoint