--- /dev/null
+package org.simantics.g3d.math;\r
+\r
+import javax.vecmath.AxisAngle4d;\r
+import javax.vecmath.Matrix3d;\r
+import javax.vecmath.Matrix4d;\r
+import javax.vecmath.Quat4d;\r
+import javax.vecmath.Tuple3d;\r
+import javax.vecmath.Tuple4d;\r
+import javax.vecmath.Vector2f;\r
+import javax.vecmath.Vector3d;\r
+\r
+import org.simantics.g3d.math.EulerTools.Order;\r
+\r
+\r
+/**\r
+ * Some useful geometry related math functions. Beware, methods may modify their input parameters!\r
+ * \r
+ * @author Marko Luukkainen\r
+ *\r
+ */\r
+public class MathTools {\r
+ \r
+ public static double NEAR_ZERO = 0.0000001;\r
+ public static double NEAR_HALF = 0.4999999;\r
+ \r
+ public static final Vector3d Z_AXIS = new Vector3d(0.0,0.0,1.0);\r
+ public static final Vector3d Y_AXIS = new Vector3d(0.0,1.0,0.0);\r
+ public static final Vector3d X_AXIS = new Vector3d(1.0,0.0,0.0);\r
+ public static final Vector3d ORIGIN = new Vector3d(0.0,0.0,0.0);\r
+ \r
+ final static double EPS = 1.0e-12;\r
+ \r
+ \r
+ public static boolean equals(double d1, double d2) {\r
+ return Math.abs(d1-d2) < EPS;\r
+ }\r
+ \r
+ public static boolean equals(Tuple3d p1, Tuple3d p2) {\r
+ return distanceSquared(p1, p2) < NEAR_ZERO;\r
+ }\r
+ \r
+ public static boolean equals(Tuple4d p1, Tuple4d p2) {\r
+ return distanceSquared(p1, p2) < NEAR_ZERO;\r
+ }\r
+ \r
+ public static double distance(Tuple3d p1, Tuple3d p2) {\r
+ double dx, dy, dz;\r
+\r
+ dx = p2.x - p1.x;\r
+ dy = p2.y - p1.y;\r
+ dz = p2.z - p1.z;\r
+ return Math.sqrt(dx*dx+dy*dy+dz*dz);\r
+ }\r
+ \r
+ public static double distance(Tuple4d p1, Tuple4d p2) {\r
+ double dx, dy, dz, dw;\r
+\r
+ dx = p2.x - p1.x;\r
+ dy = p2.y - p1.y;\r
+ dz = p2.z - p1.z;\r
+ dw = p2.w - p1.w;\r
+ return Math.sqrt(dx*dx+dy*dy+dz*dz+dw*dw);\r
+ }\r
+ \r
+ public static double distanceSquared(Tuple3d p1, Tuple3d p2) {\r
+ double dx, dy, dz;\r
+\r
+ dx = p2.x - p1.x;\r
+ dy = p2.y - p1.y;\r
+ dz = p2.z - p1.z;\r
+ return dx*dx+dy*dy+dz*dz;\r
+ }\r
+ \r
+ public static double distanceSquared(Tuple4d p1, Tuple4d p2) {\r
+ double dx, dy, dz, dw;\r
+\r
+ dx = p2.x - p1.x;\r
+ dy = p2.y - p1.y;\r
+ dz = p2.z - p1.z;\r
+ dw = p2.w - p1.w;\r
+ return dx*dx+dy*dy+dz*dz+dw*dw;\r
+ }\r
+ \r
+ public static boolean isValid(Tuple3d t) {\r
+ return !(Double.isInfinite(t.x) || Double.isNaN(t.x) ||\r
+ Double.isInfinite(t.y) || Double.isNaN(t.y) ||\r
+ Double.isInfinite(t.z) || Double.isNaN(t.z));\r
+ }\r
+ \r
+ public static Vector3d closestPointOnEdge(Vector3d point, Vector3d edgePoint1, Vector3d edgePoint2) {\r
+ point.sub(edgePoint1);\r
+ Vector3d v = new Vector3d(edgePoint2);\r
+ v.sub(edgePoint1);\r
+ double t = v.dot(point);\r
+ t /= v.lengthSquared();\r
+ if (t <= 0.0f)\r
+ return edgePoint1;\r
+ if (t >= 1.0f)\r
+ return edgePoint2;\r
+ v.scale(t);\r
+ v.add(edgePoint1);\r
+ return v; \r
+ }\r
+ \r
+ public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir) {\r
+ Vector3d v = new Vector3d(point);\r
