diff options
Diffstat (limited to 'src/jogl/classes/com/jogamp/graph')
| -rwxr-xr-x | src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java | 1258 | ||||
| -rwxr-xr-x | src/jogl/classes/com/jogamp/graph/math/Quaternion.java | 764 | ||||
| -rwxr-xr-x | src/jogl/classes/com/jogamp/graph/math/VectorUtil.java | 866 |
3 files changed, 1444 insertions, 1444 deletions
diff --git a/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java b/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java index 025a998d8..e60fba02b 100755 --- a/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java +++ b/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java @@ -1,629 +1,629 @@ -/**
- * Copyright 2010 JogAmp Community. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without modification, are
- * permitted provided that the following conditions are met:
- *
- * 1. Redistributions of source code must retain the above copyright notice, this list of
- * conditions and the following disclaimer.
- *
- * 2. 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.
- *
- * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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.
- *
- * The views and conclusions contained in the software and documentation are those of the
- * authors and should not be interpreted as representing official policies, either expressed
- * or implied, of JogAmp Community.
- */
-package com.jogamp.graph.curve;
-
-import java.util.ArrayList;
-import java.util.Collections;
-
-import com.jogamp.graph.curve.tess.Triangulation;
-import com.jogamp.graph.curve.tess.Triangulator;
-import com.jogamp.graph.geom.AABBox;
-import com.jogamp.graph.geom.Outline;
-import com.jogamp.graph.geom.Triangle;
-import com.jogamp.graph.geom.Vertex;
-import com.jogamp.graph.math.VectorUtil;
-
-
-/** A Generic shape objects which is defined by a list of Outlines.
- * This Shape can be transformed to Triangulations.
- * The list of triangles generated are render-able by a Region object.
- * The triangulation produced by this Shape will define the
- * closed region defined by the outlines.
- *
- * One or more OutlineShape Object can be associated to a region
- * this is left as a high-level representation of the Objects. For
- * optimizations, flexibility requirements for future features.
- *
- * <br><br>
- * Example to creating an Outline Shape:
- * <pre>
- addVertex(...)
- addVertex(...)
- addVertex(...)
- addEmptyOutline()
- addVertex(...)
- addVertex(...)
- addVertex(...)
- * </pre>
- *
- * The above will create two outlines each with three vertices. By adding these two outlines to
- * the OutlineShape, we are stating that the combination of the two outlines represent the shape.
- * <br>
- *
- * To specify that the shape is curved at a region, the on-curve flag should be set to false
- * for the vertex that is in the middle of the curved region (if the curved region is defined by 3
- * vertices (quadratic curve).
- * <br>
- * In case the curved region is defined by 4 or more vertices the middle vertices should both have
- * the on-curve flag set to false.
- *
- * <br>Example: <br>
- * <pre>
- addVertex(0,0, true);
- addVertex(0,1, false);
- addVertex(1,1, false);
- addVertex(1,0, true);
- * </pre>
- *
- * The above snippet defines a cubic nurbs curve where (0,1 and 1,1)
- * do not belong to the final rendered shape.
- *
- * <i>Implementation Notes:</i><br>
- * <ul>
- * <li> The first vertex of any outline belonging to the shape should be on-curve</li>
- * <li> Intersections between off-curved parts of the outline is not handled</li>
- * </ul>
- *
- * @see Outline
- * @see Region
- */
-public class OutlineShape implements Comparable<OutlineShape> {
- /**
- * Outline's vertices have undefined state until transformed.
- */
- public enum VerticesState {
- UNDEFINED(0), QUADRATIC_NURBS(1);
-
- public final int state;
-
- VerticesState(int state){
- this.state = state;
- }
- }
-
- public static final int DIRTY_BOUNDS = 1 << 0;
-
- private final Vertex.Factory<? extends Vertex> vertexFactory;
- private VerticesState outlineState;
-
- /** The list of {@link Outline}s that are part of this
- * outline shape.
- */
- private ArrayList<Outline> outlines;
- private AABBox bbox;
-
- /** dirty bits DIRTY_BOUNDS */
- private int dirtyBits;
-
- /** Create a new Outline based Shape
- */
- public OutlineShape(Vertex.Factory<? extends Vertex> factory) {
- this.vertexFactory = factory;
- this.outlines = new ArrayList<Outline>(3);
- this.outlines.add(new Outline());
- this.outlineState = VerticesState.UNDEFINED;
- this.bbox = new AABBox();
- this.dirtyBits = 0;
- }
-
- /** Clears all data and reset all states as if this instance was newly created */
- public void clear() {
- outlines.clear();
- outlines.add(new Outline());
- outlineState = VerticesState.UNDEFINED;
- bbox.reset();
- dirtyBits = 0;
- }
-
- /** Returns the associated vertex factory of this outline shape
- * @return Vertex.Factory object
- */
- public final Vertex.Factory<? extends Vertex> vertexFactory() { return vertexFactory; }
-
- public int getOutlineNumber() {
- return outlines.size();
- }
-
- /** Add a new empty {@link Outline}
- * to the end of this shape's outline list.
- * <p>If the {@link #getLastOutline()} is empty already, no new one will be added.</p>
- *
- * After a call to this function all new vertices added
- * will belong to the new outline
- */
- public void addEmptyOutline() {
- if( !getLastOutline().isEmpty() ) {
- outlines.add(new Outline());
- }
- }
-
- /** Appends the {@link Outline} element to the end,
- * ensuring a clean tail.
- *
- * <p>A clean tail is ensured, no double empty Outlines are produced
- * and a pre-existing empty outline will be replaced with the given one. </p>
- *
- * @param outline Outline object to be added
- * @throws NullPointerException if the {@link Outline} element is null
- */
- public void addOutline(Outline outline) throws NullPointerException {
- addOutline(outlines.size(), outline);
- }
-
- /** Insert the {@link Outline} element at the given {@code position}.
- *
- * <p>If the {@code position} indicates the end of this list,
- * a clean tail is ensured, no double empty Outlines are produced
- * and a pre-existing empty outline will be replaced with the given one. </p>
- *
- * @param position of the added Outline
- * @param outline Outline object to be added
- * @throws NullPointerException if the {@link Outline} element is null
- * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position > getOutlineNumber())
- */
- public void addOutline(int position, Outline outline) throws NullPointerException, IndexOutOfBoundsException {
- if (null == outline) {
- throw new NullPointerException("outline is null");
- }
- if( outlines.size() == position ) {
- final Outline lastOutline = getLastOutline();
- if( outline.isEmpty() && lastOutline.isEmpty() ) {
- return;
- }
- if( lastOutline.isEmpty() ) {
- outlines.set(position-1, outline);
- if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
- bbox.resize(outline.getBounds());
- }
- return;
- }
- }
- outlines.add(position, outline);
- if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
- bbox.resize(outline.getBounds());
- }
- }
-
- /** Insert the {@link OutlineShape} elements of type {@link Outline}, .. at the end of this shape,
- * using {@link #addOutline(Outline)} for each element.
- * <p>Closes the current last outline via {@link #closeLastOutline()} before adding the new ones.</p>
- * @param outlineShape OutlineShape elements to be added.
- * @throws NullPointerException if the {@link OutlineShape} is null
- * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position > getOutlineNumber())
- */
- public void addOutlineShape(OutlineShape outlineShape) throws NullPointerException {
- if (null == outlineShape) {
- throw new NullPointerException("OutlineShape is null");
- }
- closeLastOutline();
- for(int i=0; i<outlineShape.getOutlineNumber(); i++) {
- addOutline(outlineShape.getOutline(i));
- }
- }
-
- /** Replaces the {@link Outline} element at the given {@code position}.
- * <p>Sets the bounding box dirty, hence a next call to {@link #getBounds()} will validate it.</p>
- *
- * @param position of the replaced Outline
- * @param outline replacement Outline object
- * @throws NullPointerException if the {@link Outline} element is null
- * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber())
- */
- public void setOutline(int position, Outline outline) throws NullPointerException, IndexOutOfBoundsException {
- if (null == outline) {
- throw new NullPointerException("outline is null");
- }
- outlines.set(position, outline);
- dirtyBits |= DIRTY_BOUNDS;
- }
-
- /** Removes the {@link Outline} element at the given {@code position}.
- * <p>Sets the bounding box dirty, hence a next call to {@link #getBounds()} will validate it.</p>
- *
- * @param position of the to be removed Outline
- * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber())
- */
- public final Outline removeOutline(int position) throws IndexOutOfBoundsException {
- dirtyBits |= DIRTY_BOUNDS;
- return outlines.remove(position);
- }
-
- /** Get the last added outline to the list
- * of outlines that define the shape
- * @return the last outline
- */
- public final Outline getLastOutline() {
- return outlines.get(outlines.size()-1);
- }
-
- /** @return the {@code Outline} at {@code position}
- * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber())
- */
- public Outline getOutline(int position) throws IndexOutOfBoundsException {
- return outlines.get(position);
- }
-
- /** Adds a vertex to the last open outline in the
- * shape.
- * @param v the vertex to be added to the OutlineShape
- */
- public final void addVertex(Vertex v) {
- final Outline lo = getLastOutline();
- lo.addVertex(v);
- if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
- bbox.resize(lo.getBounds());
- }
- }
-
- /** Adds a vertex to the last open outline in the shape.
- * at {@code position}
- * @param position indx at which the vertex will be added
- * @param v the vertex to be added to the OutlineShape
- */
- public final void addVertex(int position, Vertex v) {
- final Outline lo = getLastOutline();
- lo.addVertex(position, v);
- if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
- bbox.resize(lo.getBounds());
- }
- }
-
- /** Add a 2D {@link Vertex} to the last outline by defining the coordniate attribute
- * of the vertex. The 2D vertex will be represented as Z=0.
- *
- * @param x the x coordinate
- * @param y the y coordniate
- * @param onCurve flag if this vertex is on the final curve or defines a curved region
- * of the shape around this vertex.
- */
- public final void addVertex(float x, float y, boolean onCurve) {
- addVertex(vertexFactory.create(x, y, 0f, onCurve));
- }
-
- /** Add a 3D {@link Vertex} to the last outline by defining the coordniate attribute
- * of the vertex.
- * @param x the x coordinate
- * @param y the y coordinate
- * @param z the z coordinate
- * @param onCurve flag if this vertex is on the final curve or defines a curved region
- * of the shape around this vertex.
- */
- public final void addVertex(float x, float y, float z, boolean onCurve) {
- addVertex(vertexFactory.create(x, y, z, onCurve));
- }
-
- /** Add a vertex to the last outline by passing a float array and specifying the
- * offset and length in which. The attributes of the vertex are located.
- * The attributes should be continuous (stride = 0).
- * Attributes which value are not set (when length less than 3)
- * are set implicitly to zero.
- * @param coordsBuffer the coordinate array where the vertex attributes are to be picked from
- * @param offset the offset in the buffer to the x coordinate
- * @param length the number of attributes to pick from the buffer (maximum 3)
- * @param onCurve flag if this vertex is on the final curve or defines a curved region
- * of the shape around this vertex.
- */
- public final void addVertex(float[] coordsBuffer, int offset, int length, boolean onCurve) {
- addVertex(vertexFactory.create(coordsBuffer, offset, length, onCurve));
- }
-
- /** Closes the last outline in the shape.
