VoxelArray

java.lang.Object
- frink.graphics.VoxelArray

All Implemented Interfaces:

Field3DFloat
```
public class VoxelArray
extends java.lang.Object
implements Field3DFloat
```
This is a 3-D Voxel array which can be used to generate 3-D graphics. The voxel array consists of a fixed-sized 3-dimensional array of boolean values at integer coordinates.
The convention for most graphics is that you should round real-valued points to their closest integer value.
Bits are stored in the BiggerBitSet in Z-major order, then Y, then X. This means that it's usually most efficient to iterate over the z-axis in the outer loop for cache efficiency.
This is the main class for Frink's 3-D modeling routines. Most of its high-level modeling routines are here.

Author:

Alan Eliasen, eliasen@mindspring.com

Field Summary

Fields
Modifier and Type	Field and Description
`private long`	`area` The area of the XY plane.
`private int`	`offX` The offset of the x axis.
`private int`	`offY` The offset of the y axis.
`private int`	`offZ` The offset of the z axis.
`private int`	`sizeX` The size of the x axis.
`private int`	`sizeY` The size of the y axis.
`private int`	`sizeZ` The size of the z axis.
`private static double`	`TWOPI` 2 * pi
`private BiggerBitSet`	`voxels` The `BiggerBitSet` that contains all of the bits.

