sprite coordinates

[berka]

Hi,

It has been so long since I have not posted anything here. But I have never stopped scripting. I am currently creating a game engine The player can move in any direction pixel by pixel.
I added a function to the Sprite class which determines the coordinates of the vertices of a sprite based on the angle of rotation.


[ruby]class Sprite
  attr_accessor :rectangle
 
  alias :rectangle_initialize :initialize unless $@
  alias :rectangle_angle :angle= unless $@
 
  def initialize(*args)
    rectangle_initialize(*args)
    @rectangle=Rectangle.new
  end
 
  def angle=(a)
    rectangle_angle(a)
    c=Math.cos(r=a*PI/180.0)
    s=Math.sin(r)
   
    hs=self.bitmap.height*s/2
    ls=self.bitmap.width*s/2
    hc=self.bitmap.height*c/2
    lc=self.bitmap.width*c/2
   
    @rectangle.a.set(self.x-lc-hs,self.y-hc+ls)
    @rectangle.b.set(self.x+lc-hs,self.y-hc-ls)
    @rectangle.b.set(self.x+lc-hs,self.y-hc-ls)
    @rectangle.c.set(self.x+lc+hs,self.y+hc-ls)
    @rectangle.d.set(self.x-lc+hs,self.y+hc+ls)
  end
end
[/ruby]

Note: Rectangle#a=[x,y]

This code works when Sprite#ox and Sprite#oy are the center of the sprite.
How to calculate the coordinates as ox and oy are not the center ? (e.g: ox = self.bitmap.width/5)

Trigonometry is so far :sad:

Thanks in advance,
Regards,

Berka

 

[SephirothSpawn]

Let me think on it for a minute. When I get back to the computer I should have a solution.

 

[berka]

ok, thanks !

 

[SephirothSpawn]

Still working on simplifying my formula for this. Basically, for any arbitrary point [ox, oy], you are finding:

- Distances from each point of original rect to [ox, oy].
- An angle value back to 0.

Then adding your new sprite.angle to each of those angles and re-calculating each rectangle point based off the hypot (distance from offset) and the original angle + new angle.


The only part that is making this tricky is say

: +ox, +oy
: +ox, -oy
: -ox, +oy
: -ox, -oy

I haven't had time to sit down yet and work on this, but should sometime in the next 12 hours.

 

[SephirothSpawn]

Wow been out of Trig to long. Forgot a valuable formula:

(x1, y1) = ((x*cos(theta) - y*sin(theta)), (x*sin(theta) + y*cos(theta)))

So here is what I came up with:

module Math

  def self.degrees_to_radians(d)

    return d * PI / 180

  end

  def self.radians_to_degrees(r)

    return r * 180 / PI

  end

  @q_cos = {}

  @q_sin = {}

  for i in 0...360

    @q_cos[i] = self.cos(self.degrees_to_radians(i))

    @q_sin[i] = self.sin(self.degrees_to_radians(i))

  end

  def self.q_cos(i, degrees = true)

    i = self.radians_to_degrees(i) unless degrees

    return @q_cos[i.round % 360]

  end

  def self.q_sin(i, degrees)

    i = self.radians_to_degrees(i) unless degrees

    return @q_sin[i.round % 360]

  end

end

 

class Rotating_Rect

  attr_accessor :angle

  attr_accessor :a, :b, :c, :d

  def initialize

    @angle = 0

    @a, @b, @c, @d = [], [], [], []

  end

  def rotate_points(x, y, angle)

    ax = @a[0] - x ; ay = @a[1] - y

    bx = @b[0] - x ; by = @b[1] - y

    cx = @c[0] - x ; cy = @c[1] - y

    dx = @d[0] - x ; dy = @d[1] - y

    nax = ax * Math.q_cos(angle) - ay * Math.q_sin(angle)

    nay = ax * Math.q_sin(angle) - ay * Math.q_cos(angle)

    nbx = bx * Math.q_cos(angle) - by * Math.q_sin(angle)

    nby = bx * Math.q_sin(angle) - by * Math.q_cos(angle)

    ncx = cx * Math.q_cos(angle) - cy * Math.q_sin(angle)

    ncy = cx * Math.q_sin(angle) - cy * Math.q_cos(angle)

    ndx = dx * Math.q_cos(angle) - dy * Math.q_sin(angle)

    ndy = dx * Math.q_sin(angle) - dy * Math.q_cos(angle)

    @angle = angle

    @a = [nax + x, nay + y]

    @b = [nbx + x, nby + y]

    @c = [ncx + x, ncy + y]

    @d = [ndx + x, ndy + y]  

  end

end

 

class Sprite

  attr_reader :angle_rect

  alias_method :seph_spriterects_init, :initialize

  def initialize(*args)

    seph_spriterects_init(*args)

    @angle_rect = Rotating_Rect.new

    @angle_rect.a = [0, 0]

    @angle_rect.b = [self.bitmap.width, 0]

    @angle_rect.c = [0, self.bitmap.height]

