/*
 * Copyright (C) 2011-2020, 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.geometry.GeometryMath_F64;
import georegression.misc.GrlConstants;
import georegression.struct.line.LineParametric3D_F64;
import georegression.struct.line.LineSegment3D_F64;
import georegression.struct.plane.PlaneGeneral3D_F64;
import georegression.struct.plane.PlaneNormal3D_F64;
import georegression.struct.point.Point3D_F64;
import georegression.struct.point.Vector3D_F64;
import georegression.struct.shapes.Box3D_F64;
import georegression.struct.shapes.BoxLength3D_F64;
import georegression.struct.shapes.Sphere3D_F64;
import georegression.struct.shapes.Triangle3D_F64;
import org.ddogleg.struct.FastAccess;

/**
 * @author Peter Abeles
 */
public class Intersection3D_F64 {

	/**
	 * Finds the intersection of a line and a plane.  Returns true if they intersect at a unique point or false if
	 * there is no intersection or an infinite number of intersections.
	 *
	 * @param plane (Input) Plane
	 * @param line (Input) Line
	 * @param intersection (Output) Where the intersection is written to
	 * @return True if the intersection is at a unique point.  If false then no intersection or infinite.
	 */
	public static boolean intersect( PlaneNormal3D_F64 plane , LineParametric3D_F64 line , Point3D_F64 intersection ) {
		double dx = plane.p.x - line.p.x;
		double dy = plane.p.y - line.p.y;
		double dz = plane.p.z - line.p.z;

		double top = dx*plane.n.x + dy*plane.n.y + dz*plane.n.z;
		double bottom = line.slope.dot(plane.n);

		if( bottom == 0 )
			return false;

		double d = top/bottom;

		intersection.x = line.p.x + d*line.slope.x;
		intersection.y = line.p.y + d*line.slope.y;
		intersection.z = line.p.z + d*line.slope.z;

		return true;
	}

	/**
	 * Finds the intersection of a line and a plane.  Returns true if they intersect at a unique point or false if
	 * there is no intersection or an infinite number of intersections.
	 *
	 * @param plane (Input) Plane
	 * @param line (Input) Line
	 * @param intersection (Output) Where the intersection is written to
	 * @return True if the intersection is at a unique point.  If false then no intersection or infinite.
	 */
	public static boolean intersect( PlaneGeneral3D_F64 plane , LineParametric3D_F64 line , Point3D_F64 intersection ) {

		double top = plane.D - plane.A*line.p.x - plane.B*line.p.y - plane.C*line.p.z;
		double bottom = plane.A*line.slope.x + plane.B*line.slope.y + plane.C*line.slope.z;

		if( bottom == 0 )
			return false;

		double d = top/bottom;

		intersection.x = line.p.x + d*line.slope.x;
		intersection.y = line.p.y + d*line.slope.y;
		intersection.z = line.p.z + d*line.slope.z;

		return true;
	}

	/**
	 * Finds the line which is the intersection between the two planes.  For a valid solution to be returned
	 * the planes must not be parallel to each other.  If the planes are parallel then the slope of the returned line
	 * will have a value of zero for each element.
	 *
	 * @param a (Input) Plane
	 * @param b (Input) Plane
	 * @param line (Output) Intersection.
	 * @return true if they intersect ata line or false if not
	 */
	public static boolean intersect( PlaneGeneral3D_F64 a , PlaneGeneral3D_F64 b , LineParametric3D_F64 line ) {

		// Line's slope is the cross product of the two normal vectors
		GeometryMath_F64.cross(a.A,a.B,a.C,b.A,b.B,b.C,line.slope);

		if( line.slope.normSq() == 0 )
			return false;

		// Closest point on plane 'a' to origin (0,0,0)
		double n2 = a.A*a.A + a.B*a.B + a.C*a.C;

		double closestX = a.A*a.D/n2;
		double closestY = a.B*a.D/n2;
		double closestZ = a.C*a.D/n2;

		// Cross product between normal of 'a' and the line's slope.  This points towards the intersection
		double slopeX = a.B * line.slope.z - a.C * line.slope.y;
		double slopeY = a.C * line.slope.x - a.A * line.slope.z;
		double slopeZ = a.A * line.slope.y - a.B * line.slope.x;