Constructor Summary

Constructors
Constructor and Description
`VoxelArray(int sizeX, int sizeY, int sizeZ)` Construct a VoxelArray with the specified size on each axis and each element set to false.
`VoxelArray(int sizeX, int sizeY, int sizeZ, boolean value)` Construct a VoxelArray with the specified size on each axis and each element set to the specified value.
`VoxelArray(int minX, int sizeX, int minY, int sizeY, int minZ, int sizeZ, boolean value)` Construct a VoxelArray with the specified minimum value and size on each axis and each element set to the specific value.
`VoxelArray(VoxelArray other)` Copy constructor.
`VoxelArray(VoxelArray other, boolean value)` Copy the dimensions but set every voxel to the specified value.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`add(VoxelArray b)` Adds the pixels in this VoxelArray that are true in VoxelArray b, modifying this VoxelArray in place.
`void`	`addAlongLine(VoxelArray b, int x1, int y1, int z1, int x2, int y2, int z2, int xc, int yc, int zc)` Adds the pixels in this VoxelArray by moving the VoxelArray b along a line and adding the points in VoxelArray b that are true, modifying this VoxelArray in place.
`Point3DDouble`	`centerOfMass()` Calculate the center of mass of all set voxels (assuming each voxel has the same density).
`private void`	`checkPoint(long x, long y, long z)` This method checks a point to see if it is within a valid range for this VoxelArray and throws an `IndexOutOfBoundsException` if it doesn't.
`static VoxelArray`	`construct(BoundingBox3DFloat bb, boolean value)` Construct a new rectangular VoxelArray that encloses the specific bounding box.
`static VoxelArray`	`construct(double x1, double x2, double y1, double y2, double z1, double z2, boolean value)` Construct a new rectangular VoxelArray that encloses the specific min and max coordinates.
`static VoxelArray`	`construct(Point3DIntList points)` Construct a new rectangular VoxelArray that represents the points in the Point3DIntList.
`long`	`countSetBits()` Counts the number of set bits.
`static VoxelArray`	`cube(double x1, double x2, double y1, double y2, double z1, double z2, boolean value)` Construct a new rectangular VoxelArray that is a cuboid with the specified minimum and maximum values.
`VoxelArray`	`cylindricalEmboss(frink.graphics.FrinkImage img, float cx, float cy, float cz, double angleCenter, double angleWidth, float targetHeight, float d0, float d1, VoxelArray tool, int toolcx, int toolcy, int toolcz)` Embosses an image using a cylindrical mapping into the outer hull of an object.
`VoxelArray`	`cylindricalEmboss(frink.graphics.FrinkImage img, float cx, float cy, float cz, double angleCenter, double angleWidth, float targetHeight, int grayMin, int grayMax, float d0min, float d0max, float d1min, float d1max, VoxelArray tool, int toolcx, int toolcy, int toolcz)` Embosses an image using a cylindrical mapping into the outer hull of an object.
`void`	`drawCappedCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius)` Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
`void`	`drawCappedCylinder(Point3DFloat p1, Point3DFloat p2, float radius)` Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
`void`	`drawCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius)` Draws a cylinder with the specified endpoints and radius into this VoxelArray, modifying it in place.
`void`	`drawCylinder(Point3DFloat p1, Point3DFloat p2, float radius)` Draws a cylinder with the specified endpoints and radius into this VoxelArray, modifying it in place.
`void`	`drawTaperedCappedCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius1, float radius2)` Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
`void`	`drawTaperedCappedCylinder(Point3DFloat p1, Point3DFloat p2, float radius1, float radius2)` Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
`void`	`drawTaperedCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius1, float radius2)` Draws a cylinder with the specified endpoints and radii into this VoxelArray, modifying it in place.
`void`	`drawTaperedCylinder(Point3DFloat p1, Point3DFloat p2, float radius1, float radius2)` Draws a cylinder with the specified endpoints and radiii into this VoxelArray, modifying it in place.
`Point3DIntList`	`externalHullPoints()` Returns a list of points on the hull of the object.
`static VoxelArray`	`extrudeOnPlane(frink.graphics.FrinkImage img, float x, float y, float z, float u, float v, float w, float depth, double thetaZ)` Extrudes an image along a plane specified by a point on the plane (x, ,y, z) and a normal vector to the plane specified by (u,v,w).
`static VoxelArray`	`extrudeTapered(Point2DFloatList polygon, float x1, float y1, float z1, float x2, float y2, float z2, float cx, float cy, float scale1, float scale2, double thetaZ)` Extrudes a filled polygon along a line from p1 to p2 and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeTaperedRotated(Point2DFloatList polygon, float x1, float y1, float z1, float x2, float y2, float z2, float cx, float cy, float scale1, float scale2, double angle1, double angle2)` Extrudes a filled polygon along a line from p1 to p2 and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeZ(frink.graphics.FrinkImage img, int heightZ)` Extrudes an image along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeZ(frink.graphics.FrinkImage img, int minZ, int maxZ)` Extrudes an image along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeZ(Point2DFloatList polygon, float minZ, float maxZ)` Extrudes a filled polygon along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeZTapered(Point2DFloatList polygon, float minZ, float maxZ, float scale1, float scale2)` Extrudes a filled polygon (centered around its centroid) along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeZTapered(Point2DFloatList polygon, float minZ, float maxZ, float cx, float cy, float scale1, float scale2)` Extrudes a filled polygon along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`extrudeZTapered(Point2DFloatList polygon, float minZ, float maxZ, float cx, float cy, float scale1, float scale2, double angle1, double angle2)` Extrudes a filled polygon along the Z axis and returns a new VoxelArray of it.
`Point3DInt`	`farthestSetPoint(LineSegment3DFloat line)` Returns the farthest set point from the specified (infinite) line.
`void`	`fillCube(float minX, float maxX, float minY, float maxY, float minZ, float maxZ, boolean value)` Sets the values in the specified cube to a specific value (true or false.) Coordinates are rounded to the nearest voxel.
`VoxelArray`	`floodFill(int minx, int maxx, int miny, int maxy, int minz, int maxz, int startx, int starty, int startz)` Performs a flood fill of the specified VoxelArray, filling only to the specified bounds.
`boolean`	`get(int x, int y, int z)` Returns the value of the point at (x,y,z) (true or false)
`Point3DFloat`	`getCenter()` Returns a `Point3DFloat` representing the center of this VoxelArray.
`Point3DInt`	`getMaximumSetPoints()` Find the maximum set pixels on the (x,y,z) axes in this VoxelArray and returns a Point3DInt containing their coordinates.
`int`	`getMaxSetZ()` Quick function to obtain the highest set Z coordinate.
`int`	`getMaxX()` Returns the max value in the x dimension.
`int`	`getMaxY()` Returns the maximum value in the y dimension.
`int`	`getMaxZ()` Returns the maximum value in the z dimension.
`Point3DInt`	`getMinimumSetPoints()` Find the minimum set pixels on the (x,y,z) axes in this VoxelArray and returns a Point3DInt containing their coordinates.
`int`	`getMinSetZ()` Quick function to obtain the lowest set Z coordinate.
`int`	`getMinX()` Returns the minimum value in the x dimension.
`int`	`getMinY()` Returns the minimum value in the y dimension.
`int`	`getMinZ()` Returns the minimum value in the z dimension.
`long`	`getNextSetBitIndex(long index)` Returns the index of the next set bit that occurs on or after ther specified starting index.
`private boolean`	`getNoCheck(int x, int y, int z)` Returns the value of the point at (x,y,z) without doing any boundary checks.
`private boolean`	`getNoCheck(Point3DInt p)` Returns the value of the point without doing any boundary checks.
`long`	`getPreviousSetBitIndex(long index)` Returns the index of the previous set bit that occurs on or before the specified starting index.
`int`	`getSizeX()` Returns the size in the x dimension.
`int`	`getSizeY()` Returns the size in the y dimension.
`int`	`getSizeZ()` Returns the size in the z dimension.
`boolean`	`hasSameBoundary(VoxelArray other)` Returns true if the bounds of the other VoxelArray is the same size and location as this one.
`Point3DIntList`	`hullPoints()` Returns a list of points on the hull of the object.
`void`	`indexToXYZ(long index, long[] coords)` Convert an index into the `BiggerBitSet` into x,y,z coordinates.
`boolean`	`intersectsWith(int xmin, int ymin, int zmin, int xmax, int ymax, int zmax)` Returns true if the bounding box of this VoxelArray intersects with a box containing the specified boundaries.
`boolean`	`intersectsWith(VoxelArray b)` Returns true if the bounding box of this VoxelArray intersects with the other VoxelArray, false otherwise.
`void`	`invert()` Inverts all of the pixels in this VoxelArray.
`boolean`	`isInRange(long x, long y, long z)` This method checks a point to see if it is within a valid range for this VoxelArray.
`boolean`	`isInRange(Point3DInt p)` This method checks a point to see if it is within a valid range for this VoxelArray.
`static VoxelArray`	`makeCappedCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius)` Makes a cylinder with spherical end caps with the specified endpoints and radius.
`static VoxelArray`	`makeCappedCylinder(Point3DFloat p1, Point3DFloat p2, float radius)` Makes a cylinder with spherical end caps with the specified endpoints and radius.
`static VoxelArray`	`makeCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius)` Makes a cylinder with with the specified endpoints and radius.
`static VoxelArray`	`makeCylinder(Point3DFloat p1, Point3DFloat p2, float radius)` Makes a cylinder with with the specified endpoints and radius.
`static VoxelArray`	`makeRoundedCube(float x1, float x2, float y1, float y2, float z1, float z2, float radius)` Construct a new rounded cuboid VoxelArray that encloses the specific min and max coordinates and with corner diameter radius.
`static VoxelArray`	`makeSphere(float radius)` Makes a new VoxelArray with a sphere centered at (0,0,0) with the specified radius.
`static VoxelArray`	`makeSpheroid(float rx, float ry, float rz)` Makes a new VoxelArray with a spheroid centered at (0,0,0) with the specified radius on each axis [rx, ry, rz] TODO: Make a version of this centered at any specified point.
`static VoxelArray`	`makeSuperellipsoid(double rx, double ry, double rz, double n1, double n2)` Creates a "superellipsoid" which is a generalization of the ellipsoid family which is a superset of the spheroid family.
`static VoxelArray`	`makeSupertoroid(double r, double rx, double ry, double rz, double e1, double e2)` Creates a "supertoroid" which is a generalization of the toroid family.
`static VoxelArray`	`makeTaperedCappedCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius1, float radius2)` Makes a cylinder with spherical end caps with the specified endpoints and radius.
`static VoxelArray`	`makeTaperedCappedCylinder(Point3DFloat p1, Point3DFloat p2, float radius1, float radius2)` Makes a cylinder with spherical end caps with the specified endpoints and radius.
`static VoxelArray`	`makeTaperedCylinder(float x1, float y1, float z1, float x2, float y2, float z2, float radius1, float radius2)` Makes a tapered cylinder with with the specified endpoints and radius.
`static VoxelArray`	`makeTaperedCylinder(Point3DFloat p1, Point3DFloat p2, float radius1, float radius2)` Makes a tapered cylinder with with the specified endpoints and radius.
`private double`	`mod(double x, double y)` Define a modulus operator where x % y = x - y * floor[x/y] .
`static VoxelArray`	`paintAlongAllPoints(VoxelArray v1, VoxelArray tool, int cx, int cy, int cz)` Moves a tool along all set points in a VoxelArray and returns a new VoxelArray of it.
`VoxelArray`	`paintAlongHull(VoxelArray tool, int cx, int cy, int cz, boolean add)` Moves a tool along a path of integer points and returns a new VoxelArray of it, either adding to or removing points with the tool.
`void`	`paintAlongLine(VoxelArray tool, int x1, int y1, int z1, int x2, int y2, int z2, int xc, int yc, int zc, boolean add)` Modifies the pixels in this VoxelArray by moving the VoxelArray tool along a line and adding or removing the points in VoxelArray tool that are true, modifying this VoxelArray in place.
`static VoxelArray`	`paintAlongPath(Point3DIntList points, VoxelArray tool, int cx, int cy, int cz)` Moves a tool along a path of integer points and returns a new VoxelArray of it.
`VoxelArray`	`planarEmboss(frink.graphics.FrinkImage img, float cx, float cy, float xWidth, float yHeight, int grayMin, int grayMax, float d0min, float d0max, float d1min, float d1max, VoxelArray tool, int toolcx, int toolcy, int toolcz)` Embosses an image using a planar mapping into the top of an object (that is, downward on the Z-axis.) A tool will be used to carve into the object.
`frink.graphics.FrinkImageExpression`	`projectX(frink.expr.Environment env)` Projects a silhouette image looking along the X axis.
`frink.graphics.FrinkImageExpression`	`projectY(frink.expr.Environment env)` Projects a silhouette image looking along the Y axis.
`frink.graphics.FrinkImageExpression`	`projectZ(frink.expr.Environment env)` Projects a silhouette image looking along the Z axis.
`void`	`remove(VoxelArray b)` Removes the pixels in this VoxelArray that are true in VoxelArray b, modifying this VoxelArray in place.
`void`	`removeAlongLine(VoxelArray b, int x1, int y1, int z1, int x2, int y2, int z2, int xc, int yc, int zc)` Removes the pixels in this VoxelArray by moving the VoxelArray b along a line and removing the points in VoxelArray b that are true, modifying this VoxelArray in place.
`void`	`removeOutside(Plane3DFloat plane)` Removes all the voxels on the "outside" of a plane.
`void`	`removeOutsideLine(float cx1, float cy1, float cz1, float cx2, float cy2, float cz2, float radius, int minX, int maxX, int minY, int maxY, int minZ, int maxZ)` Removes the points outside of a specified distance (radius) from an infinite line.
`void`	`removeOutsideSphere(float cx, float cy, float cz, float radius, int minX, int maxX, int minY, int maxY, int minZ, int maxZ)` Removes all of the points outside a sphere.
`VoxelArray`	`rotate(float a, float b, float c, float u, float v, float w, double theta)` Rotates this VoxelArray around a line through a point (a, b, c) parallel to the vector [u,v,w] by the angle theta.
`VoxelArray`	`rotateXYZ(float a, float b, float c, double thetaX, double thetaY, double thetaZ)` Performs three rotations around the point (a, b, c) by performing 3 successive rotations about the x, y, and z axes in that order.
`boolean`	`sampleBoolean(int x, int y, int z)` Sample the field at the specified 3-dimensional point and return its value as true or false.
`boolean`	`sampleBoolean(Point3DInt p)` Sample the field at the specified 3-dimensional point and return its value as true or false.
`float`	`sampleFloat(float x, float y, float z)` Sample the field at the specified 3-dimensional point and return its value.
`float`	`sampleFloat(Point3DFloat p)` Sample the field at the specified 3-dimensional point and return its value.
`void`	`set(int x, int y, int z, boolean value)` Sets the voxel in the specific coordinate to the specific value.
`void`	`set(Point3DInt p, boolean value)` Sets the voxel in the specific coordinate to the specific value.
`private void`	`setNoCheck(int x, int y, int z, boolean value)` Sets the specific coordinate to the specific value, doing no checking of the validity of the coordinates for speed.
`private void`	`setNoCheck(Point3DInt p, boolean value)` Sets the specific coordinate to the specific value.
`void`	`setRange(int minX, int maxX, int minY, int maxY, int minZ, int maxZ, boolean value)` Sets the values in the specified range to the certain value.
`VoxelArray`	`solidOfRotation(float x, float y, float z, float u, float v, float w, double angle1, double angle2)` Creates a solid of rotation by rotating this VoxelArray around an axis going through point (x,y,z) and the normal (u,v,w).
`VoxelArray`	`solidOfRotation(LineSegment3DFloat axis, double angle1, double angle2)` Creates a solid of rotation by rotating this VoxelArray around an axis specified by axis.
`VoxelArray`	`solidOfRotation(Point3DFloat point, Point3DFloat axis, double angle1, double angle2)` Creates a solid of rotation by rotating this VoxelArray around an axis going through point (x,y,z) and the normal (u,v,w).
`VoxelArray`	`sphericalEmboss(frink.graphics.FrinkImage img, float cx, float cy, float cz, double azCenter, double azWidth, double altCenter, double altHeight, float d0, float d1, VoxelArray tool, int toolcx, int toolcy, int toolcz)` Embosses an image using a spherical mapping into the outer hull of an object.
`VoxelArray`	`sphericalEmboss(frink.graphics.FrinkImage img, float cx, float cy, float cz, double azCenter, double azWidth, double altCenter, double altHeight, int grayMin, int grayMax, float d0min, float d0max, float d1min, float d1max, VoxelArray tool, int toolcx, int toolcy, int toolcz)` Embosses an image using a spherical mapping into the outer hull of an object.
`static VoxelArray`	`strokeZ(Point2DFloatList polygon, float z1, float z2, float strokeRadius, boolean closed)` Extrudes the stroke of a polygon (using a cylindrical "pen") along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`strokeZ(Point2DFloatList polygon, VoxelArray tool, float cx, float cy, float cz, boolean closed)` Extrudes the stroke of a polygon (using a the specified VoxelArray as a "tool") along the Z axis and returns a new VoxelArray of it.
`static VoxelArray`	`strokeZTapered(Point2DFloatList polygon, float z1, float z2, float r1, float r2, boolean closed)` Extrudes the stroke of a polygon (using a tapered cylindrical "pen") along the Z axis and returns a new VoxelArray of it.
`long`	`toIndex(long x, long y, long z)` Convert x,y,z coordinates to an index into the `BiggerBitSet`.
`private long`	`toIndexNoCheck(long x, long y, long z)` Convert x,y,z coordinates to an index into the `BiggerBitSet`.
`java.lang.String`	`toObjFormat(java.lang.String name)` This triangulates the external hull of this object and returns it as a string in Wavefront .obj format that can be 3-D printed.
`java.lang.String`	`toObjFormat(java.lang.String name, float scale)` This triangulates the external hull of this object and returns it as a string in Wavefront .obj format that can be 3-D printed.
`java.lang.String`	`toSTLFormat(java.lang.String name)` This triangulates the external hull of this object and returns it as a string in STL format that can be 3-D printed.
`java.lang.String`	`toSTLFormat(java.lang.String name, float scale)` This triangulates the external hull of this object and returns it as a string in STL format that can be 3-D printed.
`VoxelArray`	`transform(CoordinateTransformer3DFloat transform)` Transforms this VoxelArray (rotations, scalings, translations, etc.) using an arbitrary `CoordinateTransformer3DFloat`
`void`	`translate(int x, int y, int z)` Translates this whole object by the specified amounts on each axis.
`java.util.Vector<Triangle3DFloat>`	`triangulateHull()` Triangulates the external hull of the voxels and returns a `Vector` of triangles that represent its external hull.
`VoxelArray`	`union(VoxelArray other)` Creates the union of this VoxelArray and another VoxelArray and returns a new VoxelArray that is just big enough to contain their union.
`static VoxelArray`	`union(VoxelArray v1, VoxelArray v2)` Returns the union of two VoxelArrays as a new VoxelArray that is just big enough to hold both of them.
`long`	`volume()` Returns the volume of a VoxelArray in number of voxels.