    @angle_rect.d = [self.bitmap.width, self.bitmap.height]

  end

  alias_method :seph_spriterects_setbitmap, :bitmap=

  def bitmap=(bitmap)

    seph_spriterects_setbitmap(bitmap)

    @angle_rect.angle = 0

    @angle_rect.a = [0, 0]

    @angle_rect.b = [self.bitmap.width, 0]

    @angle_rect.c = [0, self.bitmap.height]

    @angle_rect.d = [self.bitmap.width, self.bitmap.height]

    @angle_rect.rotate_points(self.ox, self.oy, self.angle)

  end

  alias_method :seph_spriterects_setangle, :angle=

  def angle=(angle)

    seph_spriterects_setangle(angle)

    @angle_rect.angle = 0

    @angle_rect.a = [0, 0]

    @angle_rect.b = [self.bitmap.width, 0]

    @angle_rect.c = [0, self.bitmap.height]

    @angle_rect.d = [self.bitmap.width, self.bitmap.height]

    @angle_rect.rotate_points(self.ox, self.oy, angle)

  end

end

The Rotating_Rect class holds the 4 points of the rect. I put the function for rotating the rect counter-clockwise in that class. That's where the Math is.

Hope this helps you.

 

[berka]

Thank you. I'll try that as soon as possible and I'll simplify the code, because the angle_rect is calculated each frame.

 

[SephirothSpawn]

It shouldn't calculate every frame, unless you are changing your angle instance in your sprite. If that is the case, you can cache the coordinates like so:

module Math

  def self.degrees_to_radians(d)

    return d * PI / 180

  end

  def self.radians_to_degrees(r)

    return r * 180 / PI

  end

  @q_cos = {}

  @q_sin = {}

  for i in 0...360

    @q_cos[i] = self.cos(self.degrees_to_radians(i))

    @q_sin[i] = self.sin(self.degrees_to_radians(i))

  end

  def self.q_cos(i, degrees = true)

    i = self.radians_to_degrees(i) unless degrees

    return @q_cos[i.round % 360]

  end

  def self.q_sin(i, degrees)

    i = self.radians_to_degrees(i) unless degrees

    return @q_sin[i.round % 360]

  end

end

 

class Rotating_Rect

  attr_accessor :angle

  attr_reader   :ox, :oy

  def initialize

    @angle, @ox, @oy = 0, 0, 0

    @a, @b, @c, @d = [], [], [], []

  end

  def a

    return @values[['a', @angle]]

  end

  def b

    return @values[['b', @angle]]

  end

  def c

    return @values[['c', @angle]]

  end

  def d

    return @values[['d', @angle]]

  end

  def set(a, b, c, d, ox, oy)

    @a, @b, @c, @d, @ox, @oy = a, b, c, d, ox, oy

    set_values

  end

  def set_values

    @values = {}

    keys = {'a' => @a, 'b' => @b, 'c' => @c, 'd' => @d}

    keys.each do |l, instance|

      for i in 0...360

        key = [l, i]

        @values[key] = get_value(@a, i)

        Graphics.update

      end

    end

  end

  def get_value(pos, angle)

    x, y = *pos

    x1, y1 = x - @ox, y - @oy

    x2 = x1 * Math.q_cos(angle) - y1 * Math.q_sin(angle)

    y2 = x1 * Math.q_sin(angle) + y1 * Math.q_cos(angle)

    return [x2 + @ox, y2 + @oy]

  end

end

 

class Sprite

  attr_reader :angle_rect

  alias_method :seph_spriterects_init, :initialize

  def initialize(*args)

    seph_spriterects_init(*args)

    @angle_rect = Rotating_Rect.new

  end

  alias_method :seph_spriterects_setbitmap, :bitmap=

  def bitmap=(bitmap)

    seph_spriterects_setbitmap(bitmap)

    set_angle_rect

  end

  alias_method :seph_spriterects_setox, :ox=

  def ox=(ox)

    seph_spriterects_setox(ox)

    set_angle_rect

  end

  alias_method :seph_spriterects_setoy, :oy=

  def oy=(oy)

    seph_spriterects_setoy(oy)

    set_angle_rect

  end

  alias_method :seph_spriterects_setangle, :angle=

  def angle=(angle)

    seph_spriterects_setangle(angle)

    @angle_rect.angle = self.angle

  end

  def set_angle_rect

    if bitmap != nil

      a = [@x, @y]

      b = [@x + bitmap.width, @y]

      c = [@x, @y + bitmap.height]

      d = [@x + bitmap.width, @y + bitmap.height]

      @angle_rect.set(a, b, c, d, self.ox, self.oy)

      @angle_rect.angle = self.angle

    end

  end

end

Now when the bitmap, ox or oy are set, it calculates all the a-d coordinates for all angles 0 to 359. Now the a-d methods are dynamic and return a cache value determined by the angle. Also before the coordinates assumed that the sprites @x and @y were 0. Now it takes into consideration of the sprite's position (see set_angle_rect).

Again, hope that helps.

 

[berka]

Okay, thanks. I'll modify your last script to embed it in my system. Of course, I'll post the whole script there.

 

[SephirothSpawn]

Great. Can't wait to see what you are cooking up... :thumb: