/* * Copyright (C) 2011-2015, Peter Abeles. All Rights Reserved. * * This file is part of Geometric Regression Library (GeoRegression). * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package georegression.metric; import georegression.metric.alg.DistancePointTriangle3D_F64; import georegression.struct.line.LineParametric3D_F64; import georegression.struct.line.LineSegment3D_F64; import georegression.struct.plane.PlaneGeneral3D_F64; import georegression.struct.point.Point3D_F64; import georegression.struct.shapes.Cylinder3D_F64; import georegression.struct.shapes.Sphere3D_F64; import georegression.struct.shapes.Triangle3D_F64; /** * @author Peter Abeles */ public class Distance3D_F64 { /** * Distance of the closest point between two lines. Parallel lines are correctly * handled. * * @param l0 First line. Not modified. * @param l1 Second line. Not modified. * @return Distance between the closest point on both lines. */ public static double distance( LineParametric3D_F64 l0, LineParametric3D_F64 l1 ) { double x = l0.p.x - l1.p.x; double y = l0.p.y - l1.p.y; double z = l0.p.z - l1.p.z; // this solution is from: http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline3d/ double dv01v1 = MiscOps.dot( x,y,z, l1.slope ); double dv1v0 = MiscOps.dot( l1.slope, l0.slope ); double dv1v1 = MiscOps.dot( l1.slope, l1.slope ); double bottom = MiscOps.dot( l0.slope, l0.slope ) * dv1v1 - dv1v0 * dv1v0; double t0; if( bottom == 0 ) { // handle parallel lines t0 = 0; } else { t0 = (dv01v1 * dv1v0 - MiscOps.dot( x,y,z, l0.slope ) * dv1v1)/bottom; } // ( d1343 + mua d4321 ) / d4343 double t1 = ( dv01v1 + t0 * dv1v0 ) / dv1v1; double dx = ( l0.p.x + t0 * l0.slope.x ) - ( l1.p.x + t1 * l1.slope.x ); double dy = ( l0.p.y + t0 * l0.slope.y ) - ( l1.p.y + t1 * l1.slope.y ); double dz = ( l0.p.z + t0 * l0.slope.z ) - ( l1.p.z + t1 * l1.slope.z ); // round off error can make distanceSq go negative when it is very close to zero double distanceSq = dx * dx + dy * dy + dz * dz; if( distanceSq < 0 ) return 0; else return Math.sqrt( distanceSq ); } /** * Distance from the point to the closest point on the line. * * @param l Line. Not modified. * @param p Point. Not modified. * @return distance. */ public static double distance( LineParametric3D_F64 l, Point3D_F64 p ) { double x = l.p.x - p.x; double y = l.p.y - p.y; double z = l.p.z - p.z; double cc = x*x + y*y + z*z; // could avoid a square root here by computing b*b directly // however that is most likely more prone to numerical overflow since the numerator will need to be squared // before division can reduce its "power" double b = MiscOps.dot(x,y,z,l.slope)/l.slope.norm(); double distanceSq = cc-b*b; // round off error can make distanceSq go negative when it is very close to zero if( distanceSq < 0 ) { return 0; } else { return Math.sqrt(distanceSq); } } /** * Distance from the point to the closest point on the line segment. * * @param l Line. Not modified. * @param p Point. Not modified. * @return distance. */ public static double distance( LineSegment3D_F64 l, Point3D_F64 p ) { double dx = p.x - l.a.x; double dy = p.y - l.a.y; double dz = p.z - l.a.z; double cc = dx*dx + dy*dy + dz*dz; double slope_x = l.b.x - l.a.x; double slope_y = l.b.y - l.a.y; double slope_z = l.b.z - l.a.z; double n = (double) Math.sqrt(slope_x*slope_x + slope_y*slope_y + slope_z*slope_z); double d = (slope_x*dx + slope_y*dy + slope_z*dz) / n; // check end points if( d <= 0 ) return p.distance(l.a); else if( d >= n ) return p.distance(l.b); double distanceSq = cc-d*d; // round off error can make distanceSq go negative when it is very close to zero if( distanceSq < 0 ) { return 0; } else { return Math.sqrt(distanceSq); } } /** * Distance between a plane and a point. A signed distance is returned, where a positive value is returned if * the point is on the same side of the plane as the normal and the opposite if it's on the other. * * @param plane The plane * @param point The point * @return Signed distance */ public static double distance( PlaneGeneral3D_F64 plane , Point3D_F64 point ) { double top = plane.A*point.x + plane.B*point.y + plane.C*point.z - plane.D; return top / Math.sqrt( plane.A*plane.A + plane.B*plane.B + plane.C*plane.C); } /** * Returns the signed distance a point is from the sphere's surface. If the point is outside of the sphere * it's distance will be positive. If it is inside it will be negative. * <p></p> * distance = ||sphere.center - point|| - r * * @param sphere The sphere * @param point The point * @return Signed distance */ public static double distance( Sphere3D_F64 sphere , Point3D_F64 point ) { double r = point.distance(sphere.center); return r-sphere.radius; } /** * Returns the signed distance a point is from the cylinder's surface. If the point is outside of the cylinder * it's distance will be positive. If it is inside it will be negative. * * @param cylinder The cylinder * @param point The point * @return Signed distance */ public static double distance( Cylinder3D_F64 cylinder, Point3D_F64 point ) { double r = Distance3D_F64.distance(cylinder.line,point); return r - cylinder.radius; } /** * Signed distance from a 3D point to 3D triangle. The sign indicates which side of the triangle the point * is on. See {@link georegression.metric.alg.DistancePointTriangle3D_F64} for the details. * * @param triangle 3D triangle * @param point Point for which the closest point on the triangle is found * @return The closest point */ public static double distance( Triangle3D_F64 triangle, Point3D_F64 point ) { DistancePointTriangle3D_F64 alg = new DistancePointTriangle3D_F64(); alg.setTriangle(triangle.v0,triangle.v1,triangle.v2); Point3D_F64 cp = new Point3D_F64(); alg.closestPoint(point,cp); double d = point.distance(cp); return alg.sign(point)*d; } }