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

- Field Detail
  - voxels
```
private BiggerBitSet voxels
```
    The BiggerBitSet that contains all of the bits.
  - sizeX
```
private int sizeX
```
    The size of the x axis.
  - sizeY
```
private int sizeY
```
    The size of the y axis.
  - sizeZ
```
private int sizeZ
```
    The size of the z axis.
  - offX
```
private int offX
```
    The offset of the x axis.
  - offY
```
private int offY
```
    The offset of the y axis.
  - offZ
```
private int offZ
```
    The offset of the z axis.
  - area
```
private long area
```
    The area of the XY plane. Multiply this by sizeZ to get the volume.
  - TWOPI
```
private static final double TWOPI
```
    2 * pi
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - VoxelArray
```
public VoxelArray(int sizeX,
                  int sizeY,
                  int sizeZ)
```
    Construct a VoxelArray with the specified size on each axis and each element set to false.
  - VoxelArray
```
public VoxelArray(int sizeX,
                  int sizeY,
                  int sizeZ,
                  boolean value)
```
    Construct a VoxelArray with the specified size on each axis and each element set to the specified value.
  - VoxelArray
```
public VoxelArray(int minX,
                  int sizeX,
                  int minY,
                  int sizeY,
                  int minZ,
                  int sizeZ,
                  boolean value)
```
    Construct a VoxelArray with the specified minimum value and size on each axis and each element set to the specific value.
  - VoxelArray
```
public VoxelArray(VoxelArray other)
```
    Copy constructor.
  - VoxelArray
```
public VoxelArray(VoxelArray other,
                  boolean value)
```
    Copy the dimensions but set every voxel to the specified value.
- Method Detail
  - construct
```
public static VoxelArray construct(double x1,
                                   double x2,
                                   double y1,
                                   double y2,
                                   double z1,
                                   double z2,
                                   boolean value)
```
    Construct a new rectangular VoxelArray that encloses the specific min and max coordinates. This should be easier to use than the constructors that require specific integer offsets and widths.
  - cube
```
public static VoxelArray cube(double x1,
                              double x2,
                              double y1,
                              double y2,
                              double z1,
                              double z2,
                              boolean value)
```
    Construct a new rectangular VoxelArray that is a cuboid with the specified minimum and maximum values. This differs from construct(double, double, double, double, double, double, boolean) above in that it *rounds* to the nearest voxel coordinate instead of doing the probably-erroneous ceil and floor of construct. This is recommended instead of construct for rendering cuboids.
  - construct
```
public static VoxelArray construct(Point3DIntList points)
```
    Construct a new rectangular VoxelArray that represents the points in the Point3DIntList.
  - construct
```
public static VoxelArray construct(BoundingBox3DFloat bb,
                                   boolean value)
```
    Construct a new rectangular VoxelArray that encloses the specific bounding box.
  - toIndex
```
public long toIndex(long x,
                    long y,
                    long z)
             throws java.lang.IndexOutOfBoundsException
```
    Convert x,y,z coordinates to an index into the BiggerBitSet.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - toIndexNoCheck
```
private long toIndexNoCheck(long x,
                            long y,
                            long z)
```
    Convert x,y,z coordinates to an index into the BiggerBitSet. This is a private method that doesn't do any range checking, assuming the ranges have already been checked in the calling function.
  - indexToXYZ
```
public void indexToXYZ(long index,
                       long[] coords)
```
    Convert an index into the BiggerBitSet into x,y,z coordinates. The array passed in should be able to hold 3 longs.
  - setRange
```
public void setRange(int minX,
                     int maxX,
                     int minY,
                     int maxY,
                     int minZ,
                     int maxZ,
                     boolean value)
              throws java.lang.IndexOutOfBoundsException
```
    Sets the values in the specified range to the certain value.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - fillCube
```
public void fillCube(float minX,
                     float maxX,
                     float minY,
                     float maxY,
                     float minZ,
                     float maxZ,
                     boolean value)
              throws java.lang.IndexOutOfBoundsException
```
    Sets the values in the specified cube to a specific value (true or false.) Coordinates are rounded to the nearest voxel.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - set
```
public void set(int x,
                int y,
                int z,
                boolean value)
         throws java.lang.IndexOutOfBoundsException
```
    Sets the voxel in the specific coordinate to the specific value.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - set
```
public void set(Point3DInt p,
                boolean value)
         throws java.lang.IndexOutOfBoundsException
```
    Sets the voxel in the specific coordinate to the specific value.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - setNoCheck
```
private void setNoCheck(int x,
                        int y,
                        int z,
                        boolean value)
```
    Sets the specific coordinate to the specific value, doing no checking of the validity of the coordinates for speed. It is assumed that some other routine has checked the coordinates.
  - setNoCheck
```
private void setNoCheck(Point3DInt p,
                        boolean value)
```
    Sets the specific coordinate to the specific value. doing no checking of the validity of the coordinates for speed. It is assumed that some other routine has checked the coordinates.
  - isInRange
```
public boolean isInRange(long x,
                         long y,
                         long z)
```
    This method checks a point to see if it is within a valid range for this VoxelArray. If so, it returns true.
  - isInRange
```
public boolean isInRange(Point3DInt p)
```
    This method checks a point to see if it is within a valid range for this VoxelArray. If so, it returns true.
  - checkPoint
```
private void checkPoint(long x,
                        long y,
                        long z)
                 throws java.lang.IndexOutOfBoundsException
```
    This method checks a point to see if it is within a valid range for this VoxelArray and throws an IndexOutOfBoundsException if it doesn't.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - get
```
public boolean get(int x,
                   int y,
                   int z)
            throws java.lang.IndexOutOfBoundsException
```
    Returns the value of the point at (x,y,z) (true or false)
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - getNoCheck
```
private boolean getNoCheck(int x,
                           int y,
                           int z)
                    throws java.lang.IndexOutOfBoundsException
```
    Returns the value of the point at (x,y,z) without doing any boundary checks. This will still throw an exception if the resultant index is negative.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - getNoCheck
```
private boolean getNoCheck(Point3DInt p)
                    throws java.lang.IndexOutOfBoundsException
```
    Returns the value of the point without doing any boundary checks. This will still throw an exception if the resultant index is negative.
    
