Providing frustum planes derived by different inputs (P*MV, ..) used to classify objects

and to test whether they are outside

Extracting the world-frustum planes from the P*Mv:

Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
  Gil Gribb 
  Klaus Hartmann 
  http://graphics.cs.ucf.edu/cap4720/fall2008/plane_extraction.pdf

Classifying Point, Sphere and AABBox:

Efficient View Frustum Culling
  Daniel Sýkora 
  Josef Jelínek 
  http://www.cg.tuwien.ac.at/hostings/cescg/CESCG-2002/DSykoraJJelinek/index.html

Lighthouse3d.com
http://www.lighthouse3d.com/tutorials/view-frustum-culling/

Fundamentals about Planes, Half-Spaces and Frustum-Culling:

Planes and Half-Spaces,  Max Wagner 
http://www.emeyex.com/site/tuts/PlanesHalfSpaces.pdf

Frustum Culling,  Max Wagner 
http://www.emeyex.com/site/tuts/FrustumCulling.pdf

Nested and Inner Type Summary

Modifier and Type	Class and Description
public static class	Frustum.FovDesc `Frustum` description by `fovhv` and `zNear`, `zFar`.
public static enum	Frustum.Location
public static class	Frustum.Plane Plane equation := dot(n, x - p) = 0 -> ax + bc + cx + d == 0 In order to work w/ `isOutside(..)` methods, the normals have to point to the inside of the frustum.

Field Summary

Modifier and Type	Field and Description
public static final int	BOTTOM Index for bottom plane:
public static final int	FAR Index for far plane:
public static final int	LEFT Index for left plane:
public static final int	NEAR Index for near plane:
protected final Frustum.Plane[]	planes Normalized planes[l, r, b, t, n, f]
public static final int	RIGHT Index for right plane:
public static final int	TOP Index for top plane:

Constructor Summary

Access	Constructor and Description
public	Frustum() Creates an undefined instance w/o calculating the frustum.

Method Summary

Modifier and Type	Method and Description
public final Frustum.Location	Returns: `Location` of point related to frustum planes classifyPoint(final float[] the point p) Check to see if a point is outside, inside or on a plane of the frustum.
public final Frustum.Location	Returns: `Location` of point related to frustum planes classifySphere(final float[] center of the sphere p, final float radius of the sphere radius) Check to see if a sphere is outside, intersecting or inside of the frustum.
public final Frustum.Plane[]	Returns: array of normalized `Plane`s, order see above. getPlanes() `Plane`s are ordered in the returned array as follows: `LEFT` `RIGHT` `BOTTOM` `TOP` `NEAR` `FAR`
public final boolean	isAABBoxOutside(final AABBox box) Check to see if an axis aligned bounding box is completely outside of the frustum.
private static final boolean	isOutsideImpl(final Frustum.Plane p, final AABBox box)
public final boolean	Returns: true if outside of the frustum, otherwise inside or on a plane isPointOutside(final float[] the point p) Check to see if a point is outside of the frustum.
public final boolean	Returns: true if outside of the frustum, otherwise inside or intersecting isSphereOutside(final float[] center of the sphere p, final float radius of the sphere radius) Check to see if a sphere is outside of the frustum.
public StringBuilder	toString(StringBuilder sb)
public String	toString() Overrides java.lang.Object.toString. Returns a string representation of the object.
public float[]	Returns: given matrix for chaining updateByFovDesc(final float[] 4x4 matrix in column-major order (also result) m, final int offset in given array m, i.e. start of the 4x4 matrix m_offset, final boolean if true, given matrix will be initialized w/ identity matrix, otherwise only the frustum fields are set. initM, final Frustum.FovDesc `Frustum` `FovDesc` fovDesc) Calculate the frustum planes in world coordinates using the passed `FovDesc`.
public final void	updateByPlanes(final Frustum.Plane[] the 6 source planes src) Copy the given `src` planes into this this instance's planes.
public void	updateByPMV(final float[] pmv, final int pmv_off) Calculate the frustum planes in world coordinates using the passed float[16] as premultiplied P*MV (column major order).

