*
*/
public class MathTools {
-
- public static double NEAR_ZERO = 0.000000001;
- public static double NEAR_HALF = 0.499999999;
-
- public static final Vector3d Z_AXIS = new Vector3d(0.0,0.0,1.0);
+
+ public static double NEAR_ZERO = 0.000000001;
+ public static double NEAR_HALF = 0.499999999;
+
+ public static final Vector3d Z_AXIS = new Vector3d(0.0,0.0,1.0);
public static final Vector3d Y_AXIS = new Vector3d(0.0,1.0,0.0);
public static final Vector3d X_AXIS = new Vector3d(1.0,0.0,0.0);
public static final Vector3d ORIGIN = new Vector3d(0.0,0.0,0.0);
public static boolean isValid(Tuple3d t) {
return !(Double.isInfinite(t.x) || Double.isNaN(t.x) ||
- Double.isInfinite(t.y) || Double.isNaN(t.y) ||
- Double.isInfinite(t.z) || Double.isNaN(t.z));
- }
-
- public static Vector3d closestPointOnEdge(Vector3d point, Vector3d edgePoint1, Vector3d edgePoint2) {
- point.sub(edgePoint1);
- Vector3d v = new Vector3d(edgePoint2);
- v.sub(edgePoint1);
- double t = v.dot(point);
- t /= v.lengthSquared();
- if (t <= 0.0f)
- return edgePoint1;
- if (t >= 1.0f)
- return edgePoint2;
- v.scale(t);
- v.add(edgePoint1);
- return v;
- }
-
- public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir) {
- Vector3d v = new Vector3d(point);
- v.sub(straightPoint);
- double t = straightDir.dot(v);
- t /= straightDir.lengthSquared();
- v.set(straightDir);
- v.scale(t);
- v.add(straightPoint);
- return v;
- }
-
- public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir, double u[]) {
- Vector3d v = new Vector3d(point);
- v.sub(straightPoint);
- u[0] = straightDir.dot(v);
- u[0] /= straightDir.lengthSquared();
- v.set(straightDir);
- v.scale(u[0]);
- v.add(straightPoint);
- return v;
- }
-
- public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, Tuple3d planePoint) {
- point.sub(planePoint);
-
- return planeNormal.dot(point);
- }
-
- public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, float d) {
- return (planeNormal.dot(point) + d);
- }
-
- public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Tuple3d intersectPoint) {
- intersectPoint.set(planePoint);
- intersectPoint.sub(linePoint);
- double u = planeNormal.dot(new Vector3d(intersectPoint));
- double v = planeNormal.dot(lineDir);
- if (Math.abs(v) < NEAR_ZERO)
- return false;
- u /= v;
- intersectPoint.set(lineDir);
- intersectPoint.scale(u);
- intersectPoint.add(linePoint);
- return true;
- }
-
- public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Vector3d intersectPoint, double[] u) {
- intersectPoint.set(planePoint);
- intersectPoint.sub(linePoint);
- u[0] = planeNormal.dot(intersectPoint);
- double v = planeNormal.dot(lineDir);
- if (Math.abs(v) < NEAR_ZERO)
- return false;
- u[0] /= v;
- intersectPoint.set(lineDir);
- intersectPoint.scale(u[0]);
- intersectPoint.add(linePoint);
- return true;
- }
-
- public static boolean intersectLineLine(Tuple3d l1_start,Tuple3d l1_end,Tuple3d l2_start,Tuple3d l2_end,Tuple3d l1_pos, Tuple3d l2_pos) {
- Vector3d p13 = new Vector3d();
- Vector3d p43 = new Vector3d();
- Vector3d p21 = new Vector3d();
- double d1343,d4321,d1321,d4343,d2121;
- double numer,denom;
- p13.sub(l1_start, l2_start);
- p43.sub(l2_end,l2_start);
- if (Math.abs(p43.x) < NEAR_ZERO && Math.abs(p43.y) < NEAR_ZERO && Math.abs(p43.z) < NEAR_ZERO)
- return false;
- p21.sub(l1_end,l1_start);
- if (Math.abs(p21.x) < NEAR_ZERO && Math.abs(p21.y) < NEAR_ZERO && Math.abs(p21.z) < NEAR_ZERO)
- return false;
-
- d1343 = p13.dot(p43);
- d4321 = p43.dot(p21);
- d1321 = p13.dot(p21);
- d4343 = p43.lengthSquared();
- d2121 = p21.lengthSquared();
-
- denom = d2121 * d4343 - d4321 * d4321;
- if (Math.abs(denom) < NEAR_ZERO)
- return false;
- numer = d1343 * d4321 - d1321 * d4343;
-
- double mua = numer / denom;
- double mub = (d1343 + d4321 * mua) / d4343;
-
- l1_pos.x = l1_start.x + mua * p21.x;
- l1_pos.y = l1_start.y + mua * p21.y;
- l1_pos.z = l1_start.z + mua * p21.z;
- l2_pos.x = l2_start.x + mub * p43.x;
- l2_pos.y = l2_start.y + mub * p43.y;
- l2_pos.z = l2_start.z + mub * p43.z;
-
- return true;
- }
-
- public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb) {
- Vector3d p13 = new Vector3d();
+ Double.isInfinite(t.y) || Double.isNaN(t.y) ||
+ Double.isInfinite(t.z) || Double.isNaN(t.z));
+ }
+
+ public static Vector3d closestPointOnEdge(Vector3d point, Vector3d edgePoint1, Vector3d edgePoint2) {
+ point.sub(edgePoint1);
+ Vector3d v = new Vector3d(edgePoint2);
+ v.sub(edgePoint1);
