GeomUtil.hpp

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/*
 * MOAB, a Mesh-Oriented datABase, is a software component for creating,
 * storing and accessing finite element mesh data.
 *
 * Copyright 2004 Sandia Corporation.  Under the terms of Contract
 * DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government
 * retains certain rights in this software.
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 */

/**\file Geometry.hpp
 *\author Jason Kraftcheck ([email protected])
 *\date 2006-07-27
 */

#ifndef MB_GEOM_UTIL_HPP
#define MB_GEOM_UTIL_HPP

#include "moab/CartVect.hpp"
#include <cmath>

namespace moab
{

/** \class GeomUtil
 * \brief Functions for computational geometry on triangles, rays, and boxes
 */
namespace GeomUtil
{

    /** Given a line segment and an axis-aligned box,
     *  return the sub-segment of the line segment that
     *  itersects the box.
     *
     *  Can be used to intersect ray with box by passing seg_end
     *  as HUGE_VAL or std::numeric_limits<double>::maximum().
     *
     *\param box_min   Minimum corner of axis-aligned box
     *\param box_max   Maximum corner of axis-aligned box
     *\param seg_pt    A point in the line containing the segement
     *\param seg_unit_dir A unit vector in the direction of the line
     *                 containing the semgent.
     *\param seg_start The distance from seg_pt in the direction of
     *                 seg_unit_dir at which the segment begins.
     *                 As input, the start of the original segment, as output, the
     *                 start of the sub-segment intersecting the box.
     *                 Note:  seg_start must be less than seg_end
     *\param seg_end   The distance from seg_pt in the direction of
     *                 seg_unit_dir at which the segment ends.
     *                 As input, the end of the original segment, as output, the
     *                 end of the sub-segment intersecting the box.
     *                 Note:  seg_start must be less than seg_end
     *\return true if line semgent intersects box, false otherwise.
     */
    bool segment_box_intersect( CartVect box_min,
                                CartVect box_max,
                                const CartVect& seg_pt,
                                const CartVect& seg_unit_dir,
                                double& seg_start,
                                double& seg_end );

    /**\brief Test for intersection between a ray and a triangle.
     *\param ray_point  The start point of the ray.
     *\param ray_unit_direciton  The direction of the ray. Must be a unit vector.
     *\param t_out Output: The distance along the ray from ray_point in the
     *                  direction of ray_unit_direction at which the ray
     *                  itersected the triangle.
     *\param ray_length Optional:  If non-null, a pointer a maximum length
     *                  for the ray, converting this function to a segment-tri-
     *                  intersect test.
     *\return true if intersection, false otherwise.
     */
    bool ray_tri_intersect( const CartVect vertices[3],
                            const CartVect& ray_point,
                            const CartVect& ray_unit_direction,
                            double& t_out,
                            const double* ray_length = 0 );

    /**\brief Plücker test for intersection between a ray and a triangle.
     *\param vertices            Nodes of the triangle.
     *\param ray_point           The start point of the ray.
     *\param ray_unit_direction  The direction of the ray. Must be a unit vector.
     *\param t_out               Output: The distance along the ray from ray_point in the
     *                           direction of ray_unit_direction at which the ray
     *                           intersected the triangle.
     *\param nonneg_ray_length   Optional: If non-null, a maximum length for the ray,
     *                           converting this function to a segment-tri-intersect
     *                           test.
     *\param neg_ray_length      Optional: If non-null, a maximum length for the ray
     *                           behind the origin, converting this function to a
     *                           segment-tri-intersect test.
     *\param orientation         Optional: Reject intersections without the specified
     *                           orientation of ray with respect to triangle normal
     *                           vector. Indicate desired orientation by passing
     *                           1 (forward), -1 (reverse), or 0 (no preference).
     *\param int_type            Optional Output: The type of intersection; used to
     *                           identify edge/node intersections.
     *\return true if intersection, false otherwise.
     */
    enum intersection_type
    {
        NONE = 0,
        INTERIOR,
        NODE0,
        NODE1,
        NODE2,
        EDGE0,
        EDGE1,
        EDGE2
    };
    /* intersection type is determined by which of the intermediate values are == 0.  There
       are three such values that can therefore be encoded in a 3 bit integer.
       0 = none are == 0 -> interior type
       1 = pip0 == 0 -> EDGE0
       2 = pip1 == 1 -> EDGE1
       4 = pip2 == 2 -> EDGE2
       5 = pip2 = pip0 == 0 -> NOEE0
       3 = pip0 = pip1 == 0 -> NODE1
       6 = pip1 = pip2 == 0 -> NODE2 */
    const intersection_type type_list[] = { INTERIOR, EDGE0, EDGE1, NODE1, EDGE2, NODE0, NODE2 };

    bool plucker_ray_tri_intersect( const CartVect vertices[3],
                                    const CartVect& ray_point,
                                    const CartVect& ray_unit_direction,
                                    double& dist_out,
                                    const double* nonneg_ray_length = 0,
                                    const double* neg_ray_length    = 0,
                                    const int* orientation          = 0,
                                    intersection_type* int_type     = 0 );
    double plucker_edge_test( const CartVect& vertexa,
                              const CartVect& vertexb,
                              const CartVect& ray,
                              const CartVect& ray_normal );

