Type Parameters:

ST - is the type of the general implementation.

IT - is the type of the implementation of this shape.

IE - is the type of the path elements.

P - is the type of the points.

V - is the type of the vectors.

B - is the type of the bounding boxes.

All Superinterfaces:

Cloneable, JsonableObject, Path3D<ST,IT,PathIterator3ai<IE>,P,V,B>, Serializable, Shape3ai<ST,IT,IE,P,V,B>, Shape3D<ST,IT,PathIterator3ai<IE>,P,V,B>

All Known Implementing Classes:

Path3i, Path3ifx
```
public interface Path3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
extends Shape3ai<ST,IT,IE,P,V,B>, Path3D<ST,IT,PathIterator3ai<IE>,P,V,B>
```
Fonctional interface that represented a 2D path on a plane.

Since:

13.0

Version:

17.0 2020-01-04 14:41:43

Author:

Stéphane GALLAND, Hamza JAFFALI

Maven Group Id:

org.arakhne.afc.core

Maven Artifact Id:

mathgeom

Nested Class Summary

Nested Classes
Modifier and Type	Interface	Description
`static class`	`Path3ai.AbstractPathIterator<E extends PathElement3ai>`	An abstract path iterator.
`static class`	`Path3ai.FlatteningPathIterator<E extends PathElement3ai>`	A path iterator that is flattening the path.
`static class`	`Path3ai.PathPathIterator<E extends PathElement3ai>`	A path iterator that does not transform the coordinates.
`static class`	`Path3ai.PixelIterator<P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>>`	Iterator on the pixels of the path.
`static class`	`Path3ai.PointCollection<P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>>`	An collection of the points of the path.
`static class`	`Path3ai.PointIterator<P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>>`	Iterator on the points of the path.
`static class`	`Path3ai.PrivateAPI`	Private API for Path3ai.
`static class`	`Path3ai.TransformedPathIterator<E extends PathElement3ai>`	A path iterator that transforms the coordinates.

Nested classes/interfaces inherited from interface org.arakhne.afc.math.geometry.d3.Path3D
Path3D.ArcType

Field Summary

Fields
Modifier and Type	Field	Description
`static int`	`DEFAULT_FLATTENING_LIMIT`	Default depth for the flattening of the path.
`static PathWindingRule`	`DEFAULT_WINDING_RULE`	The default winding rule: `PathWindingRule.NON_ZERO`.
`static int`	`GROW_SIZE`	Multiple of cubic & quad curve size.

Method Summary

All Methods Static Methods Instance Methods Abstract Methods Default Methods
Modifier and Type	Method	Description
`default void`	`add(Iterator<? extends PathElement3ai> iterator)`	Add the elements replied by the iterator into this path.
`static boolean`	`computeControlPointBoundingBox(PathIterator3ai<?> iterator, RectangularPrism3ai<?,?,?,?,?,?> box)`	Compute the box that corresponds to the control points of the path.
`static int`	`computeCrossingsFromPath(int crossings, PathIterator3ai<?> iterator, BasicPathShadow3ai shadow, CrossingComputationType type)`	Accumulate the number of times the path crosses the shadow extending to the right of the second path.
`static int`	`computeCrossingsFromPoint(int crossings, PathIterator3ai<?> pi, int px, int py, int pz, CrossingComputationType type)`	Calculates the number of times the given path crosses the ray extending to the right from (px,py).
`static int`	`computeCrossingsFromRect(int crossings, PathIterator3ai<?> pi, int rxmin, int rymin, int rzmin, int rxmax, int rymax, int rzmax, CrossingComputationType type)`	Accumulate the number of times the path crosses the shadow extending to the right of the rectangle.
`static int`	`computeCrossingsFromSegment(int crossings, PathIterator3ai<?> pi, int x1, int y1, int z1, int x2, int y2, int z2, CrossingComputationType type)`	Calculates the number of times the given path crosses the given circle extending to the right.
`static int`	`computeCrossingsFromSphere(int crossings, PathIterator3ai<?> pi, int cx, int cy, int cz, int radius, CrossingComputationType type)`	Calculates the number of times the given path crosses the given circle extending to the right.
`static boolean`	`computeDrawableElementBoundingBox(PathIterator3ai<?> iterator, RectangularPrism3ai<?,?,?,?,?,?> box)`	Compute the box that corresponds to the drawable elements of the path.
`default boolean`	`contains(int x, int y, int z)`	Replies if the given point is inside this shape.
`static boolean`	`contains(PathIterator3ai<?> pi, int x, int y, int z)`	Tests if the specified coordinates are inside the closed boundary of the specified `PathIterator3ai`.
`static boolean`	`contains(PathIterator3ai<?> pi, int rx, int ry, int rz, int rwidth, int rheight, int rdepth)`	Tests if the specified rectangle is inside the closed boundary of the specified `PathIterator3ai`.
`default boolean`	`contains(RectangularPrism3ai<?,?,?,?,?,?> box)`	Replies if the given rectangle is inside this shape.
`void`	`curveTo(int x1, int y1, int z1, int x2, int y2, int z2, int x3, int y3, int z3)`	Adds a curved segment, defined by three new points, to the path by drawing a Bézier curve that intersects both the current coordinates and the specified coordinates `(x3,y3)`, using the specified points `(x1,y1)` and `(x2,y2)` as Bézier control points.
`default void`	`curveTo(Point3D<?,?> ctrl1, Point3D<?,?> ctrl2, Point3D<?,?> to)`	Adds a curved segment, defined by three new points, to the path by drawing a Bézier curve that intersects both the current coordinates and the specified coordinates `(x3,y3)`, using the specified points `(x1,y1)` and `(x2,y2)` as Bézier control points.
`default boolean`	`equalsToShape(IT shape)`	Replies this shape is equal to the given shape.
`default P`	`getClosestPointTo(MultiShape3ai<?,?,?,?,?,?,?> multishape)`	Replies the closest point on this shape to the given rectangle.
`default P`	`getClosestPointTo(Path3ai<?,?,?,?,?,?> path)`	Replies the closest point on this shape to the given rectangle.
`static void`	`getClosestPointTo(PathIterator3ai<? extends PathElement3ai> pi, int x, int y, int z, Point3D<?,?> result)`	Replies the point on the path that is closest to the given point.
`default P`	`getClosestPointTo(RectangularPrism3ai<?,?,?,?,?,?> rectangle)`	Replies the closest point on this shape to the given rectangle.
`default P`	`getClosestPointTo(Segment3ai<?,?,?,?,?,?> segment)`	Replies the closest point on this shape to the given rectangle.
`default P`	`getClosestPointTo(Sphere3ai<?,?,?,?,?,?> circle)`	Replies the closest point on this shape to the given rectangle.
`default P`	`getClosestPointTo(Point3D<?,?> pt)`	Replies the point on the shape that is closest to the given point.
`int`	`getCoordAt(int index)`	Replies the coordinate at the given index.
`default P`	`getCurrentPoint()`	Replies the last point in the path.
`int`	`getCurrentX()`	Replies the x coordinate of the last point in the path.
`int`	`getCurrentY()`	Replies the x coordinate of the last point in the path.
`int`	`getCurrentZ()`	Replies the z coordinate of the last point in the path.
`default double`	`getDistanceL1(Point3D<?,?> point)`	Computes the L-1 (Manhattan) distance between this shape and point p1.
`default double`	`getDistanceLinf(Point3D<?,?> point)`	Computes the L-infinite distance between this shape and point p1.
`default double`	`getDistanceSquared(Point3D<?,?> point)`	Replies the squared value of the minimal distance from this shape to the given point.
`static void`	`getFarthestPointTo(PathIterator3ai<? extends PathElement3ai> pi, int x, int y, int z, Point3D<?,?> result)`	Replies the point on the path that is farthest to the given point.
`default P`	`getFarthestPointTo(Point3D<?,?> pt)`	Replies the point on the shape that is farthest the given point.
`default double`	`getLengthSquared()`	Replies the total squared length of the path.
`default PathIterator3ai<IE>`	`getPathIterator(double flatness)`	Replies an iterator on the path elements.
`default PathIterator3ai<IE>`	`getPathIterator(Transform3D transform)`	Replies the elements of the paths.
`default Iterator<P>`	`getPointIterator()`	Replies an iterator on the points covered by the perimeter of this shape.
`default boolean`	`intersects(MultiShape3ai<?,?,?,?,?,?,?> multishape)`	Replies if this shape is intersecting the given multishape.
`default boolean`	`intersects(PathIterator3ai<?> iterator)`	Replies if this shape is intersecting the path described by the given iterator.
`static boolean`	`intersects(PathIterator3ai<?> pi, int x, int y, int z, int width, int height, int depth)`	Tests if the interior of the specified `PathIterator3ai` intersects the interior of a specified set of rectangular coordinates.
`default boolean`	`intersects(RectangularPrism3ai<?,?,?,?,?,?> rectangularPrism)`	Replies if this shape is intersecting the given rectangular prism.
`default boolean`	`intersects(Segment3ai<?,?,?,?,?,?> segment)`	Replies if this shape is intersecting the given segment.
`default boolean`	`intersects(Sphere3ai<?,?,?,?,?,?> sphere)`	Replies if this shape is intersecting the given sphere.
`void`	`lineTo(int x, int y, int z)`	Adds a point to the path by drawing a straight line from the current coordinates to the new specified coordinates specified in double precision.
`default void`	`lineTo(Point3D<?,?> to)`	Adds a point to the path by drawing a straight line from the current coordinates to the new specified coordinates specified in double precision.
`void`	`moveTo(int x, int y, int z)`	Adds a point to the path by moving to the specified coordinates specified in double precision.
`default void`	`moveTo(Point3D<?,?> position)`	Adds a point to the path by moving to the specified coordinates specified in double precision.
`void`	`quadTo(int x1, int y1, int z1, int x2, int y2, int z2)`	Adds a curved segment, defined by two new points, to the path by drawing a Quadratic curve that intersects both the current coordinates and the specified coordinates `(x2,y2)`, using the specified point `(x1,y1)` as a quadratic parametric control point.
`default void`	`quadTo(Point3D<?,?> ctrl, Point3D<?,?> to)`	Adds a curved segment, defined by two new points, to the path by drawing a Quadratic curve that intersects both the current coordinates and the specified coordinates `(x2,y2)`, using the specified point `(x1,y1)` as a quadratic parametric control point.
`boolean`	`remove(int x, int y, int z)`	Remove the point with the given coordinates.
`default void`	`set(Path3ai<?,?,?,?,?,?> path)`	Set the path.
`void`	`setLastPoint(int x, int y, int z)`	Change the coordinates of the last inserted point.
`default void`	`setLastPoint(Point3D<?,?> point)`	Change the coordinates of the last inserted point.
`default Collection<P>`	`toCollection()`	Replies the collection that is contains all the points of the path.
`void`	`transform(Transform3D transform)`	Transform the current path.

