module Silicium::Geometry
Constants
- Point
Represents a point as two coordinates in two-dimensional space
- Point3d
Represents a point as three coordinates in three-dimensional space
Public Instance Methods
Determines if a clockwise crawl is performed for defined order of points
# File lib/geometry.rb, line 83 def clockwise(a, b, c) oriented_area(a, b, c).negative? end
Determines if a counter-clockwise crawl is performed for defined order of points
# File lib/geometry.rb, line 90 def counter_clockwise(a, b, c) oriented_area(a, b, c).positive? end
# File lib/geometry.rb, line 147 def cut_by_eq(line_equation) line_equation.slice(line_equation.index('='), line_equation.length).sub('=', '') end
Creates an array- directing vector in three-dimensional space . The equation is specified in the canonical form. Example, (x-0) / 26 = (y + 300) / * (- 15) = (z-200) / 51
Important: mandatory order of variables: x, y, z
# File lib/geometry.rb, line 169 def directing_vector3d(line_equation) process_line_by_coordinates(line_equation, :process_cf) end
The distance from a point to a line on a plane The line is defined by two points en.wikipedia.org/wiki/Distance_from_a_point_to_a_line
# File lib/geometry.rb, line 60 def distance_point_line2d(p1, p2, a) line_segment_length = distance_point_to_point2d(p1, p2) ((p2.y - p1.y) * a.x - (p2.x - p1.x) * a.y + p2.x * p1.y - p2.y * p1.x).abs / (line_segment_length * 1.0) end
The distance from a point to a line on a plane Line defined by an equation return 0 if the equation does not define a line.
# File lib/geometry.rb, line 69 def distance_point_line_equation2d(a, b, c, p) if a == 0 and b == 0 return 0 end (a * p.x + b * p.y + c).abs / Math.sqrt(a**2 + b**2) end
Calculates the distance from given points in two-dimensional space
# File lib/geometry.rb, line 19 def distance_point_to_point2d(a, b) Math.sqrt((b.x - a.x)**2 + (b.y - a.y)**2) end
Calculates the distance from given points in three-dimensional space
# File lib/geometry.rb, line 52 def distance_point_to_point3d(a, b) Math.sqrt((b.x - a.x)**2 + (b.y - a.y)**2 + (b.z - a.z)**2) end
Creates an array of coordinates of the point ([x, y, z] on the line given by the equation in the canonical form. Example, (x-0) / 26 = (y + 300) / * (- 15) = (z-200) / 51
Important: mandatory order of variables: x, y, z
# File lib/geometry.rb, line 201 def height_point_3d(line_equation) process_line_by_coordinates(line_equation, :process_free_member) end
# File lib/geometry.rb, line 232 def insert_eq(line_equation) line_equation.gsub(' ', '').insert(line_equation.length, '=') end
Returns an array containing points that are included in the minimal convex hull for a given array of points e-maxx.ru/algo/convex_hull_graham
# File lib/geometry.rb, line 110 def minimal_convex_hull_2d(points) return points if not_polygon?(points) points.sort_by! { |p| [p.x, p.y] } first = points[0] last = points.last up = [first] down = [first] (1...points.size).each do |i| point = points[i] is_last = i == points.size - 1 if is_last || clockwise(first, point, last) put_point_in_part(up, point, :clockwise) end if is_last || counter_clockwise(first, point, last) put_point_in_part(down, point, :counter_clockwise) end end hull = up (1..(down.size - 2)).reverse_each do |j| hull.push(down[j]) end hull end
# File lib/geometry.rb, line 176 def needed_variables_order?(before, after) before < after end
# File lib/geometry.rb, line 94 def not_polygon?(points) points.empty? || points.size == 1 || points.size == 2 end
# File lib/geometry.rb, line 76 def oriented_area(a, b, c) a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) end
Calculates the distance from a point given by a Point3d
structure to a straight line given by a canonical equation. Example, (x-0) / 26 = (y + 300) / * (- 15) = (z-200) / 51
Important: mandatory order of variables: x, y, z
# File lib/geometry.rb, line 223 def point_to_line_distance_3d(point, line_eq) dir_vector = directing_vector3d(line_eq) line_point = height_point_3d(line_eq) height_vector = [line_point[0] - point.x, line_point[1] - point.y, line_point[2] - point.z] height_on_dir = vectors_product(height_vector, dir_vector) vector_length(height_on_dir) / vector_length(dir_vector) end
# File lib/geometry.rb, line 137 def process_cf(line_equation, variable) if line_equation.include?(variable) before = line_equation.index('/') + 1 after = line_equation.index('=') line_equation.slice(before..after).gsub('=', '').sub('*', '').gsub('(', '').gsub(')', '').to_f else 0.0 end end
# File lib/geometry.rb, line 180 def process_free_member(line_equation, variable) if line_equation.include?(variable) before = line_equation.index(variable) + 1 after = line_equation.index('/') unless needed_variables_order?(before, after) throw VariablesOrderException end line_equation.slice(before..after).gsub('/', '').to_f * (-1) else 0.0 end end
# File lib/geometry.rb, line 151 def process_line_by_coordinates(line_equation, func) copy_line = insert_eq(line_equation) func = method(func) res = [] res[0] = func.call(copy_line, 'x') copy_line = cut_by_eq(copy_line) res[1] = func.call(copy_line, 'y') copy_line = cut_by_eq(copy_line) res[2] = func.call(copy_line, 'z') res end
# File lib/geometry.rb, line 98 def put_point_in_part(part, point, direction) direction = method(direction) while part.size >= 2 && !direction.call(part[part.size - 2], part[part.size - 1], point) part.pop end part.push(point) end
# File lib/geometry.rb, line 213 def vector_length(vector) Math.sqrt(vector[0]**2 + vector[1]**2 + vector[2]**2) end
# File lib/geometry.rb, line 205 def vectors_product(v1, v2) res = Array.new(3) (0..2).each do |i| res[i] = v1[(i + 1) % 3] * v2[(i + 2) % 3] - v1[(i + 2) % 3] * v2[(i + 1) % 3] end res end