		// Now find the intersection of the plane and a line containing point 'closest' and pointing towards the
		// the intersection.
		double top = b.D - b.A*closestX - b.B*closestY - b.C*closestZ;
		double bottom = b.A*slopeX + b.B*slopeY + b.C*slopeZ;

		double d = top/bottom;

		line.p.x = closestX + d*slopeX;
		line.p.y = closestY + d*slopeY;
		line.p.z = closestZ + d*slopeZ;

		return true;
	}

	/**
	 * <p>Finds the intersection between a 3D triangle and a line-segment.  Code ported from [1].</p>
	 *
	 * <p>
	 * [1] http://geomalgorithms.com/a06-_intersect-2.html
	 * </p>
	 *
	 * @param T (Input) Triangle in 3D space
	 * @param R (Input) Line segment in 3D space.
	 * @param output (Output) Storage for the intersection, if there is one
	 * @return -1 = triangle is degenerate (a segment or point)<br>
	 *          0 =  disjoint (no intersect)<br>
	 *          1 =  intersect in unique point I1<br>
	 *          2 =  are in the same plane
	 **/
	public static int intersect(Triangle3D_F64 T , LineSegment3D_F64 R , Point3D_F64 output ) {
		return intersect(T,R,output,
				new Vector3D_F64(),new Vector3D_F64(),new Vector3D_F64(),new Vector3D_F64(),new Vector3D_F64());
	}

	/**
	 * <p>Finds the intersection between a 3D triangle and a line-segment.  Code ported from [1].  Internal
	 * working variables are provided in this interface to reduce memory creation/destruction.</p>
	 *
	 * <p>
	 * [1] http://geomalgorithms.com/a06-_intersect-2.html
	 * </p>
	 *
	 * @param T (Input) Triangle in 3D space
	 * @param R (Input) Line segment in 3D space.
	 * @param output (Output) Storage for the intersection, if there is one
	 * @param u   (internal use) triangle vectors
	 * @param v   (internal use) triangle vectors
	 * @param n   (internal use) triangle vectors
	 * @param dir (internal use) ray vector
	 * @param w0  (internal use) ray vector
	 * @return -1 = triangle is degenerate (a segment or point)
	 *          0 =  disjoint (no intersect)
	 *          1 =  intersect in unique point I1
	 *          2 =  are in the same plane
	 **/
	public static int intersect(Triangle3D_F64 T , LineSegment3D_F64 R , Point3D_F64 output ,
								Vector3D_F64 u , Vector3D_F64 v , Vector3D_F64 n,
								Vector3D_F64 dir , Vector3D_F64 w0 ) {
		double r, a, b;              // params to calc ray-plane intersect

		// get triangle edge vectors and plane normal
		u.minus(T.v1,T.v0);   // NOTE: these could be precomputed
		v.minus(T.v2,T.v0);
		n.cross(u,v);

		if ( n.normSq() == 0 )        // triangle is degenerate
			return -1;                  // do not deal with this case

		dir.minus(R.b,R.a);             // ray direction vector
		w0.minus(R.a,T.v0);
		a = -n.dot(w0);
		b = n.dot(dir);
		if (Math.abs(b) < GrlConstants.EPS) { // ray is  parallel to triangle plane
			if (a == 0)                       // ray lies in triangle plane
				return 2;
			else return 0;                    // ray disjoint from plane
		}

		// get intersect point of ray with triangle plane
		r = a / b;
		if (r < 0.0)                    // ray goes away from triangle
			return 0;                   // => no intersect
		else if( r > 1.0 )              // is past the end of the line segment
			return 0;

		// intersect point of ray and plane
		output.x = R.a.x + r*dir.x;
		output.y = R.a.y + r*dir.y;
		output.z = R.a.z + r*dir.z;

		// is I inside T?
		if( containedPlane(T.v0,output,u,v,w0)) {
			return 1;
		} else {
			return 0;
		}
	}

	/**
	 * <p>Finds the intersection between a 3D triangle and a line.  Code ported from [1].  Internal
	 * working variables are provided in this interface to reduce memory creation/destruction.</p>
	 *
	 * <p>
	 * [1] http://geomalgorithms.com/a06-_intersect-2.html
	 * </p>
	 *
	 * @param T (Input) Triangle in 3D space
	 * @param R (Input) Line segment in 3D space.
	 * @param output (Output) Storage for the intersection, if there is one
	 * @return <ul style="list-style-type:none">
	 *         <li>-1 = triangle is degenerate (a segment or point)</li>
	 *          <li>0 =  disjoint (no intersect)</li>
	 *          <li>1 =  intersect in unique point. Positive direction or zero</li>
	 *          <li>2 =  are in the same plane</li>
	 *          <li>3 =  intersect in unique point. Negative direction</li>
	 *          </ul>
	 **/
	public static int intersect(Triangle3D_F64 T , LineParametric3D_F64 R , Point3D_F64 output) {
		return intersect(T,R,output,
				new Vector3D_F64(),new Vector3D_F64(),new Vector3D_F64(),new Vector3D_F64());
	}