+ double t = v.dot(point);
+ t /= v.lengthSquared();
+ if (t <= 0.0f)
+ return edgePoint1;
+ if (t >= 1.0f)
+ return edgePoint2;
+ v.scale(t);
+ v.add(edgePoint1);
+ return v;
+ }
+
+ public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir) {
+ Vector3d v = new Vector3d(point);
+ v.sub(straightPoint);
+ double t = straightDir.dot(v);
+ t /= straightDir.lengthSquared();
+ v.set(straightDir);
+ v.scale(t);
+ v.add(straightPoint);
+ return v;
+ }
+
+ public static Vector3d closestPointOnStraight(Tuple3d point, Tuple3d straightPoint, Vector3d straightDir, double u[]) {
+ Vector3d v = new Vector3d(point);
+ v.sub(straightPoint);
+ u[0] = straightDir.dot(v);
+ u[0] /= straightDir.lengthSquared();
+ v.set(straightDir);
+ v.scale(u[0]);
+ v.add(straightPoint);
+ return v;
+ }
+
+ public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, Tuple3d planePoint) {
+ point.sub(planePoint);
+
+ return planeNormal.dot(point);
+ }
+
+ public static double distanceFromPlane(Vector3d point, Vector3d planeNormal, float d) {
+ return (planeNormal.dot(point) + d);
+ }
+
+ public static Vector3d projectToPlane(Vector3d v, Vector3d planeNormal) {
+ //v.normalize();
+ //planeNormal.normalize();
+ Vector3d t = new Vector3d();
+ t.cross(v,planeNormal);
+ t.cross(planeNormal, t);
+ return t;
+
+ }
+
+ public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Tuple3d intersectPoint) {
+ intersectPoint.set(planePoint);
+ intersectPoint.sub(linePoint);
+ double u = planeNormal.dot(new Vector3d(intersectPoint));
+ double v = planeNormal.dot(lineDir);
+ if (Math.abs(v) < NEAR_ZERO)
+ return false;
+ u /= v;
+ intersectPoint.set(lineDir);
+ intersectPoint.scale(u);
+ intersectPoint.add(linePoint);
+ return true;
+ }
+
+ public static boolean intersectStraightPlane(Tuple3d linePoint, Vector3d lineDir, Tuple3d planePoint, Vector3d planeNormal, Vector3d intersectPoint, double[] u) {
+ intersectPoint.set(planePoint);
+ intersectPoint.sub(linePoint);
+ u[0] = planeNormal.dot(intersectPoint);
+ double v = planeNormal.dot(lineDir);
+ if (Math.abs(v) < NEAR_ZERO)
+ return false;
+ u[0] /= v;
+ intersectPoint.set(lineDir);
+ intersectPoint.scale(u[0]);
+ intersectPoint.add(linePoint);
+ return true;
+ }
+
+ public static boolean intersectLineLine(Tuple3d l1_start,Tuple3d l1_end,Tuple3d l2_start,Tuple3d l2_end,Tuple3d l1_pos, Tuple3d l2_pos) {
+ Vector3d p13 = new Vector3d();
+ Vector3d p43 = new Vector3d();
+ Vector3d p21 = new Vector3d();
+ double d1343,d4321,d1321,d4343,d2121;
+ double numer,denom;
+ p13.sub(l1_start, l2_start);
+ p43.sub(l2_end,l2_start);
+ if (Math.abs(p43.x) < NEAR_ZERO && Math.abs(p43.y) < NEAR_ZERO && Math.abs(p43.z) < NEAR_ZERO)
+ return false;
+ p21.sub(l1_end,l1_start);
+ if (Math.abs(p21.x) < NEAR_ZERO && Math.abs(p21.y) < NEAR_ZERO && Math.abs(p21.z) < NEAR_ZERO)
+ return false;
- double d1343,d4321,d1321,d4343,d2121;
- double numer,denom;
-
- p13.sub(p1, p3);
- if (Math.abs(p43.x) < NEAR_ZERO && Math.abs(p43.y) < NEAR_ZERO && Math.abs(p43.z) < NEAR_ZERO)
- return false;
- if (Math.abs(p21.x) < NEAR_ZERO && Math.abs(p21.y) < NEAR_ZERO && Math.abs(p21.z) < NEAR_ZERO)
- return false;
-
- d1343 = p13.dot(p43);
- d4321 = p43.dot(p21);
- d1321 = p13.dot(p21);
- d4343 = p43.lengthSquared();
- d2121 = p21.lengthSquared();
-
- denom = d2121 * d4343 - d4321 * d4321;
- if (Math.abs(denom) < NEAR_ZERO)
- return false;
- numer = d1343 * d4321 - d1321 * d4343;
-
- double mua = numer / denom;
- double mub = (d1343 + d4321 * mua) / d4343;
-
- pa.x = p1.x + mua * p21.x;
- pa.y = p1.y + mua * p21.y;
- pa.z = p1.z + mua * p21.z;
- pb.x = p3.x + mub * p43.x;
- pb.y = p3.y + mub * p43.y;
- pb.z = p3.z + mub * p43.z;
+ d1343 = p13.dot(p43);
+ d4321 = p43.dot(p21);
+ d1321 = p13.dot(p21);
+ d4343 = p43.lengthSquared();
+ d2121 = p21.lengthSquared();
- return true;
- }
-
- /**
- * Calculate the line segment PaPb that is the shortest route between
- * two lines P1P2 and P3P4. Calculate also the values of mua and mub where
- * Pa = P1 + mua (P2 - P1)
- * Pb = P3 + mub (P4 - P3)
- * @param p1
- * @param p21
- * @param p3
- * @param p43
- * @param pa
- * @param pb
- * @param mu
- * @return
- */
- public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb, double mu[]) {
- Vector3d p13 = new Vector3d();
-
- double d1343,d4321,d1321,d4343,d2121;
- double numer,denom;
- double EPS = 0.001;
- p13.sub(p1, p3);
- if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS)
