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-rwxr-xr-xsrc/jogl/classes/com/jogamp/graph/math/Quaternion.java764
-rwxr-xr-xsrc/jogl/classes/com/jogamp/graph/math/VectorUtil.java866
2 files changed, 815 insertions, 815 deletions
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;
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-25 00:04:20 +0000