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Math Help - Need Geo. Expert Here With Checking Intersection Of Parallelograms!

  1. #1
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    Angry Need Geo. Expert Here With Checking Intersection Of Parallelograms!

    I need some help with this problem that I just cant seen to understand how to do.
    I just need help coming up with an algorithm that can check to see if two parallelograms have an intersection. This involves where they are on a 2d grid (x,y) coordinates of the vertex's.

    The other thing is the grid I am working with, the (0,0) or origin is at the top left
    and as you go down, the y number is increasing and is >= 0
    An example is:
    (0,0) (5,0)
    __________
    |_|_|_|_|_|
    |_|_|_|_|_|
    |_|_|_|_|_|
    |_|_|_|_|_|
    |_|_|_|_|_|
    (0,5) (5,5)


    If you know can you write out the steps to solve it ex. [find of the length of this, then subtract this from this, etc...]

    given 16 arguments

    1)parallelogram1_x1
    2)parallelogram1_y1
    3)parallelogram1_x2
    4)parallelogram1_y2
    5)parallelogram1_x3
    6)parallelogram1_y3
    7)parallelogram1_x4
    8)parallelogram1_y4
    9)parallelogram2_x1
    10)parallelogram2_y1
    11)parallelogram2_x2
    12)parallelogram2_y2
    13)parallelogram2_x3
    14)parallelogram2_y3
    15)parallelogram2_x4
    16)parallelogram2_y4

    the (x,y)#1 will be the top_left of the parallelogram
    the (x,y)#2 will be the top_right of the parallelogram
    the (x,y)#3 will be the bottom_left of the parallelogram
    the (x,y)#4 will be the bottom_right of the parallelogram

    NOTE: the parallelogram may be a rectangle
    NOTE2: I am working with variables here, not actual values.
    NOTE3: there are no negative x or y coordinates in the grid. its just [for x] 0,...,room_width, and [for y] 0,...,room_height. This is the whole grid.

    With this data, how do I find out if there is an intersection anywhere between both the parallelograms? One of them doesn't have to lie directly inside the other, I just want to know if they touch.

    Any help is appreciated.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Sneaky View Post
    (0,0) (5,0)
    __________
    |_|_|_|_|_|
    |_|_|_|_|_|
    |_|_|_|_|_|
    |_|_|_|_|_|
    |_|_|_|_|_|
    (0,5) (5,5)
    Are you sure you "understand" coordinates?
    The 2 lower ones should be (0, -5) and (5,-5).

    Say you have this parallelogram:
    Code:
           A                 B
    
    
    
    C                 D
    AB = CD = 9 and AC = BD = 5; height from A to CD = 4.
    If you place A at origin and B on x axis, what will be the coordinates of B, C and D?

    If you can't answer that, you're sure not ready for this.
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  3. #3
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    I understand coordinates, but the specific software I am using uses this type of coordinates in order for things to work.

    also i dont understand your last question, the coordinates of all 4 points of both shapes are provided as variables, so they are all defined.

    if your translating a shape to be placed on the origin, then do the same operations on the other 3 points as well.
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  4. #4
    MHF Contributor
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    My question has NOTHING to do with your program.
    It is a simple geometry problem.
    Can you answer it or not?
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  5. #5
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    B=(9,0)
    C=(-3,4)
    D=(6,4)
    i think these are right

    but i think i know how to do this, for p1, u can take each of the lines and compare it with each of the lines of p2, if there are any intersections then there is a intersection with the shapes. But before you do this u check to see if p1 lies completely inside p2 and if p2 is in p1. But i am not sure how to write mathematically how to check if there is a intersection between lines.
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