Methods inherited from interface org.arakhne.afc.vmutil.json.JsonableObject
toJson

Methods inherited from interface org.arakhne.afc.math.geometry.d3.Path3D
closePath, containsControlPoint, getLength, getPathElementCount, getPathElementTypeAt, getPointAt, getWindingRule, isCurved, isMultiParts, isPolygon, isPolyline, removeLast, setWindingRule, size, toBoundingBoxWithCtrlPoints, toBoundingBoxWithCtrlPoints, toDoubleArray, toDoubleArray, toFloatArray, toFloatArray, toIntArray, toIntArray, toPointArray, toPointArray

Methods inherited from interface org.arakhne.afc.math.geometry.d3.ai.Shape3ai
contains, contains, createTransformedShape, getClosestPointTo, getDistanceSquared, getDistanceSquared, getDistanceSquared, getDistanceSquared, getDistanceSquared, getDistanceSquared, getGeomFactory, intersects, intersects, toBoundingBox, translate, translate

Methods inherited from interface org.arakhne.afc.math.geometry.d3.Shape3D
clear, clone, equalsToPathIterator, getDistance, getDistance, getPathIterator, isEmpty, operator_add, operator_and, operator_and, operator_minus, operator_multiply, operator_plus, operator_remove, operator_upTo, set, toBoundingBox

- Field Detail
  - GROW_SIZE
```
static final int GROW_SIZE
```
    Multiple of cubic & quad curve size.
    
    See Also:
    
    Constant Field Values
  - DEFAULT_FLATTENING_LIMIT
```
static final int DEFAULT_FLATTENING_LIMIT
```
    Default depth for the flattening of the path.
    
    See Also:
    
    Constant Field Values
  - DEFAULT_WINDING_RULE
```
static final PathWindingRule DEFAULT_WINDING_RULE
```
    The default winding rule: PathWindingRule.NON_ZERO.
- Method Detail
  - computeDrawableElementBoundingBox
```
static boolean computeDrawableElementBoundingBox(PathIterator3ai<?> iterator,
                                                 RectangularPrism3ai<?,?,?,?,?,?> box)
```
    Compute the box that corresponds to the drawable elements of the path.
    An element is drawable if it is a line, a curve, or a closing path element.
    
    Parameters:
    
    iterator - the iterator on the path elements.
    
    box - the box to set.
    
    Returns:
    
    true if a drawable element was found.
  - computeControlPointBoundingBox
```
static boolean computeControlPointBoundingBox(PathIterator3ai<?> iterator,
                                              RectangularPrism3ai<?,?,?,?,?,?> box)
```
    Compute the box that corresponds to the control points of the path.
    An element is drawable if it is a line, a curve, or a closing path element. The box fits the drawn lines and the drawn curves. The control points of the curves may be outside the output box. For obtaining the bounding box of the drawn lines and cruves, use computeDrawableElementBoundingBox(PathIterator3ai, RectangularPrism3ai).
    
    Parameters:
    
    iterator - the iterator on the path elements.
    
    box - the box to set.
    
    Returns:
    
    true if a control point was found.
    
    See Also:
    
    computeDrawableElementBoundingBox(PathIterator3ai, RectangularPrism3ai)
  - computeCrossingsFromSegment
```
static int computeCrossingsFromSegment(int crossings,
                                       PathIterator3ai<?> pi,
                                       int x1,
                                       int y1,
                                       int z1,
                                       int x2,
                                       int y2,
                                       int z2,
                                       CrossingComputationType type)
```
    Calculates the number of times the given path crosses the given circle extending to the right.
    
    Parameters:
    
    crossings - is the initial value for crossing.
    
    pi - is the description of the path.
    
    x1 - is the first point of the segment.
    
    y1 - is the first point of the segment.
    
    z1 - is the first point of the segment.
    
    x2 - is the first point of the segment.
    
    y2 - is the first point of the segment.
    
    z2 - is the first point of the segment.
    
    type - is the type of special computation to apply. If null, it is equivalent to CrossingComputationType.STANDARD.
    
    Returns:
    
    the crossing
  - computeCrossingsFromSphere
```
static int computeCrossingsFromSphere(int crossings,
                                      PathIterator3ai<?> pi,
                                      int cx,
                                      int cy,
                                      int cz,
                                      int radius,
                                      CrossingComputationType type)
```
    Calculates the number of times the given path crosses the given circle extending to the right.
    