+ v.sub(straightPoint);\r
+ double t = straightDir.dot(v);\r
+ t /= straightDir.lengthSquared();\r
+ v.set(straightDir);\r
+ v.scale(t);\r
+ v.add(straightPoint);\r
+ return v; \r
+ }\r
+ \r
+ public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir, double u[]) {\r
+ Vector3d v = new Vector3d(point);\r
+ v.sub(straightPoint);\r
+ u[0] = straightDir.dot(v);\r
+ u[0] /= straightDir.lengthSquared();\r
+ v.set(straightDir);\r
+ v.scale(u[0]);\r
+ v.add(straightPoint);\r
+ return v; \r
+ }\r
+ \r
+ public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, Tuple3d planePoint) {\r
+ point.sub(planePoint);\r
+ \r
+ return planeNormal.dot(point);\r
+ }\r
+ \r
+ public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, float d) {\r
+ return (planeNormal.dot(point) + d);\r
+ }\r
+ \r
+ public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Tuple3d intersectPoint) {\r
+ intersectPoint.set(planePoint);\r
+ intersectPoint.sub(linePoint);\r
+ double u = planeNormal.dot(new Vector3d(intersectPoint));\r
+ double v = planeNormal.dot(lineDir);\r
+ if (Math.abs(v) < NEAR_ZERO)\r
+ return false;\r
+ u /= v;\r
+ intersectPoint.set(lineDir);\r
+ intersectPoint.scale(u);\r
+ intersectPoint.add(linePoint);\r
+ return true;\r
+ }\r
+ \r
+ public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Vector3d intersectPoint, double[] u) {\r
+ intersectPoint.set(planePoint);\r
+ intersectPoint.sub(linePoint);\r
+ u[0] = planeNormal.dot(intersectPoint);\r
+ double v = planeNormal.dot(lineDir);\r
+ if (Math.abs(v) < NEAR_ZERO)\r
+ return false;\r
+ u[0] /= v;\r
+ intersectPoint.set(lineDir);\r
+ intersectPoint.scale(u[0]);\r
+ intersectPoint.add(linePoint);\r
+ return true;\r
+ }\r
+ \r
+ public static boolean intersectLineLine(Tuple3d l1_start,Tuple3d l1_end,Tuple3d l2_start,Tuple3d l2_end,Tuple3d l1_pos, Tuple3d l2_pos) {\r
+ Vector3d p13 = new Vector3d();\r
+ Vector3d p43 = new Vector3d();\r
+ Vector3d p21 = new Vector3d();\r
+ double d1343,d4321,d1321,d4343,d2121;\r
+ double numer,denom;\r
+ p13.sub(l1_start, l2_start);\r
+ p43.sub(l2_end,l2_start);\r
+ if (Math.abs(p43.x) < NEAR_ZERO && Math.abs(p43.y) < NEAR_ZERO && Math.abs(p43.z) < NEAR_ZERO)\r
+ return false;\r
+ p21.sub(l1_end,l1_start);\r
+ if (Math.abs(p21.x) < NEAR_ZERO && Math.abs(p21.y) < NEAR_ZERO && Math.abs(p21.z) < NEAR_ZERO)\r
+ return false;\r
+\r
+ d1343 = p13.dot(p43);\r
+ d4321 = p43.dot(p21);\r
+ d1321 = p13.dot(p21);\r
+ d4343 = p43.lengthSquared();\r
+ d2121 = p21.lengthSquared();\r
+\r
+ denom = d2121 * d4343 - d4321 * d4321;\r
+ if (Math.abs(denom) < NEAR_ZERO)\r
+ return false;\r
+ numer = d1343 * d4321 - d1321 * d4343;\r
+\r
+ double mua = numer / denom;\r
+ double mub = (d1343 + d4321 * mua) / d4343;\r
+ \r
+ l1_pos.x = l1_start.x + mua * p21.x;\r
+ l1_pos.y = l1_start.y + mua * p21.y;\r
+ l1_pos.z = l1_start.z + mua * p21.z;\r
+ l2_pos.x = l2_start.x + mub * p43.x;\r
+ l2_pos.y = l2_start.y + mub * p43.y;\r
+ l2_pos.z = l2_start.z + mub * p43.z;\r
+\r