- return false;
- if (Math.abs(p21.x) < EPS && Math.abs(p21.y) < EPS && Math.abs(p21.z) < EPS)
- return false;
-
- d1343 = p13.dot(p43);
- d4321 = p43.dot(p21);
- d1321 = p13.dot(p21);
- d4343 = p43.lengthSquared();
- d2121 = p21.lengthSquared();
-
- denom = d2121 * d4343 - d4321 * d4321;
- if (Math.abs(denom) < EPS)
- return false;
- numer = d1343 * d4321 - d1321 * d4343;
-
- mu[0] = numer / denom;
- mu[1] = (d1343 + d4321 * mu[0]) / d4343;
-
- pa.x = p1.x + mu[0] * p21.x;
- pa.y = p1.y + mu[0] * p21.y;
- pa.z = p1.z + mu[0] * p21.z;
- pb.x = p3.x + mu[1] * p43.x;
- pb.y = p3.y + mu[1] * p43.y;
- pb.z = p3.z + mu[1] * p43.z;
+ denom = d2121 * d4343 - d4321 * d4321;
+ if (Math.abs(denom) < NEAR_ZERO)
+ return false;
+ numer = d1343 * d4321 - d1321 * d4343;
- return true;
- }
-
-
-
- public static void rotate(Quat4d q, Tuple3d in, Tuple3d out) {
- // p' = q * p * q'
- double tw = - q.x*in.x - q.y*in.y - q.z*in.z;
- double tx = q.w*in.x + q.y*in.z - q.z*in.y;
- double ty = q.w*in.y - q.x*in.z + q.z*in.x;
- double tz = q.w*in.z + q.x*in.y - q.y*in.x ;
-
- //temp * q' -> x = -x, y = -y z = -z
- //out.w = tw*q.w + tx*q.x + ty*q.y + tz*q.z;
- out.x = -tw*q.x + tx*q.w - ty*q.z + tz*q.y;
- out.y = -tw*q.y + tx*q.z + ty*q.w - tz*q.x;
- out.z = -tw*q.z - tx*q.y + ty*q.x + tz*q.w;
- }
-
- public static void getMatrix(Quat4d quat, Matrix3d m) {
- m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
- m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
- m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
- m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
- m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
- m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
- m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
- m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
- m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
-
- }
-
- public static void getMatrix(Quat4d quat, Matrix4d m) {
- m.setZero();
- m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
- m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
- m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
- m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
- m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
- m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
- m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
- m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
- m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
- m.m33 = 1.0;
- }
-
- private static double q[] = new double[3];
- private static int nxt[] = { 1, 2, 0 };
- /**
- * Converts Matrix to Quaternion
- *
- * Note: non-thread safe.
- *
- * @param mat
- * @param quat
- */
- public static void getQuat(Matrix3d mat, Quat4d quat) {
- double tr = mat.m00 + mat.m11 + mat.m22;
+ double mua = numer / denom;
+ double mub = (d1343 + d4321 * mua) / d4343;
+
+ l1_pos.x = l1_start.x + mua * p21.x;
+ l1_pos.y = l1_start.y + mua * p21.y;
+ l1_pos.z = l1_start.z + mua * p21.z;
+ l2_pos.x = l2_start.x + mub * p43.x;
+ l2_pos.y = l2_start.y + mub * p43.y;
+ l2_pos.z = l2_start.z + mub * p43.z;
+
+ return true;
+ }
+
+ public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb) {
+ Vector3d p13 = new Vector3d();
+
+ double d1343,d4321,d1321,d4343,d2121;
+ double numer,denom;
+
+ p13.sub(p1, p3);
+ if (Math.abs(p43.x) < NEAR_ZERO && Math.abs(p43.y) < NEAR_ZERO && Math.abs(p43.z) < NEAR_ZERO)
+ return false;
+ if (Math.abs(p21.x) < NEAR_ZERO && Math.abs(p21.y) < NEAR_ZERO && Math.abs(p21.z) < NEAR_ZERO)
+ return false;
+
+ d1343 = p13.dot(p43);
+ d4321 = p43.dot(p21);
+ d1321 = p13.dot(p21);
+ d4343 = p43.lengthSquared();
+ d2121 = p21.lengthSquared();
+
+ denom = d2121 * d4343 - d4321 * d4321;
+ if (Math.abs(denom) < NEAR_ZERO)
+ return false;
+ numer = d1343 * d4321 - d1321 * d4343;
+
+ double mua = numer / denom;
+ double mub = (d1343 + d4321 * mua) / d4343;
+
+ pa.x = p1.x + mua * p21.x;
+ pa.y = p1.y + mua * p21.y;
+ pa.z = p1.z + mua * p21.z;
+ pb.x = p3.x + mub * p43.x;
+ pb.y = p3.y + mub * p43.y;
+ pb.z = p3.z + mub * p43.z;
+
+ return true;
+ }
+
+ /**
+ * Calculate the line segment PaPb that is the shortest route between
+ * two lines P1P2 and P3P4. Calculate also the values of mua and mub where
+ * Pa = P1 + mua (P2 - P1)
+ * Pb = P3 + mub (P4 - P3)
+ * @param p1
+ * @param p21
+ * @param p3
+ * @param p43
+ * @param pa
+ * @param pb
+ * @param mu
+ * @return
+ */