    Parameters:
    
    crossings - is the initial value for crossing.
    
    pi - is the description of the path.
    
    cx - is the center of the circle.
    
    cy - is the center of the circle.
    
    cz - is the center of the circle.
    
    radius - is the radius of the circle.
    
    type - is the type of special computation to apply. If null, it is equivalent to CrossingComputationType.STANDARD.
    
    Returns:
    
    the crossing
  - computeCrossingsFromPoint
```
static int computeCrossingsFromPoint(int crossings,
                                     PathIterator3ai<?> pi,
                                     int px,
                                     int py,
                                     int pz,
                                     CrossingComputationType type)
```
    Calculates the number of times the given path crosses the ray extending to the right from (px,py). If the point lies on a part of the path, then no crossings are counted for that intersection. +1 is added for each crossing where the Y coordinate is increasing -1 is added for each crossing where the Y coordinate is decreasing The return value is the sum of all crossings for every segment in the path. The path must start with a MOVE_TO, otherwise an exception is thrown.
    
    Parameters:
    
    crossings - the initial crossing.
    
    pi - is the description of the path.
    
    px - is the reference point to test.
    
    py - is the reference point to test.
    
    pz - is the reference point to test.
    
    type - is the type of special computation to apply. If null, it is equivalent to CrossingComputationType.STANDARD.
    
    Returns:
    
    the crossing, or GeomConstants.SHAPE_INTERSECTS
  - computeCrossingsFromPath
```
static int computeCrossingsFromPath(int crossings,
                                    PathIterator3ai<?> iterator,
                                    BasicPathShadow3ai shadow,
                                    CrossingComputationType type)
```
    Accumulate the number of times the path crosses the shadow extending to the right of the second path. See the comment for the SHAPE_INTERSECTS constant for more complete details. The return value is the sum of all crossings for both the top and bottom of the shadow for every segment in the path, or the special value SHAPE_INTERSECTS if the path ever enters the interior of the rectangle. The path must start with a SEG_MOVETO, otherwise an exception is thrown. The caller must check r[xy]{min,max} for NaN values.
    
    Parameters:
    
    crossings - the intial crossing.
    
    iterator - is the iterator on the path elements.
    
    shadow - is the description of the shape to project to the right.
    
    type - is the type of special computation to apply. If null, it is equivalent to CrossingComputationType.STANDARD.
    
    Returns:
    
    the crossings.
    
    See Also:
    
    "Weiler–Atherton clipping algorithm"
  - contains
```
static boolean contains(PathIterator3ai<?> pi,
                        int x,
                        int y,
                        int z)
```
    Tests if the specified coordinates are inside the closed boundary of the specified PathIterator3ai.
    This method provides a basic facility for implementors of the Shape3ai interface to implement support for the Shape3ai.contains(int, int, int) method.
    
    Parameters:
    
    pi - the specified PathIterator2f
    
    x - the specified X coordinate
    
    y - the specified Y coordinate
    
    z - the specified Z coordinate
    
    Returns:
    
    true if the specified coordinates are inside the specified PathIterator2f; false otherwise
  - contains
```
static boolean contains(PathIterator3ai<?> pi,
                        int rx,
                        int ry,
                        int rz,
                        int rwidth,
                        int rheight,
                        int rdepth)
```
    Tests if the specified rectangle is inside the closed boundary of the specified PathIterator3ai.
    The points on the path are assumed to be outside the path area. It means that is the rectangle is intersecting the path, this function replies false.
    
    Parameters:
    
    pi - the specified PathIterator3ai
    
    rx - the lowest corner of the rectangle.
    
    ry - the lowest corner of the rectangle.
    
    rz - the lowest corner of the rectangle.
    
    rwidth - is the width of the rectangle.
    
    rheight - is the width of the rectangle.
    
    rdepth - is the width of the rectangle.
    
    Returns:
    
    true if the specified rectangle is inside the specified PathIterator2f; false otherwise.
  - contains
```
@Pure
default boolean contains(RectangularPrism3ai<?,?,?,?,?,?> box)
```
    Description copied from interface: Shape3ai
    
    Replies if the given rectangle is inside this shape.
    
    Specified by:
    
    contains in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    box - the rectangle to test.
    
    Returns:
    
    true if the given box is inside the shape.
  - contains
```
default boolean contains(int x,
                         int y,
                         int z)
```
    Description copied from interface: Shape3ai
    
    Replies if the given point is inside this shape.
    
    Specified by:
    
    contains in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    x - x coordinate of the point to test.
    
    y - y coordinate of the point to test.
    
    z - z coordinate of the point to test.
    