+ return true;\r
+ }\r
+ \r
+ public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb) {\r
+ Vector3d p13 = new Vector3d();\r
+\r
+ double d1343,d4321,d1321,d4343,d2121;\r
+ double numer,denom;\r
+ \r
+ p13.sub(p1, p3);\r
+ if (Math.abs(p43.x) < NEAR_ZERO && Math.abs(p43.y) < NEAR_ZERO && Math.abs(p43.z) < NEAR_ZERO)\r
+ return false;\r
+ if (Math.abs(p21.x) < NEAR_ZERO && Math.abs(p21.y) < NEAR_ZERO && Math.abs(p21.z) < NEAR_ZERO)\r
+ return false;\r
+\r
+ d1343 = p13.dot(p43);\r
+ d4321 = p43.dot(p21);\r
+ d1321 = p13.dot(p21);\r
+ d4343 = p43.lengthSquared();\r
+ d2121 = p21.lengthSquared();\r
+\r
+ denom = d2121 * d4343 - d4321 * d4321;\r
+ if (Math.abs(denom) < NEAR_ZERO)\r
+ return false;\r
+ numer = d1343 * d4321 - d1321 * d4343;\r
+\r
+ double mua = numer / denom;\r
+ double mub = (d1343 + d4321 * mua) / d4343;\r
+\r
+ pa.x = p1.x + mua * p21.x;\r
+ pa.y = p1.y + mua * p21.y;\r
+ pa.z = p1.z + mua * p21.z;\r
+ pb.x = p3.x + mub * p43.x;\r
+ pb.y = p3.y + mub * p43.y;\r
+ pb.z = p3.z + mub * p43.z;\r
+\r
+ return true;\r
+ }\r
+ \r
+ /**\r
+ * Calculate the line segment PaPb that is the shortest route between\r
+ * two lines P1P2 and P3P4. Calculate also the values of mua and mub where\r
+ * Pa = P1 + mua (P2 - P1)\r
+ * Pb = P3 + mub (P4 - P3)\r
+ * @param p1\r
+ * @param p21\r
+ * @param p3\r
+ * @param p43\r
+ * @param pa\r
+ * @param pb\r
+ * @param mu\r
+ * @return\r
+ */\r
+ public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb, double mu[]) {\r
+ Vector3d p13 = new Vector3d();\r
+\r
+ double d1343,d4321,d1321,d4343,d2121;\r
+ double numer,denom;\r
+ double EPS = 0.001;\r
+ p13.sub(p1, p3);\r
+ if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS)\r
+ return false;\r
+ if (Math.abs(p21.x) < EPS && Math.abs(p21.y) < EPS && Math.abs(p21.z) < EPS)\r
+ return false;\r
+\r
+ d1343 = p13.dot(p43);\r
+ d4321 = p43.dot(p21);\r
+ d1321 = p13.dot(p21);\r
+ d4343 = p43.lengthSquared();\r
+ d2121 = p21.lengthSquared();\r
+\r
+ denom = d2121 * d4343 - d4321 * d4321;\r
+ if (Math.abs(denom) < EPS)\r
+ return false;\r
+ numer = d1343 * d4321 - d1321 * d4343;\r
+\r
+ mu[0] = numer / denom;\r
+ mu[1] = (d1343 + d4321 * mu[0]) / d4343;\r
+\r
+ pa.x = p1.x + mu[0] * p21.x;\r
+ pa.y = p1.y + mu[0] * p21.y;\r
+ pa.z = p1.z + mu[0] * p21.z;\r
+ pb.x = p3.x + mu[1] * p43.x;\r
+ pb.y = p3.y + mu[1] * p43.y;\r
+ pb.z = p3.z + mu[1] * p43.z;\r
+\r
+ return true;\r
+ }\r
+ \r
+ \r
+ \r
+ public static void rotate(Quat4d q, Tuple3d in, Tuple3d out) {\r
+ // p' = q * p * q'\r
+ double tw = - q.x*in.x - q.y*in.y - q.z*in.z;\r
+ double tx = q.w*in.x + q.y*in.z - q.z*in.y;\r
+ double ty = q.w*in.y - q.x*in.z + q.z*in.x;\r
+ double tz = q.w*in.z + q.x*in.y - q.y*in.x ;\r
+ \r
+ //temp * q' -> x = -x, y = -y z = -z\r
+ //out.w = tw*q.w + tx*q.x + ty*q.y + tz*q.z;\r
+ out.x = -tw*q.x + tx*q.w - ty*q.z + tz*q.y;\r
+ out.y = -tw*q.y + tx*q.z + ty*q.w - tz*q.x;\r
+ out.z = -tw*q.z - tx*q.y + ty*q.x + tz*q.w; \r
+ }\r
+ \r