    Throws:
    
    java.lang.IndexOutOfBoundsException
  - getSizeX
```
public int getSizeX()
```
    Returns the size in the x dimension.
  - getSizeY
```
public int getSizeY()
```
    Returns the size in the y dimension.
  - getSizeZ
```
public int getSizeZ()
```
    Returns the size in the z dimension.
  - getMinX
```
public int getMinX()
```
    Returns the minimum value in the x dimension.
  - getMinY
```
public int getMinY()
```
    Returns the minimum value in the y dimension.
  - getMinZ
```
public int getMinZ()
```
    Returns the minimum value in the z dimension.
  - getMaxX
```
public int getMaxX()
```
    Returns the max value in the x dimension.
  - getMaxY
```
public int getMaxY()
```
    Returns the maximum value in the y dimension.
  - getMaxZ
```
public int getMaxZ()
```
    Returns the maximum value in the z dimension.
  - getCenter
```
public Point3DFloat getCenter()
```
    Returns a Point3DFloat representing the center of this VoxelArray. This is not the center of the set voxels, but the center of the containing VoxelArray.
  - translate
```
public void translate(int x,
                      int y,
                      int z)
```
    Translates this whole object by the specified amounts on each axis. This doesn't alter the voxels but just the offsets so it's fast but it's dangerous because it fundamentally changes the location of this VoxelArray.
  - sampleFloat
```
public float sampleFloat(float x,
                         float y,
                         float z)
```
    Sample the field at the specified 3-dimensional point and return its value. This returns 1.0f whenever the voxel is true, and 0.0f whenever the voxel is false or out of bounds.
    
    Specified by:
    
    sampleFloat in interface Field3DFloat
  - sampleBoolean
```
public boolean sampleBoolean(int x,
                             int y,
                             int z)
```
    Sample the field at the specified 3-dimensional point and return its value as true or false. This returns true whenever the voxel is true, and false whenever the voxel is false or out of bounds.
  - sampleBoolean
```
public boolean sampleBoolean(Point3DInt p)
```
    Sample the field at the specified 3-dimensional point and return its value as true or false. This returns true whenever the voxel is true, and false whenever the voxel is false or out of bounds.
  - sampleFloat
```
public float sampleFloat(Point3DFloat p)
```
    Sample the field at the specified 3-dimensional point and return its value. This returns 1.0f whenever the voxel is true, and 0.0f whenever the voxel is false or out of bounds.
  - triangulateHull
```
public java.util.Vector<Triangle3DFloat> triangulateHull()
```
    Triangulates the external hull of the voxels and returns a Vector of triangles that represent its external hull.
  - toObjFormat
```
public java.lang.String toObjFormat(java.lang.String name)
```
    This triangulates the external hull of this object and returns it as a string in Wavefront .obj format that can be 3-D printed.
    
    Parameters:
    
    name - The name of the object in the obj file. This should be text only.
  - toObjFormat
```
public java.lang.String toObjFormat(java.lang.String name,
                                    float scale)
```
    This triangulates the external hull of this object and returns it as a string in Wavefront .obj format that can be 3-D printed.
    
    Parameters:
    
    name - The name of the object in the obj file. This should be text only.
    
    scale - The scale to multiply each coordinate by.
  - toSTLFormat
```
public java.lang.String toSTLFormat(java.lang.String name)
```
    This triangulates the external hull of this object and returns it as a string in STL format that can be 3-D printed.
    
    Parameters:
    
    name - The name of the object in the obj file. This should be text only.
  - toSTLFormat
```
public java.lang.String toSTLFormat(java.lang.String name,
                                    float scale)
```
    This triangulates the external hull of this object and returns it as a string in STL format that can be 3-D printed.
    
    Parameters:
    
    name - The name of the object in the obj file. This should be text only.
    
    scale - A scaling factor to multiply by.
  - hullPoints
```
public Point3DIntList hullPoints()
```
    Returns a list of points on the hull of the object. The hull points are the set points where at least one of the 6 adjacent points is unset. (Should this be 26?) Note that this includes points on the hollow inside surface of an object. If you do not want internal points, call the more-expensive externalHullPoints() method. The resultant Point3DIntList can be passed to paintAlongPath(frink.graphics.Point3DIntList, frink.graphics.VoxelArray, int, int, int) to extend (or erode) the hull of an object.
  - externalHullPoints
```
public Point3DIntList externalHullPoints()
```
    Returns a list of points on the hull of the object. The hull points are the set points where at least one of the 6 adjacent points is unset. (Should this be 26?) Note that this does not include points on the hollow inside surface of an object. This performs a potentially-expensive flood fill. If you *do* want internal points, call the less-expensive hullPoints() method. The resultant Point3DIntList can be passed to paintAlongPath(frink.graphics.Point3DIntList, frink.graphics.VoxelArray, int, int, int) to extend (or erode) the hull of an object.
  - floodFill
```
public VoxelArray floodFill(int minx,
                            int maxx,
                            int miny,
                            int maxy,
                            int minz,
                            int maxz,
                            int startx,
                            int starty,
                            int startz)
```
    Performs a flood fill of the specified VoxelArray, filling only to the specified bounds. The flood fill starts at startX, startY, startZ, which should be unset. The original VoxelArray is not modified, but returns a new VoxelArray (which can be added back to the original with the add(frink.graphics.VoxelArray) method.) Returning a new VoxelArray is useful because then you can then determine the volume (number of set bits) in the result by calling countSetBits(). This can be used to highly-accurately measure weird-shaped measuring cups or spoons, etc.
  - projectX
```
public frink.graphics.FrinkImageExpression projectX(frink.expr.Environment env)
                                             throws frink.expr.NotSupportedException
```
    Projects a silhouette image looking along the X axis. Black pixels are occluded.
    
    Throws:
    
    frink.expr.NotSupportedException
  - projectY
```
public frink.graphics.FrinkImageExpression projectY(frink.expr.Environment env)
                                             throws frink.expr.NotSupportedException
```
    Projects a silhouette image looking along the Y axis. Black pixels are occluded.
    
    Throws:
    
    frink.expr.NotSupportedException
  - projectZ
```
public frink.graphics.FrinkImageExpression projectZ(frink.expr.Environment env)
                                             throws frink.expr.NotSupportedException
```
    Projects a silhouette image looking along the Z axis. Black pixels are occluded.
    
    Throws:
    
