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jMonkeyEngine is a 3-D game engine for adventurous Java developers
/*
* Copyright (c) 2009-2020 jMonkeyEngine
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name of 'jMonkeyEngine' nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package com.jme3.math;
import com.jme3.export.*;
import com.jme3.util.TempVars;
import java.io.IOException;
/**
* LineSegment represents a segment in the space. This is a portion of a Line
* that has a limited start and end points.
* A LineSegment is defined by an origin, a direction and an extent (or length).
* Direction should be a normalized vector. It is not internally normalized.
* This class provides methods to calculate distances between LineSegments, Rays and Vectors.
* It is also possible to retrieve both end points of the segment {@link LineSegment#getPositiveEnd(Vector3f)}
* and {@link LineSegment#getNegativeEnd(Vector3f)}. There are also methods to check whether
* a point is within the segment bounds.
*
* @see Ray
* @author Mark Powell
* @author Joshua Slack
*/
public class LineSegment implements Cloneable, Savable, java.io.Serializable {
static final long serialVersionUID = 1;
private Vector3f origin;
private Vector3f direction;
private float extent;
/**
* Instantiate a zero-length segment at the origin.
*/
public LineSegment() {
origin = new Vector3f();
direction = new Vector3f();
}
/**
* Instantiate a copy of the specified segment.
*
* @param ls the LineSegment to copy (not null, unaffected)
*/
public LineSegment(LineSegment ls) {
this.origin = new Vector3f(ls.getOrigin());
this.direction = new Vector3f(ls.getDirection());
this.extent = ls.getExtent();
}
/**
* Creates a new LineSegment with the given origin, direction and extent.
* Note that the origin is not one of the ends of the LineSegment, but its center.
*
* @param origin the location of the desired midpoint (alias created)
* @param direction the desired direction vector (alias created)
* @param extent the extent: 1/2 of the desired length, assuming direction
* is a unit vector
*/
public LineSegment(Vector3f origin, Vector3f direction, float extent) {
this.origin = origin;
this.direction = direction;
this.extent = extent;
}
/**
* Creates a new LineSegment with a given origin and end. This constructor will calculate the
* center, the direction and the extent.
*
* @param start location of the negative endpoint (not null, unaffected)
* @param end location of the negative endpoint (not null, unaffected)
*/
public LineSegment(Vector3f start, Vector3f end) {
this.origin = new Vector3f(0.5f * (start.x + end.x), 0.5f * (start.y + end.y), 0.5f * (start.z + end.z));
this.direction = end.subtract(start);
this.extent = direction.length() * 0.5f;
direction.normalizeLocal();
}
/**
* Copy the specified segment to this one.
*
* @param ls the LineSegment to copy (not null, unaffected)
*/
public void set(LineSegment ls) {
this.origin = new Vector3f(ls.getOrigin());
this.direction = new Vector3f(ls.getDirection());
this.extent = ls.getExtent();
}
/**
* Calculate the distance between this segment and the specified point.
*
* @param point a location vector (not null, unaffected)
* @return the minimum distance (≥0)
*/
public float distance(Vector3f point) {
return FastMath.sqrt(distanceSquared(point));
}
/**
* Calculate the distance between this segment and another.
*
* @param ls the other LineSegment (not null, unaffected)
* @return the minimum distance (≥0)
*/
public float distance(LineSegment ls) {
return FastMath.sqrt(distanceSquared(ls));
}
/**
* Calculate the distance between this segment and the specified Ray.
*
* @param r the input Ray (not null, unaffected)
* @return the minimum distance (≥0)
*/
public float distance(Ray r) {
return FastMath.sqrt(distanceSquared(r));
}
/**
* Calculate the squared distance between this segment and the specified
* point.
*
* @param point location vector of the input point (not null, unaffected)
* @return the square of the minimum distance (≥0)
*/
public float distanceSquared(Vector3f point) {
TempVars vars = TempVars.get();
Vector3f compVec1 = vars.vect1;
point.subtract(origin, compVec1);
float segmentParameter = direction.dot(compVec1);
if (-extent < segmentParameter) {
if (segmentParameter < extent) {
origin.add(direction.mult(segmentParameter, compVec1),
compVec1);
} else {
origin.add(direction.mult(extent, compVec1), compVec1);
}
} else {
origin.subtract(direction.mult(extent, compVec1), compVec1);
}
compVec1.subtractLocal(point);
float len = compVec1.lengthSquared();
vars.release();
return len;
}
/**
* Calculate the squared distance between this segment and another.
*
* @param test the other LineSegment (not null, unaffected)
* @return the square of the minimum distance (≥0)
*/
public float distanceSquared(LineSegment test) {
TempVars vars = TempVars.get();
Vector3f compVec1 = vars.vect1;
origin.subtract(test.getOrigin(), compVec1);
float negativeDirectionDot = -(direction.dot(test.getDirection()));
float diffThisDot = compVec1.dot(direction);
float diffTestDot = -(compVec1.dot(test.getDirection()));
float lengthOfDiff = compVec1.lengthSquared();
vars.release();
float determinant = FastMath.abs(1.0f - negativeDirectionDot
* negativeDirectionDot);
float s0, s1, squareDistance, extentDeterminant0, extentDeterminant1, tempS0, tempS1;
if (determinant >= FastMath.FLT_EPSILON) {
// segments are not parallel
s0 = negativeDirectionDot * diffTestDot - diffThisDot;
s1 = negativeDirectionDot * diffThisDot - diffTestDot;
extentDeterminant0 = extent * determinant;
extentDeterminant1 = test.getExtent() * determinant;
if (s0 >= -extentDeterminant0) {
if (s0 <= extentDeterminant0) {
if (s1 >= -extentDeterminant1) {
if (s1 <= extentDeterminant1) // region 0 (interior)
{
// minimum at two interior points of 3D lines
float inverseDeterminant = ((float) 1.0)
/ determinant;
s0 *= inverseDeterminant;
s1 *= inverseDeterminant;
squareDistance = s0
* (s0 + negativeDirectionDot * s1 + (2.0f) * diffThisDot)
+ s1
* (negativeDirectionDot * s0 + s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else // region 3 (side)
{
s1 = test.getExtent();
tempS0 = -(negativeDirectionDot * s1 + diffThisDot);
if (tempS0 < -extent) {
s0 = -extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0)
+ s1 * (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else if (tempS0 <= extent) {
s0 = tempS0;
squareDistance = -s0 * s0 + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else {
s0 = extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0)
+ s1 * (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
}
}
} else // region 7 (side)
{
s1 = -test.getExtent();
tempS0 = -(negativeDirectionDot * s1 + diffThisDot);
if (tempS0 < -extent) {
s0 = -extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0) + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else if (tempS0 <= extent) {
s0 = tempS0;
squareDistance = -s0 * s0 + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else {
s0 = extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0) + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
}
}
} else {
if (s1 >= -extentDeterminant1) {
if (s1 <= extentDeterminant1) // region 1 (side)
{
s0 = extent;
tempS1 = -(negativeDirectionDot * s0 + diffTestDot);
if (tempS1 < -test.getExtent()) {
s1 = -test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1)
+ s0 * (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else if (tempS1 <= test.getExtent()) {
s1 = tempS1;
squareDistance = -s1 * s1 + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else {
s1 = test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1)
+ s0 * (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
}
} else // region 2 (corner)
{
s1 = test.getExtent();
tempS0 = -(negativeDirectionDot * s1 + diffThisDot);
if (tempS0 < -extent) {
s0 = -extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0)
+ s1 * (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else if (tempS0 <= extent) {
s0 = tempS0;
squareDistance = -s0 * s0 + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else {
s0 = extent;
tempS1 = -(negativeDirectionDot * s0 + diffTestDot);
if (tempS1 < -test.getExtent()) {