+ public static void getMatrix(Quat4d quat, Matrix3d m) {\r
+ m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);\r
+ m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);\r
+ m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);\r
+ m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);\r
+ m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);\r
+ m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);\r
+ m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);\r
+ m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);\r
+ m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);\r
+\r
+ }\r
+ \r
+ \r
+ private static double q[] = new double[3];\r
+ private static int nxt[] = { 1, 2, 0 };\r
+ /**\r
+ * Converts Matrix to Quaternion\r
+ * \r
+ * Note: non-thread safe.\r
+ * \r
+ * @param mat\r
+ * @param quat\r
+ */\r
+ public static void getQuat(Matrix3d mat, Quat4d quat) {\r
+ double tr = mat.m00 + mat.m11 + mat.m22;\r
+ if (tr > 0.0) {\r
+ double s = Math.sqrt(tr + 1.0);\r
+ quat.w = 0.5 * s;\r
+ s = 0.5 / s;\r
+ quat.x = (mat.m21 - mat.m12) * s;\r
+ quat.y = (mat.m02 - mat.m20) * s;\r
+ quat.z = (mat.m10 - mat.m01) * s;\r
+ } else {\r
+ int i = 0, j, k;\r
+ if (mat.m11 > mat.m00)\r
+ i = 1;\r
+ if (mat.m22 > mat.getElement(i, i))\r
+ i = 2;\r
+ \r
+\r
+ j = nxt[i];\r
+ k = nxt[j];\r
+\r
+ double s = Math.sqrt((mat.getElement(i, i) - (mat.getElement(j, j) + mat.getElement(k, k))) + 1.0);\r
+\r
+ q[i] = s * 0.5;\r
+\r
+ if (Math.abs(s) > 0.001)\r
+ s = 0.5 / s;\r
+\r
+ quat.w = (mat.getElement(k, j) - mat.getElement(j, k)) * s;\r
+ q[j] = (mat.getElement(j, i) + mat.getElement(i, j)) * s;\r
+ q[k] = (mat.getElement(k, i) + mat.getElement(i, k)) * s;\r
+\r
+ quat.x = q[0];\r
+ quat.y = q[1];\r
+ quat.z = q[2];\r
+ }\r
+ }\r
+ \r
+ public static Quat4d getQuat(Matrix3d mat) {\r
+ Quat4d q = new Quat4d();\r
+ getQuat(mat, q);\r
+ return q;\r
+ }\r
+ \r
+ public static AxisAngle4d getFromPseudoEuler(Vector3d euler) {\r
+ AxisAngle4d aa = new AxisAngle4d();\r
+ aa.angle = euler.length();\r
+ Vector3d normal = new Vector3d(euler);\r
+ if (aa.angle > NEAR_ZERO) {\r
+ normal.normalize();\r
+ aa.x = normal.x;\r
+ aa.y = normal.y;\r
+ aa.z = normal.z;\r
+ } else {\r
+ aa.x = 1.0;\r
+ aa.y = 0.0;\r
+ aa.z = 0.0;\r
+ }\r
+ \r
+ return aa;\r
+ }\r
+ \r
+ public static Vector3d getPseudoEuler(AxisAngle4d aa) {\r
+ Vector3d euler = new Vector3d(aa.x,aa.y,aa.z);\r
+ euler.scale(aa.angle);\r
+ return euler;\r
+ }\r
+ \r
+ \r
+ public static void getQuat(Vector3d euler, Quat4d quat) {\r
+ Quat4d q = EulerTools.getQuatFromEuler(Order.YXZ, euler.y,euler.x,euler.z);\r
+ quat.set(q);\r
+ // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms\r
+ // Using the x-convention, the 3-1-3 Euler angles phi, theta and psi (around the Z, X and again the Z-axis) \r
+// quat.x = -Math.cos((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);\r
+// quat.y = -Math.sin((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);\r