+ public static boolean intersectStraightStraight(Tuple3d p1,Vector3d p21,Tuple3d p3,Vector3d p43,Tuple3d pa,Tuple3d pb, double mu[]) {
+ Vector3d p13 = new Vector3d();
+
+ double d1343,d4321,d1321,d4343,d2121;
+ double numer,denom;
+ double EPS = 0.001;
+ p13.sub(p1, p3);
+ if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS)
+ return false;
+ if (Math.abs(p21.x) < EPS && Math.abs(p21.y) < EPS && Math.abs(p21.z) < EPS)
+ return false;
+
+ d1343 = p13.dot(p43);
+ d4321 = p43.dot(p21);
+ d1321 = p13.dot(p21);
+ d4343 = p43.lengthSquared();
+ d2121 = p21.lengthSquared();
+
+ denom = d2121 * d4343 - d4321 * d4321;
+ if (Math.abs(denom) < EPS)
+ return false;
+ numer = d1343 * d4321 - d1321 * d4343;
+
+ mu[0] = numer / denom;
+ mu[1] = (d1343 + d4321 * mu[0]) / d4343;
+
+ pa.x = p1.x + mu[0] * p21.x;
+ pa.y = p1.y + mu[0] * p21.y;
+ pa.z = p1.z + mu[0] * p21.z;
+ pb.x = p3.x + mu[1] * p43.x;
+ pb.y = p3.y + mu[1] * p43.y;
+ pb.z = p3.z + mu[1] * p43.z;
+
+ return true;
+ }
+
+
+
+ public static void rotate(Quat4d q, Tuple3d in, Tuple3d out) {
+ // p' = q * p * q'
+ double tw = - q.x*in.x - q.y*in.y - q.z*in.z;
+ double tx = q.w*in.x + q.y*in.z - q.z*in.y;
+ double ty = q.w*in.y - q.x*in.z + q.z*in.x;
+ double tz = q.w*in.z + q.x*in.y - q.y*in.x ;
+
+ //temp * q' -> x = -x, y = -y z = -z
+ //out.w = tw*q.w + tx*q.x + ty*q.y + tz*q.z;
+ out.x = -tw*q.x + tx*q.w - ty*q.z + tz*q.y;
+ out.y = -tw*q.y + tx*q.z + ty*q.w - tz*q.x;
+ out.z = -tw*q.z - tx*q.y + ty*q.x + tz*q.w;
+ }
+
+ public static void getMatrix(Quat4d quat, Matrix3d m) {
+ m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
+ m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
+ m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
+ m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
+ m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
+ m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
+ m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
+ m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
+ m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
+
+ }
+
+ public static void getMatrix(Quat4d quat, Matrix4d m) {
+ m.setZero();
+ m.m00 = 1.0f - 2.0 * (quat.y * quat.y + quat.z * quat.z);
+ m.m01 = 2.0 * (quat.x * quat.y + quat.w * quat.z);
+ m.m02 = 2.0 * (quat.x * quat.z - quat.w * quat.y);
+ m.m10 = 2.0 * (quat.x * quat.y - quat.w * quat.z);
+ m.m11 = 1.0 - 2.0f * (quat.x * quat.x + quat.z * quat.z);
+ m.m12 = 2.0 * (quat.y * quat.z + quat.w * quat.x);
+ m.m20 = 2.0 * (quat.x * quat.z + quat.w * quat.y);
+ m.m21 = 2.0 * (quat.y * quat.z - quat.w * quat.x);
+ m.m22 = 1.0 - 2.0f * (quat.x * quat.x + quat.y * quat.y);
+ m.m33 = 1.0;
+ }
+
+ private static double q[] = new double[3];
+ private static int nxt[] = { 1, 2, 0 };
+ /**
+ * Converts Matrix to Quaternion
+ *
+ * Note: non-thread safe.
+ *
+ * @param mat
+ * @param quat
+ */
+ public static void getQuat(Matrix3d mat, Quat4d quat) {
+ double tr = mat.m00 + mat.m11 + mat.m22;
if (tr > 0.0) {
double s = Math.sqrt(tr + 1.0);
quat.w = 0.5 * s;
quat.z = q[2];
}
}
-
- public static Quat4d getQuat(Matrix3d mat) {
- Quat4d q = new Quat4d();
- getQuat(mat, q);
- return q;
- }
-
- public static AxisAngle4d getFromPseudoEuler(Vector3d euler) {
- AxisAngle4d aa = new AxisAngle4d();
- aa.angle = euler.length();
- Vector3d normal = new Vector3d(euler);
- if (aa.angle > NEAR_ZERO) {
- normal.normalize();
- aa.x = normal.x;
- aa.y = normal.y;
- aa.z = normal.z;
- } else {
- aa.x = 1.0;
- aa.y = 0.0;
- aa.z = 0.0;
- }
-
- return aa;
- }
-
- public static Vector3d getPseudoEuler(AxisAngle4d aa) {
- Vector3d euler = new Vector3d(aa.x,aa.y,aa.z);
- euler.scale(aa.angle);
- return euler;
- }
-
-
- public static void getQuat(Vector3d euler, Quat4d quat) {
- Quat4d q = EulerTools.getQuatFromEuler(Order.YXZ, euler.y,euler.x,euler.z);
- quat.set(q);
+
+ public static Quat4d getQuat(Matrix3d mat) {
+ Quat4d q = new Quat4d();
+ getQuat(mat, q);
+ return q;
+ }
+
+ public static AxisAngle4d getFromPseudoEuler(Vector3d euler) {
+ AxisAngle4d aa = new AxisAngle4d();
+ aa.angle = euler.length();
+ Vector3d normal = new Vector3d(euler);
+ if (aa.angle > NEAR_ZERO) {
+ normal.normalize();
+ aa.x = normal.x;
+ aa.y = normal.y;
+ aa.z = normal.z;
+ } else {
+ aa.x = 1.0;
+ aa.y = 0.0;
+ aa.z = 0.0;
+ }
+
+ return aa;
+ }
+
+ public static Vector3d getPseudoEuler(AxisAngle4d aa) {
+ Vector3d euler = new Vector3d(aa.x,aa.y,aa.z);