    Returns:
    
    true if the given point is inside this shape, otherwise false.
  - computeCrossingsFromRect
```
static int computeCrossingsFromRect(int crossings,
                                    PathIterator3ai<?> pi,
                                    int rxmin,
                                    int rymin,
                                    int rzmin,
                                    int rxmax,
                                    int rymax,
                                    int rzmax,
                                    CrossingComputationType type)
```
    Accumulate the number of times the path crosses the shadow extending to the right of the rectangle. See the comment for the SHAPE_INTERSECTS constant for more complete details. The return value is the sum of all crossings for both the top and bottom of the shadow for every segment in the path, or the special value SHAPE_INTERSECTS if the path ever enters the interior of the rectangle. The path must start with a SEG_MOVETO, otherwise an exception is thrown. The caller must check r[xy]{min,max} for NaN values.
    
    Parameters:
    
    crossings - the initial crossing.
    
    pi - is the iterator on the path elements.
    
    rxmin - is the first corner of the rectangle.
    
    rymin - is the first corner of the rectangle.
    
    rzmin - is the first corner of the rectangle.
    
    rxmax - is the second corner of the rectangle.
    
    rymax - is the second corner of the rectangle.
    
    rzmax - is the second corner of the rectangle.
    
    type - is the type of special computation to apply. If null, it is equivalent to CrossingComputationType.STANDARD.
    
    Returns:
    
    the crossings.
  - intersects
```
static boolean intersects(PathIterator3ai<?> pi,
                          int x,
                          int y,
                          int z,
                          int width,
                          int height,
                          int depth)
```
    Tests if the interior of the specified PathIterator3ai intersects the interior of a specified set of rectangular coordinates.
    This method provides a basic facility for implementors of the Shape3ai interface to implement support for the intersects() method.
    This method object may conservatively return true in cases where the specified rectangular area intersects a segment of the path, but that segment does not represent a boundary between the interior and exterior of the path. Such a case may occur if some set of segments of the path are retraced in the reverse direction such that the two sets of segments cancel each other out without any interior area between them. To determine whether segments represent true boundaries of the interior of the path would require extensive calculations involving all of the segments of the path and the winding rule and are thus beyond the scope of this implementation.
    
    Parameters:
    
    pi - the specified PathIterator
    
    x - the specified X coordinate
    
    y - the specified Y coordinate
    
    z - the specified Z coordinate
    
    width - the width of the specified rectangular coordinates
    
    height - the height of the specified rectangular coordinates
    
    depth - the depth of the specified rectangular coordinates
    
    Returns:
    
    true if the specified PathIterator and the interior of the specified set of rectangular coordinates intersect each other; false otherwise.
  - intersects
```
@Pure
default boolean intersects(Sphere3ai<?,?,?,?,?,?> sphere)
```
    Description copied from interface: Shape3ai
    
    Replies if this shape is intersecting the given sphere.
    
    Specified by:
    
    intersects in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    sphere - the sphere
    
    Returns:
    
    true if this shape is intersecting the given shape; false if there is no intersection.
  - intersects
```
@Pure
default boolean intersects(RectangularPrism3ai<?,?,?,?,?,?> rectangularPrism)
```
    Description copied from interface: Shape3ai
    
    Replies if this shape is intersecting the given rectangular prism.
    
    Specified by:
    
    intersects in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    rectangularPrism - the rectangular prism.
    
    Returns:
    
    true if this shape is intersecting the given shape; false if there is no intersection.
  - intersects
```
@Pure
default boolean intersects(Segment3ai<?,?,?,?,?,?> segment)
```
    Description copied from interface: Shape3ai
    
    Replies if this shape is intersecting the given segment.
    
    Specified by:
    
    intersects in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    segment - the segment
    
    Returns:
    
    true if this shape is intersecting the given shape; false if there is no intersection.
  - intersects
```
default boolean intersects(PathIterator3ai<?> iterator)
```
    Description copied from interface: Shape3ai
    
    Replies if this shape is intersecting the path described by the given iterator.
    
    Specified by:
    
    intersects in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    iterator - the path Iterator
    
    Returns:
    
    true if this shape is intersecting the given shape; false if there is no intersection.
  - intersects
```
@Pure
default boolean intersects(MultiShape3ai<?,?,?,?,?,?,?> multishape)
```
    Description copied from interface: Shape3ai
    
    Replies if this shape is intersecting the given multishape.
    
    Specified by:
    
    intersects in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    multishape - the ùmultishape
    
    Returns:
    
    true if this shape is intersecting the given shape; false if there is no intersection.
  - getClosestPointTo
```
static void getClosestPointTo(PathIterator3ai<? extends PathElement3ai> pi,
                              int x,
                              int y,
                              int z,
                              Point3D<?,?> result)
```
    Replies the point on the path that is closest to the given point.
    CAUTION: This function works only on path iterators that are replying polyline primitives, ie. if the PathIterator3D.isPolyline()of pi is replying true. getClosestPointTo(Point3D) avoids this restriction.
    
    Parameters:
    
    pi - is the iterator on the elements of the path.
    
    x - x coordinate of the point.
    
    y - y coordinate of the point.
    
    z - z coordinate of the point.
    
    result - the closest point on the shape; or the point itself if it is inside the shape.
  - getClosestPointTo
```
default P getClosestPointTo(Point3D<?,?> pt)
```
    Description copied from interface: Shape3D
    
    Replies the point on the shape that is closest to the given point.
    
    Specified by:
    
    getClosestPointTo in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    pt - the point.
    
    Returns:
    
    the closest point on the shape; or the point itself if it is inside the shape.
  - getClosestPointTo
```
default P getClosestPointTo(RectangularPrism3ai<?,?,?,?,?,?> rectangle)
```
    Description copied from interface: Shape3ai
    
    Replies the closest point on this shape to the given rectangle.
    
    Specified by:
    
    getClosestPointTo in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    rectangle - the rectangle.
    
    Returns:
    
    the closest point on this shape to the given shape; or the point if the point is in this shape.
  - getClosestPointTo
```
default P getClosestPointTo(Sphere3ai<?,?,?,?,?,?> circle)
```
    Description copied from interface: Shape3ai
    
    Replies the closest point on this shape to the given rectangle.
    
    Specified by:
    
    getClosestPointTo in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    circle - the circle.
    
    Returns:
    
    the closest point on this shape to the given shape; or the point if the point is in this shape.
  - getClosestPointTo
```
default P getClosestPointTo(Segment3ai<?,?,?,?,?,?> segment)
```
    Description copied from interface: Shape3ai
    
    Replies the closest point on this shape to the given rectangle.
    
    Specified by:
    
    getClosestPointTo in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    segment - the segment.
    
    Returns:
    
    the closest point on this shape to the given shape; or the point if the point is in this shape.
  - getClosestPointTo
```
default P getClosestPointTo(MultiShape3ai<?,?,?,?,?,?,?> multishape)
```
    Description copied from interface: Shape3ai
    
    Replies the closest point on this shape to the given rectangle.
    
    Specified by:
    
    getClosestPointTo in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    multishape - the multishape.
    
    Returns:
    
    the closest point on this shape to the given shape; or the point if the point is in this shape.
  - getClosestPointTo
```
default P getClosestPointTo(Path3ai<?,?,?,?,?,?> path)
```
    Description copied from interface: Shape3ai
    
    Replies the closest point on this shape to the given rectangle.
    
    Specified by:
    
    getClosestPointTo in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    path - the path.
    
    Returns:
    
    the closest point on this shape to the given shape; or the point if the point is in this shape.
  - getFarthestPointTo
```
static void getFarthestPointTo(PathIterator3ai<? extends PathElement3ai> pi,
                               int x,
                               int y,
                               int z,
                               Point3D<?,?> result)
```
    Replies the point on the path that is farthest to the given point.
    CAUTION: This function works only on path iterators that are replying polyline primitives, ie. if the PathIterator3D.isPolyline() of pi is replying true. getFarthestPointTo(Point3D) avoids this restriction.
    
    Parameters:
    
    pi - is the iterator on the elements of the path.
    
    x - x coordinate of the point.
    
    y - y coordinate of the point.
    
    z - z coordinate of the point.
    
    result - the farthest point on the shape.
  - getFarthestPointTo
```
default P getFarthestPointTo(Point3D<?,?> pt)
```
    Description copied from interface: Shape3D
    
    Replies the point on the shape that is farthest the given point.
    
    Specified by:
    
    getFarthestPointTo in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    pt - the point.
    
    Returns:
    
    the farthest point on the shape.
  - equalsToShape
```
@Pure
default boolean equalsToShape(IT shape)
```
    Description copied from interface: Shape3D
    
    Replies this shape is equal to the given shape.
    
    Specified by:
    
    equalsToShape in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    shape - the shape to compare to.
    
    Returns:
    
    true if this shape is equal is equal to the given path.
  - add
```
default void add(Iterator<? extends PathElement3ai> iterator)
```
    Add the elements replied by the iterator into this path.
    
    Parameters:
    
    iterator - the iterator on the elements to add.
  - set
```
default void set(Path3ai<?,?,?,?,?,?> path)
```
    Set the path.
    
    Parameters:
    
    path - the path to copy.
  - moveTo
```
void moveTo(int x,
            int y,
            int z)
```
    Adds a point to the path by moving to the specified coordinates specified in double precision.
    
    Parameters:
    
    x - the specified X coordinate
    
    y - the specified Y coordinate
    
    z - the specified Y coordinate
  - moveTo
```
default void moveTo(Point3D<?,?> position)
```
    Description copied from interface: Path3D
    
    Adds a point to the path by moving to the specified coordinates specified in double precision.
    
    Specified by:
    
    moveTo in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    position - the new position.
  - lineTo
```
void lineTo(int x,
            int y,
            int z)
```
    Adds a point to the path by drawing a straight line from the current coordinates to the new specified coordinates specified in double precision.
    
    Parameters:
    
    x - the specified X coordinate
    
    y - the specified Y coordinate
    
    z - the specified Y coordinate
  - lineTo
```
default void lineTo(Point3D<?,?> to)
```
    Description copied from interface: Path3D
    
    Adds a point to the path by drawing a straight line from the current coordinates to the new specified coordinates specified in double precision.
    
