# Copyright (c) 2021 Andy Maleh
#
# Permission is hereby granted, free of charge, to any person obtaining
# a copy of this software and associated documentation files (the
# "Software"), to deal in the Software without restriction, including
# without limitation the rights to use, copy, modify, merge, publish,
# distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so, subject to
# the following conditions:
#
# The above copyright notice and this permission notice shall be
# included in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
# LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
# OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
# WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

require 'perfect_shape/shape'
require 'perfect_shape/multi_point'

module PerfectShape
  # Mostly ported from java.awt.geom: https://docs.oracle.com/javase/8/docs/api/java/awt/geom/Line2D.html
  class Line < Shape
    class << self
      # Returns an indicator of where the specified point (px,py) lies with respect to the line segment from
      # (x1,y1) to (x2,y2).
      #
      # The return value can be either 1, -1, or 0 and indicates in which direction the specified line must pivot around its first end point, (x1,y1), in order to point at the specified point (px,py).
      # A return value of 1 indicates that the line segment must turn in the direction that takes the positive X axis towards the negative Y axis. In the default coordinate system used by Java 2D, this direction is counterclockwise.
      #
      # A return value of -1 indicates that the line segment must turn in the direction that takes the positive X axis towards the positive Y axis. In the default coordinate system, this direction is clockwise.
      #
      # A return value of 0 indicates that the point lies exactly on the line segment. Note that an indicator value of 0 is rare and not useful for determining collinearity because of floating point rounding issues.
      #
      # If the point is colinear with the line segment, but not between the end points, then the value will be -1 if the point lies “beyond (x1,y1)” or 1 if the point lies “beyond (x2,y2)”.
      #
      # @param x1 the X coordinate of the start point of the
      #           specified line segment
      # @param y1 the Y coordinate of the start point of the
      #           specified line segment
      # @param x2 the X coordinate of the end point of the
      #           specified line segment
      # @param y2 the Y coordinate of the end point of the
      #           specified line segment
      # @param px the X coordinate of the specified point to be
      #           compared with the specified line segment
      # @param py the Y coordinate of the specified point to be
      #           compared with the specified line segment
      # @return an integer that indicates the position of the third specified
      #                  coordinates with respect to the line segment formed
      #                  by the first two specified coordinates.
      def relative_counterclockwise(x1, y1, x2, y2, px, py)
        x2 -= x1;
        y2 -= y1;
        px -= x1;
        py -= y1;
        ccw = px * y2 - py * x2;
        if ccw == 0.0
          # The point is colinear, classify based on which side of
          # the segment the point falls on.  We can calculate a
          # relative value using the projection of px,py onto the
          # segment - a negative value indicates the point projects
          # outside of the segment in the direction of the particular
          # endpoint used as the origin for the projection.
          ccw = px * x2 + py * y2;
          if ccw > 0.0
            # Reverse the projection to be relative to the original x2,y2
            # x2 and y2 are simply negated.
            # px and py need to have (x2 - x1) or (y2 - y1) subtracted
            #    from them (based on the original values)
            # Since we really want to get a positive answer when the
            #    point is "beyond (x2,y2)", then we want to calculate
            #    the inverse anyway - thus we leave x2 & y2 negated.
            px -= x2;
            py -= y2;
            ccw = px * x2 + py * y2;
            ccw = 0.0 if ccw < 0.0
          end
        end
        (ccw < 0.0) ? -1 : ((ccw > 0.0) ? 1 : 0);
      end
      
      # Returns the square of the distance from a point to a line segment.
      # The distance measured is the distance between the specified
      # point and the closest point between the specified end points.
      # If the specified point intersects the line segment in between the
      # end points, this method returns 0.0.
      #
      # @param x1 the X coordinate of the start point of the
      #           specified line segment
      # @param y1 the Y coordinate of the start point of the
      #           specified line segment
      # @param x2 the X coordinate of the end point of the
      #           specified line segment
      # @param y2 the Y coordinate of the end point of the
      #           specified line segment
      # @param px the X coordinate of the specified point being
      #           measured against the specified line segment
      # @param py the Y coordinate of the specified point being
      #           measured against the specified line segment
      # @return a double value that is the square of the distance from the
      #                  specified point to the specified line segment.
      def point_segment_distance_square(x1, y1,
                                       x2, y2,
                                       px, py)
        x1 = BigDecimal(x1.to_s)
        y1 = BigDecimal(y1.to_s)
        x2 = BigDecimal(x2.to_s)
        y2 = BigDecimal(y2.to_s)
        px = BigDecimal(px.to_s)
        py = BigDecimal(py.to_s)
        # Adjust vectors relative to x1,y1
        # x2,y2 becomes relative vector from x1,y1 to end of segment
        x2 -= x1
        y2 -= y1
        # px,py becomes relative vector from x1,y1 to test point
        px -= x1
        py -= y1
        dot_product = px * x2 + py * y2;
        if dot_product <= 0.0
          # px,py is on the side of x1,y1 away from x2,y2
          # distance to segment is length of px,py vector
          # "length of its (clipped) projection" is now 0.0
          projected_length_square = BigDecimal('0.0');
        else
          # switch to backwards vectors relative to x2,y2
          # x2,y2 are already the negative of x1,y1=>x2,y2
          # to get px,py to be the negative of px,py=>x2,y2
          # the dot product of two negated vectors is the same
          # as the dot product of the two normal vectors
          px = x2 - px
          py = y2 - py
          dot_product = px * x2 + py * y2
          if dot_product <= 0.0
            # px,py is on the side of x2,y2 away from x1,y1
            # distance to segment is length of (backwards) px,py vector
            # "length of its (clipped) projection" is now 0.0
            projected_length_square = BigDecimal('0.0')
          else
            # px,py is between x1,y1 and x2,y2
            # dot_product is the length of the px,py vector
            # projected on the x2,y2=>x1,y1 vector times the
            # length of the x2,y2=>x1,y1 vector
            projected_length_square = dot_product * dot_product / (x2 * x2 + y2 * y2)
          end
        end
        # Distance to line is now the length of the relative point
        # vector minus the length of its projection onto the line
        # (which is zero if the projection falls outside the range
        #  of the line segment).
        length_square = px * px + py * py - projected_length_square
        length_square = BigDecimal('0.0') if length_square < 0
        length_square
      end
      