	/**
	 * <p>Finds the intersection between a 3D triangle and a line.  Code ported from [1].  Internal
	 * working variables are provided in this interface to reduce memory creation/destruction.</p>
	 *
	 * <p>
	 * [1] http://geomalgorithms.com/a06-_intersect-2.html
	 * </p>
	 *
	 * @param T (Input) Triangle in 3D space
	 * @param R (Input) Line segment in 3D space.
	 * @param output (Output) Storage for the intersection, if there is one
	 * @param u   (internal use) triangle vectors
	 * @param v   (internal use) triangle vectors
	 * @param n   (internal use) triangle vectors
	 * @param w0  (internal use) ray vector
	 * @return <ul style="list-style-type:none">
	 *         <li>-1 = triangle is degenerate (a segment or point)</li>
	 *          <li>0 =  disjoint (no intersect)</li>
	 *          <li>1 =  intersect in unique point. Positive direction or zero</li>
	 *          <li>2 =  are in the same plane</li>
	 *          <li>3 =  intersect in unique point. Negative direction</li>
	 *          </ul>
	 **/
	public static int intersect(Triangle3D_F64 T , LineParametric3D_F64 R , Point3D_F64 output ,
								Vector3D_F64 u , Vector3D_F64 v , Vector3D_F64 n,
								Vector3D_F64 w0 ) {
		double r, a, b;              // params to calc ray-plane intersect

		// get triangle edge vectors and plane normal
		u.minus(T.v1,T.v0);   // NOTE: these could be precomputed
		v.minus(T.v2,T.v0);
		n.cross(u,v);

		if ( n.normSq() == 0 )        // triangle is degenerate
			return -1;                  // do not deal with this case

		Vector3D_F64 dir = R.slope;
		w0.minus(R.p,T.v0);
		a = -n.dot(w0);
		b = n.dot(dir);
		if (Math.abs(b) < GrlConstants.EPS) { // ray is  parallel to triangle plane
			if (a == 0)                       // ray lies in triangle plane
				return 2;
			else return 0;                    // ray disjoint from plane
		}

		// get intersect point of ray with triangle plane
		r = a / b;

		// intersect point of ray and plane
		output.x = R.p.x + r*dir.x;
		output.y = R.p.y + r*dir.y;
		output.z = R.p.z + r*dir.z;

		// is I inside T?
		if( containedPlane(T.v0,output,u,v,w0)) {
			if( r >= 0 )
				return 1;
			else
				return 3;
		} else {
			return 0;
		}
	}

	/**
	 * Detects if a 2D convex polygon that has been moved into a 3D world is intersected by the 3D line.
	 * <pre>
	 * Transformation:
	 * 1) Each 2D point is converted into 3D: X=(x,y,0)
	 * 2) X' = R*X + T, where (R,T) are a rigid body transform from poly to world frames
	 * </pre>
	 *
	 * @param polygon (Input) Convex polygon. All points must lie on a plane.
	 * @param line (Input) Line.
	 * @param output (Output) Point of intersection (if any)
	 * @param n (internal use)
	 * @param u (internal use)
	 * @param v (internal use)
	 * @param w0 (internal use)
	 * @return <ul style="list-style-type:none">
	 *         <li>-1 = triangle is degenerate (a segment or point)</li>
	 *          <li>0 =  disjoint (no intersect)</li>
	 *          <li>1 =  intersect in unique point. Positive direction or zero</li>
	 *          <li>2 =  are in the same plane</li>
	 *          <li>3 =  intersect in unique point. Negative direction</li>
	 *          </ul>
	 */
	public static int intersectConvex(FastAccess<Point3D_F64> polygon,
									  LineParametric3D_F64 line , Point3D_F64 output,
									  Vector3D_F64 n, Vector3D_F64 u, Vector3D_F64 v, Vector3D_F64 w0) {
		if( polygon.size < 3 )
			throw new IllegalArgumentException("There must be 3 or more points");

		double r, a, b;              // params to calc ray-plane intersect

		Point3D_F64 v0 = polygon.get(0);
		Point3D_F64 v1 = polygon.get(1);
		Point3D_F64 v2 = polygon.get(2);

