Polygon3D

java.lang.Object
- org.edisonwj.draw3d.Polygon3D

All Implemented Interfaces:

Draw3DDefaults
```
public class Polygon3D
extends java.lang.Object
implements Draw3DDefaults
```
Polygon3D class captures information defining a Polygon3D instantiation with: - Point3D array defining the vertices of the polygon (in user coordinate scale) - Specified or computed a, b, c, d coefficients of the plane equation: ax + by + cz = d - Computed distance to origin from associated plane - normal vector of the plane - unit normal vector of the plane - Boolean flag, drawEdges, indicating whether to draw polygon edges - Boolean flag, drawVertices, indicating whether to draw polygon vertices - Boolean flag, drawVertexLabels, indicating whether to draw polygon vertex labels - PhongMaterial (optional) for filling polygon - PhongMaterial (optional) for edge color - DrawMode setting (optional) - Cullface setting (optional) The Polygon3D object is drawn using a custom polygon MeshView. The class implements defaults specified in Draw3DDefaults.

Version:

1.01 August 2015

Author:

William Edison

Field Summary
- Fields inherited from interface org.edisonwj.draw3d.Draw3DDefaults
  AMBIENT_LIGHT_ON, ARROW_POINT_HEIGHT, ARROW_POINT_RADIUS, ARROW_RADIUS, AV_POINT_DIVISIONS, AXIS_LENGTH, AXIS_RADIUS, BACKGROUND_COLOR, BOUNDRY_RADIUS, CAMERA_FAR_CLIP, CAMERA_INITIAL_DISTANCE, CAMERA_INITIAL_X_ANGLE, CAMERA_INITIAL_Y_ANGLE, CAMERA_NEAR_CLIP, CONE_DIVISIONS, CUMULATE_DEFAULT, CUMULATE_MANUAL_DEFAULT, CYLINDER_DIVISIONS, DEFAULT_ORIGIN, EDGE_RADIUS, EPSILON, LABEL_FONT, LABEL_FONT_SIZE, LINE_RADIUS, MIN_MAX_X, MIN_MAX_Y, MIN_MAX_Z, MOUSE_SPEED, OVAL_DIVISIONS, POINT_LIGHT_1_X, POINT_LIGHT_1_Y, POINT_LIGHT_1_Z, POINT_LIGHT_2_X, POINT_LIGHT_2_Y, POINT_LIGHT_2_Z, POINT_LIGHT_ON, POINT_SIZE, ROTATION_SPEED, SCENE_HEIGHT, SCENE_WIDTH, SCROLL_DELTA, SCROLL_FACTOR, SHOW_AXES, SHOW_BOUNDARY_CUBE, SHOW_DEFAULT_GRID, SHOW_TICK_MARKS, SHOW_X_Y_ONLY, SHOW_Z_AXIS_UP, SPHERE_DIVISIONS, TICK_MARK_LENGTH, TICK_MARK_RADIUS, VECTOR_POINT_HEIGHT, VECTOR_POINT_RADIUS, VECTOR_RADIUS, VERTEX_SIZE