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll wait wait wait

Field Detail

BOTTOM	back to summary
public static final int BOTTOM Index for bottom plane:

FAR	back to summary
public static final int FAR Index for far plane:

LEFT	back to summary
public static final int LEFT Index for left plane:

NEAR	back to summary
public static final int NEAR Index for near plane:

planes	back to summary
protected final Frustum.Plane[] planes Normalized planes[l, r, b, t, n, f]

RIGHT	back to summary
public static final int RIGHT Index for right plane:

TOP	back to summary
public static final int TOP Index for top plane:

Constructor Detail

Frustum back to summary

Frustum	back to summary
public Frustum() Creates an undefined instance w/o calculating the frustum. Use one of the `update(..)` methods to set the `planes`. See Also `updateByPlanes(Plane[])`, `updateByPMV(float[], int)`

public Frustum()

Creates an undefined instance w/o calculating the frustum.

Use one of the update(..) methods to set the planes.

See Also: updateByPlanes(Plane[]), updateByPMV(float[], int)

Method Detail

classifyPoint back to summary

classifyPoint	back to summary
public final Frustum.Location classifyPoint(final float[] p) Check to see if a point is outside, inside or on a plane of the frustum. Parameters p:float[] the point Returns:Frustum.Location `Location` of point related to frustum planes

public final Frustum.Location classifyPoint(final float[] p)

Check to see if a point is outside, inside or on a plane of the frustum.

Parameters

p:float[]: the point

Returns:Frustum.Location

Location of point related to frustum planes

classifySphere back to summary

classifySphere	back to summary
public final Frustum.Location classifySphere(final float[] p, final float radius) Check to see if a sphere is outside, intersecting or inside of the frustum. Parameters p:float[] center of the sphere radius:float radius of the sphere Returns:Frustum.Location `Location` of point related to frustum planes

public final Frustum.Location classifySphere(final float[] p, final float radius)

Check to see if a sphere is outside, intersecting or inside of the frustum.

Parameters

p:float[]: center of the sphere
radius:float: radius of the sphere

Returns:Frustum.Location

Location of point related to frustum planes

getPlanes back to summary

getPlanes	back to summary
public final Frustum.Plane[] getPlanes() `Plane`s are ordered in the returned array as follows: `LEFT` `RIGHT` `BOTTOM` `TOP` `NEAR` `FAR` `Plane`'s normals are pointing to the inside of the frustum in order to work w/ `isOutside(..)` methods. Returns:Frustum.Plane[] array of normalized `Plane`s, order see above.

public final Frustum.Plane[] getPlanes()

Planes are ordered in the returned array as follows:

Plane's normals are pointing to the inside of the frustum in order to work w/ isOutside(..) methods.

Returns:Frustum.Plane[]: array of normalized Planes, order see above.

isAABBoxOutside	back to summary
public final boolean isAABBoxOutside(final AABBox box) Check to see if an axis aligned bounding box is completely outside of the frustum. Note If method returns false, the box may only be partially inside.

isOutsideImpl	back to summary
private static final boolean isOutsideImpl(final Frustum.Plane p, final AABBox box)

isPointOutside	back to summary
public final boolean isPointOutside(final float[] p) Check to see if a point is outside of the frustum. Parameters p:float[] the point Returns:boolean true if outside of the frustum, otherwise inside or on a plane

isPointOutside

back to summary

public final boolean isPointOutside(final float[] p)

Check to see if a point is outside of the frustum.

Parameters

p:float[]: the point

Returns:boolean

true if outside of the frustum, otherwise inside or on a plane

isSphereOutside	back to summary
public final boolean isSphereOutside(final float[] p, final float radius) Check to see if a sphere is outside of the frustum. Parameters p:float[] center of the sphere radius:float radius of the sphere Returns:boolean true if outside of the frustum, otherwise inside or intersecting

isSphereOutside

back to summary

public final boolean isSphereOutside(final float[] p, final float radius)

Check to see if a sphere is outside of the frustum.

Parameters

p:float[]: center of the sphere
radius:float: radius of the sphere

Returns:boolean

true if outside of the frustum, otherwise inside or intersecting

toString	back to summary
public StringBuilder toString(StringBuilder sb)

toString	back to summary
public String toString() Overrides java.lang.Object.toString. Doc from java.lang.Object.toString. Returns a string representation of the object. Returns:String a string representation of the object Annotations @Override

toString

back to summary

public String toString()

Overrides java.lang.Object.toString.

Doc from java.lang.Object.toString.

Returns a string representation of the object.