    Specified by:
    
    lineTo in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    to - the end point
  - quadTo
```
void quadTo(int x1,
            int y1,
            int z1,
            int x2,
            int y2,
            int z2)
```
    Adds a curved segment, defined by two new points, to the path by drawing a Quadratic curve that intersects both the current coordinates and the specified coordinates (x2,y2), using the specified point (x1,y1) as a quadratic parametric control point. All coordinates are specified in double precision.
    
    Parameters:
    
    x1 - the X coordinate of the quadratic control point
    
    y1 - the Y coordinate of the quadratic control point
    
    z1 - the Z coordinate of the quadratic control point
    
    x2 - the X coordinate of the final end point
    
    y2 - the Y coordinate of the final end point
    
    z2 - the Z coordinate of the final end point
  - quadTo
```
default void quadTo(Point3D<?,?> ctrl,
                    Point3D<?,?> to)
```
    Description copied from interface: Path3D
    
    Adds a curved segment, defined by two new points, to the path by drawing a Quadratic curve that intersects both the current coordinates and the specified coordinates (x2,y2), using the specified point (x1,y1) as a quadratic parametric control point. All coordinates are specified in double precision.
    
    Specified by:
    
    quadTo in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    ctrl - the quadratic control point
    
    to - the final end point
  - curveTo
```
void curveTo(int x1,
             int y1,
             int z1,
             int x2,
             int y2,
             int z2,
             int x3,
             int y3,
             int z3)
```
    Adds a curved segment, defined by three new points, to the path by drawing a Bézier curve that intersects both the current coordinates and the specified coordinates (x3,y3), using the specified points (x1,y1) and (x2,y2) as Bézier control points. All coordinates are specified in double precision.
    
    Parameters:
    
    x1 - the X coordinate of the first Bézier control point
    
    y1 - the Y coordinate of the first Bézier control point
    
    z1 - the Z coordinate of the first Bézier control point
    
    x2 - the X coordinate of the second Bézier control point
    
    y2 - the Y coordinate of the second Bézier control point
    
    z2 - the Z coordinate of the second Bézier control point
    
    x3 - the X coordinate of the final end point
    
    y3 - the Y coordinate of the final end point
    
    z3 - the Z coordinate of the final end point
  - curveTo
```
default void curveTo(Point3D<?,?> ctrl1,
                     Point3D<?,?> ctrl2,
                     Point3D<?,?> to)
```
    Description copied from interface: Path3D
    
    Adds a curved segment, defined by three new points, to the path by drawing a Bézier curve that intersects both the current coordinates and the specified coordinates (x3,y3), using the specified points (x1,y1) and (x2,y2) as Bézier control points. All coordinates are specified in double precision.
    
    Specified by:
    
    curveTo in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    ctrl1 - the first Bézier control point
    
    ctrl2 - the second Bézier control point
    
    to - the final end point
  - getDistanceSquared
```
@Pure
default double getDistanceSquared(Point3D<?,?> point)
```
    Description copied from interface: Shape3D
    
    Replies the squared value of the minimal distance from this shape to the given point.
    
    Specified by:
    
    getDistanceSquared in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    point - the point.
    
    Returns:
    
    squared value of the minimal distance between this shape and the point.
  - getDistanceL1
```
@Pure
default double getDistanceL1(Point3D<?,?> point)
```
    Description copied from interface: Shape3D
    
    Computes the L-1 (Manhattan) distance between this shape and point p1. The L-1 distance is equal to abs(x1-x2) + abs(y1-y2).
    
    Specified by:
    
    getDistanceL1 in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    point - the point
    
    Returns:
    
    the distance.
  - getDistanceLinf
```
@Pure
default double getDistanceLinf(Point3D<?,?> point)
```
    Description copied from interface: Shape3D
    
    Computes the L-infinite distance between this shape and point p1. The L-infinite distance is equal to MAX[abs(x1-x2), abs(y1-y2), abs(z1-z2)].
    
    Specified by:
    
    getDistanceLinf in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    point - the point.
    
    Returns:
    
    the distance.
  - getLengthSquared
```
default double getLengthSquared()
```
    Description copied from interface: Path3D
    
    Replies the total squared length of the path.
    
    Specified by:
    
    getLengthSquared in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Returns:
    
    the length of the path.
  - getCurrentPoint
```
@Pure
default P getCurrentPoint()
```
    Description copied from interface: Path3D
    
    Replies the last point in the path.
    
    Specified by:
    
    getCurrentPoint in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Returns:
    
    the last point.
  - getCurrentX
```
@Pure
int getCurrentX()
```
    Replies the x coordinate of the last point in the path.
    
    Returns:
    
    the x coordinate of the last point in the path.
  - getCurrentY
```
@Pure
int getCurrentY()
```
    Replies the x coordinate of the last point in the path.
    
    Returns:
    
    the x coordinate of the last point in the path.
  - getCurrentZ
```
@Pure
int getCurrentZ()
```
    Replies the z coordinate of the last point in the path.
    
    Returns:
    
    the z coordinate of the last point in the path.
  - getCoordAt
```
@Pure
int getCoordAt(int index)
```
    Replies the coordinate at the given index. The index is in [0;Path3D.size()*3).
    