    //! Find range of overlap between ray and axis-aligned box.
    //!
    //!\param box_min   Box corner with minimum coordinate values
    //!\param box_max   Box corner with minimum coordinate values
    //!\param ray_pt    Coordinates of start point of ray
    //!\param ray_dir   Directionion vector for ray such that
    //!                 the ray is defined by r(t) = ray_point + t * ray_vect
    //!                 for t > 0.
    //!\param t_enter   Output: if return value is true, this value
    //!                 is the parameter location along the ray at which
    //!                 the ray entered the leaf.  If return value is false,
    //!                 then this value is undefined.
    //!\param t_exit    Output: if return value is true, this value
    //!                 is the parameter location along the ray at which
    //!                 the ray exited the leaf.  If return value is false,
    //!                 then this value is undefined.
    //!\return true if ray intersects leaf, false otherwise.
    bool ray_box_intersect( const CartVect& box_min,
                            const CartVect& box_max,
                            const CartVect& ray_pt,
                            const CartVect& ray_dir,
                            double& t_enter,
                            double& t_exit );

    /**\brief Test if plane intersects axis-aligned box
     *
     * Test for intersection between an unbounded plane and
     * an axis-aligned box.
     *\param plane_normal Vector in plane normal direction (need *not*
     *                    be a unit vector).  The N in
     *                    the plane equation: N . X + D = 0
     *\param plane_coeff  The scalar 'D' term in the plane equation:
     *                    N . X + D = 0
     *\param box_min_corner The smallest coordinates of the box along each
     *                    axis.  The corner of the box for which all three
     *                    coordinate values are smaller than those of any
     *                    other corner.  The X, Y, Z values for the planes
     *                    normal to those axes and bounding the box on the
     *                    -X, -Y, and -Z sides respectively.
     *\param box_max_corner The largest coordinates of the box along each
     *                    axis.  The corner of the box for which all three
     *                    coordinate values are larger than those of any
     *                    other corner.  The X, Y, Z values for the planes
     *                    normal to those axes and bounding the box on the
     *                    +X, +Y, and +Z sides respectively.
     *\return true if overlap, false otherwise.
     */
    bool box_plane_overlap( const CartVect& plane_normal,
                            double plane_coeff,
                            CartVect box_min_corner,
                            CartVect box_max_corner );

    /**\brief Test if triangle intersects axis-aligned box
     *
     * Test if a triangle intersects an axis-aligned box.
     *\param triangle_corners  The corners of the triangle.
     *\param box_min_corner The smallest coordinates of the box along each
     *                    axis.  The corner of the box for which all three
     *                    coordinate values are smaller than those of any
     *                    other corner.  The X, Y, Z values for the planes
     *                    normal to those axes and bounding the box on the
     *                    -X, -Y, and -Z sides respectively.
     *\param box_max_corner The largest coordinates of the box along each
     *                    axis.  The corner of the box for which all three
     *                    coordinate values are larger than those of any
     *                    other corner.  The X, Y, Z values for the planes
     *                    normal to those axes and bounding the box on the
     *                    +X, +Y, and +Z sides respectively.
     *\param tolerance    The tolerance used in the intersection test.  The box
     *                    size is increased by this amount before the intersection
     *                    test.
     *\return true if overlap, false otherwise.
     */
    bool box_tri_overlap( const CartVect triangle_corners[3],
                          const CartVect& box_min_corner,
                          const CartVect& box_max_corner,
                          double tolerance );

    /**\brief Test if triangle intersects axis-aligned box
     *
     * Test if a triangle intersects an axis-aligned box.
     *\param triangle_corners  The corners of the triangle.
     *\param box_center   The center of the box.
     *\param box_hanf_dims The distance along each axis, respectively, from the
     *                    box_center to the boundary of the box.
     *\return true if overlap, false otherwise.
     */
    bool box_tri_overlap( const CartVect triangle_corners[3],
                          const CartVect& box_center,
                          const CartVect& box_half_dims );

    bool box_point_overlap( const CartVect& box_min_corner,
                            const CartVect& box_max_corner,
                            const CartVect& point,
                            double tolerance );

    /**\brief Test if the specified element intersects an axis-aligned box.
     *
     * Test if element intersects axis-aligned box.  Use element-specific
     * optimization if available, otherwise call box_general_elem_overlap.
     *
     *\param elem_corners The coordinates of the element vertices
     *\param elem_type    The toplogy of the element.
     *\param box_center   The center of the axis-aligned box
     *\param box_half_dims Half of the width of the box in each axial
     *                     direction.
     */
    bool box_elem_overlap( const CartVect* elem_corners,
                           EntityType elem_type,
                           const CartVect& box_center,
                           const CartVect& box_half_dims,
                           int nodecount = 0 );