Constructor Summary

Constructors
Constructor and Description
`Polygon3D(javafx.geometry.Point3D[] v)` Constructs a Polygon3D object given a Point3d[] Array containing polygon vertices.
`Polygon3D(javafx.geometry.Point3D[] v, boolean drawEdges, boolean drawVertices, boolean drawVertexLabels)` Constructs a Polygon3D object given a Point3d[] Array containing the polygon vertices, drawEdges flag, drawVertices flag, drawVertexLabels, and PhongMaterial.
`Polygon3D(javafx.geometry.Point3D[] v, javafx.scene.paint.PhongMaterial m)` Constructs a Polygon3D object given a Point3d[] Array containing the polygon vertices and PhongMaterial.
`Polygon3D(java.lang.String lineString)` Constructs a Polygon3D object given specification of the parameters in Save Data File format.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`changeXYZ(double x, double y, double z)` Modifies each vertex xyz coordinate tuple by adding to it the x, y, and z parameter values, updating the v array set of Polygon vertices.
`boolean`	`checkLeft(javafx.geometry.Point3D a, javafx.geometry.Point3D b, javafx.geometry.Point3D c)` Provides an indication when traversing the Point3D Polygon vertices from a to b to c, as to whether the path turns left or right when going from the side ab to vertex c.
`int`	`findLongestComponent()` Finds the "main plane", i.e.
`Triangle3D[]`	`findPolygonTriangles(int[][] tri)`
`javafx.scene.shape.CullFace`	`getCullFace()` Gets the Polygon CullFace property
`double`	`getD()` Returns the d coefficient of the plane equation of the Polygon ax + by + cz = d
`boolean`	`getDrawEdges()` Gets the Polygon drawEdges flag
`javafx.scene.shape.DrawMode`	`getDrawMode()` Gets the Polygon DrawMode property
`boolean`	`getDrawVertexLabels()` Gets the Polygon drawVertexLabels flag
`boolean`	`getDrawVertices()` Gets the Polygon drawVertices flag
`javafx.scene.paint.PhongMaterial`	`getEdgeMaterial()` Gets the Polygon edgeMaterial property
`javafx.scene.paint.PhongMaterial`	`getMaterial()` Gets the Polygon PhongMaterial property
`Vector3D`	`getNormal()` Gets the normal vector for the Plane of the Polygon
`double`	`getP()` Returns the distance to the origin from the plane of the Triangle
`Vector3D`	`getUnitNormal()` Gets the unit normal vector for the plane of the Polygon based on its vertices
`javafx.geometry.Point3D[]`	`getV()` Gets the Point3D array of vertices defining the Polygon
`double`	`getVolumeSign()` Gets the volumeSign field for the Polygon.
`boolean`	`isConvexPoly()` Provides an indication as to whether the Polygon specified by the Point3D array, v, of vertices is convex
`int`	`isInAxisPlane()` Provides an indication as to whether the Polygon determined by Point3D array v lies in a plane determined by the coordinate axes.
`boolean`	`isPlanar()` Provides an indication as to whether the Point3D array v contains a set of Polygon vertices that lie in the plane specified by coordinates a, b, c, d.
`double`	`meanX(javafx.geometry.Point3D[] vi)` Returns the mean x coordinate value from the provided set of Polygon vertices.
`double`	`meanY(javafx.geometry.Point3D[] vi)` Returns the mean y coordinate value from the provided set of Polygon vertices.
`double`	`meanZ(javafx.geometry.Point3D[] vi)` Returns the mean z coordinate value from the provided set of Polygon vertices.
`java.lang.String`	`outString()` Returns a String containing all Polygon3D values for saving to a data file.
`void`	`reverse()` Reverses the order of vertices in array v
`void`	`scale(double d)` Modifies each vertex xyz coordinate tuple by multiplying it by the d parameter value, updating the v array set of Polygon vertices.
`void`	`setCullFace(javafx.scene.shape.CullFace cf)` Sets the Polygon CullFace property
`void`	`setDrawEdges(boolean b)` Sets the Polygon drawEdges flag
`void`	`setDrawMode(javafx.scene.shape.DrawMode dm)` Sets the Polygon DrawMode property
`void`	`setDrawVertexLabels(boolean b)` Sets the Polygon drawVertexLabels flag
`void`	`setDrawVertices(boolean b)` Sets the Polygon drawVertices flag
`void`	`setEdgeMaterial(javafx.scene.paint.PhongMaterial edgeMaterial)` Sets the Polygon edgeMaterial property
`void`	`setMaterial(javafx.scene.paint.PhongMaterial m)` Sets the Polygon PhongMaterial property
`void`	`setOrientation()` Sets the volumeSign field value that indicates the orientation of the Polygon based on the z-axis coordinate value of the unit normal vector and the sign of the coefficient d.
`void`	`setX(double a, double b, double c, double d)` Given a set of y and z coordinates, this method computes a corresponding x coordinate resulting in an update to v, the array of Polygon vertices.
`void`	`setY(double a, double b, double c, double d)` Given a set of x and z coordinates, this method computes a corresponding y coordinate resulting in an update to v, the array of Polygon vertices.
`void`	`setZ(double a, double b, double c, double d)` Given a set of x and y coordinates, this method computes a corresponding z coordinate resulting in an update to v, the array of Polygon vertices.
`void`	`sortVertices()` Sorts the array of vertices v Adapted from: Gernot Hoffman, Cube Plane Intersection, http://docs-hoffmann.de/cubeplane12112006.pdf
`java.lang.String`	`toString()` Returns a String for printing all Polygon3D values
`int[][]`	`triangulateConvexPolygon()` Triangulate convex polygon
`int[][]`	`triangulatePolygon()` Triangulate polygon defined by the Point3D[] v array of polygon vertices in counter clockwise order.
`double`	`volume(javafx.geometry.Point3D a, javafx.geometry.Point3D b, javafx.geometry.Point3D c)` Returns the volume of the tetrahedron with vertices a, b, c, and d (the origin at 0,0,0).

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

- Constructor Detail
  - Polygon3D
```
public Polygon3D(javafx.geometry.Point3D[] v)
```
    Constructs a Polygon3D object given a Point3d[] Array containing polygon vertices.
    
    Parameters:
    
    v - Point3D[] Array containing the polygon vertices
  - Polygon3D
```
public Polygon3D(javafx.geometry.Point3D[] v,
                 javafx.scene.paint.PhongMaterial m)
```
    Constructs a Polygon3D object given a Point3d[] Array containing the polygon vertices and PhongMaterial.
    
    Parameters:
    
    v - Point3D[] Array containing the polygon vertices
    
    m - PhongMaterial determining polygon color
  - Polygon3D
```
public Polygon3D(javafx.geometry.Point3D[] v,
                 boolean drawEdges,
                 boolean drawVertices,
                 boolean drawVertexLabels)
```
    Constructs a Polygon3D object given a Point3d[] Array containing the polygon vertices, drawEdges flag, drawVertices flag, drawVertexLabels, and PhongMaterial.
    
    Parameters:
    
    v - Point3D[] Array containing the polygon vertices
    
    drawEdges - Flag indicating to draw polygon edges
    
    drawVertices - Flag indicating to draw polygon vertices
    
    drawVertexLabels - Flag indicating to draw polygon vertex labels
  - Polygon3D
```
public Polygon3D(java.lang.String lineString)
```
    Constructs a Polygon3D object given specification of the parameters in Save Data File format.
    
    Parameters:
    
    lineString - Polygon: format data string
- Method Detail
  - getV
```
public javafx.geometry.Point3D[] getV()
```
    Gets the Point3D array of vertices defining the Polygon
    
    Returns:
    
    v Point3D array of Polygon vertices
  - getDrawEdges
```
public boolean getDrawEdges()
```
    Gets the Polygon drawEdges flag
    
    Returns:
    
    drawEdges
  - setDrawEdges
```
public void setDrawEdges(boolean b)
```
    Sets the Polygon drawEdges flag
    
    Parameters:
    
    b - drawEdges value
  - getDrawVertices
```
public boolean getDrawVertices()
```
    Gets the Polygon drawVertices flag
    
    Returns:
    
    drawVertices
  - setDrawVertices
```
public void setDrawVertices(boolean b)
```
    Sets the Polygon drawVertices flag
    
    Parameters:
    
    b - drawVertices value
  - getDrawVertexLabels
```
public boolean getDrawVertexLabels()
```
    Gets the Polygon drawVertexLabels flag
    
    Returns:
    
    drawVertexLabels
  - setDrawVertexLabels
```
public void setDrawVertexLabels(boolean b)
```
    Sets the Polygon drawVertexLabels flag
    
    Parameters:
    
    b - drawVertexLabels value
  - getMaterial
```
public javafx.scene.paint.PhongMaterial getMaterial()
```
    Gets the Polygon PhongMaterial property
    
    Returns:
    
    m PhongMaterial value of the Polygon
  - setMaterial
```
public void setMaterial(javafx.scene.paint.PhongMaterial m)
```
    Sets the Polygon PhongMaterial property
    
    Parameters:
    
    m - PhongMaterial property of the Polygon
  - getEdgeMaterial
```
public javafx.scene.paint.PhongMaterial getEdgeMaterial()
```
    Gets the Polygon edgeMaterial property
    
    Returns:
    
    edgeMaterial PhongMaterial value for drawing polygon edges
  - setEdgeMaterial
```
public void setEdgeMaterial(javafx.scene.paint.PhongMaterial edgeMaterial)
```
    Sets the Polygon edgeMaterial property
    
    Parameters:
    
    edgeMaterial - PhongMaterial value for drawing polygon edges
  - getDrawMode
```
public javafx.scene.shape.DrawMode getDrawMode()
```
    Gets the Polygon DrawMode property
    
    Returns:
    
    dm DrawMode property of the Polygon
  - setDrawMode
```
public void setDrawMode(javafx.scene.shape.DrawMode dm)
```
    Sets the Polygon DrawMode property
    
    Parameters:
    
    dm - DrawMode property of the Polygon
  - getCullFace
```
public javafx.scene.shape.CullFace getCullFace()
```
    Gets the Polygon CullFace property
    
    Returns:
    
    cf CullFace property of the Polygon
  - setCullFace
```
public void setCullFace(javafx.scene.shape.CullFace cf)
```
    Sets the Polygon CullFace property
    
    Parameters:
    
    cf - CullFace property of the Polygon
  - getNormal
```
public Vector3D getNormal()
```
    Gets the normal vector for the Plane of the Polygon
    
    Returns:
    
    normal Vector3D normal vector of the Plane
  - getUnitNormal
```
public Vector3D getUnitNormal()
```
    Gets the unit normal vector for the plane of the Polygon based on its vertices
    