Returns:String

a string representation of the object

Annotations

@Override

updateByFovDesc back to summary

updateByFovDesc	back to summary
public float[] updateByFovDesc(final float[] m, final int m_offset, final boolean initM, final Frustum.FovDesc fovDesc) Calculate the frustum planes in world coordinates using the passed `FovDesc`. Operation Details: The given `FovDesc` will be transformed into the given float[16] as a perspective matrix (column major order) first, see `FloatUtil#makePerspective(float[], int, boolean, FovHVHalves, float, float)`. Then the float[16] perspective matrix is used to `updateByPMV(float[], int)` this instance. Frustum plane's normals will point to the inside of the viewing frustum, as required by this class. Parameters m:float[] 4x4 matrix in column-major order (also result) m_offset:int offset in given array m, i.e. start of the 4x4 matrix initM:boolean if true, given matrix will be initialized w/ identity matrix, otherwise only the frustum fields are set. fovDesc:Frustum.FovDesc `Frustum` `FovDesc` Returns:float[] given matrix for chaining See Also `FloatUtil#makePerspective(float[], int, boolean, FovHVHalves, float, float)`

public float[] updateByFovDesc(final float[] m, final int m_offset, final boolean initM, final Frustum.FovDesc fovDesc)

Calculate the frustum planes in world coordinates using the passed FovDesc.

Operation Details:

The given FovDesc will be transformed into the given float[16] as a perspective matrix (column major order) first, see FloatUtil#makePerspective(float[], int, boolean, FovHVHalves, float, float).
Then the float[16] perspective matrix is used to updateByPMV(float[], int) this instance.

Frustum plane's normals will point to the inside of the viewing frustum, as required by this class.

Parameters

m:float[]: 4x4 matrix in column-major order (also result)
m_offset:int: offset in given array m, i.e. start of the 4x4 matrix
initM:boolean: if true, given matrix will be initialized w/ identity matrix, otherwise only the frustum fields are set.
fovDesc:Frustum.FovDesc: Frustum FovDesc

Returns:float[]

given matrix for chaining

updateByPlanes back to summary

updateByPlanes	back to summary
public final void updateByPlanes(final Frustum.Plane[] src) Copy the given `src` planes into this this instance's planes. Parameters src:Frustum.Plane[] the 6 source planes

public final void updateByPlanes(final Frustum.Plane[] src)

Copy the given src planes into this this instance's planes.

Parameters

src:Frustum.Plane[]: the 6 source planes

updateByPMV	back to summary
public void updateByPMV(final float[] pmv, final int pmv_off) Calculate the frustum planes in world coordinates using the passed float[16] as premultiplied P*MV (column major order). Frustum plane's normals will point to the inside of the viewing frustum, as required by this class.

updateByPMV

back to summary

public void updateByPMV(final float[] pmv, final int pmv_off)

Calculate the frustum planes in world coordinates using the passed float[16] as premultiplied P*MV (column major order).

Frustum plane's normals will point to the inside of the viewing frustum, as required by this class.

com.jogamp.opengl.math.geom back to summary

public Class Frustum.FovDesc

Class Inheritance

extends Object

java.lang.Object
com.jogamp.opengl.math.geom.Frustum.FovDesc

Frustum description by fovhv and zNear, zFar.

Field Summary

Modifier and Type	Field and Description
public final FovHVHalves	fovhv Field of view in both directions, may not be centered, either `FovHVHalves#inTangents` or radians.
public final float	zFar Far Z
public final float	zNear Near Z

Constructor Summary

Access	Constructor and Description
public	FovDesc(final FovHVHalves field of view in both directions, may not be centered, either `FovHVHalves#inTangents` or radians fovhv, final float zNear, final float zFar)

Method Summary

Modifier and Type	Method and Description
public final String	toString() Overrides java.lang.Object.toString. Returns a string representation of the object.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll wait wait wait

Field Detail

fovhv	back to summary
public final FovHVHalves fovhv Field of view in both directions, may not be centered, either `FovHVHalves#inTangents` or radians.

zFar	back to summary
public final float zFar Far Z

zNear	back to summary
public final float zNear Near Z

Constructor Detail

FovDesc	back to summary
public FovDesc(final FovHVHalves fovhv, final float zNear, final float zFar) throws IllegalArgumentException Parameters fovhv:FovHVHalves field of view in both directions, may not be centered, either `FovHVHalves#inTangents` or radians Exceptions IllegalArgumentException: if `zNear <= 0` or `zFar <= zNear`.

Method Detail

toString	back to summary
public final String toString() Overrides java.lang.Object.toString. Doc from java.lang.Object.toString. Returns a string representation of the object. Returns:String a string representation of the object

toString

back to summary

public final String toString()

Overrides java.lang.Object.toString.

Doc from java.lang.Object.toString.

Returns a string representation of the object.

Returns:String: a string representation of the object

com.jogamp.opengl.math.geom back to summary

public final Enum Frustum.Location

Class Inheritance

extends Enum<Frustum.Location>

java.lang.Object
java.lang.Enum
com.jogamp.opengl.math.geom.Frustum.Location

Field Summary

Modifier and Type	Field and Description
public static final Frustum.Location	INSIDE
public static final Frustum.Location	INTERSECT
public static final Frustum.Location	OUTSIDE

Constructor Summary

Access	Constructor and Description
private	Location()

Method Summary

Modifier and Type	Method and Description
public static Frustum.Location	valueOf(String name)
public static Frustum.Location[]	values()

Inherited from java.lang.Enum:: clone compareTo describeConstable equals finalize getDeclaringClass hashCode name ordinal toString valueOf

Field Detail

INSIDE	back to summary
public static final Frustum.Location INSIDE

INTERSECT	back to summary
public static final Frustum.Location INTERSECT

OUTSIDE	back to summary
public static final Frustum.Location OUTSIDE

Constructor Detail

Location	back to summary
private Location()

Method Detail

valueOf	back to summary
public static Frustum.Location valueOf(String name)

values	back to summary
public static Frustum.Location[] values()

com.jogamp.opengl.math.geom back to summary

public Class Frustum.Plane

Class Inheritance

extends Object

java.lang.Object
com.jogamp.opengl.math.geom.Frustum.Plane

Plane equation := dot(n, x - p) = 0 -> ax + bc + cx + d == 0

In order to work w/ isOutside(..) methods, the normals have to point to the inside of the frustum.

Field Summary

Modifier and Type	Field and Description
public float	d Distance to origin
public final float[]	n Normal of the plane

Constructor Summary

Access	Constructor and Description
public	Plane()

Method Summary

Modifier and Type	Method and Description
public final float	distanceTo(final float x, final float y, final float z) Return signed distance of plane to given point.
public final float	distanceTo(final float[] p) Return distance of plane to given point, see `distanceTo(float, float, float)`.
public String	toString() Overrides java.lang.Object.toString. Returns a string representation of the object.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll wait wait wait

Field Detail

d	back to summary
public float d Distance to origin

n	back to summary
public final float[] n Normal of the plane

Constructor Detail

Plane	back to summary
public Plane()

Method Detail

distanceTo	back to summary
public final float distanceTo(final float x, final float y, final float z) Return signed distance of plane to given point. If dist < 0 , then the point p lies in the negative halfspace. If dist = 0 , then the point p lies in the plane. If dist > 0 , then the point p lies in the positive halfspace. A plane cuts 3D space into 2 half spaces. Positive halfspace is where the plane’s normals vector points into. Negative halfspace is the other side of the plane, i.e. *-1

distanceTo

back to summary

public final float distanceTo(final float x, final float y, final float z)

Return signed distance of plane to given point.

If dist < 0 , then the point p lies in the negative halfspace.
If dist = 0 , then the point p lies in the plane.
If dist > 0 , then the point p lies in the positive halfspace.

A plane cuts 3D space into 2 half spaces.

Positive halfspace is where the plane’s normals vector points into.

Negative halfspace is the other side of the plane, i.e. *-1

distanceTo	back to summary
public final float distanceTo(final float[] p) Return distance of plane to given point, see `distanceTo(float, float, float)`.

toString	back to summary
public String toString() Overrides java.lang.Object.toString. Doc from java.lang.Object.toString. Returns a string representation of the object. Returns:String a string representation of the object Annotations @Override

toString

back to summary

public String toString()

Overrides java.lang.Object.toString.

Doc from java.lang.Object.toString.

Returns a string representation of the object.

Returns:String

a string representation of the object

Annotations

@Override