AP_GeodesicGrid.h

Go to the documentation of this file.

/*
 * Copyright (C) 2016  Intel Corporation. All rights reserved.
 *
 * This file is free software: you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This file is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * See the GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License along
 * with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
#pragma once

#include "AP_Math.h"

class AP_GeodesicGrid {
    friend class GeodesicGridTest;

public:
    /*
     * The following concepts are used by the description of this class'
     * members.
     *
     * Vector crossing objects
     * -----------------------
     * We say that a vector v crosses an object in space (point, line, line
     * segment, plane etc) iff the line, being Q the set of points of that
     * object, the vector v crosses it iff there exists a positive scalar alpha
     * such that alpha * v is in Q.
     */

    static const int NUM_SUBTRIANGLES = 4;

    static int section(const Vector3f &v, bool inclusive = false);

private:
    /*
     * The following are concepts used in the description of the private
     * members.
     *
     * Neighbor triangle with respect to an edge
     * -----------------------------------------
     * Let T be a triangle. The triangle W is a neighbor of T with respect to
     * edge e if T and W share that edge. If e is formed by vectors a and b,
     * then W can be said to be a neighbor of T with respect to a and b.
     *
     * Umbrella of a vector
     * --------------------
     * Let v be one vertex of the icosahedron. The umbrella of v is the set of
     * icosahedron triangles that share that vertex. The vector v is called the
     * umbrella's pivot.
     *
     * Let T have vertices v, a and b. Then, with respect to (a, b):
     *  - The vector a is the umbrella's 0-th vertex.
     *  - The vector b is the 1-th vertex.
     *  - The triangle formed by the v, the i-th and ((i + 1) % 5)-th vertex is
     *  the umbrella's i-th component.
     *  - For i in [2,5), the i-th vertex is the vertex that, with the
     *  (i - 1)-th and v, forms the neighbor of the (i - 2)-th component with
     *  respect to v and the (i - 1)-th vertex.
     *
     * Still with respect to (a, b), the umbrella's i-th component is the
     * triangle formed by the i-th and ((i + 1) % 5)-th vertices and the pivot.
     *
     * Neighbor umbrella with respect to an icosahedron triangle's edge
     * ----------------------------------------------------------------
     * Let T be an icosahedron triangle. Let W be the T's neighbor triangle wrt
     * the edge e. Let w be the W's vertex that is opposite to e. Then the
     * neighbor umbrella of T with respect to e is the umbrella of w.
     */

    static const Matrix3f _inverses[10];

    static const Matrix3f _mid_inverses[10];

    static const struct neighbor_umbrella {
        uint8_t components[5];
        uint8_t v0_c0;
        uint8_t v1_c1;
        uint8_t v2_c1;
        uint8_t v4_c4;
        uint8_t v0_c4;
    } _neighbor_umbrellas[3];

    static int _neighbor_umbrella_component(int umbrella_index, int component_idx);

    static int _from_neighbor_umbrella(int umbrella_index,
                                       const Vector3f &v,
                                       const Vector3f &u,
                                       bool inclusive);

    static int _triangle_index(const Vector3f &v, bool inclusive);

    static int _subtriangle_index(const unsigned int triangle_index,
                                  const Vector3f &v,
                                  bool inclusive);
};