    Returns:
    
    unitNormal Vector3D unit normal vector for the plane of the Polygon
  - getD
```
public double getD()
```
    Returns the d coefficient of the plane equation of the Polygon ax + by + cz = d
    
    Returns:
    
    d Double coefficent d
  - getP
```
public double getP()
```
    Returns the distance to the origin from the plane of the Triangle
    
    Returns:
    
    p Double distance from the Polygon plane to the origin
  - setOrientation
```
public void setOrientation()
```
    Sets the volumeSign field value that indicates the orientation of the Polygon based on the z-axis coordinate value of the unit normal vector and the sign of the coefficient d. The volumeSign field is used in interpreting the result of the volume() to determine whether vertices are in clockwise or counterclockwise order.
  - getVolumeSign
```
public double getVolumeSign()
```
    Gets the volumeSign field for the Polygon.
    
    Returns:
    
    volumeSign Double value of the volumeSign field.
  - setX
```
public void setX(double a,
                 double b,
                 double c,
                 double d)
```
    Given a set of y and z coordinates, this method computes a corresponding x coordinate resulting in an update to v, the array of Polygon vertices. The resulting polygon is in the plane determined by the a, b, c, d input parameters that have the relationship ax + by + cz = d.
    
    Parameters:
    
    a - Double value of the a coefficient of the plane equation
    
    b - Double value of the b coefficient of the plane equation
    
    c - Double value of the c coefficient of the plane equation
    
    d - Double value of the d coefficient of the plane equation
  - setY
```
public void setY(double a,
                 double b,
                 double c,
                 double d)
```
    Given a set of x and z coordinates, this method computes a corresponding y coordinate resulting in an update to v, the array of Polygon vertices. The resulting polygon is in the plane determined by the a, b, c, d input parameters that have the relationship ax + by + cz = d.
    
    Parameters:
    
    a - Double value of the a coefficient of the plane equation
    
    b - Double value of the b coefficient of the plane equation
    
    c - Double value of the c coefficient of the plane equation
    
    d - Double value of the d coefficient of the plane equation
  - setZ
```
public void setZ(double a,
                 double b,
                 double c,
                 double d)
```
    Given a set of x and y coordinates, this method computes a corresponding z coordinate resulting in an update to v, the array of Polygon vertices. The resulting polygon is in the plane determined by the a, b, c, d input parameters that have the relationship ax + by + cz = d.
    
    Parameters:
    
    a - Double value of the a coefficient of the plane equation
    
    b - Double value of the b coefficient of the plane equation
    
    c - Double value of the c coefficient of the plane equation
    
    d - Double value of the d coefficient of the plane equation
  - changeXYZ
```
public void changeXYZ(double x,
                      double y,
                      double z)
```
    Modifies each vertex xyz coordinate tuple by adding to it the x, y, and z parameter values, updating the v array set of Polygon vertices.
    
    Parameters:
    
    x - Double value to be added to each vertex x coordinate value
    
    y - Double value to be added to each vertex y coordinate value
    
    z - Double value to be added to each vertex z coordinate value
  - scale
```
public void scale(double d)
```
    Modifies each vertex xyz coordinate tuple by multiplying it by the d parameter value, updating the v array set of Polygon vertices.
    
    Parameters:
    
    d - Double value to be multiplied times each x, y, z coordinate value of the vertices
  - reverse
```
public void reverse()
```
    Reverses the order of vertices in array v
  - sortVertices
```
public void sortVertices()
```
    Sorts the array of vertices v Adapted from: Gernot Hoffman, Cube Plane Intersection, http://docs-hoffmann.de/cubeplane12112006.pdf
  - findLongestComponent
```
public int findLongestComponent()
```
    Finds the "main plane", i.e. the plane orthogonal to the longest component of the normal vector
    
    Returns:
    
    result 1 if x coordinate is longest result 2 if y coordinate is longest result 3 if z coordinate is longest
  - meanX
```
public double meanX(javafx.geometry.Point3D[] vi)
```
    Returns the mean x coordinate value from the provided set of Polygon vertices.
    
    Parameters:
    
    vi - Point3D array of vertices
    
    Returns:
    
    meanX Double mean x value from the provided set of Polygon vertices.
  - meanY
```
public double meanY(javafx.geometry.Point3D[] vi)
```
    Returns the mean y coordinate value from the provided set of Polygon vertices.
    
    Parameters:
    
    vi - Point3D array of vertices
    
    Returns:
    
    meanY Double mean y value from the provided set of Polygon vertices.
  - meanZ
```
public double meanZ(javafx.geometry.Point3D[] vi)
```
    Returns the mean z coordinate value from the provided set of Polygon vertices.
    