    frink.expr.NotSupportedException
  - remove
```
public void remove(VoxelArray b)
```
    Removes the pixels in this VoxelArray that are true in VoxelArray b, modifying this VoxelArray in place.
  - addAlongLine
```
public void addAlongLine(VoxelArray b,
                         int x1,
                         int y1,
                         int z1,
                         int x2,
                         int y2,
                         int z2,
                         int xc,
                         int yc,
                         int zc)
```
    Adds the pixels in this VoxelArray by moving the VoxelArray b along a line and adding the points in VoxelArray b that are true, modifying this VoxelArray in place.
  - removeAlongLine
```
public void removeAlongLine(VoxelArray b,
                            int x1,
                            int y1,
                            int z1,
                            int x2,
                            int y2,
                            int z2,
                            int xc,
                            int yc,
                            int zc)
```
    Removes the pixels in this VoxelArray by moving the VoxelArray b along a line and removing the points in VoxelArray b that are true, modifying this VoxelArray in place.
  - paintAlongLine
```
public void paintAlongLine(VoxelArray tool,
                           int x1,
                           int y1,
                           int z1,
                           int x2,
                           int y2,
                           int z2,
                           int xc,
                           int yc,
                           int zc,
                           boolean add)
```
    Modifies the pixels in this VoxelArray by moving the VoxelArray tool along a line and adding or removing the points in VoxelArray tool that are true, modifying this VoxelArray in place.
  - add
```
public void add(VoxelArray b)
```
    Adds the pixels in this VoxelArray that are true in VoxelArray b, modifying this VoxelArray in place.
  - intersectsWith
```
public boolean intersectsWith(VoxelArray b)
```
    Returns true if the bounding box of this VoxelArray intersects with the other VoxelArray, false otherwise. This does *not* test that pixels overlap.
  - intersectsWith
```
public boolean intersectsWith(int xmin,
                              int ymin,
                              int zmin,
                              int xmax,
                              int ymax,
                              int zmax)
```
    Returns true if the bounding box of this VoxelArray intersects with a box containing the specified boundaries.
  - union
```
public static VoxelArray union(VoxelArray v1,
                               VoxelArray v2)
```
    Returns the union of two VoxelArrays as a new VoxelArray that is just big enough to hold both of them. Exacly one of the arguments is allowed to be null, in which case it returns a copy of the non-null argument.
  - union
```
public VoxelArray union(VoxelArray other)
```
    Creates the union of this VoxelArray and another VoxelArray and returns a new VoxelArray that is just big enough to contain their union. If the argument other is null, this just returns a new copy of this.
  - invert
```
public void invert()
```
    Inverts all of the pixels in this VoxelArray. Pixels that were true become false and vice-versa.
  - volume
```
public long volume()
```
    Returns the volume of a VoxelArray in number of voxels.
  - hasSameBoundary
```
public boolean hasSameBoundary(VoxelArray other)
```
    Returns true if the bounds of the other VoxelArray is the same size and location as this one. This potentially allows two VoxelArrays to be added, intersected, very rapidly using just operators like and, andNot, etc.
  - makeSphere
```
public static VoxelArray makeSphere(float radius)
```
    Makes a new VoxelArray with a sphere centered at (0,0,0) with the specified radius. TODO: Make a version of this centered at any specified point.
  - makeSpheroid
```
public static VoxelArray makeSpheroid(float rx,
                                      float ry,
                                      float rz)
```
    Makes a new VoxelArray with a spheroid centered at (0,0,0) with the specified radius on each axis [rx, ry, rz] TODO: Make a version of this centered at any specified point.
  - makeCylinder
```
public static VoxelArray makeCylinder(Point3DFloat p1,
                                      Point3DFloat p2,
                                      float radius)
```
    Makes a cylinder with with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - makeCylinder
```
public static VoxelArray makeCylinder(float x1,
                                      float y1,
                                      float z1,
                                      float x2,
                                      float y2,
                                      float z2,
                                      float radius)
```
    Makes a cylinder with with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - drawCylinder
```
public void drawCylinder(Point3DFloat p1,
                         Point3DFloat p2,
                         float radius)
```
    Draws a cylinder with the specified endpoints and radius into this VoxelArray, modifying it in place.
  - drawCylinder
```
public void drawCylinder(float x1,
                         float y1,
                         float z1,
                         float x2,
                         float y2,
                         float z2,
                         float radius)
```
    Draws a cylinder with the specified endpoints and radius into this VoxelArray, modifying it in place.
  - makeTaperedCylinder
```
public static VoxelArray makeTaperedCylinder(Point3DFloat p1,
                                             Point3DFloat p2,
                                             float radius1,
                                             float radius2)
```
    Makes a tapered cylinder with with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - makeTaperedCylinder
```
public static VoxelArray makeTaperedCylinder(float x1,
                                             float y1,
                                             float z1,
                                             float x2,
                                             float y2,
                                             float z2,
                                             float radius1,
                                             float radius2)
```
    Makes a tapered cylinder with with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - drawTaperedCylinder
```
public void drawTaperedCylinder(Point3DFloat p1,
                                Point3DFloat p2,
                                float radius1,
                                float radius2)
```
    Draws a cylinder with the specified endpoints and radiii into this VoxelArray, modifying it in place.
  - drawTaperedCylinder
```
public void drawTaperedCylinder(float x1,
                                float y1,
                                float z1,
                                float x2,
                                float y2,
                                float z2,
                                float radius1,
                                float radius2)
```
    Draws a cylinder with the specified endpoints and radii into this VoxelArray, modifying it in place.
  - makeCappedCylinder
```
public static VoxelArray makeCappedCylinder(Point3DFloat p1,
                                            Point3DFloat p2,
                                            float radius)
```
    Makes a cylinder with spherical end caps with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - makeCappedCylinder
```
public static VoxelArray makeCappedCylinder(float x1,
                                            float y1,
                                            float z1,
                                            float x2,
                                            float y2,
                                            float z2,
                                            float radius)
```
    Makes a cylinder with spherical end caps with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - drawCappedCylinder
```
public void drawCappedCylinder(Point3DFloat p1,
                               Point3DFloat p2,
                               float radius)
```
    Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
  - drawCappedCylinder
```
public void drawCappedCylinder(float x1,
                               float y1,
                               float z1,
                               float x2,
                               float y2,
                               float z2,
                               float radius)
```
    Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
  - makeTaperedCappedCylinder
```
public static VoxelArray makeTaperedCappedCylinder(Point3DFloat p1,
                                                   Point3DFloat p2,
                                                   float radius1,
                                                   float radius2)
```
    Makes a cylinder with spherical end caps with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - makeTaperedCappedCylinder
```
public static VoxelArray makeTaperedCappedCylinder(float x1,
                                                   float y1,
                                                   float z1,
                                                   float x2,
                                                   float y2,
                                                   float z2,
                                                   float radius1,
                                                   float radius2)
```
    Makes a cylinder with spherical end caps with the specified endpoints and radius. This version creates a new VoxelArray that is just big enough to contain the cylinder, draws the cylinder into it, and returns the new VoxelArray.
  - drawTaperedCappedCylinder
```
public void drawTaperedCappedCylinder(Point3DFloat p1,
                                      Point3DFloat p2,
                                      float radius1,
                                      float radius2)
```
    Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
  - drawTaperedCappedCylinder
```
public void drawTaperedCappedCylinder(float x1,
                                      float y1,
                                      float z1,
                                      float x2,
                                      float y2,
                                      float z2,
                                      float radius1,
                                      float radius2)
```
    Draws a cylinder with spherical end caps with the specified endpoints and radius into this VoxelArray, modifying it in place.
  - removeOutside
```
public void removeOutside(Plane3DFloat plane)
```
    Removes all the voxels on the "outside" of a plane. This can be used for lots of constructive solid geometry, especially for constructing convex objects.
    See Plane3DFloat for definition of what "inside" and "outside" of the plane means and how to construct a plane in a few different ways.
    TODO: This can probably be optimized a lot.
    For each y and z, the point where x intersects the plane is x = - (D + B y + C z) / A
    and the points to be removed can be quickly found along that x line. Note that if A == 0, this could cause a divide by zero. This means that line is entirely inside or outside the object.
    For each x and z, the point where y intersects the plane is y = - (D + A x + C z) / B
    For each x and y, the point where z intersects the plane is given by z = - (D + A x + B y) / C
  - extrudeZ
```
public static VoxelArray extrudeZ(frink.graphics.FrinkImage img,
                                  int heightZ)
                           throws frink.expr.NotSupportedException
```
    Extrudes an image along the Z axis and returns a new VoxelArray of it. Pixels that are black will be extruded. The image will be centered at (x=0, y=0, z=0) and will be heightZ voxels thick in the Z direction.
    
    Throws:
    
    frink.expr.NotSupportedException
  - extrudeZ
```
public static VoxelArray extrudeZ(frink.graphics.FrinkImage img,
                                  int minZ,
                                  int maxZ)
                           throws frink.expr.NotSupportedException
```
    Extrudes an image along the Z axis and returns a new VoxelArray of it. Pixels that are black will be extruded. The image will be centered at (x=0, y=0) and range from minZ to maxZ on the Z axis.
    
    Throws:
    
    frink.expr.NotSupportedException
  - extrudeOnPlane
```
public static VoxelArray extrudeOnPlane(frink.graphics.FrinkImage img,
                                        float x,
                                        float y,
                                        float z,
                                        float u,
                                        float v,
                                        float w,
                                        float depth,
                                        double thetaZ)
                                 throws frink.expr.NotSupportedException,
                                        frink.expr.InvalidArgumentException
```
    Extrudes an image along a plane specified by a point on the plane (x, ,y, z) and a normal vector to the plane specified by (u,v,w). The image can be rotated by thetaZ radians to orient it on the plane.
    