+ euler.scale(aa.angle);
+ return euler;
+ }
+
+
+ public static void getQuat(Vector3d euler, Quat4d quat) {
+ Quat4d q = EulerTools.getQuatFromEuler(Order.YXZ, euler.y,euler.x,euler.z);
+ quat.set(q);
// http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
// Using the x-convention, the 3-1-3 Euler angles phi, theta and psi (around the Z, X and again the Z-axis)
// quat.x = -Math.cos((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);
// quat.y = -Math.sin((euler.x - euler.z)*0.5)*Math.sin(euler.y*0.5);
// quat.z = -Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);
// quat.w = Math.sin((euler.x + euler.z)*0.5)*Math.cos(euler.y*0.5);
-
- // http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
- // Y, Z, X order
+
+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
+ // Y, Z, X order
// double c1 = Math.cos(euler.y*0.5);
// double s1 = Math.sin(euler.y*0.5);
// double c2 = Math.cos(euler.z*0.5);
// quat.x = (c2 * s3 + c1 * s3 + s1 * s2 * c3) / w4 ;
// quat.y = (s1 * c2 + s1 * c3 + c1 * s2 * s3) / w4 ;
// quat.z = (-s1 * s3 + c1 * s2 * c3 +s2) / w4 ;
- }
-
-
-
-
- public static void getEuler(Quat4d quat,Vector3d euler) {
- Vector3d e = EulerTools.getEulerFromQuat(Order.YXZ, quat);
- euler.x = e.y;
- euler.y = e.x;
- euler.z = e.z;
-
- // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
+ }
+
+
+
+
+ public static void getEuler(Quat4d quat,Vector3d euler) {
+ Vector3d e = EulerTools.getEulerFromQuat(Order.YXZ, quat);
+ euler.x = e.y;
+ euler.y = e.x;
+ euler.z = e.z;
+
+ // http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Conversion_formulae_between_formalisms
// euler.x = Math.atan2(quat.x * quat.z + quat.y* quat.w, quat.y*quat.z - quat.x * quat.w);
// euler.y = Math.acos(-square(quat.x) - square(quat.y) + square(quat.z) + square(quat.w));
// euler.z = -Math.atan2(quat.x * quat.z - quat.y* quat.w, quat.y*quat.z + quat.x * quat.w);
-
- // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm
- // Y, Z, X order
+
+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm
+ // Y, Z, X order
// double test = quat.x * quat.y + quat.z * quat.w;
// if (test > NEAR_HALF) {
// euler.y = 2.0 * Math.atan2(quat.x,quat.w);
// euler.y = Math.atan2(2*quat.y*quat.w-2*quat.x*quat.z , sqx - sqy - sqz + sqw);
// euler.z = Math.asin(2*test/unit);
// euler.x = Math.atan2(2*quat.x*quat.w-2*quat.y*quat.z , -sqx + sqy - sqz + sqw);
- }
-
- public static Quat4d getQuat(Vector3d euler) {
- Quat4d q = new Quat4d();
- getQuat(euler,q);
- return q;
- }
-
-
- public static Vector3d getEuler(Quat4d quat) {
- Vector3d v = new Vector3d();
- getEuler(quat, v);
- return v;
- }
-
- public static Quat4d getQuat(AxisAngle4d aa) {
- Quat4d q = new Quat4d();
- getQuat(aa, q);
- return q;
- }
-
+ }
+
+ public static Quat4d getQuat(Vector3d euler) {
+ Quat4d q = new Quat4d();
+ getQuat(euler,q);
+ return q;
+ }
+
+
+ public static Vector3d getEuler(Quat4d quat) {
+ Vector3d v = new Vector3d();
+ getEuler(quat, v);
+ return v;
+ }
+
+ public static Quat4d getQuat(AxisAngle4d aa) {
+ Quat4d q = new Quat4d();
+ getQuat(aa, q);
+ return q;
+ }
+
public static AxisAngle4d getAxisAngle(Quat4d q) {
AxisAngle4d aa = new AxisAngle4d();
double mag = q.x * q.x + q.y * q.y + q.z * q.z;
// aa.set(q);
return aa;
}
-
- public static Quat4d getIdentityQuat() {
- return new Quat4d(0, 0, 0, 1);
- }
-
- public static void getQuat(AxisAngle4d aa, Quat4d q) {
- double mag,amag;
+
+ public static Quat4d getIdentityQuat() {
+ return new Quat4d(0, 0, 0, 1);
+ }
+
+ public static void getQuat(AxisAngle4d aa, Quat4d q) {
+ double mag,amag;
// Quat = cos(theta/2) + sin(theta/2)(roation_axis)
amag = Math.sqrt( aa.x*aa.x + aa.y*aa.y + aa.z*aa.z);
if( amag < NEAR_ZERO ) {
- q.w = 1.0;
- q.x = 0.0;
- q.y = 0.0;
- q.z = 0.0;
+ q.w = 1.0;
+ q.x = 0.0;
+ q.y = 0.0;
+ q.z = 0.0;
} else {
- amag = 1.0/amag;
- double a2 = aa.angle * 0.5;
- mag = Math.sin(a2);
- q.w = Math.cos(a2);
- q.x = aa.x*amag*mag;
- q.y = aa.y*amag*mag;
- q.z = aa.z*amag*mag;
+ amag = 1.0/amag;
+ double a2 = aa.angle * 0.5;
+ mag = Math.sin(a2);
+ q.w = Math.cos(a2);
+ q.x = aa.x*amag*mag;
+ q.y = aa.y*amag*mag;
+ q.z = aa.z*amag*mag;
}
- }
-
-
+ }
+
+
/*
* Cohen-Sutherland
*/
}
- public static void multiplyOrientation(AxisAngle4d aa, AxisAngle4d rot) {
+ public static void multiplyOrientation(AxisAngle4d aa, AxisAngle4d rot) {
Quat4d q1 = new Quat4d();
getQuat(aa, q1);
Quat4d q2 = new Quat4d();
getQuat(rot, q2);