- * <p>If last vertex is not equal to first vertex.
- * A new temp vertex is added at the end which
- * is equal to the first.</p>
- */
- public void closeLastOutline() {
- getLastOutline().setClosed(true);
- }
-
- /**
- * @return the outline's vertices state, {@link OutlineShape.VerticesState}
- */
- public final VerticesState getOutlineState() {
- return outlineState;
- }
-
- /** Ensure the outlines represent
- * the specified destinationType.
- * and removes all overlaps in boundary triangles
- * @param destinationType the target outline's vertices state. Currently only
- * {@link OutlineShape.VerticesState#QUADRATIC_NURBS} are supported.
- */
- public void transformOutlines(VerticesState destinationType) {
- if(outlineState != destinationType){
- if(destinationType == VerticesState.QUADRATIC_NURBS){
- transformOutlines2Quadratic();
- checkOverlaps();
- } else {
- throw new IllegalStateException("destinationType "+destinationType.name()+" not supported (currently "+outlineState.name()+")");
- }
- }
- }
-
- private void subdivideTriangle(final Outline outline, Vertex a, Vertex b, Vertex c, int index){
- float[] v1 = VectorUtil.mid(a.getCoord(), b.getCoord());
- float[] v3 = VectorUtil.mid(b.getCoord(), c.getCoord());
- float[] v2 = VectorUtil.mid(v1, v3);
-
- //drop off-curve vertex to image on the curve
- b.setCoord(v2, 0, 3);
- b.setOnCurve(true);
-
- outline.addVertex(index, vertexFactory.create(v1, 0, 3, false));
- outline.addVertex(index+2, vertexFactory.create(v3, 0, 3, false));
- }
-
- /** Check overlaps between curved triangles
- * first check if any vertex in triangle a is in triangle b
- * second check if edges of triangle a intersect segments of triangle b
- * if any of the two tests is true we divide current triangle
- * and add the other to the list of overlaps
- *
- * Loop until overlap array is empty. (check only in first pass)
- */
- private void checkOverlaps() {
- ArrayList<Vertex> overlaps = new ArrayList<Vertex>(3);
- int count = getOutlineNumber();
- boolean firstpass = true;
- do {
- for (int cc = 0; cc < count; cc++) {
- final Outline outline = getOutline(cc);
- int vertexCount = outline.getVertexCount();
- for(int i=0; i < outline.getVertexCount(); i++) {
- final Vertex currentVertex = outline.getVertex(i);
- if ( !currentVertex.isOnCurve()) {
- final Vertex nextV = outline.getVertex((i+1)%vertexCount);
- final Vertex prevV = outline.getVertex((i+vertexCount-1)%vertexCount);
- Vertex overlap =null;
-
- //check for overlap even if already set for subdivision
- //ensuring both trianglur overlaps get divided
- //for pref. only check in first pass
- //second pass to clear the overlaps arrray(reduces precision errors)
- if(firstpass) {
- overlap = checkTriOverlaps(prevV, currentVertex, nextV);
- }
- if(overlaps.contains(currentVertex) || overlap != null) {
- overlaps.remove(currentVertex);
-
- subdivideTriangle(outline, prevV, currentVertex, nextV, i);
- i+=3;
- vertexCount+=2;
-
- if(overlap != null && !overlap.isOnCurve()) {
- if(!overlaps.contains(overlap))
- overlaps.add(overlap);
- }
- }
- }
- }
- }
- firstpass = false;
- }while(!overlaps.isEmpty());
- }
-
- private Vertex checkTriOverlaps(Vertex a, Vertex b, Vertex c) {
- int count = getOutlineNumber();
- for (int cc = 0; cc < count; cc++) {
- final Outline outline = getOutline(cc);
- int vertexCount = outline.getVertexCount();
- for(int i=0; i < vertexCount; i++) {
- final Vertex current = outline.getVertex(i);
- if(current.isOnCurve() || current == a || current == b || current == c) {
- continue;
- }
- final Vertex nextV = outline.getVertex((i+1)%vertexCount);
- final Vertex prevV = outline.getVertex((i+vertexCount-1)%vertexCount);
-
- //skip neighboring triangles
- if(prevV == c || nextV == a) {
- continue;
- }
-
- if(VectorUtil.vertexInTriangle(a.getCoord(), b.getCoord(), c.getCoord(), current.getCoord())
- || VectorUtil.vertexInTriangle(a.getCoord(), b.getCoord(), c.getCoord(), nextV.getCoord())
- || VectorUtil.vertexInTriangle(a.getCoord(), b.getCoord(), c.getCoord(), prevV.getCoord())) {
-
- return current;
- }
- if(VectorUtil.tri2SegIntersection(a, b, c, prevV, current)
- || VectorUtil.tri2SegIntersection(a, b, c, current, nextV)
- || VectorUtil.tri2SegIntersection(a, b, c, prevV, nextV)) {
- return current;
- }
- }
- }
- return null;
- }
-
- private void transformOutlines2Quadratic() {
- int count = getOutlineNumber();
- for (int cc = 0; cc < count; cc++) {
- final Outline outline = getOutline(cc);
- int vertexCount = outline.getVertexCount();
-
- for(int i=0; i < vertexCount; i++) {
- final Vertex currentVertex = outline.getVertex(i);
- final Vertex nextVertex = outline.getVertex((i+1)%vertexCount);
- if ( !currentVertex.isOnCurve() && !nextVertex.isOnCurve() ) {
- final float[] newCoords = VectorUtil.mid(currentVertex.getCoord(),
- nextVertex.getCoord());
- final Vertex v = vertexFactory.create(newCoords, 0, 3, true);
- i++;
- vertexCount++;
- outline.addVertex(i, v);
- }
- }
- if(vertexCount <= 0) {
- outlines.remove(outline);
- cc--;
- count--;
- continue;
- }
-
- if( vertexCount > 0 ) {
- if(VectorUtil.checkEquality(outline.getVertex(0).getCoord(),
- outline.getLastVertex().getCoord())) {
- outline.removeVertex(vertexCount-1);
- }
- }
- }
- outlineState = VerticesState.QUADRATIC_NURBS;
- }
-
- private void generateVertexIds() {
- int maxVertexId = 0;
- for(int i=0; i<outlines.size(); i++) {
- final ArrayList<Vertex> vertices = outlines.get(i).getVertices();
- for(int pos=0; pos<vertices.size(); pos++) {
- Vertex vert = vertices.get(pos);
- vert.setId(maxVertexId);
- maxVertexId++;
- }
- }
- }
-
- /** @return the list of concatenated vertices associated with all
- * {@code Outline}s of this object
- */
- public ArrayList<Vertex> getVertices() {
- ArrayList<Vertex> vertices = new ArrayList<Vertex>();
- for(int i=0; i<outlines.size(); i++) {
- vertices.addAll(outlines.get(i).getVertices());
- }
- return vertices;
- }
-
- /**
- * Triangulate the {@link OutlineShape} generating a list of triangles
- * @return an arraylist of triangles representing the filled region
- * which is produced by the combination of the outlines
- */
- public ArrayList<Triangle> triangulate() {
- if(outlines.size() == 0){
- return null;
- }
- sortOutlines();
- generateVertexIds();
-
- Triangulator triangulator2d = Triangulation.create();
- for(int index = 0; index<outlines.size(); index++) {
- triangulator2d.addCurve(outlines.get(index));
- }
-
- ArrayList<Triangle> triangles = triangulator2d.generate();
- triangulator2d.reset();
-
- return triangles;
- }
-
- /** Sort the outlines from large
- * to small depending on the AABox
- */
- private void sortOutlines() {
- Collections.sort(outlines);
- Collections.reverse(outlines);
- }
-
- /** Compare two outline shapes with Bounding Box area
- * as criteria.
- * @see java.lang.Comparable#compareTo(java.lang.Object)
- */
- public final int compareTo(OutlineShape outline) {
- float size = getBounds().getSize();
- float newSize = outline.getBounds().getSize();
- if(size < newSize){
- return -1;
- }
- else if(size > newSize){
- return 1;
- }
- return 0;
- }
-
- private final void validateBoundingBox() {
- dirtyBits &= ~DIRTY_BOUNDS;
- bbox.reset();
- for (int i=0; i<outlines.size(); i++) {
- bbox.resize(outlines.get(i).getBounds());
- }
- }
-
- public final AABBox getBounds() {
- if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
- validateBoundingBox();
- }
- return bbox;
- }
-
- /**
- * @param obj the Object to compare this OutlineShape with
- * @return true if {@code obj} is an OutlineShape, not null,
- * same outlineState, equal bounds and equal outlines in the same order
- */
- public boolean equals(Object obj) {
- if( obj == this) {
- return true;
- }
- if( null == obj || !(obj instanceof OutlineShape) ) {
- return false;
- }
- final OutlineShape o = (OutlineShape) obj;
- if(getOutlineState() != o.getOutlineState()) {
- return false;
- }
- if(getOutlineNumber() != o.getOutlineNumber()) {
- return false;
- }
- if( !getBounds().equals( o.getBounds() ) ) {
- return false;
- }
- for (int i=getOutlineNumber()-1; i>=0; i--) {
- if( ! getOutline(i).equals( o.getOutline(i) ) ) {
- return false;
- }
- }
- return true;
- }
-
- /**
- * @return deep clone of this OutlineShape w/o Region
- */
- public OutlineShape clone() {
- OutlineShape o;
- try {
- o = (OutlineShape) super.clone();
- } catch (CloneNotSupportedException e) { throw new InternalError(); }
- o.bbox = bbox.clone();
- o.outlines = new ArrayList<Outline>(outlines.size());
- for(int i=0; i<outlines.size(); i++) {
- o.outlines.add(outlines.get(i).clone());
- }
- return o;
- }
-}
+/** + * Copyright 2010 JogAmp Community. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without modification, are + * permitted provided that the following conditions are met: + * + * 1. Redistributions of source code must retain the above copyright notice, this list of + * conditions and the following disclaimer. + * + * 2. 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. + * + * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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. + * + * The views and conclusions contained in the software and documentation are those of the + * authors and should not be interpreted as representing official policies, either expressed + * or implied, of JogAmp Community. + */ +package com.jogamp.graph.curve; + +import java.util.ArrayList; +import java.util.Collections; + +import com.jogamp.graph.curve.tess.Triangulation; +import com.jogamp.graph.curve.tess.Triangulator; +import com.jogamp.graph.geom.AABBox; +import com.jogamp.graph.geom.Outline; +import com.jogamp.graph.geom.Triangle; +import com.jogamp.graph.geom.Vertex; +import com.jogamp.graph.math.VectorUtil; + + +/** A Generic shape objects which is defined by a list of Outlines. + * This Shape can be transformed to Triangulations. + * The list of triangles generated are render-able by a Region object. + * The triangulation produced by this Shape will define the + * closed region defined by the outlines. + * + * One or more OutlineShape Object can be associated to a region + * this is left as a high-level representation of the Objects. For + * optimizations, flexibility requirements for future features. + * + * <br><br> + * Example to creating an Outline Shape: + * <pre> + addVertex(...) + addVertex(...) + addVertex(...) + addEmptyOutline() + addVertex(...) + addVertex(...) + addVertex(...) + * </pre> + * + * The above will create two outlines each with three vertices. By adding these two outlines to + * the OutlineShape, we are stating that the combination of the two outlines represent the shape. + * <br> + * + * To specify that the shape is curved at a region, the on-curve flag should be set to false + * for the vertex that is in the middle of the curved region (if the curved region is defined by 3 + * vertices (quadratic curve). + * <br> + * In case the curved region is defined by 4 or more vertices the middle vertices should both have + * the on-curve flag set to false. + * + * <br>Example: <br> + * <pre> + addVertex(0,0, true); + addVertex(0,1, false); + addVertex(1,1, false); + addVertex(1,0, true); + * </pre> + * + * The above snippet defines a cubic nurbs curve where (0,1 and 1,1) + * do not belong to the final rendered shape. + * + * <i>Implementation Notes:</i><br> + * <ul> + * <li> The first vertex of any outline belonging to the shape should be on-curve</li> + * <li> Intersections between off-curved parts of the outline is not handled</li> + * </ul> + * + * @see Outline + * @see Region + */ +public class OutlineShape implements Comparable<OutlineShape> { + /** + * Outline's vertices have undefined state until transformed. + */ + public enum VerticesState { + UNDEFINED(0), QUADRATIC_NURBS(1); + + public final int state; + + VerticesState(int state){ + this.state = state; + } + } + + public static final int DIRTY_BOUNDS = 1 << 0; + + private final Vertex.Factory<? extends Vertex> vertexFactory; + private VerticesState outlineState; + + /** The list of {@link Outline}s that are part of this + * outline shape. + */ + private ArrayList<Outline> outlines; + private AABBox bbox; + + /** dirty bits DIRTY_BOUNDS */ + private int dirtyBits; + + /** Create a new Outline based Shape + */ + public OutlineShape(Vertex.Factory<? extends Vertex> factory) { + this.vertexFactory = factory; + this.outlines = new ArrayList<Outline>(3); + this.outlines.add(new Outline()); + this.outlineState = VerticesState.UNDEFINED; + this.bbox = new AABBox(); + this.dirtyBits = 0; + } + + /** Clears all data and reset all states as if this instance was newly created */ + public void clear() { + outlines.clear(); + outlines.add(new Outline()); + outlineState = VerticesState.UNDEFINED; + bbox.reset(); + dirtyBits = 0; + } + + /** Returns the associated vertex factory of this outline shape + * @return Vertex.Factory object + */ + public final Vertex.Factory<? extends Vertex> vertexFactory() { return vertexFactory; } + + public int getOutlineNumber() { + return outlines.size(); + } + + /** Add a new empty {@link Outline} + * to the end of this shape's outline list. + * <p>If the {@link #getLastOutline()} is empty already, no new one will be added.</p> + * + * After a call to this function all new vertices added + * will belong to the new outline + */ + public void addEmptyOutline() { + if( !getLastOutline().isEmpty() ) { + outlines.add(new Outline()); + } + } + + /** Appends the {@link Outline} element to the end, + * ensuring a clean tail. + * + * <p>A clean tail is ensured, no double empty Outlines are produced + * and a pre-existing empty outline will be replaced with the given one. </p> + * + * @param outline Outline object to be added + * @throws NullPointerException if the {@link Outline} element is null + */ + public void addOutline(Outline outline) throws NullPointerException { + addOutline(outlines.size(), outline); + } + + /** Insert the {@link Outline} element at the given {@code position}. + * + * <p>If the {@code position} indicates the end of this list, + * a clean tail is ensured, no double empty Outlines are produced + * and a pre-existing empty outline will be replaced with the given one. </p> + * + * @param position of the added Outline + * @param outline Outline object to be added + * @throws NullPointerException if the {@link Outline} element is null + * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position > getOutlineNumber()) + */ + public void addOutline(int position, Outline outline) throws NullPointerException, IndexOutOfBoundsException { + if (null == outline) { + throw new NullPointerException("outline is null"); + } + if( outlines.size() == position ) { + final Outline lastOutline = getLastOutline(); + if( outline.isEmpty() && lastOutline.isEmpty() ) { + return; + } + if( lastOutline.isEmpty() ) { + outlines.set(position-1, outline); + if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) { + bbox.resize(outline.getBounds()); + } + return; + } + } + outlines.add(position, outline); + if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) { + bbox.resize(outline.getBounds()); + } + } + + /** Insert the {@link OutlineShape} elements of type {@link Outline}, .. at the end of this shape, + * using {@link #addOutline(Outline)} for each element. + * <p>Closes the current last outline via {@link #closeLastOutline()} before adding the new ones.</p> + * @param outlineShape OutlineShape elements to be added. + * @throws NullPointerException if the {@link OutlineShape} is null + * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position > getOutlineNumber()) + */ + public void addOutlineShape(OutlineShape outlineShape) throws NullPointerException { + if (null == outlineShape) { + throw new NullPointerException("OutlineShape is null"); + } + closeLastOutline(); + for(int i=0; i<outlineShape.getOutlineNumber(); i++) { + addOutline(outlineShape.getOutline(i)); + } + } + + /** Replaces the {@link Outline} element at the given {@code position}. + * <p>Sets the bounding box dirty, hence a next call to {@link #getBounds()} will validate it.</p> + * + * @param position of the replaced Outline + * @param outline replacement Outline object + * @throws NullPointerException if the {@link Outline} element is null + * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber()) + */ + public void setOutline(int position, Outline outline) throws NullPointerException, IndexOutOfBoundsException { + if (null == outline) { + throw new NullPointerException("outline is null"); + } + outlines.set(position, outline); + dirtyBits |= DIRTY_BOUNDS; + } + + /** Removes the {@link Outline} element at the given {@code position}. + * <p>Sets the bounding box dirty, hence a next call to {@link #getBounds()} will validate it.</p> + * + * @param position of the to be removed Outline + * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber()) + */ + public final Outline removeOutline(int position) throws IndexOutOfBoundsException { + dirtyBits |= DIRTY_BOUNDS; + return outlines.remove(position); + } + + /** Get the last added outline to the list + * of outlines that define the shape + * @return the last outline + */ + public final Outline getLastOutline() { + return outlines.get(outlines.size()-1); + } + + /** @return the {@code Outline} at {@code position} + * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber()) + */ + public Outline getOutline(int position) throws IndexOutOfBoundsException { + return outlines.get(position); + } + + /** Adds a vertex to the last open outline in the + * shape. + * @param v the vertex to be added to the OutlineShape + */ + public final void addVertex(Vertex v) { + final Outline lo = getLastOutline(); + lo.addVertex(v); + if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) { + bbox.resize(lo.getBounds()); + } + } + + /** Adds a vertex to the last open outline in the shape. + * at {@code position} + * @param position indx at which the vertex will be added + * @param v the vertex to be added to the OutlineShape + */ + public final void addVertex(int position, Vertex v) { + final Outline lo = getLastOutline(); + lo.addVertex(position, v); + if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) { + bbox.resize(lo.getBounds()); + } + } + + /** Add a 2D {@link Vertex} to the last outline by defining the coordniate attribute + * of the vertex. The 2D vertex will be represented as Z=0. + * + * @param x the x coordinate + * @param y the y coordniate + * @param onCurve flag if this vertex is on the final curve or defines a curved region + * of the shape around this vertex. + */ + public final void addVertex(float x, float y, boolean onCurve) { + addVertex(vertexFactory.create(x, y, 0f, onCurve)); + } + + /** Add a 3D {@link Vertex} to the last outline by defining the coordniate attribute + * of the vertex. + * @param x the x coordinate + * @param y the y coordinate + * @param z the z coordinate + * @param onCurve flag if this vertex is on the final curve or defines a curved region + * of the shape around this vertex. + */ + public final void addVertex(float x, float y, float z, boolean onCurve) { + addVertex(vertexFactory.create(x, y, z, onCurve)); + } + + /** Add a vertex to the last outline by passing a float array and specifying the + * offset and length in which. The attributes of the vertex are located. + * The attributes should be continuous (stride = 0). + * Attributes which value are not set (when length less than 3) + * are set implicitly to zero. + * @param coordsBuffer the coordinate array where the vertex attributes are to be picked from + * @param offset the offset in the buffer to the x coordinate + * @param length the number of attributes to pick from the buffer (maximum 3) + * @param onCurve flag if this vertex is on the final curve or defines a curved region + * of the shape around this vertex. + */ + public final void addVertex(float[] coordsBuffer, int offset, int length, boolean onCurve) { + addVertex(vertexFactory.create(coordsBuffer, offset, length, onCurve)); + } + + /** Closes the last outline in the shape. + * <p>If last vertex is not equal to first vertex. + * A new temp vertex is added at the end which + * is equal to the first.</p> + */ + public void closeLastOutline() { + getLastOutline().setClosed(true); + } + + /** + * @return the outline's vertices state, {@link OutlineShape.VerticesState} + */ + public final VerticesState getOutlineState() { + return outlineState; + } + + /** Ensure the outlines represent + * the specified destinationType. + * and removes all overlaps in boundary triangles + * @param destinationType the target outline's vertices state. Currently only + * {@link OutlineShape.VerticesState#QUADRATIC_NURBS} are supported. + */ + public void transformOutlines(VerticesState destinationType) { + if(outlineState != destinationType){ + if(destinationType == VerticesState.QUADRATIC_NURBS){ + transformOutlines2Quadratic(); + checkOverlaps(); + } else { + throw new IllegalStateException("destinationType "+destinationType.name()+" not supported (currently "+outlineState.name()+")"); + } + } + } + + private void subdivideTriangle(final Outline outline, Vertex a, Vertex b, Vertex c, int index){ + float[] v1 = VectorUtil.mid(a.getCoord(), b.getCoord()); + float[] v3 = VectorUtil.mid(b.getCoord(), c.getCoord()); + float[] v2 = VectorUtil.mid(v1, v3); + + //drop off-curve vertex to image on the curve + b.setCoord(v2, 0, 3); + b.setOnCurve(true); + + outline.addVertex(index, vertexFactory.create(v1, 0, 3, false)); + outline.addVertex(index+2, vertexFactory.create(v3, 0, 3, false)); + } + + /** Check overlaps between curved triangles + * first check if any vertex in triangle a is in triangle b + * second check if edges of triangle a intersect segments of triangle b + * if any of the two tests is true we divide current triangle + * and add the other to the list of overlaps + * + * Loop until overlap array is empty. (check only in first pass) + */ + private void checkOverlaps() { + ArrayList<Vertex> overlaps = new ArrayList<Vertex>(3); + int count = getOutlineNumber(); + boolean firstpass = true; + do { + for (int cc = 0; cc < count; cc++) { + final Outline outline = getOutline(cc); + int vertexCount = outline.getVertexCount(); + for(int i=0; i < outline.getVertexCount(); i++) { + final Vertex currentVertex = outline.getVertex(i); + if ( !currentVertex.isOnCurve()) { + final Vertex nextV = outline.getVertex((i+1)%vertexCount); + final Vertex prevV = outline.getVertex((i+vertexCount-1)%vertexCount); + Vertex overlap =null; + + //check for overlap even if already set for subdivision + //ensuring both trianglur overlaps get divided + //for pref. only check in first pass + //second pass to clear the overlaps arrray(reduces precision errors) + if(firstpass) { + overlap = checkTriOverlaps(prevV, currentVertex, nextV); + } + if(overlaps.contains(currentVertex) || overlap != null) { + overlaps.remove(currentVertex); + + subdivideTriangle(outline, prevV, currentVertex, nextV, i); + i+=3; + vertexCount+=2; + + if(overlap != null && !overlap.isOnCurve()) { + if(!overlaps.contains(overlap)) + overlaps.add(overlap); + } + } + } + } + } + firstpass = false; + }while(!overlaps.isEmpty()); + } + + private Vertex checkTriOverlaps(Vertex a, Vertex b, Vertex c) { + int count = getOutlineNumber(); + for (int cc = 0; cc < count; cc++) { + final Outline outline = getOutline(cc); + int vertexCount = outline.getVertexCount(); + for(int i=0; i < vertexCount; i++) { + final Vertex current = outline.getVertex(i); + if(current.isOnCurve() || current == a || current == b || current == c) { + continue; + } + final Vertex nextV = outline.getVertex((i+1)%vertexCount); + final Vertex prevV = outline.getVertex((i+vertexCount-1)%vertexCount); + + //skip neighboring triangles + if(prevV == c || nextV == a) { + continue; + } + + if(VectorUtil.vertexInTriangle(a.getCoord(), b.getCoord(), c.getCoord(), current.getCoord()) + || VectorUtil.vertexInTriangle(a.getCoord(), b.getCoord(), c.getCoord(), nextV.getCoord()) + || VectorUtil.vertexInTriangle(a.getCoord(), b.getCoord(), c.getCoord(), prevV.getCoord())) { + + return current; + } + if(VectorUtil.tri2SegIntersection(a, b, c, prevV, current) + || VectorUtil.tri2SegIntersection(a, b, c, current, nextV) + || VectorUtil.tri2SegIntersection(a, b, c, prevV, nextV)) { + return current; + } + } + } + return null; + } + + private void transformOutlines2Quadratic() { + int count = getOutlineNumber(); + for (int cc = 0; cc < count; cc++) { + final Outline outline = getOutline(cc); + int vertexCount = outline.getVertexCount(); + + for(int i=0; i < vertexCount; i++) { + final Vertex currentVertex = outline.getVertex(i); + final Vertex nextVertex = outline.getVertex((i+1)%vertexCount); + if ( !currentVertex.isOnCurve() && !nextVertex.isOnCurve() ) { + final float[] newCoords = VectorUtil.mid(currentVertex.getCoord(), + nextVertex.getCoord()); + final Vertex v = vertexFactory.create(newCoords, 0, 3, true); + i++; + vertexCount++; + outline.addVertex(i, v); + } + } + if(vertexCount <= 0) { + outlines.remove(outline); + cc--; + count--; + continue; + } + + if( vertexCount > 0 ) { + if(VectorUtil.checkEquality(outline.getVertex(0).getCoord(), + outline.getLastVertex().getCoord())) { + outline.removeVertex(vertexCount-1); + } + } + } + outlineState = VerticesState.QUADRATIC_NURBS; + } + + private void generateVertexIds() { + int maxVertexId = 0; + for(int i=0; i<outlines.size(); i++) { + final ArrayList<Vertex> vertices = outlines.get(i).getVertices(); + for(int pos=0; pos<vertices.size(); pos++) { + Vertex vert = vertices.get(pos); + vert.setId(maxVertexId); + maxVertexId++; + } + } + } + + /** @return the list of concatenated vertices associated with all + * {@code Outline}s of this object + */ + public ArrayList<Vertex> getVertices() { + ArrayList<Vertex> vertices = new ArrayList<Vertex>(); + for(int i=0; i<outlines.size(); i++) { + vertices.addAll(outlines.get(i).getVertices()); + } + return vertices; + } + + /** + * Triangulate the {@link OutlineShape} generating a list of triangles + * @return an arraylist of triangles representing the filled region + * which is produced by the combination of the outlines + */ + public ArrayList<Triangle> triangulate() { + if(outlines.size() == 0){ + return null; + } + sortOutlines(); + generateVertexIds(); + + Triangulator triangulator2d = Triangulation.create(); + for(int index = 0; index<outlines.size(); index++) { + triangulator2d.addCurve(outlines.get(index)); + } + + ArrayList<Triangle> triangles = triangulator2d.generate(); + triangulator2d.reset(); + + return triangles; + } + + /** Sort the outlines from large + * to small depending on the AABox + */ + private void sortOutlines() { + Collections.sort(outlines); + Collections.reverse(outlines); + } + + /** Compare two outline shapes with Bounding Box area + * as criteria. + * @see java.lang.Comparable#compareTo(java.lang.Object) + */ + public final int compareTo(OutlineShape outline) { + float size = getBounds().getSize(); + float newSize = outline.getBounds().getSize(); + if(size < newSize){ + return -1; + } + else if(size > newSize){ + return 1; + } + return 0; + } + + private final void validateBoundingBox() { + dirtyBits &= ~DIRTY_BOUNDS; + bbox.reset(); + for (int i=0; i<outlines.size(); i++) { + bbox.resize(outlines.get(i).getBounds()); + } + } + + public final AABBox getBounds() { + if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) { + validateBoundingBox(); + } + return bbox; + } + + /** + * @param obj the Object to compare this OutlineShape with + * @return true if {@code obj} is an OutlineShape, not null, + * same outlineState, equal bounds and equal outlines in the same order + */ + public boolean equals(Object obj) { + if( obj == this) { + return true; + } + if( null == obj || !(obj instanceof OutlineShape) ) { + return false; + } + final OutlineShape o = (OutlineShape) obj; + if(getOutlineState() != o.getOutlineState()) { + return false; + } + if(getOutlineNumber() != o.getOutlineNumber()) { + return false; + } + if( !getBounds().equals( o.getBounds() ) ) { + return false; + } + for (int i=getOutlineNumber()-1; i>=0; i--) { + if( ! getOutline(i).equals( o.getOutline(i) ) ) { + return false; + } + } + return true; + } + + /** + * @return deep clone of this OutlineShape w/o Region + */ + public OutlineShape clone() { + OutlineShape o; + try { + o = (OutlineShape) super.clone(); + } catch (CloneNotSupportedException e) { throw new InternalError(); } + o.bbox = bbox.clone(); + o.outlines = new ArrayList<Outline>(outlines.size()); + for(int i=0; i<outlines.size(); i++) { + o.outlines.add(outlines.get(i).clone()); + } + return o; + } +} diff --git a/src/jogl/classes/com/jogamp/graph/math/Quaternion.java b/src/jogl/classes/com/jogamp/graph/math/Quaternion.java index 38638dc5a..adaf073e3 100755 --- a/src/jogl/classes/com/jogamp/graph/math/Quaternion.java +++ b/src/jogl/classes/com/jogamp/graph/math/Quaternion.java @@ -1,382 +1,382 @@ -/**
- * Copyright 2010 JogAmp Community. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without modification, are
- * permitted provided that the following conditions are met:
- *
- * 1. Redistributions of source code must retain the above copyright notice, this list of
- * conditions and the following disclaimer.
- *
- * 2. 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.
- *
- * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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.
- *
- * The views and conclusions contained in the software and documentation are those of the
- * authors and should not be interpreted as representing official policies, either expressed
- * or implied, of JogAmp Community.
- */
-package com.jogamp.graph.math;
-
-import jogamp.graph.math.MathFloat;
-
-public class Quaternion {
- protected float x,y,z,w;
-
- public Quaternion(){
-
- }
-
- public Quaternion(float x, float y, float z, float w) {
- this.x = x;
- this.y = y;
- this.z = z;
- this.w = w;
- }
-
- /** Constructor to create a rotation based quaternion from two vectors
- * @param vector1
- * @param vector2
- */
- public Quaternion(float[] vector1, float[] vector2)
- {
- float theta = (float)MathFloat.acos(dot(vector1, vector2));
- float[] cross = cross(vector1,vector2);
- cross = normalizeVec(cross);
-
- this.x = (float)MathFloat.sin(theta/2)*cross[0];
- this.y = (float)MathFloat.sin(theta/2)*cross[1];
- this.z = (float)MathFloat.sin(theta/2)*cross[2];
- this.w = (float)MathFloat.cos(theta/2);
- this.normalize();
- }
-
- /** Transform the rotational quaternion to axis based rotation angles
- * @return new float[4] with ,theta,Rx,Ry,Rz
- */
- public float[] toAxis()
- {
- float[] vec = new float[4];
- float scale = (float)MathFloat.sqrt(x * x + y * y + z * z);
- vec[0] =(float) MathFloat.acos(w) * 2.0f;
- vec[1] = x / scale;
- vec[2] = y / scale;
- vec[3] = z / scale;
- return vec;
- }
-
- /** Normalize a vector
- * @param vector input vector
- * @return normalized vector
- */
- private float[] normalizeVec(float[] vector)
- {
- float[] newVector = new float[3];
-
- float d = MathFloat.sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]);
- if(d> 0.0f)
- {
- newVector[0] = vector[0]/d;
- newVector[1] = vector[1]/d;
- newVector[2] = vector[2]/d;
- }
- return newVector;
- }
- /** compute the dot product of two points
- * @param vec1 vector 1
- * @param vec2 vector 2
- * @return the dot product as float
- */
- private float dot(float[] vec1, float[] vec2)
- {
- return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]);
- }
- /** cross product vec1 x vec2
- * @param vec1 vector 1
- * @param vec2 vecttor 2
- * @return the resulting vector
- */
- private float[] cross(float[] vec1, float[] vec2)
- {
- float[] out = new float[3];
-
- out[0] = vec2[2]*vec1[1] - vec2[1]*vec1[2];
- out[1] = vec2[0]*vec1[2] - vec2[2]*vec1[0];
- out[2] = vec2[1]*vec1[0] - vec2[0]*vec1[1];
-
- return out;
- }
- public float getW() {
- return w;
- }
- public void setW(float w) {
- this.w = w;
- }
- public float getX() {
- return x;
- }
- public void setX(float x) {
- this.x = x;
- }
- public float getY() {
- return y;
- }
- public void setY(float y) {
- this.y = y;
- }
- public float getZ() {
- return z;
- }
- public void setZ(float z) {
- this.z = z;
- }
-
- /** Add a quaternion
- * @param q quaternion
- */
- public void add(Quaternion q)
- {
- x+=q.x;
- y+=q.y;
- z+=q.z;
- }
-
- /** Subtract a quaternion
- * @param q quaternion
- */
- public void subtract(Quaternion q)
- {
- x-=q.x;
- y-=q.y;
- z-=q.z;
- }
-
- /** Divide a quaternion by a constant
- * @param n a float to divide by
- */
- public void divide(float n)
- {
- x/=n;
- y/=n;
- z/=n;
- }
-
- /** Multiply this quaternion by
- * the param quaternion
- * @param q a quaternion to multiply with
- */
- public void mult(Quaternion q)
- {
- float w1 = w*q.w - (x*q.x + y*q.y + z*q.z);
-
- float x1 = w*q.z + q.w*z + y*q.z - z*q.y;
- float y1 = w*q.x + q.w*x + z*q.x - x*q.z;
- float z1 = w*q.y + q.w*y + x*q.y - y*q.x;
-
- w = w1;
- x = x1;
- y = y1;
- z = z1;
- }
-
- /** Multiply a quaternion by a constant
- * @param n a float constant
- */
- public void mult(float n)
- {
- x*=n;
- y*=n;
- z*=n;
- }
-
- /** Normalize a quaternion required if
- * to be used as a rotational quaternion
- */
- public void normalize()
- {
- float norme = (float)MathFloat.sqrt(w*w + x*x + y*y + z*z);
- if (norme == 0.0f)
- {
- w = 1.0f;
- x = y = z = 0.0f;
- }
- else
- {
- float recip = 1.0f/norme;
-
- w *= recip;
- x *= recip;
- y *= recip;
- z *= recip;
- }
- }
-
- /** Invert the quaternion If rotational,
- * will produce a the inverse rotation
- */
- public void inverse()
- {
- float norm = w*w + x*x + y*y + z*z;
-
- float recip = 1.0f/norm;
-
- w *= recip;
- x = -1*x*recip;
- y = -1*y*recip;
- z = -1*z*recip;
- }
-
- /** Transform this quaternion to a
- * 4x4 column matrix representing the rotation
- * @return new float[16] column matrix 4x4
- */
- public float[] toMatrix()
- {
- float[] matrix = new float[16];
- matrix[0] = 1.0f - 2*y*y - 2*z*z;
- matrix[1] = 2*x*y + 2*w*z;
- matrix[2] = 2*x*z - 2*w*y;
- matrix[3] = 0;
-
- matrix[4] = 2*x*y - 2*w*z;
- matrix[5] = 1.0f - 2*x*x - 2*z*z;
- matrix[6] = 2*y*z + 2*w*x;
- matrix[7] = 0;
-
- matrix[8] = 2*x*z + 2*w*y;
- matrix[9] = 2*y*z - 2*w*x;
- matrix[10] = 1.0f - 2*x*x - 2*y*y;
- matrix[11] = 0;
-
- matrix[12] = 0;
- matrix[13] = 0;
- matrix[14] = 0;
- matrix[15] = 1;
- return matrix;
- }
-
- /** Set this quaternion from a Sphereical interpolation
- * of two param quaternion, used mostly for rotational animation
- * @param a initial quaternion
- * @param b target quaternion
- * @param t float between 0 and 1 representing interp.
