--- /dev/null
+/*******************************************************************************\r
+ * Copyright (c) 2007- VTT Technical Research Centre of Finland.\r
+ * All rights reserved. This program and the accompanying materials\r
+ * are made available under the terms of the Eclipse Public License v1.0\r
+ * which accompanies this distribution, and is available at\r
+ * http://www.eclipse.org/legal/epl-v10.html\r
+ *\r
+ * Contributors:\r
+ * VTT Technical Research Centre of Finland - initial API and implementation\r
+ *******************************************************************************/\r
+package org.simantics.proconf.g3d.base;\r
+\r
+import javax.vecmath.AxisAngle4d;\r
+import javax.vecmath.Matrix3d;\r
+import javax.vecmath.Point3d;\r
+import javax.vecmath.Quat4d;\r
+import javax.vecmath.Tuple3d;\r
+import javax.vecmath.Vector3d;\r
+\r
+import com.jme.math.Vector2f;\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
+ static double EPS = 0.001;\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(Point3d point, Point3d 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(Point3d point, Point3d 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) < EPS)\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) < EPS)\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(Vector3d p1,Vector3d p2,Vector3d p3,Vector3d p4,Vector3d pa,Vector3d pb) {\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(p1, p3);\r
+ p43.sub(p4,p3);\r
+ if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS)\r
+ return false;\r
+ p21.sub(p2,p1);\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
+ 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
+ public static boolean intersectStraightStraight(Vector3d p1,Vector3d p21,Vector3d 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) < 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
+ 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
+ public static AxisAngle4d getFromEuler2(Vector3d euler) {\r
+ AxisAngle4d aa = new AxisAngle4d();\r
+ aa.angle = euler.length();\r
+ Vector3d normal = new Vector3d(euler);\r
+ if (aa.angle > EPS) {\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 getEuler(AxisAngle4d aa) {\r
+ Vector3d euler = new Vector3d(aa.x,aa.y,aa.z);\r
+ euler.scale(aa.angle);\r
+ return euler;\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
+ 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
+ int nxt[] = { 1, 2, 0 };\r
+\r
+ j = nxt[i];\r
+ k = nxt[j];\r
+\r
+ double s = Math\r
+ .sqrt((mat.getElement(i, i) - (mat.getElement(j, j) + mat\r
+ .getElement(k, k))) + 1.0);\r
+\r
+ double q[] = new double[3];\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
+ \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
Code Review / simantics / 3d.git / blobdiff