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Math Help - Anamorphic Art Work

  1. #1
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    Anamorphic Art Work

    Hi, new to the forum and in need of a bit of help!

    I'm working on a piece of art work that will require a lot of maths. I use maths generally in my work whether it be to make a structure or plan out an animation etc... However the maths involved in my most recent idea is a little beyond me (im not great at maths to be honest).

    Anyway here is a link to the kinda thing im going to be making:

    Jim Bond

    So basically when you look through the hole (view point) at the front of the cube the figure appears whole and in correct proportions. It might help you to think of the channel 4 ads with the massive number 4 that comes together! Anyway I know objects at the back will need to be larger and objects at the front smaller (but thats about all i know).

    It might be worth me mentioning im going to be doing this with objects (not the human figure) on a life size scale in a gallery so as the viewer can walk passed each individual item. For example i could use a door, each item such as the door bell, letter box, door number, door, door frame will be deconstructed and spaces out throughout the gallery, but when the instillation is viewed at a particular point will morph into a whole image.

    I would really appreciate any help at all. Im no maths genius so keep it simple if you can.

    Thanks
    Kevin
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  2. #2
    MHF Contributor

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    Paris, France
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    Hi,

    this is a nice project. Luckily for you, this kind of anamorphosis doesn't require advanced maths. The only result you need is Thales theorem, and in fact you can probably do most of the work on sketches.

    The basic idea is that if the real distance from the viewer to an object is multiplied by a factor k, then the size of the object should be multiplied by the same factor k.

    In the example (Jim Bond), the elements look very much like scaled versions of the hand, leg, head, etc. You can in fact allow much more freedom than that: for instance, a deformed head could look like normal from the appropriate viewpoint.

    On the other hand, there are also possible simplifications, i.e. cases when you can avoid deforming object by just scaling them. This is the case for almost-planar objects (like a door) under some condition (the real door has to be parallel to the "virtual" door), and this is the case for relatively small objects (like a door knob, or body parts in Bond's artwork), where slight deformation will keep unnoticed.

    The best is to start with a sketch. Draw the view from above (to get the location on the ground), and the view from the side (to get the height). In each case, you should begin by choosing the viewer's location. Then draw the objects of the scene like they should be viewed, for instance a real-size door with a real-size door number on it (on the sketches from above and from the side, these are line segments, or rectangles). On this sketch, draw thin lines from the viewpoint through the corners of the door (cf. attached sketch). These lines determine where the corners of the real door (the one you will build) should be; anywhere they are on these lines, they will appear to be at the same point for the viewer. On the sketch, the real door is chosen to be parallel to the "virtual" door (the real-size one); this way, the real door is not deformed, it is just scaled by a factor that you can measure on the sketch. You can do the same for any object: draw what it should look like, then choose what you're going to build by picking points that keep being on the same line from the viewpoint.

    This is the main idea; your imagination will do the rest!

    If something is not clear, or not sufficiently precise, feel free to ask.
    Attached Thumbnails Attached Thumbnails Anamorphic Art Work-mhf.png  
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  3. #3
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    Thank so much for the help! Got me sketching and making some kind of logic of it all! Im still pretty confused however so please excuse my stupidity!

    Here is the sketch of the idea i want to take forwads:

    IMG_0983 on Flickr - Photo Sharing!

    As you can see the viewer is sitting on a chair while looking through the VP. I want the viewer to see a replica of the chair he is seated on (the chair will appear 3D unlike the door). The chair must appear as if it is sitting in actual space (not floating). How do i ground the chair? Is it also best to use the center point of the cube as my focal point as it will let me space out objects equally in the cube or is there a better method?

    Say my chair is 80cm in height and my cube has a total length of 300cm, so 150cm will be the chairs focal point. How big will my 80cm chair appear at 150cm from the VP for the viewer? This will be key in making sure the chair appears correct will it not? Then how do i enlarge the bits i wish to be further away and reduce the bits i wish to be closer?

    Sorry once again this kind of maths is probably real basic. I just need to get my head around the general principals so i can start playing around with hanging the objects for best effect in the space (or scale model making). Really appreciate it!

    Thanks once again for the help
    Kevin
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