    Throws:
    
    frink.expr.NotSupportedException
    
    frink.expr.InvalidArgumentException
  - strokeZ
```
public static VoxelArray strokeZ(Point2DFloatList polygon,
                                 VoxelArray tool,
                                 float cx,
                                 float cy,
                                 float cz,
                                 boolean closed)
```
    Extrudes the stroke of a polygon (using a the specified VoxelArray as a "tool") along the Z axis and returns a new VoxelArray of it.
  - strokeZ
```
public static VoxelArray strokeZ(Point2DFloatList polygon,
                                 float z1,
                                 float z2,
                                 float strokeRadius,
                                 boolean closed)
```
    Extrudes the stroke of a polygon (using a cylindrical "pen") along the Z axis and returns a new VoxelArray of it. The pen will range from z1 to z2 on the Z axis.
  - strokeZTapered
```
public static VoxelArray strokeZTapered(Point2DFloatList polygon,
                                        float z1,
                                        float z2,
                                        float r1,
                                        float r2,
                                        boolean closed)
```
    Extrudes the stroke of a polygon (using a tapered cylindrical "pen") along the Z axis and returns a new VoxelArray of it. The pen will range from z1 to z2 on the Z axis. The radius of the cylindrical pen is r1 at z1 and r2 at z2.
  - extrudeZ
```
public static VoxelArray extrudeZ(Point2DFloatList polygon,
                                  float minZ,
                                  float maxZ)
```
    Extrudes a filled polygon along the Z axis and returns a new VoxelArray of it. The shape will range from minZ to maxZ on the Z axis.
  - extrudeZTapered
```
public static VoxelArray extrudeZTapered(Point2DFloatList polygon,
                                         float minZ,
                                         float maxZ,
                                         float scale1,
                                         float scale2)
```
    Extrudes a filled polygon (centered around its centroid) along the Z axis and returns a new VoxelArray of it. The shape will range from minZ to maxZ on the Z axis. The object will be scaled by a factor of scale1 at minZ and scale2 at maxZ around the centroid.
  - extrudeZTapered
```
public static VoxelArray extrudeZTapered(Point2DFloatList polygon,
                                         float minZ,
                                         float maxZ,
                                         float cx,
                                         float cy,
                                         float scale1,
                                         float scale2)
```
    Extrudes a filled polygon along the Z axis and returns a new VoxelArray of it. The shape will range from minZ to maxZ on the Z axis. The object will be scaled by a factor of scale1 at minZ and scale2 at maxZ around the point (cx, cy)
  - extrudeZTapered
```
public static VoxelArray extrudeZTapered(Point2DFloatList polygon,
                                         float minZ,
                                         float maxZ,
                                         float cx,
                                         float cy,
                                         float scale1,
                                         float scale2,
                                         double angle1,
                                         double angle2)
```
    Extrudes a filled polygon along the Z axis and returns a new VoxelArray of it. The shape will range from minZ to maxZ on the Z axis. The object will be scaled by a factor of scale1 at minZ and scale2 at maxZ around the point (cx, cy) This also rotates from angle1 at minZ to angle2 at maxZ. This is harder to calculate a bounding box for.
  - extrudeTapered
```
public static VoxelArray extrudeTapered(Point2DFloatList polygon,
                                        float x1,
                                        float y1,
                                        float z1,
                                        float x2,
                                        float y2,
                                        float z2,
                                        float cx,
                                        float cy,
                                        float scale1,
                                        float scale2,
                                        double thetaZ)
                                 throws frink.expr.InvalidArgumentException
```
    Extrudes a filled polygon along a line from p1 to p2 and returns a new VoxelArray of it. The object will be scaled by a factor of scale1 at p1 and scale2 at p2 around point (cx, cy). This first rotates around the angle thetaZ (specified in radians). Positive angles are counterclockwise.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - extrudeTaperedRotated
```
public static VoxelArray extrudeTaperedRotated(Point2DFloatList polygon,
                                               float x1,
                                               float y1,
                                               float z1,
                                               float x2,
                                               float y2,
                                               float z2,
                                               float cx,
                                               float cy,
                                               float scale1,
                                               float scale2,
                                               double angle1,
                                               double angle2)
                                        throws frink.expr.InvalidArgumentException
```
    Extrudes a filled polygon along a line from p1 to p2 and returns a new VoxelArray of it. The object will be scaled by a factor of scale1 at p1 and scale2 at p2 around point (cx, cy). This rotates from angle1 at point 1 to angle2 at point2 (specified in radians). Positive angles are counterclockwise
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - makeRoundedCube
```
public static VoxelArray makeRoundedCube(float x1,
                                         float x2,
                                         float y1,
                                         float y2,
                                         float z1,
                                         float z2,
                                         float radius)
```
    Construct a new rounded cuboid VoxelArray that encloses the specific min and max coordinates and with corner diameter radius.
  - removeOutsideSphere
```
public void removeOutsideSphere(float cx,
                                float cy,
                                float cz,
                                float radius,
                                int minX,
                                int maxX,
                                int minY,
                                int maxY,
                                int minZ,
                                int maxZ)
```
    Removes all of the points outside a sphere. This is used for creating the corners of a rounded cuboid.
  - removeOutsideLine
```
public void removeOutsideLine(float cx1,
                              float cy1,
                              float cz1,
                              float cx2,
                              float cy2,
                              float cz2,
                              float radius,
                              int minX,
                              int maxX,
                              int minY,
                              int maxY,
                              int minZ,
                              int maxZ)
```
    Removes the points outside of a specified distance (radius) from an infinite line. This is used to round edges on a rounded cube.
  - paintAlongPath
```
public static VoxelArray paintAlongPath(Point3DIntList points,
                                        VoxelArray tool,
                                        int cx,
                                        int cy,
                                        int cz)
```
    Moves a tool along a path of integer points and returns a new VoxelArray of it. The point (cx, cy, cz) represents the point in the tool that should be moved along the path.
  - paintAlongAllPoints
```
public static VoxelArray paintAlongAllPoints(VoxelArray v1,
                                             VoxelArray tool,
                                             int cx,
                                             int cy,
                                             int cz)
```
    Moves a tool along *all* set points in a VoxelArray and returns a new VoxelArray of it. The point (cx, cy, cz) represents the point in the tool that should be moved along the path. You generally never want to use this except for embossing. For doing something like the Minkowski sum, you should use paintAlongHull.
  - paintAlongHull
```
public VoxelArray paintAlongHull(VoxelArray tool,
                                 int cx,
                                 int cy,
                                 int cz,
                                 boolean add)
```
    Moves a tool along a path of integer points and returns a new VoxelArray of it, either adding to or removing points with the tool. The point (cx, cy, cz) represents the point in the tool that should be moved along the hull. This is also called the Minkowski sum.
  - transform
```
public VoxelArray transform(CoordinateTransformer3DFloat transform)
                     throws frink.expr.InvalidArgumentException
```
    Transforms this VoxelArray (rotations, scalings, translations, etc.) using an arbitrary CoordinateTransformer3DFloat
    
    Parameters:
    
    transform - A CoordinateTransformer3DFloat that describes the transform.
    
    Returns:
    
    A new VoxelArray which is the transformed version of this.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - rotate
```
public VoxelArray rotate(float a,
                         float b,
                         float c,
                         float u,
                         float v,
                         float w,
                         double theta)
                  throws frink.expr.InvalidArgumentException
```
    Rotates this VoxelArray around a line through a point (a, b, c) parallel to the vector [u,v,w] by the angle theta.
    
    Parameters:
    
    a - x-coordinate of a point on the line of rotation.
    
    b - y-coordinate of a point on the line of rotation.
    
    c - z-coordinate of a point on the line of rotation.
    
    u - x-coordinate of the line's direction vector (unnormalized).
    
    v - y-coordinate of the line's direction vector (unnormalized).
    
    w - z-coordinate of the line's direction vector (unnormalized).
    
    theta - The angle of rotation, in radians.
    
    Returns:
    
    A new VoxelArray which is the rotated version of this.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - rotateXYZ
```
public VoxelArray rotateXYZ(float a,
                            float b,
                            float c,
                            double thetaX,
                            double thetaY,
                            double thetaZ)
                     throws frink.expr.InvalidArgumentException
```
    Performs three rotations around the point (a, b, c) by performing 3 successive rotations about the x, y, and z axes in that order. This emulates the OpenSCAD notation
    rotate(a=[0,180,0]) which is frequently simplified to rotate([0,180,0])
    See: https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Transformations#rotate
    but is far more flexible because it allows rotation around an arbitrary point.
    It is recommended to use this method when rotating around more than one axis, especially for a VoxelArray, because it intelligently composes a single tranformation matrix and performs only one transformation which can be reversed. (VoxelArray.transform actually computes and performs the *inverse* transform of the transform you give it, eliminating holes in the target VoxelArray space.)
    
    Parameters:
    
    a - x-coordinate of a point on the line of rotation.
    
    b - y-coordinate of a point on the line of rotation.
    
    c - z-coordinate of a point on the line of rotation.
    
    thetaX - The angle of rotation around a line parallel to the X axis, in radians. Looking from a positive axis toward the origin, a positive angle gives a counterclockwise rotation.
    
    thetaY - The angle of rotation around a line parallel to the Y axis, in radians. Looking from a positive axis toward the origin, a positive angle gives a counterclockwise rotation.
    
    thetaZ - The angle of rotation around a line parallel to the Z axis, in radians. Looking from a positive axis toward the origin, a positive angle gives a counterclockwise rotation.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - makeSupertoroid
```
public static VoxelArray makeSupertoroid(double r,
                                         double rx,
                                         double ry,
                                         double rz,
                                         double e1,
                                         double e2)
```
    Creates a "supertoroid" which is a generalization of the toroid family. The supertoroid is centered around (0,0,0) and laying "flat" in the x-y plane.
    See: https://cse.buffalo.edu/~jryde/cse673/files/superquadrics.pdf for the equation
    See: http://paulbourke.net/geometry/toroidal/ for graphs of the equation families.
    TODO: The bounding box is currently only correct if rx = ry.
    
    Parameters:
    
    r - The major radius of the large circle
    
    rx - The minor radius of the small circle in the x direction
    
    ry - The minor radius of the small circle in the y direction
    
    rz - The minor radius of the small circle in the z direction
    
    e1 - The eccentricity of the small circle (1=circle, 2=square, less than 1 is puffy rounded square, greater than 2 is a pinched diamond. )
    
    e2 - The eccentricity of the large circle (1=circle, 2=square, less than 1 is puffy rounded square, greater than 2 is a pinched diamond. )
  - makeSuperellipsoid
```
public static VoxelArray makeSuperellipsoid(double rx,
                                            double ry,
                                            double rz,
                                            double n1,
                                            double n2)
```
    Creates a "superellipsoid" which is a generalization of the ellipsoid family which is a superset of the spheroid family. The ellipsoid is centered around (0,0,0) with the axis along the z axis.
    See: http://paulbourke.net/geometry/spherical/ for graphs of the equation families.
    
    Parameters:
    
    rx - The radius in the x direction
    
    ry - The radius in the y direction
    
    rz - The radius in the z direction
    
    n1 - The eccentricity around the z axis (1=circle, 2=square, less than 1 is puffy rounded square, greater than 2 is a pinched diamond. )
    
    n2 - The eccentricity around the x and y axes (1=circle, 2=square, less than 1 is puffy rounded square, greater than 2 is a pinched diamond. )
  - getNextSetBitIndex
```
public long getNextSetBitIndex(long index)
```
    Returns the index of the next set bit that occurs on or after ther specified starting index. If no such bit exists, then -1 is returned.
  - getPreviousSetBitIndex
```
public long getPreviousSetBitIndex(long index)
```
    Returns the index of the previous set bit that occurs on or before the specified starting index. If no such bit exists or if -1 is given as the starting index, then -1 is returned.
  - getMinSetZ
```
public int getMinSetZ()
```
    Quick function to obtain the lowest set Z coordinate. If there is no set bit, this returns getMaxZ().
  - getMaxSetZ
```
public int getMaxSetZ()
```
    Quick function to obtain the highest set Z coordinate. If there is no set bit, this returns getMinZ().
  - getMinimumSetPoints
```
public Point3DInt getMinimumSetPoints()
```
    Find the minimum set pixels on the (x,y,z) axes in this VoxelArray and returns a Point3DInt containing their coordinates. Note that this is not necessarily a set point!
  - getMaximumSetPoints
```
public Point3DInt getMaximumSetPoints()
```
    Find the maximum set pixels on the (x,y,z) axes in this VoxelArray and returns a Point3DInt containing their coordinates. Note that this is not necessarily a set point!
  - farthestSetPoint
```
public Point3DInt farthestSetPoint(LineSegment3DFloat line)
```
    Returns the farthest set point from the specified (infinite) line. This is useful, in, say making a solid of rotation.
  - solidOfRotation
```
public VoxelArray solidOfRotation(LineSegment3DFloat axis,
                                  double angle1,
                                  double angle2)
                           throws frink.expr.InvalidArgumentException
```
    Creates a solid of rotation by rotating this VoxelArray around an axis specified by axis. Looking from point 2 on the axis to point 1, this rotates from angle1 to angle2 with positive angles being counterclockwise. A new VoxelArray is returned.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - solidOfRotation
```
public VoxelArray solidOfRotation(Point3DFloat point,
                                  Point3DFloat axis,
                                  double angle1,
                                  double angle2)
                           throws frink.expr.InvalidArgumentException
```
    Creates a solid of rotation by rotating this VoxelArray around an axis going through point (x,y,z) and the normal (u,v,w). Looking backwards from the normal to point 1, this rotates from angle1 to angle2 with positive angles being counterclockwise.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - solidOfRotation
```
public VoxelArray solidOfRotation(float x,
                                  float y,
                                  float z,
                                  float u,
                                  float v,
                                  float w,
                                  double angle1,
                                  double angle2)
                           throws frink.expr.InvalidArgumentException
```
    Creates a solid of rotation by rotating this VoxelArray around an axis going through point (x,y,z) and the normal (u,v,w). Looking backwards from the normal to point 1, this rotates from angle1 to angle2 with positive angles being counterclockwise.
    
    Throws:
    
    frink.expr.InvalidArgumentException
  - cylindricalEmboss
```
public VoxelArray cylindricalEmboss(frink.graphics.FrinkImage img,
                                    float cx,
                                    float cy,
                                    float cz,
                                    double angleCenter,
                                    double angleWidth,
                                    float targetHeight,
                                    float d0,
                                    float d1,
                                    VoxelArray tool,
                                    int toolcx,
                                    int toolcy,
                                    int toolcz)
```
    Embosses an image using a cylindrical mapping into the outer hull of an object. This is a simplified "binary" embossing where a single depth will be used regardless of the gray level. Dark parts of the image will be embossed. A tool will be used to carve into the object. This returns a new VoxelArray of the parts to be removed or added from the original object which is unmodified.
    
    Parameters:
    
    img - The image to be embossed
    
    cx - The x-coordinate of the center of the projection.
    
    cy - The y-coordinate of the center of the projection.
    
    cz - The z-coordinate of the center of the projection.
    
    angleCenter - The angle (in radians) of the center of the projection reckoned counterclockwise from the y axis. (0 degrees is toward the y axis, 270 degrees is toward the x axis)
    
    angleWidth - The angle (in radians) wide to map the image. 2 pi radians wraps around the entire cylinder.
    
    targetHeight - The height (in voxels) to map the image.
    
    d0 - The depth to begin embossing from (in voxels). 0 is the surface of the image. Negative numbers are allowed.
    
    d1 - The depth to end embossing into the object (in voxels). 0 is the surface of the image.
    
    tool - A VoxelArray to use as the tool.
    
    toolcx - The x coordinate of the center of the tool to move along the path.
    
    toolcy - The y coordinate of the center of the tool to move along the path.
    
    toolcz - The z coordinate of the center of the tool to move along the path.
    
    Returns:
    
    A new VoxelArray representing the parts to be added or removed.
  - cylindricalEmboss
```
public VoxelArray cylindricalEmboss(frink.graphics.FrinkImage img,
                                    float cx,
                                    float cy,
                                    float cz,
                                    double angleCenter,
                                    double angleWidth,
                                    float targetHeight,
                                    int grayMin,
                                    int grayMax,
                                    float d0min,
                                    float d0max,
                                    float d1min,
                                    float d1max,
                                    VoxelArray tool,
                                    int toolcx,
                                    int toolcy,
                                    int toolcz)
```
    Embosses an image using a cylindrical mapping into the outer hull of an object. This is the most general and powerful of the cylindrical embossing routines. A tool will be used to carve into the object. This returns a new VoxelArray of the parts to be removed or added from the original object which is unmodified.
    
    Parameters:
    
    img - The image to be embossed
    
    cx - The x-coordinate of the center of the projection.
    
    cy - The y-coordinate of the center of the projection.
    
    cz - The z-coordinate of the center of the projection.
    
    angleCenter - The angle (in radians) of the center of the projection reckoned counterclockwise from the y axis. (0 degrees is toward the y axis, 270 degrees is toward the x axis)
    
    angleWidth - The angle (in radians) wide to map the image. 2 pi radians wraps around the entire cylinder.
    
    targetHeight - The height (in voxels) to map the image.
    
    grayMin - A value from 0 (black) to 255 (white) indicating the minimum pixel gray value from the image that will be embossed. Pixels with values less than this will be ignored.
    
    grayMax - A value from 0 (black) to 255 (white) indicating the maximum pixel gray value from the image that will be embossed. Pixels with values greater than this will be ignored.
    
    d0min - The depth into the object to begin embossing from (in voxels) when the color grayMin is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d0max - The depth into the object to begin embossing from (in voxels) when the color grayMax is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d1min - The depth into the object to end embossing (in voxels) when the color grayMin is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d1max - The depth into the object to end embossing (in voxels) when the color grayMax is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    tool - A VoxelArray to use as the tool.
    
    toolcx - The x coordinate of the center of the tool to move along the path.
    
    toolcy - The y coordinate of the center of the tool to move along the path.
    
    toolcz - The z coordinate of the center of the tool to move along the path.
    