    Parameters:
    
    index - the index
    
    Returns:
    
    the coordinate at the given index.
  - setLastPoint
```
void setLastPoint(int x,
                  int y,
                  int z)
```
    Change the coordinates of the last inserted point.
    
    Parameters:
    
    x - the new x coordinate of the last point.
    
    y - the new y coordinate of the last point.
    
    z - the new z coordinate of the last point.
  - setLastPoint
```
default void setLastPoint(Point3D<?,?> point)
```
    Description copied from interface: Path3D
    
    Change the coordinates of the last inserted point.
    
    Specified by:
    
    setLastPoint in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    point - the point.
  - transform
```
void transform(Transform3D transform)
```
    Transform the current path. This function changes the current path.
    
    Parameters:
    
    transform - is the affine transformation to apply.
    
    See Also:
    
    Shape3ai.createTransformedShape(org.arakhne.afc.math.geometry.d3.Transform3D)
  - remove
```
boolean remove(int x,
               int y,
               int z)
```
    Remove the point with the given coordinates.
    If the given coordinates do not match exactly a point in the path, nothing is removed.
    
    Parameters:
    
    x - the x coordinate of the point to remove.
    
    y - the y coordinate of the point to remove.
    
    z - the z coordinate of the point to remove.
    
    Returns:
    
    true if the point was removed; false otherwise.
  - getPathIterator
```
@Pure
default PathIterator3ai<IE> getPathIterator(double flatness)
```
    Description copied from interface: Path3D
    
    Replies an iterator on the path elements.
    Only PathElementType.MOVE_TO, PathElementType.LINE_TO, and PathElementType.CLOSE types are returned by the iterator.
    The amount of subdivision of the curved segments is controlled by the flatness parameter, which specifies the maximum distance that any point on the unflattened transformed curve can deviate from the returned flattened path segments. Note that a limit on the accuracy of the flattened path might be silently imposed, causing very small flattening parameters to be treated as larger values. This limit, if there is one, is defined by the particular implementation that is used.
    The iterator for this class is not multi-threaded safe.
    
    Specified by:
    
    getPathIterator in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    flatness - is the maximum distance that the line segments used to approximate the curved segments are allowed to deviate from any point on the original curve.
    
    Returns:
    
    an iterator on the path elements.
  - getPathIterator
```
@Pure
default PathIterator3ai<IE> getPathIterator(Transform3D transform)
```
    Description copied from interface: Shape3D
    
    Replies the elements of the paths.
    
    Specified by:
    
    getPathIterator in interface Shape3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Parameters:
    
    transform - is the transformation to apply to the path.
    
    Returns:
    
    the elements of the path.
  - getPointIterator
```
@Pure
default Iterator<P> getPointIterator()
```
    Description copied from interface: Shape3ai
    
    Replies an iterator on the points covered by the perimeter of this shape.
    The implementation of the iterator depends on the shape type. There is no warranty about the order of the points.
    
    Specified by:
    
    getPointIterator in interface Shape3ai<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Returns:
    
    an iterator on the points that are located at the perimeter of the shape.
  - toCollection
```
@Pure
default Collection<P> toCollection()
```
    Description copied from interface: Path3D
    
    Replies the collection that is contains all the points of the path.
    
    Specified by:
    
    toCollection in interface Path3D<ST extends Shape3ai<?,?,IE,P,V,B>,IT extends Path3ai<?,?,IE,P,V,B>,IE extends PathElement3ai,P extends Point3D<? super P,? super V>,V extends Vector3D<? super V,? super P>,B extends RectangularPrism3ai<?,?,IE,P,V,B>>
    
    Returns:
    
    the point collection.

Nested Class Summary

Nested classes/interfaces inherited from interface org.arakhne.afc.math.geometry.d3.Path3D

Field Summary

Method Summary

Methods inherited from interface org.arakhne.afc.vmutil.json.JsonableObject

Methods inherited from interface org.arakhne.afc.math.geometry.d3.Path3D

Methods inherited from interface org.arakhne.afc.math.geometry.d3.ai.Shape3ai

Methods inherited from interface org.arakhne.afc.math.geometry.d3.Shape3D

Field Detail

GROW_SIZE

DEFAULT_FLATTENING_LIMIT

DEFAULT_WINDING_RULE

Method Detail

computeDrawableElementBoundingBox

computeControlPointBoundingBox

computeCrossingsFromSegment

computeCrossingsFromSphere

computeCrossingsFromPoint

computeCrossingsFromPath

contains

contains

contains

contains

computeCrossingsFromRect

intersects

intersects

intersects

intersects

intersects

intersects

getClosestPointTo

getClosestPointTo

getClosestPointTo

getClosestPointTo

getClosestPointTo

getClosestPointTo

getClosestPointTo

getFarthestPointTo

getFarthestPointTo

equalsToShape

add

set

moveTo

moveTo

lineTo

lineTo

quadTo

quadTo

curveTo

curveTo

getDistanceSquared

getDistanceL1

getDistanceLinf

getLengthSquared

getCurrentPoint

getCurrentX

getCurrentY

getCurrentZ

getCoordAt

setLastPoint

setLastPoint

transform

remove

getPathIterator

getPathIterator

getPointIterator

toCollection