		// get triangle edge vectors and plane normal
		u.minus(v1,v0);   // NOTE: these could be precomputed
		v.minus(v2,v0);
		n.cross(u,v);

		if ( n.normSq() == 0 )        // triangle is degenerate
			return -1;                  // do not deal with this case

		Vector3D_F64 dir = line.slope;
		w0.minus(line.p,v0);
		a = -n.dot(w0);
		b = n.dot(dir);
		if (Math.abs(b) < GrlConstants.EPS) { // ray is  parallel to triangle plane
			if (a == 0)                       // ray lies in triangle plane
				return 2;
			else return 0;                    // ray disjoint from plane
		}

		// get intersect point of ray with triangle plane
		r = a / b;

		// intersect point of ray and plane
		output.x = line.p.x + r*dir.x;
		output.y = line.p.y + r*dir.y;
		output.z = line.p.z + r*dir.z;

		// See if it's inside any of the triangles
		for (int i = 2; i < polygon.size; i++) {
			// is I inside T?
			if (containedPlane(v0, output, u, v, w0)) {
				if (r >= 0)
					return 1;
				else
					return 3;
			}

			if (i < polygon.size - 1) {
				u.minus(polygon.get(i), v0);
				v.minus(polygon.get(i+1), v0);
			}
		}
		return 0;
	}

	/**
	 * @see #intersectConvex(FastAccess, LineParametric3D_F64, Point3D_F64, Vector3D_F64, Vector3D_F64, Vector3D_F64, Vector3D_F64)
	 */
	public static int intersectConvex(FastAccess<Point3D_F64> polygon,
									  LineParametric3D_F64 line , Point3D_F64 output) {
		return intersectConvex(polygon,line,output,new Vector3D_F64(),new Vector3D_F64(),new Vector3D_F64(),
				new Vector3D_F64());
	}

	/**
	 * Determines if the point on the same plane as T is contained inside of T.
	 */
	private static boolean containedPlane( Point3D_F64 T_v0,
										   Point3D_F64 output,
										   Vector3D_F64 u , Vector3D_F64 v ,
										   Vector3D_F64 w0 ) {
		double uu, uv, vv, wu, wv, D;
		uu = u.dot(u);
		uv = u.dot(v);
		vv = v.dot(v);
		w0.minus(output,T_v0);
		wu = w0.dot(u);
		wv = w0.dot(v);
		D = uv * uv - uu * vv;

		// get and test parametric coords
		double s, t;
		s = (uv * wv - vv * wu) / D;
		if (s < 0.0 || s > 1.0)        // I is outside T
			return false;
		t = (uv * wu - uu * wv) / D;
		return !(t < 0.0) && !((s + t) > 1.0);  // I is outside T
	}

	/**
	 * Returns true if the point is contained inside the box. The point is considered to be inside the box
	 * if the following test passes for each dimension.  box.x &le; point.x {@code <} box.x + box.lengthX
	 *
	 * @param box Box
	 * @param point Point which is tested to see if it is inside the box
	 * @return true for inside and false for not
	 */
	public static boolean contained( BoxLength3D_F64 box , Point3D_F64 point ) {

		return( box.p.x <= point.x && point.x < box.p.x + box.lengthX &&
				box.p.y <= point.y && point.y < box.p.y + box.lengthY &&
				box.p.z <= point.z && point.z < box.p.z + box.lengthZ );
	}

	/**
	 * <p>
	 * Returns true if the point is contained inside the box, with an exclusive upper extent.
	 * The point is considered to be inside the box if the following test passes:<br>
	 * box.p0.x &le; point.x {@code <} box.p1.x<br>
	 * box.p0.y &le; point.y {@code <} box.p1.y<br>
	 * box.p0.z &le; point.z {@code <} box.p1.z<br>
	 * </p>
	 *
	 * @param box Box
	 * @param point Point which is tested to see if it is inside the box
	 * @return true for inside and false for not
	 */
	public static boolean contained( Box3D_F64 box , Point3D_F64 point ) {

		return( box.p0.x <= point.x && point.x < box.p1.x &&
				box.p0.y <= point.y && point.y < box.p1.y &&
				box.p0.z <= point.z && point.z < box.p1.z );
	}