s1 = -test.getExtent();
squareDistance = s1
* (s1 - (2.0f) * tempS1) + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else if (tempS1 <= test.getExtent()) {
s1 = tempS1;
squareDistance = -s1 * s1 + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else {
s1 = test.getExtent();
squareDistance = s1
* (s1 - (2.0f) * tempS1) + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
}
}
}
} else // region 8 (corner)
{
s1 = -test.getExtent();
tempS0 = -(negativeDirectionDot * s1 + diffThisDot);
if (tempS0 < -extent) {
s0 = -extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0) + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else if (tempS0 <= extent) {
s0 = tempS0;
squareDistance = -s0 * s0 + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else {
s0 = extent;
tempS1 = -(negativeDirectionDot * s0 + diffTestDot);
if (tempS1 > test.getExtent()) {
s1 = test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1)
+ s0 * (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else if (tempS1 >= -test.getExtent()) {
s1 = tempS1;
squareDistance = -s1 * s1 + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else {
s1 = -test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1)
+ s0 * (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
}
}
}
}
} else {
if (s1 >= -extentDeterminant1) {
if (s1 <= extentDeterminant1) // region 5 (side)
{
s0 = -extent;
tempS1 = -(negativeDirectionDot * s0 + diffTestDot);
if (tempS1 < -test.getExtent()) {
s1 = -test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1) + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else if (tempS1 <= test.getExtent()) {
s1 = tempS1;
squareDistance = -s1 * s1 + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else {
s1 = test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1) + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
}
} else // region 4 (corner)
{
s1 = test.getExtent();
tempS0 = -(negativeDirectionDot * s1 + diffThisDot);
if (tempS0 > extent) {
s0 = extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0) + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else if (tempS0 >= -extent) {
s0 = tempS0;
squareDistance = -s0 * s0 + s1
* (s1 + (2.0f) * diffTestDot)
+ lengthOfDiff;
} else {
s0 = -extent;
tempS1 = -(negativeDirectionDot * s0 + diffTestDot);
if (tempS1 < -test.getExtent()) {
s1 = -test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1)
+ s0 * (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else if (tempS1 <= test.getExtent()) {
s1 = tempS1;
squareDistance = -s1 * s1 + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else {
s1 = test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1)
+ s0 * (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
}
}
}
} else // region 6 (corner)
{
s1 = -test.getExtent();
tempS0 = -(negativeDirectionDot * s1 + diffThisDot);
if (tempS0 > extent) {
s0 = extent;
squareDistance = s0 * (s0 - (2.0f) * tempS0) + s1
* (s1 + (2.0f) * diffTestDot) + lengthOfDiff;
} else if (tempS0 >= -extent) {
s0 = tempS0;
squareDistance = -s0 * s0 + s1
* (s1 + (2.0f) * diffTestDot) + lengthOfDiff;
} else {
s0 = -extent;
tempS1 = -(negativeDirectionDot * s0 + diffTestDot);
if (tempS1 < -test.getExtent()) {
s1 = -test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1) + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else if (tempS1 <= test.getExtent()) {
s1 = tempS1;
squareDistance = -s1 * s1 + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
} else {
s1 = test.getExtent();
squareDistance = s1 * (s1 - (2.0f) * tempS1) + s0
* (s0 + (2.0f) * diffThisDot)
+ lengthOfDiff;
}
}
}
}
} else {
// The segments are parallel. The average b0 term is designed to
// ensure symmetry of the function. That is, dist(seg0,seg1) and
// dist(seg1,seg0) should produce the same number.get
float extentSum = extent + test.getExtent();
float sign = (negativeDirectionDot > 0.0f ? -1.0f : 1.0f);
float averageB0 = (0.5f) * (diffThisDot - sign * diffTestDot);
float lambda = -averageB0;
if (lambda < -extentSum) {
lambda = -extentSum;
} else if (lambda > extentSum) {
lambda = extentSum;
}
squareDistance = lambda * (lambda + (2.0f) * averageB0)
+ lengthOfDiff;
}
return FastMath.abs(squareDistance);
}
/**
* Calculate the squared distance between this segment and the specified
* Ray.