      # Returns the distance from a point to a line segment.
      # The distance measured is the distance between the specified
      # point and the closest point between the specified end points.
      # If the specified point intersects the line segment in between the
      # end points, this method returns 0.0.
      #
      # @param x1 the X coordinate of the start point of the
      #           specified line segment
      # @param y1 the Y coordinate of the start point of the
      #           specified line segment
      # @param x2 the X coordinate of the end point of the
      #           specified line segment
      # @param y2 the Y coordinate of the end point of the
      #           specified line segment
      # @param px the X coordinate of the specified point being
      #           measured against the specified line segment
      # @param py the Y coordinate of the specified point being
      #           measured against the specified line segment
      # @return a double value that is the distance from the specified point
      #                          to the specified line segment.
      def point_segment_distance(x1, y1,
                                 x2, y2,
                                 px, py)
        BigDecimal(::Math.sqrt(point_segment_distance_square(x1, y1, x2, y2, px, py)).to_s)
      end
      
      # Calculates the number of times the line from (x1,y1) to (x2,y2)
      # crosses the ray extending to the right from (px,py).
      # If the point lies on the line, then no crossings are recorded.
      # +1 is returned for a crossing where the Y coordinate is increasing
      # -1 is returned for a crossing where the Y coordinate is decreasing
      def point_crossings(x1, y1, x2, y2, px, py)
        return 0 if (py <  y1 && py <  y2)
        return 0 if (py >= y1 && py >= y2)
        # assert(y1 != y2);
        return 0 if (px >= x1 && px >= x2)
        return ((y1 < y2) ? 1 : -1) if (px <  x1 && px <  x2)
        xintercept = x1 + (py - y1) * (x2 - x1) / (y2 - y1);
        return 0 if (px >= xintercept)
        (y1 < y2) ? 1 : -1
      end
    end
    
    include MultiPoint
    include Equalizer.new(:points)
    
    # Checks if line contains point (two-number Array or x, y args), with distance tolerance (0 by default)
    #
    # @param x The X coordinate of the point to test.
    # @param y The Y coordinate of the point to test.
    # @param distance The distance from line to tolerate (0 by default)
    #
    # @return {@code true} if the point lies within the bound of
    # the line, {@code false} if the point lies outside of the
    # line's bounds.
    def contain?(x_or_point, y = nil, distance: 0)
      x, y = normalize_point(x_or_point, y)
      return unless x && y
      distance = BigDecimal(distance.to_s)
      point_segment_distance(x, y) <= distance
    end
    
    def point_segment_distance(x_or_point, y = nil)
      x, y = normalize_point(x_or_point, y)
      return unless x && y
      Line.point_segment_distance(points[0][0], points[0][1], points[1][0], points[1][1], x, y)
    end
    
    def relative_counterclockwise(x_or_point, y = nil)
      x, y = normalize_point(x_or_point, y)
      return unless x && y
      Line.relative_counterclockwise(points[0][0], points[0][1], points[1][0], points[1][1], x, y)
    end
    
    # Calculates the number of times the line
    # crosses the ray extending to the right from (px,py).
    # If the point lies on the line, then no crossings are recorded.
    # +1 is returned for a crossing where the Y coordinate is increasing
    # -1 is returned for a crossing where the Y coordinate is decreasing
    def point_crossings(x_or_point, y = nil)
      x, y = normalize_point(x_or_point, y)
      return unless x && y
      Line.point_crossings(points[0][0], points[0][1], points[1][0], points[1][1], x, y)
    end
  end
end