Package eu.svjatoslav.sixth.e3d.geometry

Class Plane

java.lang.Object

eu.svjatoslav.sixth.e3d.geometry.Plane

public class Plane
extends Object

Represents an infinite plane in 3D space using the Hesse normal form.

Planes are fundamental to BSP (Binary Space Partitioning) tree operations in CSG. They divide 3D space into two half-spaces.

See Also:

• polygons that reference their containing plane
• BSP trees that use planes for spatial partitioning

Field Summary

Fields

Modifier and Type	Field	Description
double	distance	The signed distance from the origin to the plane along the normal.
static final double	EPSILON	Epsilon value used for floating-point comparisons in BSP operations.
Point3D	normal	The unit normal vector perpendicular to the plane surface.

Constructor Summary

Constructors

Constructor	Description
Plane(Point3D normal, double distance)	Creates a plane with the given normal and distance.

Method Summary

Modifier and Type	Method	Description
Plane	clone()	Creates a deep clone of this plane.
static boolean	computeNormal(Point3D a, Point3D b, Point3D c, Point3D result)	Computes the unit normal vector for a triangle defined by three points.
void	flip()	Flips the plane orientation by negating the normal and distance.
static Plane	fromPoints(Point3D a, Point3D b, Point3D c)	Creates a plane from three non-collinear points.
void	splitPolygon(SolidPolygon polygon, List<SolidPolygon> coplanarFront, List<SolidPolygon> coplanarBack, List<SolidPolygon> front, List<SolidPolygon> back)	Splits a polygon by this plane, classifying and potentially dividing it.

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

EPSILON

public static final double EPSILON

Epsilon value used for floating-point comparisons in BSP operations. Smaller values provide higher precision but may cause issues with near-coplanar polygons. 1e-5 is a good balance for most 3D geometry.

See Also:

• Constant Field Values

normal

public Point3D normal

The unit normal vector perpendicular to the plane surface.

distance

public double distance

The signed distance from the origin to the plane along the normal.

Constructor Details

Plane

public Plane(Point3D normal,
 double distance)

Creates a plane with the given normal and distance.

Parameters:

normal - the unit normal vector

distance - the signed distance from origin to the plane

Method Details

computeNormal

public static boolean computeNormal(Point3D a,
 Point3D b,
 Point3D c,
 Point3D result)

Computes the unit normal vector for a triangle defined by three points.

Zero-allocation method: fills the result point instead of creating a new one. This is the shared implementation used by both fromPoints(eu.svjatoslav.sixth.e3d.geometry.Point3D, eu.svjatoslav.sixth.e3d.geometry.Point3D, eu.svjatoslav.sixth.e3d.geometry.Point3D) and SolidPolygon for shading calculations.

The normal is computed as the cross product of two edge vectors (b-a and c-a), then normalized to unit length.

Parameters:

a - first point (base point for edge vectors)

b - second point

c - third point

result - Point3D to receive the unit normal vector (modified in place)

Returns:

true if normal computed successfully, false if points are collinear (cross product magnitude less than EPSILON)

fromPoints

public static Plane fromPoints(Point3D a,
 Point3D b,
 Point3D c)

Creates a plane from three non-collinear points.

Uses computeNormal(eu.svjatoslav.sixth.e3d.geometry.Point3D, eu.svjatoslav.sixth.e3d.geometry.Point3D, eu.svjatoslav.sixth.e3d.geometry.Point3D, eu.svjatoslav.sixth.e3d.geometry.Point3D) for the normal calculation, then computes the signed distance from origin using the dot product.

Parameters:

a - the first point on the plane

b - the second point on the plane

c - the third point on the plane

Returns:

a new Plane passing through the three points

Throws:

ArithmeticException - if the points are collinear (cannot define a plane)

clone

public Plane clone()

Creates a deep clone of this plane.

Overrides:

clone in class Object

Returns:

a new Plane with the same normal and distance

flip

public void flip()

Flips the plane orientation by negating the normal and distance.

splitPolygon

public void splitPolygon(SolidPolygon polygon,
 List<SolidPolygon> coplanarFront,
 List<SolidPolygon> coplanarBack,
 List<SolidPolygon> front,
 List<SolidPolygon> back)

Splits a polygon by this plane, classifying and potentially dividing it.

Parameters:

polygon - the polygon to classify and potentially split

coplanarFront - list to receive coplanar polygons with same-facing normals

coplanarBack - list to receive coplanar polygons with opposite-facing normals

front - list to receive polygons in the front half-space

back - list to receive polygons in the back half-space