*
* @param r the input Ray (not null, unaffected)
* @return the square of the minimum distance (≥0)
*/
public float distanceSquared(Ray r) {
Vector3f kDiff = r.getOrigin().subtract(origin);
float fA01 = -r.getDirection().dot(direction);
float fB0 = kDiff.dot(r.getDirection());
float fB1 = -kDiff.dot(direction);
float fC = kDiff.lengthSquared();
float fDet = FastMath.abs(1.0f - fA01 * fA01);
float fS0, fS1, fSqrDist, fExtDet;
if (fDet >= FastMath.FLT_EPSILON) {
// The ray and segment are not parallel.
fS0 = fA01 * fB1 - fB0;
fS1 = fA01 * fB0 - fB1;
fExtDet = extent * fDet;
if (fS0 >= (float) 0.0) {
if (fS1 >= -fExtDet) {
if (fS1 <= fExtDet) // region 0
{
// minimum at interior points of ray and segment
float fInvDet = ((float) 1.0) / fDet;
fS0 *= fInvDet;
fS1 *= fInvDet;
fSqrDist = fS0
* (fS0 + fA01 * fS1 + ((float) 2.0) * fB0)
+ fS1
* (fA01 * fS0 + fS1 + ((float) 2.0) * fB1) + fC;
} else // region 1
{
fS1 = extent;
fS0 = -(fA01 * fS1 + fB0);
if (fS0 > (float) 0.0) {
fSqrDist = -fS0 * fS0 + fS1
* (fS1 + ((float) 2.0) * fB1) + fC;
} else {
fS0 = (float) 0.0;
fSqrDist = fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
}
}
} else // region 5
{
fS1 = -extent;
fS0 = -(fA01 * fS1 + fB0);
if (fS0 > (float) 0.0) {
fSqrDist = -fS0 * fS0 + fS1
* (fS1 + ((float) 2.0) * fB1) + fC;
} else {
fS0 = (float) 0.0;
fSqrDist = fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
}
}
} else {
if (fS1 <= -fExtDet) // region 4
{
fS0 = -(-fA01 * extent + fB0);
if (fS0 > (float) 0.0) {
fS1 = -extent;
fSqrDist = -fS0 * fS0 + fS1
* (fS1 + ((float) 2.0) * fB1) + fC;
} else {
fS0 = (float) 0.0;
fS1 = -fB1;
if (fS1 < -extent) {
fS1 = -extent;
} else if (fS1 > extent) {
fS1 = extent;
}
fSqrDist = fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
}
} else if (fS1 <= fExtDet) // region 3
{
fS0 = (float) 0.0;
fS1 = -fB1;
if (fS1 < -extent) {
fS1 = -extent;
} else if (fS1 > extent) {
fS1 = extent;
}
fSqrDist = fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
} else // region 2
{
fS0 = -(fA01 * extent + fB0);
if (fS0 > (float) 0.0) {
fS1 = extent;
fSqrDist = -fS0 * fS0 + fS1
* (fS1 + ((float) 2.0) * fB1) + fC;
} else {
fS0 = (float) 0.0;
fS1 = -fB1;
if (fS1 < -extent) {
fS1 = -extent;
} else if (fS1 > extent) {
fS1 = extent;
}
fSqrDist = fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
}
}
}
} else {
// ray and segment are parallel
if (fA01 > (float) 0.0) {
// opposite direction vectors
fS1 = -extent;
} else {
// same direction vectors
fS1 = extent;
}
fS0 = -(fA01 * fS1 + fB0);
if (fS0 > (float) 0.0) {
fSqrDist = -fS0 * fS0 + fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
} else {
fS0 = (float) 0.0;
fSqrDist = fS1 * (fS1 + ((float) 2.0) * fB1) + fC;
}
}
return FastMath.abs(fSqrDist);
}
/**
* Access the direction of this segment.