+// quat.z = -Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);\r
+// quat.w = Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);\r
+ \r
+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm\r
+ // Y, Z, X order\r
+// double c1 = Math.cos(euler.y*0.5);\r
+// double s1 = Math.sin(euler.y*0.5);\r
+// double c2 = Math.cos(euler.z*0.5);\r
+// double s2 = Math.sin(euler.z*0.5);\r
+// double c3 = Math.cos(euler.x*0.5);\r
+// double s3 = Math.sin(euler.x*0.5);\r
+// double c1c2 = c1*c2;\r
+// double s1s2 = s1*s2;\r
+// quat.w =c1c2*c3 - s1s2*s3;\r
+// quat.x =c1c2*s3 + s1s2*c3;\r
+// quat.y =s1*c2*c3 + c1*s2*s3;\r
+// quat.z =c1*s2*c3 - s1*c2*s3;\r
+\r
+// Quat4d q2 = EulerTools.getQuatFromEuler(Order.YZX, euler.y,euler.z,euler.x);\r
+// System.out.println("Q " + quat + " Q2 " + q2);\r
+// double c1 = Math.cos(euler.y);\r
+// double s1 = Math.sin(euler.y);\r
+// double c2 = Math.cos(euler.z);\r
+// double s2 = Math.sin(euler.z);\r
+// double c3 = Math.cos(euler.x);\r
+// double s3 = Math.sin(euler.x);\r
+// quat.w = Math.sqrt(1.0 + c1 * c2 + c1*c3 - s1 * s2 * s3 + c2*c3) / 2.0;\r
+// double w4 = (4.0 * quat.w);\r
+// quat.x = (c2 * s3 + c1 * s3 + s1 * s2 * c3) / w4 ;\r
+// quat.y = (s1 * c2 + s1 * c3 + c1 * s2 * s3) / w4 ;\r
+// quat.z = (-s1 * s3 + c1 * s2 * c3 +s2) / w4 ;\r
+ }\r
+ \r
+ \r
+ \r
+ \r
+ public static void getEuler(Quat4d quat,Vector3d euler) {\r
+ Vector3d e = EulerTools.getEulerFromQuat(Order.YXZ, quat);\r
+ euler.x = e.y;\r
+ euler.y = e.x;\r
+ euler.z = e.z;\r
+ \r
+ // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms\r
+// euler.x = Math.atan2(quat.x * quat.z + quat.y* quat.w, quat.y*quat.z - quat.x * quat.w);\r
+// euler.y = Math.acos(-square(quat.x) - square(quat.y) + square(quat.z) + square(quat.w));\r
+// euler.z = -Math.atan2(quat.x * quat.z - quat.y* quat.w, quat.y*quat.z + quat.x * quat.w);\r
+ \r
+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm\r
+ // Y, Z, X order\r
+// double test = quat.x * quat.y + quat.z * quat.w;\r
+// if (test > NEAR_HALF) {\r
+// euler.y = 2.0 * Math.atan2(quat.x,quat.w);\r
+// euler.z = Math.PI * 0.5;\r
+// euler.x = 0.0;\r
+// } else if (test < -NEAR_HALF) {\r
+// euler.y = -2.0 * Math.atan2(quat.x,quat.w);\r
+// euler.z = -Math.PI * 0.5;\r
+// euler.x = 0.0;\r
+// } else {\r
+// double sqx = square(quat.x);\r
+// double sqy = square(quat.y);\r
+// double sqz = square(quat.z);\r
+// euler.y = Math.atan2(2.0*(quat.y*quat.w-quat.x*quat.z), 1.0 - 2.0*(sqy-sqz));\r
+// euler.z = Math.asin(2.0*test);\r
+// euler.x = Math.atan2(2.0*(quat.x*quat.w-quat.y*quat.z), 1.0 - 2.0*(sqx-sqz));\r
+// System.out.println(euler + " " + EulerTools.getEulerFromQuat(Order.YXZ, quat) + " " + quat);\r
+// }\r
+// double sqw = quat.w*quat.w;\r
+// double sqx = quat.x*quat.x;\r
+// double sqy = quat.y*quat.y;\r
+// double sqz = quat.z*quat.z;\r
+// double unit = sqx + sqy + sqz + sqw; // if normalised is one, otherwise is correction factor\r
+// double test = quat.x*quat.y + quat.z*quat.w;\r
