Object
NOTE: Ftor is DEPRECATED and will be removed in Rubygame 3.0! A mostly-compatible vector class will be provided at or before that time.
NOTE: you must require 'rubygame/ftor' manually to gain access to Rubygame::Ftor. It is not imported with Rubygame by default!
Ftor ("Fake vecTOR"), a vector-like class for 2D position/movement.
(NB: See angle for an important note about why angles appear to be the opposite of what you may expect.)
Ftor is useful for storing 2D coordinates (x,y) as well as vector quantities such as velocity and acceleration (representationally, points and vectors are equivalent.) Although Ftors are always represented internally as Cartesian coordinates (x, y), it is possible to deal with an Ftor as polar coordinates (angle, magnitude) instead. See new_am and set_am!, for example.
Ftor is a "fake" vector because it has certain convenient properties which differ from "true" vectors (i.e. vectors in a strict mathematical sense).
Unlike vectors, Ftors may be multiplied or divided to another Ftor. This is equivalent to multiplying or dividing each component by the corresponding component in the second Ftor. If you like, you can think of this feature as scaling each component of the Ftor by a separate factor:
Ftor(a,b) * Ftor(c,d) = Ftor(a*c, b*d)
Of course, Ftors also have the usual vector behavior for addition/subraction between two Ftors, and multiplication/division of an Ftor by a scalar:
Ftor(a,b) + Ftor(c,d) = Ftor(a+c, b+d) Ftor(a,b) * n = Ftor(a*n, b*n)
Additionally, Ftor contains functions for manipulating itself. You can both get and set such properties as angle, magnitude, unit, and normal, and the Ftor will change in-place as needed. For example, if you set angle=, the vector will change to have the new angle, but keeps the same magnitude as before.
Ftor attempts to save processing time (at the expense of memory) by storing secondary properties (angle, magnitude, etc.) whenever they are calculated,so that they need not be calculated repeatedly. If the vector changes, the properties will be calculated again the next time they are needed. (In future versions, it may be possible to disable this feature for certain Ftors, for example if they will change very often, to save memory.)
Create a new Ftor by specifying its x and y components. See also new_am and new_from_to.
# File lib/rubygame/ftor.rb, line 82 def initialize(x,y) Rubygame.deprecated("Rubygame::Ftor", "3.0") @x, @y = x, y end
Returns a new Ftor which represents the difference in position of two points p1 and p2. (p1 and p2 can be Ftors, size-2 Arrays, or anything else which has two numerical components and responds to #[].)
In other words, assuming v is the Ftor returned by this function:
p1 + v = p2
# File lib/rubygame/ftor.rb, line 101 def self.new_from_to(p1,p2) return self.new(p2[0]-p1[0],p2[1]-p1[1]) end
Perform multiplication of this Ftor by the scalar other, like so:
Ftor(a,b) * n = Ftor(a*n, b*n)
However, if this causes TypeError, attempt to extract indices 0 and 1 with other‘s #[] operator, and multiply them into the corresponding components of this Ftor, like so:
Ftor(a,b) * Ftor(c,d) = Ftor(a*c, b*d) Ftor(a,b) * [c,d] = Ftor(a*c, b*d)
# File lib/rubygame/ftor.rb, line 215 def *(other) return self.class.new(@x*other,@y*other) rescue TypeError return self.class.new(@x*other[0],@y*other[1]) end
Perform vector addition with this Ftor and other, adding them on a component-by-component basis, like so:
Ftor(a,b) + Ftor(c,d) = Ftor(a+c, b+d)
# File lib/rubygame/ftor.rb, line 198 def +(other) return self.class.new(@x+other[0],@y+other[1]) end
Like #+, but performs subtraction instead of addition.
# File lib/rubygame/ftor.rb, line 203 def -(other) return self.class.new(@x-other[0],@y-other[1]) end
Like #*, but performs division instead of multiplication.
# File lib/rubygame/ftor.rb, line 222 def /(other) x, y = @x.to_f, @y.to_f return self.class.new(x/other,y/other) rescue TypeError return self.class.new(x/other[0],y/other[1]) end
Clears stored values for angle, magnitude, normal, and unit, so that they will be recalculated the next time they are needed. Intended for internal use, but might be useful in other situations.
# File lib/rubygame/ftor.rb, line 369 def _clear @angle = nil @magnitude = nil @normal = nil @unit = nil return self end
Return the angle (radians) this Ftor forms with the positive X axis. This is the same as the Ftor’s angle in a polar coordinate system.
IMPORTANT: Because the positive Y axis on the Rubygame::Screen points downwards, an angle in the range 0..PI will appear to point downwards, rather than upwards! This also means that positive rotation will appear clockwise, and negative rotation will appear counterclockwise! This is the opposite of what you would expect in geometry class!
# File lib/rubygame/ftor.rb, line 238 def angle @angle or @angle = Math.atan2(@y,@x) end
Set the angle (radians) of this Ftor from the positive X axis. Magnitude is preserved.