*
* @return the pre-existing direction vector
*/
public Vector3f getDirection() {
return direction;
}
/**
* Alter the direction of this segment.
*
* @param direction the desired direction vector (alias created!)
*/
public void setDirection(Vector3f direction) {
this.direction = direction;
}
/**
* Read the extent of this segment.
*
* @return the extent
*/
public float getExtent() {
return extent;
}
/**
* Alter the extent of this segment.
*
* @param extent the desired extent
*/
public void setExtent(float extent) {
this.extent = extent;
}
/**
* Access the origin of this segment.
*
* @return the pre-existing location vector
*/
public Vector3f getOrigin() {
return origin;
}
/**
* Alter the origin of this segment.
*
* @param origin the desired location vector (alias created!)
*/
public void setOrigin(Vector3f origin) {
this.origin = origin;
}
/**
* Determine the location of this segment's positive end.
*
* @param store storage for the result (modified if not null)
* @return a location vector (either store or a new vector)
*/
public Vector3f getPositiveEnd(Vector3f store) {
if (store == null) {
store = new Vector3f();
}
return origin.add((direction.mult(extent, store)), store);
}
/**
* Determine the location of this segment's negative end.
*
* @param store storage for the result (modified if not null)
* @return a location vector (either store or a new vector)
*/
public Vector3f getNegativeEnd(Vector3f store) {
if (store == null) {
store = new Vector3f();
}
return origin.subtract((direction.mult(extent, store)), store);
}
/**
* Serialize this segment to the specified exporter, for example when
* saving to a J3O file.
*
* @param e (not null)
* @throws IOException from the exporter
*/
@Override
public void write(JmeExporter e) throws IOException {
OutputCapsule capsule = e.getCapsule(this);
capsule.write(origin, "origin", Vector3f.ZERO);
capsule.write(direction, "direction", Vector3f.ZERO);
capsule.write(extent, "extent", 0);
}
/**
* De-serialize this segment from the specified importer, for example
* when loading from a J3O file.
*
* @param importer (not null)
* @throws IOException from the importer
*/
@Override
public void read(JmeImporter importer) throws IOException {
InputCapsule capsule = importer.getCapsule(this);
origin = (Vector3f) capsule.readSavable("origin", Vector3f.ZERO.clone());
direction = (Vector3f) capsule.readSavable("direction", Vector3f.ZERO.clone());
extent = capsule.readFloat("extent", 0);
}
/**
* Create a copy of this segment.
*
* @return a new instance, equivalent to this one
*/
@Override
public LineSegment clone() {
try {
LineSegment segment = (LineSegment) super.clone();
segment.direction = direction.clone();
segment.origin = origin.clone();
return segment;
} catch (CloneNotSupportedException e) {
throw new AssertionError();
}
}
/**
* Evaluates whether a given point is contained within the axis aligned bounding box
* that contains this LineSegment.
This function is float error aware.
*
* @param point the location of the input point (not null, unaffected)
* @return true if contained in the box, otherwise false
*/
public boolean isPointInsideBounds(Vector3f point) {
return isPointInsideBounds(point, Float.MIN_VALUE);
}
/**
* Evaluates whether a given point is contained within the axis aligned bounding box
* that contains this LineSegment.
This function accepts an error parameter, which
* is added to the extent of the bounding box.
*
* @param point the location of the input point (not null, unaffected)
* @param error the desired margin for error
* @return true if contained in the box, otherwise false
*/
public boolean isPointInsideBounds(Vector3f point, float error) {
if (FastMath.abs(point.x - origin.x) > FastMath.abs(direction.x * extent) + error) {
return false;
}
if (FastMath.abs(point.y - origin.y) > FastMath.abs(direction.y * extent) + error) {
return false;
}
if (FastMath.abs(point.z - origin.z) > FastMath.abs(direction.z * extent) + error) {
return false;
}
return true;
}
}
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