+// if (test > 0.499*unit) { // singularity at north pole\r
+// euler.y = 2 * Math.atan2(quat.x,quat.w);\r
+// euler.z = Math.PI/2;\r
+// euler.x = 0;\r
+// return;\r
+// }\r
+// if (test < -0.499*unit) { // singularity at south pole\r
+// euler.y = -2 * Math.atan2(quat.x,quat.w);\r
+// euler.z = -Math.PI/2;\r
+// euler.x = 0;\r
+// return;\r
+// }\r
+// euler.y = Math.atan2(2*quat.y*quat.w-2*quat.x*quat.z , sqx - sqy - sqz + sqw);\r
+// euler.z = Math.asin(2*test/unit);\r
+// euler.x = Math.atan2(2*quat.x*quat.w-2*quat.y*quat.z , -sqx + sqy - sqz + sqw);\r
+ }\r
+ \r
+ public static Quat4d getQuat(Vector3d euler) {\r
+ Quat4d q = new Quat4d();\r
+ getQuat(euler,q);\r
+ return q;\r
+ }\r
+ \r
+ \r
+ public static Vector3d getEuler(Quat4d quat) {\r
+ Vector3d v = new Vector3d();\r
+ getEuler(quat, v);\r
+ return v;\r
+ }\r
+ \r
+ public static Quat4d getQuat(AxisAngle4d aa) {\r
+ Quat4d q = new Quat4d();\r
+ getQuat(aa, q);\r
+ return q;\r
+ }\r
+ \r
+ public static AxisAngle4d getAxisAngle(Quat4d q) {\r
+ AxisAngle4d aa = new AxisAngle4d();\r
+ aa.set(q);\r
+ return aa;\r
+ }\r
+ \r
+ public static Quat4d getIdentityQuat() {\r
+ return new Quat4d(0, 0, 0, 1);\r
+ }\r
+ \r
+ public static void getQuat(AxisAngle4d aa, Quat4d q) {\r
+ double mag,amag;\r
+ // Quat = cos(theta/2) + sin(theta/2)(roation_axis) \r
+ \r
+ amag = Math.sqrt( aa.x*aa.x + aa.y*aa.y + aa.z*aa.z);\r
+ if( amag < NEAR_ZERO ) {\r
+ q.w = 1.0;\r
+ q.x = 0.0;\r
+ q.y = 0.0;\r
+ q.z = 0.0;\r
+ } else { \r
+ amag = 1.0/amag; \r
+ double a2 = aa.angle * 0.5;\r
+ mag = Math.sin(a2);\r
+ q.w = Math.cos(a2);\r
+ q.x = aa.x*amag*mag;\r
+ q.y = aa.y*amag*mag;\r
+ q.z = aa.z*amag*mag;\r
+ }\r
+ }\r
+ \r
+ \r
+ /*\r
+ * Cohen-Sutherland\r
+ */\r
+ \r
+ private static final int IN = 0;\r
+ private static final int LEFT = 1;\r
+ private static final int RIGHT = 2;\r
+ private static final int BOTTOM = 4;\r
+ private static final int TOP = 8;\r
+ \r
+ \r
+ private static int bitcode(Vector2f p1, Vector2f min, Vector2f max) {\r
+ int code = IN;\r
+ if (p1.x < min.x)\r
+ code |= LEFT;\r
+ else if (p1.x > max.x)\r
+ code |= RIGHT;\r
+ if (p1.y < min.y)\r
+ code |= BOTTOM;\r
+ else if (p1.y > max.y)\r
+ code |= TOP;\r
+ return code;\r
+ }\r
+ \r
+ public static boolean clipLineRectangle(Vector2f p1,Vector2f p2, Vector2f min, Vector2f max, Vector2f r1, Vector2f r2) {\r
+ while (true) {\r
+ int o1 = bitcode(p1, min, max);\r
+ int o2 = bitcode(p2, min, max);\r
+ int and = o1 & o2;\r
+ int or = o1 | o2;\r
+ if (and != IN) {\r
+ return false;\r
+ }\r
+ if (or == IN) {\r
+ r1.set(p1);\r
+ r2.set(p2);\r
+ return true;\r
+ }\r
+ if (o1 == IN) {\r
+ Vector2f t = p1;\r
+ p1 = p2;\r
+ p2 = t;\r
+ int t2 = o1;\r
+ o1 = o2;\r
+ o2 = t2;\r
+ }\r
+ if ((o1 & TOP) != IN) {\r
+ float t = (max.y - p1.y) / (p2.y - p1.y);\r
+ p1.x += t * (p2.x - p1.x);\r
+ p1.y = max.y;\r
+ } else if ((o1 & BOTTOM) != IN) {\r
+ float t = (min.y - p1.y) / (p2.y - p1.y);\r