    Parameters:
    
    vi - Point3D array of vertices
    
    Returns:
    
    meanZ Double mean z value from the provided set of Polygon vertices.
  - isPlanar
```
public boolean isPlanar()
```
    Provides an indication as to whether the Point3D array v contains a set of Polygon vertices that lie in the plane specified by coordinates a, b, c, d.
    
    Returns:
    
    boolean value True if the points lie in a plan, otherwise false.
  - isInAxisPlane
```
public int isInAxisPlane()
```
    Provides an indication as to whether the Polygon determined by Point3D array v lies in a plane determined by the coordinate axes.
    
    Returns:
    
    0 if not in axis plane
  - isConvexPoly
```
public boolean isConvexPoly()
```
    Provides an indication as to whether the Polygon specified by the Point3D array, v, of vertices is convex
    
    Returns:
    
    boolean true if Polygon is convex
  - checkLeft
```
public boolean checkLeft(javafx.geometry.Point3D a,
                         javafx.geometry.Point3D b,
                         javafx.geometry.Point3D c)
```
    Provides an indication when traversing the Point3D Polygon vertices from a to b to c, as to whether the path turns left or right when going from the side ab to vertex c. The test determines whether the Polygon lies in an axes plane, and if so uses the sign of a two dimensional area calculation, and otherwise utilizes the sign of the volume() computation. Adapted from O'Rourke, Computational Geometry in C, p. 26-27.
    
    Parameters:
    
    a - Point3D Polygon vertex
    
    b - Point3D Polygon vertex
    
    c - Point3D Polygon vertex
    
    Returns:
    
    boolean true if left turn
  - volume
```
public double volume(javafx.geometry.Point3D a,
                     javafx.geometry.Point3D b,
                     javafx.geometry.Point3D c)
```
    Returns the volume of the tetrahedron with vertices a, b, c, and d (the origin at 0,0,0). The volume is signed and is positive if (a,b,c) form a counterclockwise circuit when viewed from the side away from d, so that the face normal determined by the right-hand rule points toward the outside. The volume(a, b, c) method is used to determine whether point c is to the left or right of line (a,b), i.e. is counterclockwise. Adapted from O'Rourke, Computational Geometry in C, p. 26-27.
    
    Parameters:
    
    a - Point3D specifying vertex a of the tetrahedron
    
    b - Point3D specifying vertex b of the tetrahedron
    
    c - Point3D specifying vertex c of the tetrahedron
    
    Returns:
    
    volume Double signed value of the volume as described above
  - findPolygonTriangles
```
public Triangle3D[] findPolygonTriangles(int[][] tri)
```
  - triangulateConvexPolygon
```
public int[][] triangulateConvexPolygon()
```
    Triangulate convex polygon
    
    Returns:
    
    tri int[][] array of indices of vertices forming the trianglulation of a convex polygon
  - triangulatePolygon
```
public int[][] triangulatePolygon()
```
    Triangulate polygon defined by the Point3D[] v array of polygon vertices in counter clockwise order. Adpapted from Ammeraal and Zang, Computer Graphics for Java Programmers, p. 44-45.
    
    Returns:
    
    tri int[v.length-2][3] array of indices of vertices forming the trianglulation of the polygon
  - outString
```
public java.lang.String outString()
```
    Returns a String containing all Polygon3D values for saving to a data file. The String is processed by the Polygon3D(String) constructor to recreate a Polygon3D object when reading a saved data file.
    
    Returns:
    
    String capturing all Cylinder3D field values
  - toString
```
public java.lang.String toString()
```
    Returns a String for printing all Polygon3D values
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    String for printing all Polygon3D field values

Class Polygon3D

Field Summary

Fields inherited from interface org.edisonwj.draw3d.Draw3DDefaults

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Polygon3D

Polygon3D

Polygon3D

Polygon3D

Method Detail

getV

getDrawEdges

setDrawEdges

getDrawVertices

setDrawVertices

getDrawVertexLabels

setDrawVertexLabels

getMaterial

setMaterial

getEdgeMaterial

setEdgeMaterial

getDrawMode

setDrawMode

getCullFace

setCullFace

getNormal

getUnitNormal

getD

getP

setOrientation

getVolumeSign

setX

setY

setZ

changeXYZ

scale

reverse

sortVertices

findLongestComponent

meanX

meanY

meanZ

isPlanar

isInAxisPlane

isConvexPoly

checkLeft

volume

findPolygonTriangles

triangulateConvexPolygon

triangulatePolygon

outString

toString