    Returns:
    
    A new VoxelArray representing the parts to be added or removed.
  - sphericalEmboss
```
public VoxelArray sphericalEmboss(frink.graphics.FrinkImage img,
                                  float cx,
                                  float cy,
                                  float cz,
                                  double azCenter,
                                  double azWidth,
                                  double altCenter,
                                  double altHeight,
                                  float d0,
                                  float d1,
                                  VoxelArray tool,
                                  int toolcx,
                                  int toolcy,
                                  int toolcz)
```
    Embosses an image using a spherical mapping into the outer hull of an object. This is a simplified "binary" embossing where a single depth will be used regardless of the gray level. Dark parts of the image will be embossed. A tool will be used to carve into the object. This returns a new VoxelArray of the parts to be removed or added from the original object which is unmodified.
    
    Parameters:
    
    img - The image to be embossed
    
    cx - The x-coordinate of the center of the projection.
    
    cy - The y-coordinate of the center of the projection.
    
    cz - The z-coordinate of the center of the projection.
    
    azCenter - The angle (in radians) of the center azimuth of the projection reckoned counterclockwise from the y axis. (0 degrees is toward the y axis, 270 degrees is toward the x axis)
    
    azWidth - The angle (in radians) wide to map the image. 2 pi radians wraps around the entire cylinder.
    
    altCenter - The center altitude angle (in radians) around which to map the image. This should be between -pi/2 (south pole) and +pi/2 radians (north pole). 0 radians is centered on the equator.
    
    altHeight - The angular height (in radians) to map the image. Pi radians will cover the whole sphere.
    
    d0 - The depth to begin embossing from (in voxels). 0 is the surface of the image. Negative numbers are allowed.
    
    d1 - The depth to end embossing into the object (in voxels). 0 is the surface of the image.
    
    tool - A VoxelArray to use as the tool.
    
    toolcx - The x coordinate of the center of the tool to move along the path.
    
    toolcy - The y coordinate of the center of the tool to move along the path.
    
    toolcz - The z coordinate of the center of the tool to move along the path.
    
    Returns:
    
    A new VoxelArray representing the parts to be added or removed.
  - sphericalEmboss
```
public VoxelArray sphericalEmboss(frink.graphics.FrinkImage img,
                                  float cx,
                                  float cy,
                                  float cz,
                                  double azCenter,
                                  double azWidth,
                                  double altCenter,
                                  double altHeight,
                                  int grayMin,
                                  int grayMax,
                                  float d0min,
                                  float d0max,
                                  float d1min,
                                  float d1max,
                                  VoxelArray tool,
                                  int toolcx,
                                  int toolcy,
                                  int toolcz)
```
    Embosses an image using a spherical mapping into the outer hull of an object. This is the most general and powerful of the spherical embossing routines. A tool will be used to carve into the object. This returns a new VoxelArray of the parts to be removed or added from the original object which is unmodified.
    
    Parameters:
    
    img - The image to be embossed
    
    cx - The x-coordinate of the center of the projection.
    
    cy - The y-coordinate of the center of the projection.
    
    cz - The z-coordinate of the center of the projection.
    
    azCenter - The angle (in radians) of the center azimuth of the projection reckoned counterclockwise from the y axis. (0 degrees is toward the y axis, 270 degrees is toward the x axis)
    
    azWidth - The angle (in radians) wide to map the image. 2 pi radians wraps around the entire cylinder.
    
    altCenter - The center altitude angle (in radians) around which to map the image. This should be between -pi/2 (south pole) and +pi/2 radians (north pole). 0 radians is centered on the equator.
    
    altHeight - The angular height (in radians) to map the image. Pi radians will cover the whole sphere.
    
    grayMin - A value from 0 (black) to 255 (white) indicating the minimum pixel gray value from the image that will be embossed. Pixels with values less than this will be ignored.
    
    grayMax - A value from 0 (black) to 255 (white) indicating the maximum pixel gray value from the image that will be embossed. Pixels with values greater than this will be ignored.
    
    d0min - The depth into the object to begin embossing from (in voxels) when the color grayMin is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d0max - The depth into the object to begin embossing from (in voxels) when the color grayMax is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d1min - The depth into the object to end embossing (in voxels) when the color grayMin is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d1max - The depth into the object to end embossing (in voxels) when the color grayMax is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    tool - A VoxelArray to use as the tool.
    
    toolcx - The x coordinate of the center of the tool to move along the path.
    
    toolcy - The y coordinate of the center of the tool to move along the path.
    
    toolcz - The z coordinate of the center of the tool to move along the path.
    
    Returns:
    
    A new VoxelArray representing the parts to be added or removed.
  - planarEmboss
```
public VoxelArray planarEmboss(frink.graphics.FrinkImage img,
                               float cx,
                               float cy,
                               float xWidth,
                               float yHeight,
                               int grayMin,
                               int grayMax,
                               float d0min,
                               float d0max,
                               float d1min,
                               float d1max,
                               VoxelArray tool,
                               int toolcx,
                               int toolcy,
                               int toolcz)
```
    Embosses an image using a planar mapping into the top of an object (that is, downward on the Z-axis.) A tool will be used to carve into the object. This returns a new VoxelArray of the parts to be removed or added from the original object which is unmodified.
    
    Parameters:
    
    img - The image to be embossed
    
    cx - The x-coordinate of the center of the projection.
    
    cy - The y-coordinate of the center of the projection.
    
    xWidth - The width (in voxels) of the x-axis of the projection
    
    yHeight - The height (in voxels) of the y-axis of the projection
    
    grayMin - A value from 0 (black) to 255 (white) indicating the minimum pixel gray value from the image that will be embossed. Pixels with values less than this will be ignored.
    
    grayMax - A value from 0 (black) to 255 (white) indicating the maximum pixel gray value from the image that will be embossed. Pixels with values greater than this will be ignored.
    
    d0min - The depth into the object to begin embossing from (in voxels) when the color grayMin is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d0max - The depth into the object to begin embossing from (in voxels) when the color grayMax is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d1min - The depth into the object to end embossing (in voxels) when the color grayMin is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    d1max - The depth into the object to end embossing (in voxels) when the color grayMax is encountered. 0 is the surface of the image. Negative numbers are allowed.
    
    tool - A VoxelArray to use as the tool.
    
    toolcx - The x coordinate of the center of the tool to move along the path.
    
    toolcy - The y coordinate of the center of the tool to move along the path.
    
    toolcz - The z coordinate of the center of the tool to move along the path.
    
    Returns:
    
    A new VoxelArray representing the parts to be added or removed.
  - countSetBits
```
public long countSetBits()
```
    Counts the number of set bits.
  - mod
```
private double mod(double x,
                   double y)
```
    Define a modulus operator where x % y = x - y * floor[x/y] . This means that the result will have the same sign as y (not x as in Java's normal math.)
  - centerOfMass
```
public Point3DDouble centerOfMass()
```
    Calculate the center of mass of all set voxels (assuming each voxel has the same density).
    To convert from voxel coordinate v to original coordinate x,
    x = xmin + v (xmax - xmin) / (vmax - vmin)
    inverse:
    
    v = (x - xmin) (vmax - vmin) / (xmax - xmin)
    
    Returns:
    
    a Point3DDouble indicating the center of mass.

Class VoxelArray

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

voxels

sizeX

sizeY

sizeZ

offX

offY

offZ

area

TWOPI

Constructor Detail

VoxelArray

VoxelArray

VoxelArray

VoxelArray

VoxelArray

Method Detail

construct

cube

construct

construct

toIndex

toIndexNoCheck

indexToXYZ

setRange

fillCube

set

set

setNoCheck

setNoCheck

isInRange

isInRange

checkPoint

get

getNoCheck

getNoCheck

getSizeX

getSizeY

getSizeZ

getMinX

getMinY

getMinZ

getMaxX

getMaxY

getMaxZ

getCenter

translate

sampleFloat

sampleBoolean

sampleBoolean

sampleFloat

triangulateHull

toObjFormat

toObjFormat

toSTLFormat

toSTLFormat

hullPoints

externalHullPoints

floodFill

projectX

projectY

projectZ

remove

addAlongLine

removeAlongLine

paintAlongLine

add

intersectsWith

intersectsWith

union

union

invert

volume

hasSameBoundary

makeSphere