q2.mul(q1);
rot.set(q2);
- }
-
- public static double radToDeg(double rad) {
- return (rad / Math.PI) * 180.0;
- }
-
- public static double degToRad(double deg) {
- return (deg / 180.0) * Math.PI;
- }
-
- public static double clamp(double min, double max,double v) {
- if (v < min)
- return min;
- if (v > max)
- return max;
- return v;
- }
-
- public static AxisAngle4d createRotation(Vector3d original, Vector3d rotated) {
+ }
+
+ public static double radToDeg(double rad) {
+ return (rad / Math.PI) * 180.0;
+ }
+
+ public static double degToRad(double deg) {
+ return (deg / 180.0) * Math.PI;
+ }
+
+ public static double clamp(double min, double max,double v) {
+ if (v < min)
+ return min;
+ if (v > max)
+ return max;
+ return v;
+ }
+
+ public static AxisAngle4d createRotation(Vector3d original, Vector3d rotated) {
AxisAngle4d result = new AxisAngle4d();
if (createRotation(original, rotated, result))
return result;
return null;
- }
-
-
- public static void setIdentity(Quat4d q) {
+ }
+
+
+ public static void setIdentity(Quat4d q) {
q.w = 1.0;
q.x = 0.0;
q.y = 0.0;
q.z = 0.0;
- }
-
+ }
+
public static void setIdentity(AxisAngle4d aa) {
aa.angle = 0.0;
aa.x = 0.0;
mat.m33 = v[15];
}
-
- public static boolean createRotation(Vector3d original, Vector3d rotated, AxisAngle4d result) {
-
- if (rotated.lengthSquared() > 0.01)
- rotated.normalize();
- else
- return false;
- double d = original.dot(rotated);
- if (d > 0.9999) {
- // original and rotated are parallel, pointing at the same direction
- result.angle = 0.0;
- result.x = 0.0;
- result.y = 1.0;
- result.z = 0.0;
- } else if (d < -0.9999) {
- // original and rotated are parallel, pointing at the opposite direction
- Vector3d a = Z_AXIS;
- if (Math.abs(a.dot(original)) > 0.8 )
- a = Y_AXIS;
- result.set(a, Math.PI);
- } else {
- double angle = original.angle(rotated);
- Vector3d axis = new Vector3d();
- axis.cross(original, rotated);
- result.set(axis,angle);
- }
- return true;
- }
-
- public static boolean createRotation(Vector3d original, Vector3d rotated, Quat4d result) {
-
- if (rotated.lengthSquared() > 0.01)
- rotated.normalize();
- else
- return false;
- double d = original.dot(rotated);
- if (d > 0.9999) {
- // original and rotated are parallel, pointing at the same direction
- result.w = 1.0;
- result.x = 0.0;
- result.y = 0.0;
- result.z = 0.0;
- } else if (d < -0.9999) {
- // original and rotated are parallel, pointing at the opposite direction
- Vector3d a = Z_AXIS;
- if (Math.abs(a.dot(original)) > 0.8 )
- a = Y_AXIS;
- getQuat(a, Math.PI, result);
-
- } else {
- double angle = original.angle(rotated);
- Vector3d axis = new Vector3d();
- axis.cross(original, rotated);
- getQuat(axis, angle, result);
- }
- return true;
- }
-
- public static void getQuat(Vector3d axis, double angle, Quat4d q)
- {
+
+ public static boolean createRotation(Vector3d original, Vector3d rotated, AxisAngle4d result) {
+
+ if (rotated.lengthSquared() > 0.01)
+ rotated.normalize();
+ else
+ return false;
+ double d = original.dot(rotated);
+ if (d > 0.9999) {
+ // original and rotated are parallel, pointing at the same direction
+ result.angle = 0.0;
+ result.x = 0.0;
+ result.y = 1.0;
+ result.z = 0.0;
+ } else if (d < -0.9999) {
+ // original and rotated are parallel, pointing at the opposite direction
+ Vector3d a = Z_AXIS;
+ if (Math.abs(a.dot(original)) > 0.8 )
+ a = Y_AXIS;
+ result.set(a, Math.PI);
+ } else {
+ double angle = original.angle(rotated);
+ Vector3d axis = new Vector3d();
+ axis.cross(original, rotated);
+ result.set(axis,angle);
+ }
+ return true;
+ }
+
+ public static boolean createRotation(Vector3d original, Vector3d rotated, Quat4d result) {
+
+ if (rotated.lengthSquared() > 0.01)
+ rotated.normalize();
+ else
+ return false;
+ double d = original.dot(rotated);
+ if (d > 0.9999) {
+ // original and rotated are parallel, pointing at the same direction
+ result.w = 1.0;
+ result.x = 0.0;
+ result.y = 0.0;
+ result.z = 0.0;
+ } else if (d < -0.9999) {
+ // original and rotated are parallel, pointing at the opposite direction
+ Vector3d a = Z_AXIS;
+ if (Math.abs(a.dot(original)) > 0.8 )
+ a = Y_AXIS;
+ getQuat(a, Math.PI, result);
+
+ } else {
+ double angle = original.angle(rotated);
+ Vector3d axis = new Vector3d();
+ axis.cross(original, rotated);
+ getQuat(axis, angle, result);
+ }
+ return true;
+ }
+
+ public static boolean createRotation(Vector3d original, Vector3d rotated, Vector3d axis, AxisAngle4d result) {
+
+ if (rotated.lengthSquared() > 0.01)
+ rotated.normalize();
+ else
+ return false;
+ if (original.lengthSquared() > 0.01)
+ original.normalize();
+ else
+ return false;
+ if (axis.lengthSquared() > 0.01)
+ axis.normalize();
+ else
+ return false;
+ double d = original.dot(rotated);
+ if (d > 0.9999) {
+ // original and rotated are parallel, pointing at the same direction
+ result.angle = 0.0;
+ result.x = axis.x;
+ result.y = axis.y;
+ result.z = axis.z;
+ } else if (d < -0.9999) {
+ // original and rotated are parallel, pointing at the opposite direction
+ result.angle = Math.PI;
+ result.x = axis.x;
+ result.y = axis.y;
+ result.z = axis.z;
+ } else {
+ Vector3d p1 = projectToPlane(original, axis);
+ Vector3d p2 = projectToPlane(rotated, axis);
+ double angle = p1.angle(p2);
+ result.set(axis,angle);
+
+ }
+ return true;
+ }
+
+ public static void getQuat(Vector3d axis, double angle, Quat4d q)
+ {
double mag,amag;
// Quat = cos(theta/2) + sin(theta/2)(roation_axis)
amag = Math.sqrt( axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
if( amag < EPS ) {
- q.w = 1.0;
- q.x = 0.0;
- q.y = 0.0;
- q.z = 0.0;
+ q.w = 1.0;
+ q.x = 0.0;
+ q.y = 0.0;
+ q.z = 0.0;
} else {
- amag = 1.0/amag;
- double a2 = angle*0.5;
- mag = Math.sin(a2);
- q.w = Math.cos(a2);
- q.x = axis.x*amag*mag;
- q.y = axis.y*amag*mag;
- q.z = axis.z*amag*mag;
+ amag = 1.0/amag;
+ double a2 = angle*0.5;
+ mag = Math.sin(a2);
+ q.w = Math.cos(a2);
+ q.x = axis.x*amag*mag;
+ q.y = axis.y*amag*mag;
+ q.z = axis.z*amag*mag;
}
- }
-
- /**
- * Linear interpolation of quaternions. Result IS set to q1.
- * @param q1
- * @param q2
- * @param alpha
- */
- public static void lip(Quat4d q1, Quat4d q2, double alpha) {
- double s1 = 1.0 - alpha;
- double s2 = alpha;
- q1.scale(s1);
- mad(q1,q2,s2);
- q1.normalize();
- }
-
- public static double dot(Quat4d q1, Quat4d q2) {
- return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
- }
-
- public static void mad(Tuple3d q1, Tuple3d q2, double s2) {
- q1.x += q2.x * s2;
- q1.y += q2.y * s2;
- q1.z += q2.z * s2;
- }
-
- public static void mad(Quat4d q1, Quat4d q2, double s2) {
- q1.x += q2.x * s2;
- q1.y += q2.y * s2;
- q1.z += q2.z * s2;
- q1.w += q2.w * s2;
- }
-
- /**
- * Slerp
- *
- * Sets results to q1. Modifies q2.
- *
- * @param q1
- * @param q2
- * @param alpha
- */
- public static void sip(Quat4d q1, Quat4d q2, double alpha) {
- double cosom = dot(q1,q2);
- if (cosom < 0.0) {
- cosom = -cosom;
- q2.negate();
- }
-
- if (cosom > 0.9999) {
- q2.sub(q1);
- q2.scale(alpha);
- q1.add(q2);
- q1.normalize();
- return;
- }
- double theta_0 = Math.acos(cosom);
- double theta = theta_0 * alpha;
- Quat4d t = new Quat4d(q1);
- t.scale(-cosom);
- t.add(q2);
- t.normalize();
- t.scale(Math.sin(theta));
- q1.scale(Math.cos(theta));
- q1.add(t);
- }
-
-
- public static void rotate(double angle, Tuple2d v1, Tuple2d v2) {
- // TODO : verify implementation
- double sin = Math.sin(angle);
- if (sin == 1.0) {
- v2.x = v1.y;
- v2.y = -v1.x;
- } else if (sin == -1.0) {
- v2.x = -v1.y;
- v2.y = v1.x;
- } else {
- double cos = Math.cos(angle);
- if (cos == -1.0) {
- v2.x = -v1.x;
- v2.y = -v1.y;
- } else if (cos != 1.0) {
- v2.x= v1.x * cos + v1.y * -sin;
- v2.y= v1.x* sin + v1.y *cos;
- }
- }
- }
-
- public static Tuple3d getPosRot(double m3x2[]) {
- Vector3d t = new Vector3d();
- t.x = m3x2[4];
- t.y = m3x2[5];
-
-
- Vector2d v2 = new Vector2d(1,0);
- Vector2d v = new Vector2d();
- // use rotation of (1,0) to calculate the rotation component
- v.x = m3x2[0];
- v.y = m3x2[2];
- double a1 = v2.angle(v);
- if (v.y < 0) {
- t.z = a1;
- } else {
- t.z = Math.PI*2.0 - a1;
- }
- return t;
- }
-
- public static Matrix4d glFrustum(double l, double r, double b, double t, double n, double f) {
- Matrix4d mat = new Matrix4d();
- mat.m00 = 2.0 * n / (r - l);
- mat.m11 = 2.0 * n / (t - b);
- mat.m02 = (r+l) / (r-l);
- mat.m12 = (t+b) / (t-b);
- mat.m22 = -(f+n) / (f-n);
- mat.m23 = -(2.0 *f * n) / (f-n);
- mat.m32 = -1.0;
- return mat;
- }
-
- public static Matrix4d glOrtho(double l, double r, double b, double t, double n, double f) {
- Matrix4d mat = new Matrix4d();
- mat.m00 = 2.0 / (r - l);
- mat.m11 = 2.0 / (t - b);
- mat.m22 = -2.0 / (f-n);
- mat.m33 = 1.0;
- mat.m03 = -(r+l)/(r-l);
- mat.m13 = -(t+b)/(t-b);
- mat.m23 = -(f+n)/(f-n);
- return mat;
- }
+ }
+
+ /**
+ * Linear interpolation of quaternions. Result IS set to q1.