+ p1.x += t * (p2.x - p1.x);\r
+ p1.y = min.y;\r
+ } else if ((o1 & LEFT) != IN) {\r
+ float t = (min.x - p1.x) / (p2.x - p1.x);\r
+ p1.y += t * (p2.y - p1.y);\r
+ p1.x = min.x;\r
+ } else if ((o1 & RIGHT) != IN) {\r
+ float t = (max.x - p1.x) / (p2.x - p1.x);\r
+ p1.y += t * (p2.y - p1.y);\r
+ p1.x = max.x;\r
+ } else {\r
+ throw new RuntimeException("Error in clipping code");\r
+ }\r
+ }\r
+ \r
+ }\r
+ \r
+ public static double square(double d) {\r
+ return d * d;\r
+ }\r
+ \r
+ \r
+ public static void multiplyOrientation(AxisAngle4d aa, AxisAngle4d rot) {\r
+ Quat4d q1 = new Quat4d();\r
+ getQuat(aa, q1);\r
+ Quat4d q2 = new Quat4d();\r
+ getQuat(rot, q2);\r
+ q2.mul(q1);\r
+ rot.set(q2);\r
+ }\r
+ \r
+ public static double radToDeg(double rad) {\r
+ return (rad / Math.PI) * 180.0;\r
+ }\r
+ \r
+ public static double degToRad(double deg) {\r
+ return (deg / 180.0) * Math.PI;\r
+ }\r
+ \r
+ public static double clamp(double min, double max,double v) {\r
+ if (v < min)\r
+ return min;\r
+ if (v > max)\r
+ return max;\r
+ return v;\r
+ }\r
+ \r
+ public static AxisAngle4d createRotation(Vector3d original, Vector3d rotated) { \r
+ AxisAngle4d result = new AxisAngle4d();\r
+ if (createRotation(original, rotated, result))\r
+ return result;\r
+ return null;\r
+ }\r
+ \r
+ \r
+ public static void setIdentity(Quat4d q) {\r
+ q.w = 1.0;\r
+ q.x = 0.0;\r
+ q.y = 0.0;\r
+ q.z = 0.0;\r
+ }\r
+ \r
+ public static void setIdentity(AxisAngle4d aa) {\r
+ aa.angle = 0.0;\r
+ aa.x = 0.0;\r
+ aa.y = 1.0;\r
+ aa.z = 0.0;\r
+ }\r
+ \r
+ public static void set(Matrix3d mat, double m00, double m01, double m02,\r
+ double m10, double m11, double m12, double m20, double m21,\r
+ double m22) {\r
+ mat.m00 = m00;\r
+ mat.m01 = m01;\r
+ mat.m02 = m02;\r
+\r
+ mat.m10 = m10;\r
+ mat.m11 = m11;\r
+ mat.m12 = m12;\r
+\r
+ mat.m20 = m20;\r
+ mat.m21 = m21;\r
+ mat.m22 = m22;\r
+ }\r
+ \r
+ public static void set(Matrix4d mat, double[] v) {\r
+ mat.m00 = v[0];\r
+ mat.m01 = v[1];\r
+ mat.m02 = v[2];\r
+ mat.m03 = v[3];\r
+\r
+ mat.m10 = v[4];\r
+ mat.m11 = v[5];\r
+ mat.m12 = v[6];\r
+ mat.m13 = v[7];\r
+\r
+ mat.m20 = v[8];\r
+ mat.m21 = v[9];\r
+ mat.m22 = v[10];\r
+ mat.m23 = v[11];\r
+\r
+ mat.m30 = v[12];\r
+ mat.m31 = v[13];\r
+ mat.m32 = v[14];\r
+ mat.m33 = v[15];\r
+\r
+ }\r
+ \r
+ public static boolean createRotation(Vector3d original, Vector3d rotated, AxisAngle4d result) {\r
+ \r
+ if (rotated.lengthSquared() > 0.01)\r
+ rotated.normalize();\r
+ else\r
+ return false;\r
+ double d = original.dot(rotated);\r
+ if (d > 0.9999) {\r
+ // original and rotated are parallel, pointing at the same direction\r
+ result.angle = 0.0;\r
+ result.x = 0.0;\r
+ result.y = 1.0;\r
+ result.z = 0.0;\r
+ } else if (d < -0.9999) {\r
+ // original and rotated are parallel, pointing at the opposite direction \r
+ Vector3d a = Z_AXIS;\r
+ if (Math.abs(a.dot(original)) > 0.8 )\r
+ a = Y_AXIS;\r
+ result.set(a, Math.PI);\r
+ } else {\r
+ double angle = original.angle(rotated);\r