# File lib/rubygame/ftor.rb, line 244 def angle=(a) m = magnitude() set!( Math.cos(a)*m, Math.sin(a)*m ) end
Return the difference in angles (radians) between this Ftor and other.
# File lib/rubygame/ftor.rb, line 322 def angle_with(other) Math.acos( self.udot(other) ) end
Return the dot product (aka inner product) of this Ftor and other. The dot product of two vectors v1 and v2 is:
v1.x * v2.x + v1.y * v2.y
# File lib/rubygame/ftor.rb, line 312 def dot(other) @x*other[0] + @y*other[1] end
Same as to_s, but this Ftor’s object_id is also displayed.
# File lib/rubygame/ftor.rb, line 131 def inspect "#<#{self.class}:#{object_id}: %f, %f>"%[@x,@y] end
Same as to_s_am, but this Ftor’s object_id is also displayed.
# File lib/rubygame/ftor.rb, line 148 def inspect_am "#<#{self.class}:AM:#{object_id}: %f, %f>"%[angle(),magnitude()] end
Returns the magnitude of the Ftor, i.e. its length from tail to head. This is the same as the Ftor’s magnitude in a polar coordinate system.
# File lib/rubygame/ftor.rb, line 254 def magnitude @magnitude or @magnitude = Math.hypot(@x,@y) end
Modifies the magnitude of the Ftor, preserving its angle.
In other words, the Ftor will point in the same direction, but it will be a different length from tail to head.
# File lib/rubygame/ftor.rb, line 262 def magnitude=(m) new = unit() * m set!(new.x, new.y) end
Return a new unit Ftor which is perpendicular to this Ftor (rotated by pi/2 radians, to be specific).
# File lib/rubygame/ftor.rb, line 272 def normal @normal or @normal = unit().rotate(HALF_PI) end
Rotate this Ftor in-place, so that it is perpendicular to other. This Ftor will be at an angle of -pi/2 to other.
# File lib/rubygame/ftor.rb, line 278 def normal=(other) set!( *(self.class.new(*other).unit().rotate(-HALF_PI) * magnitude()) ) end
“Pretty print”. Same as to_s, but components are displayed as rounded floats to 3 decimal places, for easy viewing.
# File lib/rubygame/ftor.rb, line 143 def pretty "#<#{self.class}: [%0.3f, %0.3f]>"%[@x,@y] end
“Pretty print” with angle and magnitude. Same as to_s_am, but components are displayed as rounded floats to 3 decimal places, for easy viewing.
# File lib/rubygame/ftor.rb, line 162 def pretty_am "#<#{self.class}:AM: [%0.3f, %0.3f]>"%[angle(),magnitude()] end
Like #-@, but reverses this Ftor in-place.
# File lib/rubygame/ftor.rb, line 191 def reverse! set!(-@x,-@y) end
Rotate this Ftor in-place by angle (radians). This is the same as adding angle to this Ftor’s angle.
IMPORTANT: Positive rotation will appear clockwise, and negative rotation will appear counterclockwise! See angle for the reason.
# File lib/rubygame/ftor.rb, line 344 def rotate!(angle) # case(angle) # when HALF_PI, -THREE_HALF_PI # self.set!(@y,-@x) # when THREE_HALF_PI, -HALF_PI # self.set!(-@y,@x) # when PI, -PI # self.set!(@y,-@x) # when 0, TWO_PI, -TWO_PI # self.set!(@y,-@x) # else self.a += angle # end return self end
Modify the x and y components of the Ftor in-place
# File lib/rubygame/ftor.rb, line 120 def set!(x,y) @x, @y = x,y _clear() end
Returns an Array of this Ftor’s components, [x,y].
# File lib/rubygame/ftor.rb, line 167 def to_a [@x,@y] end
Display this Ftor in the format: “#<Ftor: [x, y]>”. x and y are displayed as floats at full precision. See also pp.
# File lib/rubygame/ftor.rb, line 137 def to_s "#<#{self.class}: [%f, %f]>"%[@x,@y] end
Return the unit vector of the Ftor, i.e. an Ftor with the same direction, but a magnitude of 1. (This is sometimes called a “normalized” vector, not to be confused with a vector’s normal.)
# File lib/rubygame/ftor.rb, line 288 def unit m = magnitude().to_f @unit or @unit = Ftor.new(@x/m, @y/m) end
Rotates this Ftor in-place, so that its unit vector matches the unit vector of the given Ftor.
In other words, changes the angle of this Ftor to be the same as the angle of the given Ftor, but this Ftor’s magnitude does not change.
# File lib/rubygame/ftor.rb, line 301 def unit=(other) set!( *(self.class.new(*other).unit() * magnitude()) ) end
Set the x component of the Ftor.
# File lib/rubygame/ftor.rb, line 107 def x=(value) @x = value _clear() end
Set the y component of the Ftor.
# File lib/rubygame/ftor.rb, line 114 def y=(value) @y = value _clear() end
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