+ * @param q1
+ * @param q2
+ * @param alpha
+ */
+ public static void lip(Quat4d q1, Quat4d q2, double alpha) {
+ double s1 = 1.0 - alpha;
+ double s2 = alpha;
+ q1.scale(s1);
+ mad(q1,q2,s2);
+ q1.normalize();
+ }
+
+ public static double dot(Quat4d q1, Quat4d q2) {
+ return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
+ }
+
+ public static void mad(Tuple3d q1, Tuple3d q2, double s2) {
+ q1.x += q2.x * s2;
+ q1.y += q2.y * s2;
+ q1.z += q2.z * s2;
+ }
+
+ public static void mad(Quat4d q1, Quat4d q2, double s2) {
+ q1.x += q2.x * s2;
+ q1.y += q2.y * s2;
+ q1.z += q2.z * s2;
+ q1.w += q2.w * s2;
+ }
+
+ /**
+ * Slerp
+ *
+ * Sets results to q1. Modifies q2.
+ *
+ * @param q1
+ * @param q2
+ * @param alpha
+ */
+ public static void sip(Quat4d q1, Quat4d q2, double alpha) {
+ double cosom = dot(q1,q2);
+ if (cosom < 0.0) {
+ cosom = -cosom;
+ q2.negate();
+ }
+
+ if (cosom > 0.9999) {
+ q2.sub(q1);
+ q2.scale(alpha);
+ q1.add(q2);
+ q1.normalize();
+ return;
+ }
+ double theta_0 = Math.acos(cosom);
+ double theta = theta_0 * alpha;
+ Quat4d t = new Quat4d(q1);
+ t.scale(-cosom);
+ t.add(q2);
+ t.normalize();
+ t.scale(Math.sin(theta));
+ q1.scale(Math.cos(theta));
+ q1.add(t);
+ }
+
+
+ public static void rotate(double angle, Tuple2d v1, Tuple2d v2) {
+ // TODO : verify implementation
+ double sin = Math.sin(angle);
+ if (sin == 1.0) {
+ v2.x = v1.y;
+ v2.y = -v1.x;
+ } else if (sin == -1.0) {
+ v2.x = -v1.y;
+ v2.y = v1.x;
+ } else {
+ double cos = Math.cos(angle);
+ if (cos == -1.0) {
+ v2.x = -v1.x;
+ v2.y = -v1.y;
+ } else if (cos != 1.0) {
+ v2.x= v1.x * cos + v1.y * -sin;
+ v2.y= v1.x* sin + v1.y *cos;
+ }
+ }
+ }
+
+ public static Tuple3d getPosRot(double m3x2[]) {
+ Vector3d t = new Vector3d();
+ t.x = m3x2[4];
+ t.y = m3x2[5];
+
+
+ Vector2d v2 = new Vector2d(1,0);
+ Vector2d v = new Vector2d();
+ // use rotation of (1,0) to calculate the rotation component
+ v.x = m3x2[0];
+ v.y = m3x2[2];
+ double a1 = v2.angle(v);
+ if (v.y < 0) {
+ t.z = a1;
+ } else {
+ t.z = Math.PI*2.0 - a1;
+ }
+ return t;
+ }
+
+ public static Matrix4d glFrustum(double l, double r, double b, double t, double n, double f) {
+ Matrix4d mat = new Matrix4d();
+ mat.m00 = 2.0 * n / (r - l);
+ mat.m11 = 2.0 * n / (t - b);
+ mat.m02 = (r+l) / (r-l);
+ mat.m12 = (t+b) / (t-b);
+ mat.m22 = -(f+n) / (f-n);
+ mat.m23 = -(2.0 *f * n) / (f-n);
+ mat.m32 = -1.0;
+ return mat;
+ }
+
+ public static Matrix4d glOrtho(double l, double r, double b, double t, double n, double f) {
+ Matrix4d mat = new Matrix4d();
+ mat.m00 = 2.0 / (r - l);
+ mat.m11 = 2.0 / (t - b);
+ mat.m22 = -2.0 / (f-n);
+ mat.m33 = 1.0;
+ mat.m03 = -(r+l)/(r-l);
+ mat.m13 = -(t+b)/(t-b);
+ mat.m23 = -(f+n)/(f-n);
+ return mat;
+ }
}
Code Review / simantics / 3d.git / blobdiff