	/**
	 * <p>
	 * Returns true if the point is contained inside the box, with an inclusive upper extent.
	 * The point is considered to be inside the box if the following test passes:<br>
	 * box.p0.x &le; point.x &le; box.p1.x<br>
	 * box.p0.y &le; point.y &le; box.p1.y<br>
	 * box.p0.z &le; point.z &le; box.p1.z<br>
	 * </p>
	 *
	 * @param box Box
	 * @param point Point which is tested to see if it is inside the box
	 * @return true for inside and false for not
	 */
	public static boolean contained2( Box3D_F64 box , Point3D_F64 point ) {
		return( box.p0.x <= point.x && point.x <= box.p1.x &&
				box.p0.y <= point.y && point.y <= box.p1.y &&
				box.p0.z <= point.z && point.z <= box.p1.z );
	}

	/**
	 * Returns true if boxB is contained inside of or is identical to boxA.
	 *
	 * @param boxA Box
	 * @param boxB Box which is being tested to see if it is inside of boxA
	 * @return true if inside/identical or false if outside
	 */
	public static boolean contained( Box3D_F64 boxA , Box3D_F64 boxB ) {
		return( boxA.p0.x <= boxB.p0.x && boxA.p1.x >= boxB.p1.x &&
				boxA.p0.y <= boxB.p0.y && boxA.p1.y >= boxB.p1.y &&
				boxA.p0.z <= boxB.p0.z && boxA.p1.z >= boxB.p1.z );
	}

	/**
	 * Returns true if the two boxs intersect each other. p0 is inclusive and p1 is exclusive.
	 * So if the p0 edge and p1 edge overlap perfectly there is no intersection.
	 *
	 * @param boxA Box
	 * @param boxB Box
	 * @return true for intersection and false if no intersection
	 */
	public static boolean intersect( Box3D_F64 boxA , Box3D_F64 boxB ) {
		return( intersect(boxA.p0.x , boxB.p0.x , boxA.p1.x , boxB.p1.x ) &&
				intersect(boxA.p0.y , boxB.p0.y , boxA.p1.y , boxB.p1.y ) &&
				intersect(boxA.p0.z , boxB.p0.z , boxA.p1.z , boxB.p1.z ) );
	}

	protected static boolean intersect( double a0 , double b0 , double a1, double b1 ) {
		if( a0 <= b0 ) {
			return b0 < a1;
		} else {
			return a0 < b1;
		}
	}

	/**
	 * Finds the intersection of a line and sphere.  There can be 0, 1, or 2 intersections.  If there is
	 * 1 intersection the same point is returned twice.
	 *
	 * @param line line
	 * @param sphere sphere
	 * @param a (Output) Storage for point of intersection.  t = max(t0,t1), where t is location on line
	 * @param b (Output) Storage for point of intersection.  t = max(t0,t1), where t is location on line
	 * @return true if the line intersects the sphere
	 */
	public static boolean intersect(LineParametric3D_F64 line , Sphere3D_F64 sphere ,
									Point3D_F64 a, Point3D_F64 b ) {

		// this equation was found by solving for l:
		// ||(P + V*l) - X0|| == r

		double r2 = sphere.radius*sphere.radius;

		double PP = GeometryMath_F64.dot(line.p,line.p);
		double PV = GeometryMath_F64.dot(line.p,line.slope);
		double PX = GeometryMath_F64.dot(line.p,sphere.center);
		double VV = GeometryMath_F64.dot(line.slope,line.slope);
		double VX = GeometryMath_F64.dot(line.slope,sphere.center);
		double XX = GeometryMath_F64.dot(sphere.center,sphere.center);

		// Coefficients in the quadratic equation
		double A = VV;
		double B = 2.0*(PV-VX);
		double C = PP+XX-2.0*PX-r2;

		// solve for the quadratic equation
		double inner = B*B - 4.0*A*C;
		if( inner < 0 )
			return false;
		double sqrt = Math.sqrt(inner);

		double t0 = (-B + sqrt)/(2.0*A);
		double t1 = (-B - sqrt)/(2.0*A);

		line.setPointOnLine(t0,a);
		line.setPointOnLine(t1,b);

		return true;
	}

}
