4D graphics

[malcolm]

Dimensionality is a really abstract concept (you encounter it frequently in higher-level math). It refers to the number of independently varying parameters in any function.

Rather than referring strictly to object positions (conventional 3D), the higher dimensions could refer to light directions, viewer stimulus response, or pretty much anything else.

One application of 4D rendering is a lightfield -- instead of rendering one image, every possible viewer and light direction are rendered into an array of images. Subsequently, the original data can be reconstructed/interpolated very quickly. This technique is primarily interesting for software rendering engines; however, I've had a couple of ideas for shader-based lightfield-style rendering/reconstruction that could make for some very interesting effects.

Yes i know about dimensions in math calculations but i think here they were talking about a 4dimensional environment with 4dimensional movement and 4dimensional spherical vision (3d projected image)

Ive also been thinking about doing something like lightfield youre talking about (i think).
I think you can do real geometry bumpmapping so there are shadows in it.
Would be good especialy for things where the geometry details are much smaller than the screen pixels because you lose the small detail bumps there when you render it real time and the lighting result is very different.
With that technique you could render out different view angle textures and also the average geometry direction and reflectiveness per pixel for each mipmap for the real time specular calculation.
Some examples ive been thinking of are a cloth for a pooltable and asphalt for a racing simulation.

 

[Fred]

The temporal field as an added dimension is interesting to me.

It does not make sense to me mathematically to represent 3d graphics signature as standard 3 + 1 (for comparison our universe is actually +3 -1 technically). That is just an approximation, a hack so to speak.

Since we are dealing in reality with a quantized temporal field in 3dgraphics it should naturarly necessitate a different metric tensor, probably living in fourier transform space.

It should be possible to represent things in a precise way using this approach, and I suspect could lead to quite a few interesting results if done rigourously.

Whether its possible for realtime renderers, or even warranted by virtue of the extra overhead is anyone's guess.

 

[elimc]

http://pw1.netcom.com/~hjsmith/WireFrame4/tesseract.html

 

[g__day]

I was half expecting a post on M-theory, 11 dimensional space, string theory, and super-gravity.

As a mathematican it is easy to transform an N dimensional object in an N dimensional (linear) space into its best fit in a lower dimensional (linear) space. That's just second year University Pure linear algebra maths. The equations are straight forward once you realise you are determining the best way of describing the axis's of a N dimensional space onto the axis's of a space with fewer dimensions. Its a one line formulea for each axis.

With a maxtrix transform it'd probably be require one matrix multiply to change a N dimension object into its best equivalent form in a space of fewer dimensions. (easy peasy)! So N equations to set up the matrix and one multiply to change any object in an N dimensional space to its N-A target space. 4 dimensions to 3 dimensions, simple.

But why would you want to do this? What real world use does someone have for this need?