    /**\brief Test if the specified element intersects an axis-aligned box.
     *
     * Uses MBCN and separating axis theorem for general algorithm that
     * works for all fixed-size elements (not poly*).
     *
     *\param elem_corners The coordinates of the element vertices
     *\param elem_type    The toplogy of the element.
     *\param box_center   The center of the axis-aligned box
     *\param box_half_dims Half of the width of the box in each axial
     *                     direction.
     */
    bool box_linear_elem_overlap( const CartVect* elem_corners,
                                  EntityType elem_type,
                                  const CartVect& box_center,
                                  const CartVect& box_half_dims );

    /**\brief Test if the specified element intersects an axis-aligned box.
     *
     * Uses MBCN and separating axis theorem for general algorithm that
     * works for all fixed-size elements (not poly*).  Box and element
     * vertices must be translated such that box center is at origin.
     *
     *\param elem_corners The coordinates of the element vertices, in
     *                    local coordinate system of box.
     *\param elem_type    The toplogy of the element.
     *\param box_half_dims Half of the width of the box in each axial
     *                     direction.
     */
    bool box_linear_elem_overlap( const CartVect* elem_corners, EntityType elem_type, const CartVect& box_half_dims );

    void closest_location_on_box( const CartVect& box_min_corner,
                                  const CartVect& box_max_corner,
                                  const CartVect& point,
                                  CartVect& closest );

    /**\brief find closest location on triangle
     *
     * Find closest location on linear triangle.
     *\param location  Input position to evaluate from
     *\param vertices  Array of three corner vertex coordinates.
     *\param closest_out Result position
     */
    void closest_location_on_tri( const CartVect& location, const CartVect* vertices, CartVect& closest_out );

    /**\brief find closest location on polygon
     *
     * Find closest location on polygon
     *\param location  Input position to evaluate from
     *\param vertices  Array of corner vertex coordinates.
     *\param num_vertices Length of 'vertices' array.
     *\param closest_out Result position
     */
    void closest_location_on_polygon( const CartVect& location,
                                      const CartVect* vertices,
                                      int num_vertices,
                                      CartVect& closest_out );

    /**\brief find closest topological location on triangle
     *
     * Find closest location on linear triangle.
     *\param location  Input position to evaluate from
     *\param vertices  Array of three corner vertex coordinates.
     *\param tolerance Tolerance to use when comparing to corners and edges
     *\param closest_out Result position
     *\param closest_topo Closest topological entity
     *                     0-2 : vertex index
     *                     3-5 : edge beginning at closest_topo - 3
     *                       6 : triangle interior
     */
    void closest_location_on_tri( const CartVect& location,
                                  const CartVect* vertices,
                                  double tolerance,
                                  CartVect& closest_out,
                                  int& closest_topo );

    // Finds whether or not a box defined by the center and the half
    // width intersects a trilinear hex defined by its eight vertices.
    bool box_hex_overlap( const CartVect hexv[8], const CartVect& box_center, const CartVect& box_dims );

    // Finds whether or not a box defined by the center and the half
    // width intersects a linear tetrahedron defined by its four vertices.
    bool box_tet_overlap( const CartVect tet_corners[4], const CartVect& box_center, const CartVect& box_dims );

    // tests if 2 boxes overlap within a tolerance
    // assume that data is valid, box_min1 << box_max1, and box_min2<< box_max2
    // they are overlapping if they are overlapping in all directions
    // for example in x direction:
    //   box_max2[0] + tolerance < box_min1[0] -- false
    bool boxes_overlap( const CartVect& box_min1,
                        const CartVect& box_max1,
                        const CartVect& box_min2,
                        const CartVect& box_max2,
                        double tolerance );

    // see if boxes formed by 2 lists of "CartVect"s overlap
    bool bounding_boxes_overlap( const CartVect* list1, int num1, const CartVect* list2, int num2, double tolerance );

    // see if boxes from vertices in 2d overlap (used in gnomonic planes right now)
    bool bounding_boxes_overlap_2d( const double* list1, int num1, const double* list2, int num2, double tolerance );
    // point_in_trilinear_hex
    // Tests if a point in xyz space is within a hex element defined with
    // its eight vertex points forming a trilinear basis function.  Computes
    // the natural coordinates with respect to the hex of the xyz point
    // and checks if each are between +/-1.  If anyone is outside the range
    // the function returns false, otherwise it returns true.
    //
    bool point_in_trilinear_hex( const CartVect* hex, const CartVect& xyz, double etol );

    bool nat_coords_trilinear_hex( const CartVect* corner_coords, const CartVect& x, CartVect& xi, double tol );
}  // namespace GeomUtil

}  // namespace moab

#endif