+ Vector3d axis = new Vector3d();\r
+ axis.cross(original, rotated);\r
+ result.set(axis,angle);\r
+ }\r
+ return true;\r
+ }\r
+ \r
+ public static boolean createRotation(Vector3d original, Vector3d rotated, Quat4d result) {\r
+ \r
+ if (rotated.lengthSquared() > 0.01)\r
+ rotated.normalize();\r
+ else\r
+ return false;\r
+ double d = original.dot(rotated);\r
+ if (d > 0.9999) {\r
+ // original and rotated are parallel, pointing at the same direction\r
+ result.w = 1.0;\r
+ result.x = 0.0;\r
+ result.y = 0.0;\r
+ result.z = 0.0;\r
+ } else if (d < -0.9999) {\r
+ // original and rotated are parallel, pointing at the opposite direction \r
+ Vector3d a = Z_AXIS;\r
+ if (Math.abs(a.dot(original)) > 0.8 )\r
+ a = Y_AXIS;\r
+ getQuat(a, Math.PI, result);\r
+ \r
+ } else {\r
+ double angle = original.angle(rotated);\r
+ Vector3d axis = new Vector3d();\r
+ axis.cross(original, rotated);\r
+ getQuat(axis, angle, result);\r
+ }\r
+ return true;\r
+ }\r
+ \r
+ public static void getQuat(Vector3d axis, double angle, Quat4d q)\r
+ {\r
+ double mag,amag;\r
+ // Quat = cos(theta/2) + sin(theta/2)(roation_axis) \r
+ \r
+ amag = Math.sqrt( axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);\r
+ if( amag < EPS ) {\r
+ q.w = 1.0;\r
+ q.x = 0.0;\r
+ q.y = 0.0;\r
+ q.z = 0.0;\r
+ } else { \r
+ amag = 1.0/amag; \r
+ double a2 = angle*0.5;\r
+ mag = Math.sin(a2);\r
+ q.w = Math.cos(a2);\r
+ q.x = axis.x*amag*mag;\r
+ q.y = axis.y*amag*mag;\r
+ q.z = axis.z*amag*mag;\r
+ }\r
+ \r
+ }\r
+ \r
+ /**\r
+ * Linear interpolation of quaternions. Result IS set to q1.\r
+ * @param q1\r
+ * @param q2\r
+ * @param alpha\r
+ */\r
+ public static void lip(Quat4d q1, Quat4d q2, double alpha) {\r
+ double s1 = 1.0 - alpha;\r
+ double s2 = alpha;\r
+ q1.scale(s1);\r
+ mad(q1,q2,s2);\r
+ q1.normalize();\r
+ }\r
+ \r
+ public static double dot(Quat4d q1, Quat4d q2) {\r
+ return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;\r
+ }\r
+ \r
+ public static void mad(Tuple3d q1, Tuple3d q2, double s2) {\r
+ q1.x += q2.x * s2;\r
+ q1.y += q2.y * s2;\r
+ q1.z += q2.z * s2;\r
+ }\r
+ \r
+ public static void mad(Quat4d q1, Quat4d q2, double s2) {\r
+ q1.x += q2.x * s2;\r
+ q1.y += q2.y * s2;\r
+ q1.z += q2.z * s2;\r
+ q1.w += q2.w * s2;\r
+ }\r
+ \r
+ /**\r
+ * Slerp\r
+ * \r
+ * Sets results to q1. Modifies q2.\r
+ * \r
+ * @param q1\r
+ * @param q2\r
+ * @param alpha\r
+ */\r
+ public static void sip(Quat4d q1, Quat4d q2, double alpha) {\r
+ double cosom = dot(q1,q2);\r
+ if (cosom < 0.0) {\r
+ cosom = -cosom;\r
+ q2.negate();\r
+ }\r
+ \r
+ if (cosom > 0.9999) {\r
+ q2.sub(q1);\r
+ q2.scale(alpha);\r
+ q1.add(q2);\r
+ q1.normalize();\r
+ return;\r
+ }\r
+ double theta_0 = Math.acos(cosom);\r
+ double theta = theta_0 * alpha;\r
+ Quat4d t = new Quat4d(q1);\r
+ t.scale(-cosom);\r
+ t.add(q2);\r
+ t.normalize();\r
+ t.scale(Math.sin(theta));\r
+ q1.scale(Math.cos(theta));\r
+ q1.add(t);\r
+ }\r
+}\r
Code Review / simantics / 3d.git / blobdiff