- */
- public void slerp(Quaternion a,Quaternion b, float t)
- {
- float omega, cosom, sinom, sclp, sclq;
- cosom = a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w;
- if ((1.0f+cosom) > MathFloat.E) {
- if ((1.0f-cosom) > MathFloat.E) {
- omega = (float)MathFloat.acos(cosom);
- sinom = (float)MathFloat.sin(omega);
- sclp = (float)MathFloat.sin((1.0f-t)*omega) / sinom;
- sclq = (float)MathFloat.sin(t*omega) / sinom;
- }
- else {
- sclp = 1.0f - t;
- sclq = t;
- }
- x = sclp*a.x + sclq*b.x;
- y = sclp*a.y + sclq*b.y;
- z = sclp*a.z + sclq*b.z;
- w = sclp*a.w + sclq*b.w;
- }
- else {
- x =-a.y;
- y = a.x;
- z =-a.w;
- w = a.z;
- sclp = MathFloat.sin((1.0f-t) * MathFloat.PI * 0.5f);
- sclq = MathFloat.sin(t * MathFloat.PI * 0.5f);
- x = sclp*a.x + sclq*b.x;
- y = sclp*a.y + sclq*b.y;
- z = sclp*a.z + sclq*b.z;
- }
- }
-
- /** Check if this quaternion is empty, ie (0,0,0,1)
- * @return true if empty, false otherwise
- */
- public boolean isEmpty()
- {
- if (w==1 && x==0 && y==0 && z==0)
- return true;
- return false;
- }
-
- /** Check if this quaternion represents an identity
- * matrix, for rotation.
- * @return true if it is an identity rep., false otherwise
- */
- public boolean isIdentity()
- {
- if (w==0 && x==0 && y==0 && z==0)
- return true;
- return false;
- }
-
- /** compute the quaternion from a 3x3 column matrix
- * @param m 3x3 column matrix
- */
- public void setFromMatrix(float[] m) {
- float T= m[0] + m[4] + m[8] + 1;
- if (T>0){
- float S = 0.5f / (float)MathFloat.sqrt(T);
- w = 0.25f / S;
- x = ( m[5] - m[7]) * S;
- y = ( m[6] - m[2]) * S;
- z = ( m[1] - m[3] ) * S;
- }
- else{
- if ((m[0] > m[4])&(m[0] > m[8])) {
- float S = MathFloat.sqrt( 1.0f + m[0] - m[4] - m[8] ) * 2f; // S=4*qx
- w = (m[7] - m[5]) / S;
- x = 0.25f * S;
- y = (m[3] + m[1]) / S;
- z = (m[6] + m[2]) / S;
- }
- else if (m[4] > m[8]) {
- float S = MathFloat.sqrt( 1.0f + m[4] - m[0] - m[8] ) * 2f; // S=4*qy
- w = (m[6] - m[2]) / S;
- x = (m[3] + m[1]) / S;
- y = 0.25f * S;
- z = (m[7] + m[5]) / S;
- }
- else {
- float S = MathFloat.sqrt( 1.0f + m[8] - m[0] - m[4] ) * 2f; // S=4*qz
- w = (m[3] - m[1]) / S;
- x = (m[6] + m[2]) / S;
- y = (m[7] + m[5]) / S;
- z = 0.25f * S;
- }
- }
- }
-
- /** Check if the the 3x3 matrix (param) is in fact
- * an affine rotational matrix
- * @param m 3x3 column matrix
- * @return true if representing a rotational matrix, false otherwise
- */
- public boolean isRotationMatrix(float[] m) {
- double epsilon = 0.01; // margin to allow for rounding errors
- if (MathFloat.abs(m[0]*m[3] + m[3]*m[4] + m[6]*m[7]) > epsilon) return false;
- if (MathFloat.abs(m[0]*m[2] + m[3]*m[5] + m[6]*m[8]) > epsilon) return false;
- if (MathFloat.abs(m[1]*m[2] + m[4]*m[5] + m[7]*m[8]) > epsilon) return false;
- if (MathFloat.abs(m[0]*m[0] + m[3]*m[3] + m[6]*m[6] - 1) > epsilon) return false;
- if (MathFloat.abs(m[1]*m[1] + m[4]*m[4] + m[7]*m[7] - 1) > epsilon) return false;
- if (MathFloat.abs(m[2]*m[2] + m[5]*m[5] + m[8]*m[8] - 1) > epsilon) return false;
- return (MathFloat.abs(determinant(m)-1) < epsilon);
- }
- private float determinant(float[] m) {
- return m[0]*m[4]*m[8] + m[3]*m[7]*m[2] + m[6]*m[1]*m[5] - m[0]*m[7]*m[5] - m[3]*m[1]*m[8] - m[6]*m[4]*m[2];
- }
-}
+/** + * Copyright 2010 JogAmp Community. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without modification, are + * permitted provided that the following conditions are met: + * + * 1. Redistributions of source code must retain the above copyright notice, this list of + * conditions and the following disclaimer. + * + * 2. 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. + * + * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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. + * + * The views and conclusions contained in the software and documentation are those of the + * authors and should not be interpreted as representing official policies, either expressed + * or implied, of JogAmp Community. + */ +package com.jogamp.graph.math; + +import jogamp.graph.math.MathFloat; + +public class Quaternion { + protected float x,y,z,w; + + public Quaternion(){ + + } + + public Quaternion(float x, float y, float z, float w) { + this.x = x; + this.y = y; + this.z = z; + this.w = w; + } + + /** Constructor to create a rotation based quaternion from two vectors + * @param vector1 + * @param vector2 + */ + public Quaternion(float[] vector1, float[] vector2) + { + float theta = (float)MathFloat.acos(dot(vector1, vector2)); + float[] cross = cross(vector1,vector2); + cross = normalizeVec(cross); + + this.x = (float)MathFloat.sin(theta/2)*cross[0]; + this.y = (float)MathFloat.sin(theta/2)*cross[1]; + this.z = (float)MathFloat.sin(theta/2)*cross[2]; + this.w = (float)MathFloat.cos(theta/2); + this.normalize(); + } + + /** Transform the rotational quaternion to axis based rotation angles + * @return new float[4] with ,theta,Rx,Ry,Rz + */ + public float[] toAxis() + { + float[] vec = new float[4]; + float scale = (float)MathFloat.sqrt(x * x + y * y + z * z); + vec[0] =(float) MathFloat.acos(w) * 2.0f; + vec[1] = x / scale; + vec[2] = y / scale; + vec[3] = z / scale; + return vec; + } + + /** Normalize a vector + * @param vector input vector + * @return normalized vector + */ + private float[] normalizeVec(float[] vector) + { + float[] newVector = new float[3]; + + float d = MathFloat.sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]); + if(d> 0.0f) + { + newVector[0] = vector[0]/d; + newVector[1] = vector[1]/d; + newVector[2] = vector[2]/d; + } + return newVector; + } + /** compute the dot product of two points + * @param vec1 vector 1 + * @param vec2 vector 2 + * @return the dot product as float + */ + private float dot(float[] vec1, float[] vec2) + { + return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]); + } + /** cross product vec1 x vec2 + * @param vec1 vector 1 + * @param vec2 vecttor 2 + * @return the resulting vector + */ + private float[] cross(float[] vec1, float[] vec2) + { + float[] out = new float[3]; + + out[0] = vec2[2]*vec1[1] - vec2[1]*vec1[2]; + out[1] = vec2[0]*vec1[2] - vec2[2]*vec1[0]; + out[2] = vec2[1]*vec1[0] - vec2[0]*vec1[1]; + + return out; + } + public float getW() { + return w; + } + public void setW(float w) { + this.w = w; + } + public float getX() { + return x; + } + public void setX(float x) { + this.x = x; + } + public float getY() { + return y; + } + public void setY(float y) { + this.y = y; + } + public float getZ() { + return z; + } + public void setZ(float z) { + this.z = z; + } + + /** Add a quaternion + * @param q quaternion + */ + public void add(Quaternion q) + { + x+=q.x; + y+=q.y; + z+=q.z; + } + + /** Subtract a quaternion + * @param q quaternion + */ + public void subtract(Quaternion q) + { + x-=q.x; + y-=q.y; + z-=q.z; + } + + /** Divide a quaternion by a constant + * @param n a float to divide by + */ + public void divide(float n) + { + x/=n; + y/=n; + z/=n; + } + + /** Multiply this quaternion by + * the param quaternion + * @param q a quaternion to multiply with + */ + public void mult(Quaternion q) + { + float w1 = w*q.w - (x*q.x + y*q.y + z*q.z); + + float x1 = w*q.z + q.w*z + y*q.z - z*q.y; + float y1 = w*q.x + q.w*x + z*q.x - x*q.z; + float z1 = w*q.y + q.w*y + x*q.y - y*q.x; + + w = w1; + x = x1; + y = y1; + z = z1; + } + + /** Multiply a quaternion by a constant + * @param n a float constant + */ + public void mult(float n) + { + x*=n; + y*=n; + z*=n; + } + + /** Normalize a quaternion required if + * to be used as a rotational quaternion + */ + public void normalize() + { + float norme = (float)MathFloat.sqrt(w*w + x*x + y*y + z*z); + if (norme == 0.0f) + { + w = 1.0f; + x = y = z = 0.0f; + } + else + { + float recip = 1.0f/norme; + + w *= recip; + x *= recip; + y *= recip; + z *= recip; + } + } + + /** Invert the quaternion If rotational, + * will produce a the inverse rotation + */ + public void inverse() + { + float norm = w*w + x*x + y*y + z*z; + + float recip = 1.0f/norm; + + w *= recip; + x = -1*x*recip; + y = -1*y*recip; + z = -1*z*recip; + } + + /** Transform this quaternion to a + * 4x4 column matrix representing the rotation + * @return new float[16] column matrix 4x4 + */ + public float[] toMatrix() + { + float[] matrix = new float[16]; + matrix[0] = 1.0f - 2*y*y - 2*z*z; + matrix[1] = 2*x*y + 2*w*z; + matrix[2] = 2*x*z - 2*w*y; + matrix[3] = 0; + + matrix[4] = 2*x*y - 2*w*z; + matrix[5] = 1.0f - 2*x*x - 2*z*z; + matrix[6] = 2*y*z + 2*w*x; + matrix[7] = 0; + + matrix[8] = 2*x*z + 2*w*y; + matrix[9] = 2*y*z - 2*w*x; + matrix[10] = 1.0f - 2*x*x - 2*y*y; + matrix[11] = 0; + + matrix[12] = 0; + matrix[13] = 0; + matrix[14] = 0; + matrix[15] = 1; + return matrix; + } + + /** Set this quaternion from a Sphereical interpolation + * of two param quaternion, used mostly for rotational animation + * @param a initial quaternion + * @param b target quaternion + * @param t float between 0 and 1 representing interp. + */ + public void slerp(Quaternion a,Quaternion b, float t) + { + float omega, cosom, sinom, sclp, sclq; + cosom = a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w; + if ((1.0f+cosom) > MathFloat.E) { + if ((1.0f-cosom) > MathFloat.E) { + omega = (float)MathFloat.acos(cosom); + sinom = (float)MathFloat.sin(omega); + sclp = (float)MathFloat.sin((1.0f-t)*omega) / sinom; + sclq = (float)MathFloat.sin(t*omega) / sinom; + } + else { + sclp = 1.0f - t; + sclq = t; + } + x = sclp*a.x + sclq*b.x; + y = sclp*a.y + sclq*b.y; + z = sclp*a.z + sclq*b.z; + w = sclp*a.w + sclq*b.w; + } + else { + x =-a.y; + y = a.x; + z =-a.w; + w = a.z; + sclp = MathFloat.sin((1.0f-t) * MathFloat.PI * 0.5f); + sclq = MathFloat.sin(t * MathFloat.PI * 0.5f); + x = sclp*a.x + sclq*b.x; + y = sclp*a.y + sclq*b.y; + z = sclp*a.z + sclq*b.z; + } + } + + /** Check if this quaternion is empty, ie (0,0,0,1) + * @return true if empty, false otherwise + */ + public boolean isEmpty() + { + if (w==1 && x==0 && y==0 && z==0) + return true; + return false; + } + + /** Check if this quaternion represents an identity + * matrix, for rotation. + * @return true if it is an identity rep., false otherwise + */ + public boolean isIdentity() + { + if (w==0 && x==0 && y==0 && z==0) + return true; + return false; + } + + /** compute the quaternion from a 3x3 column matrix + * @param m 3x3 column matrix + */ + public void setFromMatrix(float[] m) { + float T= m[0] + m[4] + m[8] + 1; + if (T>0){ + float S = 0.5f / (float)MathFloat.sqrt(T); + w = 0.25f / S; + x = ( m[5] - m[7]) * S; + y = ( m[6] - m[2]) * S; + z = ( m[1] - m[3] ) * S; + } + else{ + if ((m[0] > m[4])&(m[0] > m[8])) { + float S = MathFloat.sqrt( 1.0f + m[0] - m[4] - m[8] ) * 2f; // S=4*qx + w = (m[7] - m[5]) / S; + x = 0.25f * S; + y = (m[3] + m[1]) / S; + z = (m[6] + m[2]) / S; + } + else if (m[4] > m[8]) { + float S = MathFloat.sqrt( 1.0f + m[4] - m[0] - m[8] ) * 2f; // S=4*qy + w = (m[6] - m[2]) / S; + x = (m[3] + m[1]) / S; + y = 0.25f * S; + z = (m[7] + m[5]) / S; + } + else { + float S = MathFloat.sqrt( 1.0f + m[8] - m[0] - m[4] ) * 2f; // S=4*qz + w = (m[3] - m[1]) / S; + x = (m[6] + m[2]) / S; + y = (m[7] + m[5]) / S; + z = 0.25f * S; + } + } + } + + /** Check if the the 3x3 matrix (param) is in fact + * an affine rotational matrix + * @param m 3x3 column matrix + * @return true if representing a rotational matrix, false otherwise + */ + public boolean isRotationMatrix(float[] m) { + double epsilon = 0.01; // margin to allow for rounding errors + if (MathFloat.abs(m[0]*m[3] + m[3]*m[4] + m[6]*m[7]) > epsilon) return false; + if (MathFloat.abs(m[0]*m[2] + m[3]*m[5] + m[6]*m[8]) > epsilon) return false; + if (MathFloat.abs(m[1]*m[2] + m[4]*m[5] + m[7]*m[8]) > epsilon) return false; + if (MathFloat.abs(m[0]*m[0] + m[3]*m[3] + m[6]*m[6] - 1) > epsilon) return false; + if (MathFloat.abs(m[1]*m[1] + m[4]*m[4] + m[7]*m[7] - 1) > epsilon) return false; + if (MathFloat.abs(m[2]*m[2] + m[5]*m[5] + m[8]*m[8] - 1) > epsilon) return false; + return (MathFloat.abs(determinant(m)-1) < epsilon); + } + private float determinant(float[] m) { + return m[0]*m[4]*m[8] + m[3]*m[7]*m[2] + m[6]*m[1]*m[5] - m[0]*m[7]*m[5] - m[3]*m[1]*m[8] - m[6]*m[4]*m[2]; + } +} diff --git a/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java b/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java index b1f2023f3..d51afcbab 100755 --- a/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java +++ b/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java @@ -1,433 +1,433 @@ -/**
- * Copyright 2010 JogAmp Community. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without modification, are
- * permitted provided that the following conditions are met:
- *
- * 1. Redistributions of source code must retain the above copyright notice, this list of
- * conditions and the following disclaimer.
- *
- * 2. 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.
- *
- * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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.
- *
- * The views and conclusions contained in the software and documentation are those of the
- * authors and should not be interpreted as representing official policies, either expressed
- * or implied, of JogAmp Community.
- */
-package com.jogamp.graph.math;
-
-import java.util.ArrayList;
-
-import jogamp.graph.math.MathFloat;
-
-import com.jogamp.graph.geom.Vertex;
-
-public class VectorUtil {
-
- public enum Winding {
- CW(-1), CCW(1);
-
- public final int dir;
-
- Winding(int dir) {
- this.dir = dir;
- }
- }
-
- public static final int COLLINEAR = 0;
-
- /** compute the dot product of two points
- * @param vec1 vector 1
- * @param vec2 vector 2
- * @return the dot product as float
- */
- public static float dot(float[] vec1, float[] vec2)
- {
- return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]);
- }
- /** Normalize a vector
- * @param vector input vector
- * @return normalized vector
- */
- public static float[] normalize(float[] vector)
- {
- float[] newVector = new float[3];
-
- float d = MathFloat.sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]);
- if(d> 0.0f)
- {
- newVector[0] = vector[0]/d;
- newVector[1] = vector[1]/d;
- newVector[2] = vector[2]/d;
- }
- return newVector;
- }
-
- /** Scales a vector by param
- * @param vector input vector
- * @param scale constant to scale by
- * @return scaled vector
- */
- public static float[] scale(float[] vector, float scale)
- {
- float[] newVector = new float[3];
-
- newVector[0] = vector[0]*scale;
- newVector[1] = vector[1]*scale;
- newVector[2] = vector[2]*scale;
- return newVector;
- }
-
- /** Adds to vectors
- * @param v1 vector 1
- * @param v2 vector 2
- * @return v1 + v2
- */
- public static float[] vectorAdd(float[] v1, float[] v2)
- {
- float[] newVector = new float[3];
-
- newVector[0] = v1[0] + v2[0];
- newVector[1] = v1[1] + v2[1];
- newVector[2] = v1[2] + v2[2];
- return newVector;
- }
-
- /** cross product vec1 x vec2
- * @param vec1 vector 1
- * @param vec2 vecttor 2
- * @return the resulting vector
- */
- public static float[] cross(float[] vec1, float[] vec2)
- {
- float[] out = new float[3];
-
- out[0] = vec2[2]*vec1[1] - vec2[1]*vec1[2];
- out[1] = vec2[0]*vec1[2] - vec2[2]*vec1[0];
- out[2] = vec2[1]*vec1[0] - vec2[0]*vec1[1];
-
- return out;
- }
-
- /** Column Matrix Vector multiplication
- * @param colMatrix column matrix (4x4)
- * @param vec vector(x,y,z)
- * @return result new float[3]
- */
- public static float[] colMatrixVectorMult(float[] colMatrix, float[] vec)
- {
- float[] out = new float[3];
-
- out[0] = vec[0]*colMatrix[0] + vec[1]*colMatrix[4] + vec[2]*colMatrix[8] + colMatrix[12];
- out[1] = vec[0]*colMatrix[1] + vec[1]*colMatrix[5] + vec[2]*colMatrix[9] + colMatrix[13];
- out[2] = vec[0]*colMatrix[2] + vec[1]*colMatrix[6] + vec[2]*colMatrix[10] + colMatrix[14];
-
- return out;
- }
-
- /** Matrix Vector multiplication
- * @param rawMatrix column matrix (4x4)
- * @param vec vector(x,y,z)
- * @return result new float[3]
- */
- public static float[] rowMatrixVectorMult(float[] rawMatrix, float[] vec)
- {
- float[] out = new float[3];
-
- out[0] = vec[0]*rawMatrix[0] + vec[1]*rawMatrix[1] + vec[2]*rawMatrix[2] + rawMatrix[3];
- out[1] = vec[0]*rawMatrix[4] + vec[1]*rawMatrix[5] + vec[2]*rawMatrix[6] + rawMatrix[7];
- out[2] = vec[0]*rawMatrix[8] + vec[1]*rawMatrix[9] + vec[2]*rawMatrix[10] + rawMatrix[11];
-
- return out;
- }
-
- /** Calculate the midpoint of two values
- * @param p1 first value
- * @param p2 second vale
- * @return midpoint
- */
- public static float mid(float p1, float p2)
- {
- return (p1+p2)/2.0f;
- }
- /** Calculate the midpoint of two points
- * @param p1 first point
- * @param p2 second point
- * @return midpoint
- */
- public static float[] mid(float[] p1, float[] p2)
- {
- float[] midPoint = new float[3];
- midPoint[0] = (p1[0] + p2[0])*0.5f;
- midPoint[1] = (p1[1] + p2[1])*0.5f;
- midPoint[2] = (p1[2] + p2[2])*0.5f;
-
- return midPoint;
- }
- /** Compute the norm of a vector
- * @param vec vector
- * @return vorm
- */
- public static float norm(float[] vec)
- {
- return MathFloat.sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
- }
- /** Compute distance between 2 points
- * @param p0 a ref point on the line
- * @param vec vector representing the direction of the line
- * @param point the point to compute the relative distance of
- * @return distance float
- */
- public static float computeLength(float[] p0, float[] point)
- {
- float[] w = new float[]{point[0]-p0[0],point[1]-p0[1],point[2]-p0[2]};
-
- float distance = MathFloat.sqrt(w[0]*w[0] + w[1]*w[1] + w[2]*w[2]);
-
- return distance;
- }
-
- /**Check equality of 2 vec3 vectors
- * @param v1 vertex 1
- * @param v2 vertex 2
- * @return
- */
- public static boolean checkEquality(float[] v1, float[] v2)
- {
- if(Float.compare(v1[0], v2[0]) == 0 &&
- Float.compare(v1[1], v2[1]) == 0 &&
- Float.compare(v1[2], v2[2]) == 0 )
- return true;
- return false;
- }
-
- /**Check equality of 2 vec2 vectors
- * @param v1 vertex 1
- * @param v2 vertex 2
- * @return
- */
- public static boolean checkEqualityVec2(float[] v1, float[] v2)
- {
- if(Float.compare(v1[0], v2[0]) == 0 &&
- Float.compare(v1[1], v2[1]) == 0)
- return true;
- return false;
- }
-
- /** Compute the determinant of 3 vectors
- * @param a vector 1
- * @param b vector 2
- * @param c vector 3
- * @return the determinant value
- */
- public static float computeDeterminant(float[] a, float[] b, float[] c)
- {
- float area = a[0]*b[1]*c[2] + a[1]*b[2]*c[0] + a[2]*b[0]*c[1] - a[0]*b[2]*c[1] - a[1]*b[0]*c[2] - a[2]*b[1]*c[0];
- return area;
- }
-
- /** Check if three vertices are colliniear
- * @param v1 vertex 1
- * @param v2 vertex 2
- * @param v3 vertex 3
- * @return true if collinear, false otherwise
- */
- public static boolean checkCollinear(float[] v1, float[] v2, float[] v3)
- {
- return (computeDeterminant(v1, v2, v3) == VectorUtil.COLLINEAR);
- }
-
- /** Compute Vector
- * @param v1 vertex 1
- * @param v2 vertex2 2
- * @return Vector V1V2
- */
- public static float[] computeVector(float[] v1, float[] v2)
- {
- float[] vector = new float[3];
- vector[0] = v2[0] - v1[0];
- vector[1] = v2[1] - v1[1];
- vector[2] = v2[2] - v1[2];
- return vector;
- }
-
- /** Check if vertices in triangle circumcircle
- * @param a triangle vertex 1
- * @param b triangle vertex 2
- * @param c triangle vertex 3
- * @param d vertex in question
- * @return true if the vertex d is inside the circle defined by the
- * vertices a, b, c. from paper by Guibas and Stolfi (1985).
- */
- public static boolean inCircle(Vertex a, Vertex b, Vertex c, Vertex d){
- return (a.getX() * a.getX() + a.getY() * a.getY()) * triArea(b, c, d) -
- (b.getX() * b.getX() + b.getY() * b.getY()) * triArea(a, c, d) +
- (c.getX() * c.getX() + c.getY() * c.getY()) * triArea(a, b, d) -
- (d.getX() * d.getX() + d.getY() * d.getY()) * triArea(a, b, c) > 0;
- }
-
- /** Computes oriented area of a triangle
- * @param a first vertex
- * @param b second vertex
- * @param c third vertex
- * @return compute twice the area of the oriented triangle (a,b,c), the area
- * is positive if the triangle is oriented counterclockwise.
- */
- public static float triArea(Vertex a, Vertex b, Vertex c){
- return (b.getX() - a.getX()) * (c.getY() - a.getY()) - (b.getY() - a.getY())*(c.getX() - a.getX());
- }
-
- /** Check if a vertex is in triangle using
- * barycentric coordinates computation.
- * @param a first triangle vertex
- * @param b second triangle vertex
- * @param c third triangle vertex
- * @param p the vertex in question
- * @return true if p is in triangle (a, b, c), false otherwise.
- */
- public static boolean vertexInTriangle(float[] a, float[] b, float[] c, float[] p){
- // Compute vectors
- float[] ac = computeVector(a, c); //v0
- float[] ab = computeVector(a, b); //v1
- float[] ap = computeVector(a, p); //v2
-
- // Compute dot products
- float dot00 = dot(ac, ac);
- float dot01 = dot(ac, ab);
- float dot02 = dot(ac, ap);
- float dot11 = dot(ab, ab);
- float dot12 = dot(ab, ap);
-
- // Compute barycentric coordinates
- float invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
- float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
- float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
-
- // Check if point is in triangle
- return (u >= 0) && (v >= 0) && (u + v < 1);
- }
-
- /** Check if points are in ccw order
- * @param a first vertex
- * @param b second vertex
- * @param c third vertex
- * @return true if the points a,b,c are in a ccw order
- */
- public static boolean ccw(Vertex a, Vertex b, Vertex c){
- return triArea(a,b,c) > 0;
- }
-
- /** Compute the winding of given points
- * @param a first vertex
- * @param b second vertex
- * @param c third vertex
- * @return Winding
- */
- public static Winding getWinding(Vertex a, Vertex b, Vertex c) {
- return triArea(a,b,c) > 0 ? Winding.CCW : Winding.CW ;
- }
-
- /** Computes the area of a list of vertices to check if ccw
- * @param vertices
- * @return positive area if ccw else negative area value
- */
- public static float area(ArrayList<Vertex> vertices) {
- int n = vertices.size();
- float area = 0.0f;
- for (int p = n - 1, q = 0; q < n; p = q++)
- {
- float[] pCoord = vertices.get(p).getCoord();
- float[] qCoord = vertices.get(q).getCoord();
- area += pCoord[0] * qCoord[1] - qCoord[0] * pCoord[1];
- }
- return area;
- }
-
- /** Compute the general winding of the vertices
- * @param vertices array of Vertices
- * @return CCW or CW {@link Winding}
- */
- public static Winding getWinding(ArrayList<Vertex> vertices) {
- return area(vertices) >= 0 ? Winding.CCW : Winding.CW ;
- }
-
-
- /** Compute intersection between two segments
- * @param a vertex 1 of first segment
- * @param b vertex 2 of first segment
- * @param c vertex 1 of second segment
- * @param d vertex 2 of second segment
- * @return the intersection coordinates if the segments intersect, otherwise
- * returns null
- */
- public static float[] seg2SegIntersection(Vertex a, Vertex b, Vertex c, Vertex d) {
- float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX());
-
- if (determinant == 0)
- return null;
-
- float alpha = (a.getX()*b.getY()-a.getY()*b.getX());
- float beta = (c.getX()*d.getY()-c.getY()*d.getY());
- float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant;
- float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant;
-
- float gamma = (xi - a.getX())/(b.getX() - a.getX());
- float gamma1 = (xi - c.getX())/(d.getX() - c.getX());
- if(gamma <= 0 || gamma >= 1) return null;
- if(gamma1 <= 0 || gamma1 >= 1) return null;
-
- return new float[]{xi,yi,0};
- }
-
- /** Compute intersection between two lines
- * @param a vertex 1 of first line
- * @param b vertex 2 of first line
- * @param c vertex 1 of second line
- * @param d vertex 2 of second line
- * @return the intersection coordinates if the lines intersect, otherwise
- * returns null
- */
- public static float[] line2lineIntersection(Vertex a, Vertex b, Vertex c, Vertex d) {
- float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX());
-
- if (determinant == 0)
- return null;
-
- float alpha = (a.getX()*b.getY()-a.getY()*b.getX());
- float beta = (c.getX()*d.getY()-c.getY()*d.getY());
- float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant;
- float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant;
-
- return new float[]{xi,yi,0};
- }
-
- /** Check if a segment intersects with a triangle
- * @param a vertex 1 of the triangle
- * @param b vertex 2 of the triangle
- * @param c vertex 3 of the triangle
- * @param d vertex 1 of first segment
- * @param e vertex 2 of first segment
- * @return true if the segment intersects at least one segment of the triangle, false otherwise
- */
- public static boolean tri2SegIntersection(Vertex a, Vertex b, Vertex c, Vertex d, Vertex e){
- if(seg2SegIntersection(a, b, d, e) != null)
- return true;
- if(seg2SegIntersection(b, c, d, e) != null)
- return true;
- if(seg2SegIntersection(a, c, d, e) != null)
- return true;
-
- return false;
- }
-}
+/** + * Copyright 2010 JogAmp Community. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without modification, are + * permitted provided that the following conditions are met: + * + * 1. Redistributions of source code must retain the above copyright notice, this list of + * conditions and the following disclaimer. + * + * 2. 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. + * + * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``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 JogAmp Community 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. + * + * The views and conclusions contained in the software and documentation are those of the + * authors and should not be interpreted as representing official policies, either expressed + * or implied, of JogAmp Community. + */ +package com.jogamp.graph.math; + +import java.util.ArrayList; + +import jogamp.graph.math.MathFloat; + +import com.jogamp.graph.geom.Vertex; + +public class VectorUtil { + + public enum Winding { + CW(-1), CCW(1); + + public final int dir; + + Winding(int dir) { + this.dir = dir; + } + } + + public static final int COLLINEAR = 0; + + /** compute the dot product of two points + * @param vec1 vector 1 + * @param vec2 vector 2 + * @return the dot product as float + */ + public static float dot(float[] vec1, float[] vec2) + { + return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]); + } + /** Normalize a vector + * @param vector input vector + * @return normalized vector + */ + public static float[] normalize(float[] vector) + { + float[] newVector = new float[3]; + + float d = MathFloat.sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]); + if(d> 0.0f) + { + newVector[0] = vector[0]/d; + newVector[1] = vector[1]/d; + newVector[2] = vector[2]/d; + } + return newVector; + } + + /** Scales a vector by param + * @param vector input vector + * @param scale constant to scale by + * @return scaled vector + */ + public static float[] scale(float[] vector, float scale) + { + float[] newVector = new float[3]; + + newVector[0] = vector[0]*scale; + newVector[1] = vector[1]*scale; + newVector[2] = vector[2]*scale; + return newVector; + } + + /** Adds to vectors + * @param v1 vector 1 + * @param v2 vector 2 + * @return v1 + v2 + */ + public static float[] vectorAdd(float[] v1, float[] v2) + { + float[] newVector = new float[3]; + + newVector[0] = v1[0] + v2[0]; + newVector[1] = v1[1] + v2[1]; + newVector[2] = v1[2] + v2[2]; + return newVector; + } + + /** cross product vec1 x vec2 + * @param vec1 vector 1 + * @param vec2 vecttor 2 + * @return the resulting vector + */ + public static float[] cross(float[] vec1, float[] vec2) + { + float[] out = new float[3]; + + out[0] = vec2[2]*vec1[1] - vec2[1]*vec1[2]; + out[1] = vec2[0]*vec1[2] - vec2[2]*vec1[0]; + out[2] = vec2[1]*vec1[0] - vec2[0]*vec1[1]; + + return out; + } + + /** Column Matrix Vector multiplication + * @param colMatrix column matrix (4x4) + * @param vec vector(x,y,z) + * @return result new float[3] + */ + public static float[] colMatrixVectorMult(float[] colMatrix, float[] vec) + { + float[] out = new float[3]; + + out[0] = vec[0]*colMatrix[0] + vec[1]*colMatrix[4] + vec[2]*colMatrix[8] + colMatrix[12]; + out[1] = vec[0]*colMatrix[1] + vec[1]*colMatrix[5] + vec[2]*colMatrix[9] + colMatrix[13]; + out[2] = vec[0]*colMatrix[2] + vec[1]*colMatrix[6] + vec[2]*colMatrix[10] + colMatrix[14]; + + return out; + } + + /** Matrix Vector multiplication + * @param rawMatrix column matrix (4x4) + * @param vec vector(x,y,z) + * @return result new float[3] + */ + public static float[] rowMatrixVectorMult(float[] rawMatrix, float[] vec) + { + float[] out = new float[3]; + + out[0] = vec[0]*rawMatrix[0] + vec[1]*rawMatrix[1] + vec[2]*rawMatrix[2] + rawMatrix[3]; + out[1] = vec[0]*rawMatrix[4] + vec[1]*rawMatrix[5] + vec[2]*rawMatrix[6] + rawMatrix[7]; + out[2] = vec[0]*rawMatrix[8] + vec[1]*rawMatrix[9] + vec[2]*rawMatrix[10] + rawMatrix[11]; + + return out; + } + + /** Calculate the midpoint of two values + * @param p1 first value + * @param p2 second vale + * @return midpoint + */ + public static float mid(float p1, float p2) + { + return (p1+p2)/2.0f; + } + /** Calculate the midpoint of two points + * @param p1 first point + * @param p2 second point + * @return midpoint + */ + public static float[] mid(float[] p1, float[] p2) + { + float[] midPoint = new float[3]; + midPoint[0] = (p1[0] + p2[0])*0.5f; + midPoint[1] = (p1[1] + p2[1])*0.5f; + midPoint[2] = (p1[2] + p2[2])*0.5f; + + return midPoint; + } + /** Compute the norm of a vector + * @param vec vector + * @return vorm + */ + public static float norm(float[] vec) + { + return MathFloat.sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]); + } + /** Compute distance between 2 points + * @param p0 a ref point on the line + * @param vec vector representing the direction of the line + * @param point the point to compute the relative distance of + * @return distance float + */ + public static float computeLength(float[] p0, float[] point) + { + float[] w = new float[]{point[0]-p0[0],point[1]-p0[1],point[2]-p0[2]}; + + float distance = MathFloat.sqrt(w[0]*w[0] + w[1]*w[1] + w[2]*w[2]); + + return distance; + } + + /**Check equality of 2 vec3 vectors + * @param v1 vertex 1 + * @param v2 vertex 2 + * @return + */ + public static boolean checkEquality(float[] v1, float[] v2) + { + if(Float.compare(v1[0], v2[0]) == 0 && + Float.compare(v1[1], v2[1]) == 0 && + Float.compare(v1[2], v2[2]) == 0 ) + return true; + return false; + } + + /**Check equality of 2 vec2 vectors + * @param v1 vertex 1 + * @param v2 vertex 2 + * @return + */ + public static boolean checkEqualityVec2(float[] v1, float[] v2) + { + if(Float.compare(v1[0], v2[0]) == 0 && + Float.compare(v1[1], v2[1]) == 0) + return true; + return false; + } + + /** Compute the determinant of 3 vectors + * @param a vector 1 + * @param b vector 2 + * @param c vector 3 + * @return the determinant value + */ + public static float computeDeterminant(float[] a, float[] b, float[] c) + { + float area = a[0]*b[1]*c[2] + a[1]*b[2]*c[0] + a[2]*b[0]*c[1] - a[0]*b[2]*c[1] - a[1]*b[0]*c[2] - a[2]*b[1]*c[0]; + return area; + } + + /** Check if three vertices are colliniear + * @param v1 vertex 1 + * @param v2 vertex 2 + * @param v3 vertex 3 + * @return true if collinear, false otherwise + */ + public static boolean checkCollinear(float[] v1, float[] v2, float[] v3) + { + return (computeDeterminant(v1, v2, v3) == VectorUtil.COLLINEAR); + } + + /** Compute Vector + * @param v1 vertex 1 + * @param v2 vertex2 2 + * @return Vector V1V2 + */ + public static float[] computeVector(float[] v1, float[] v2) + { + float[] vector = new float[3]; + vector[0] = v2[0] - v1[0]; + vector[1] = v2[1] - v1[1]; + vector[2] = v2[2] - v1[2]; + return vector; + } + + /** Check if vertices in triangle circumcircle + * @param a triangle vertex 1 + * @param b triangle vertex 2 + * @param c triangle vertex 3 + * @param d vertex in question + * @return true if the vertex d is inside the circle defined by the + * vertices a, b, c. from paper by Guibas and Stolfi (1985). + */ + public static boolean inCircle(Vertex a, Vertex b, Vertex c, Vertex d){ + return (a.getX() * a.getX() + a.getY() * a.getY()) * triArea(b, c, d) - + (b.getX() * b.getX() + b.getY() * b.getY()) * triArea(a, c, d) + + (c.getX() * c.getX() + c.getY() * c.getY()) * triArea(a, b, d) - + (d.getX() * d.getX() + d.getY() * d.getY()) * triArea(a, b, c) > 0; + } + + /** Computes oriented area of a triangle + * @param a first vertex + * @param b second vertex + * @param c third vertex + * @return compute twice the area of the oriented triangle (a,b,c), the area + * is positive if the triangle is oriented counterclockwise. + */ + public static float triArea(Vertex a, Vertex b, Vertex c){ + return (b.getX() - a.getX()) * (c.getY() - a.getY()) - (b.getY() - a.getY())*(c.getX() - a.getX()); + } + + /** Check if a vertex is in triangle using + * barycentric coordinates computation. + * @param a first triangle vertex + * @param b second triangle vertex + * @param c third triangle vertex + * @param p the vertex in question + * @return true if p is in triangle (a, b, c), false otherwise. + */ + public static boolean vertexInTriangle(float[] a, float[] b, float[] c, float[] p){ + // Compute vectors + float[] ac = computeVector(a, c); //v0 + float[] ab = computeVector(a, b); //v1 + float[] ap = computeVector(a, p); //v2 + + // Compute dot products + float dot00 = dot(ac, ac); + float dot01 = dot(ac, ab); + float dot02 = dot(ac, ap); + float dot11 = dot(ab, ab); + float dot12 = dot(ab, ap); + + // Compute barycentric coordinates + float invDenom = 1 / (dot00 * dot11 - dot01 * dot01); + float u = (dot11 * dot02 - dot01 * dot12) * invDenom; + float v = (dot00 * dot12 - dot01 * dot02) * invDenom; + + // Check if point is in triangle + return (u >= 0) && (v >= 0) && (u + v < 1); + } + + /** Check if points are in ccw order + * @param a first vertex + * @param b second vertex + * @param c third vertex + * @return true if the points a,b,c are in a ccw order + */ + public static boolean ccw(Vertex a, Vertex b, Vertex c){ + return triArea(a,b,c) > 0; + } + + /** Compute the winding of given points + * @param a first vertex + * @param b second vertex + * @param c third vertex + * @return Winding + */ + public static Winding getWinding(Vertex a, Vertex b, Vertex c) { + return triArea(a,b,c) > 0 ? Winding.CCW : Winding.CW ; + } + + /** Computes the area of a list of vertices to check if ccw + * @param vertices + * @return positive area if ccw else negative area value + */ + public static float area(ArrayList<Vertex> vertices) { + int n = vertices.size(); + float area = 0.0f; + for (int p = n - 1, q = 0; q < n; p = q++) + { + float[] pCoord = vertices.get(p).getCoord(); + float[] qCoord = vertices.get(q).getCoord(); + area += pCoord[0] * qCoord[1] - qCoord[0] * pCoord[1]; + } + return area; + } + + /** Compute the general winding of the vertices + * @param vertices array of Vertices + * @return CCW or CW {@link Winding} + */ + public static Winding getWinding(ArrayList<Vertex> vertices) { + return area(vertices) >= 0 ? Winding.CCW : Winding.CW ; + } + + + /** Compute intersection between two segments + * @param a vertex 1 of first segment + * @param b vertex 2 of first segment + * @param c vertex 1 of second segment + * @param d vertex 2 of second segment + * @return the intersection coordinates if the segments intersect, otherwise + * returns null + */ + public static float[] seg2SegIntersection(Vertex a, Vertex b, Vertex c, Vertex d) { + float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX()); + + if (determinant == 0) + return null; + + float alpha = (a.getX()*b.getY()-a.getY()*b.getX()); + float beta = (c.getX()*d.getY()-c.getY()*d.getY()); + float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant; + float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant; + + float gamma = (xi - a.getX())/(b.getX() - a.getX()); + float gamma1 = (xi - c.getX())/(d.getX() - c.getX()); + if(gamma <= 0 || gamma >= 1) return null; + if(gamma1 <= 0 || gamma1 >= 1) return null; + + return new float[]{xi,yi,0}; + } + + /** Compute intersection between two lines + * @param a vertex 1 of first line + * @param b vertex 2 of first line + * @param c vertex 1 of second line + * @param d vertex 2 of second line + * @return the intersection coordinates if the lines intersect, otherwise + * returns null + */ + public static float[] line2lineIntersection(Vertex a, Vertex b, Vertex c, Vertex d) { + float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX()); + + if (determinant == 0) + return null; + + float alpha = (a.getX()*b.getY()-a.getY()*b.getX()); + float beta = (c.getX()*d.getY()-c.getY()*d.getY()); + float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant; + float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant; + + return new float[]{xi,yi,0}; + } + + /** Check if a segment intersects with a triangle + * @param a vertex 1 of the triangle + * @param b vertex 2 of the triangle + * @param c vertex 3 of the triangle + * @param d vertex 1 of first segment + * @param e vertex 2 of first segment + * @return true if the segment intersects at least one segment of the triangle, false otherwise + */ + public static boolean tri2SegIntersection(Vertex a, Vertex b, Vertex c, Vertex d, Vertex e){ + if(seg2SegIntersection(a, b, d, e) != null) + return true; + if(seg2SegIntersection(b, c, d, e) != null) + return true; + if(seg2SegIntersection(a, c, d, e) != null) + return true; + + return false; + } +} |