Folded turtle2d into jogl folders

2 files changed, 677 insertions, 0 deletions

diff --git a/src/jogl/classes/com/jogamp/graph/math/Quaternion.java b/src/jogl/classes/com/jogamp/graph/math/Quaternion.java
new file mode 100755
index 000000000..b77a5fa08
--- /dev/null
+++ b/src/jogl/classes/com/jogamp/graph/math/Quaternion.java
@@ -0,0 +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];

+	}

+}

diff --git a/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java b/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java
new file mode 100755
index 000000000..cca9a454f
--- /dev/null
+++ b/src/jogl/classes/com/jogamp/graph/math/VectorUtil.java
@@ -0,0 +1,295 @@
+/**

+ * 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 static final int CW = -1;

+	public static final int CCW = 1;

+	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])/2.0f;

+		midPoint[1] = (p1[1] + p2[1])/2.0f;

+		midPoint[2] = (p1[2] + p2[2])/2.0f;

+

+		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;

+	}

+

+	/** 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 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;

+	}

+

+	/** Computes the area of a list of vertices to check if ccw

+	 * @param vertices

+	 * @return positve 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;

+	}

+}