Posts tagged: 3D

nldmut:

Specular holograms by Matthew Brand currently on display at the new Museum of Mathematics in New York.

See his site for more.

The technique used by Brand to create these pieces is not one of conventional holography. He meticulously controls the unique shape of thousands of tiny optical pieces placed on a surface creating a 3D effect when the light source or viewer moves. This is essentially a mathematical problem in differential geometry and combinatorial optimization. Brand was the first person to correctly describe this technique in 2008 even though it dates back as early as the 1930s (check out his paper for details).




This is what it would look like to spin around in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.




This is what it would look like to do a front flip in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.




Flying though a tiling of regular right angled dodecahedron in three dimensional hyperbolic space. There is more of an explanation here.

Created with Curved Spaces.


Flying through Euclidean 3-space

View as a single GIF here




Flying through Euclidean 3-space

View as 4 quadrants here

2D projections of the 3D cube


2D projections of the 3D cube

matthen:

Another cross-eye 3D image (cross your eyes so you see on 3D image in the middle; help). This shows the twisting of a flat band of paper into a Möbius strip- an interesting surface as it has only one side and one edge; it is ‘non-orientable’. [more] [my code]

matthen:

Another cross-eye 3D image (cross your eyes so you see on 3D image in the middle; help). This shows the twisting of a flat band of paper into a Möbius strip- an interesting surface as it has only one side and one edge; it is ‘non-orientable’. [more] [my code]

This is a stereoscopic image

This is a stereoscopic image

This is a stereoscopic image

This is a stereoscopic image

This is a stereoscopic image

This is a stereoscopic image

This is a stereoscopic image

This is a stereoscopic image

A stereoscopic 3D projection of a tesseract.Learn how to view here.

A stereoscopic 3D projection of a tesseract.
Learn how to view here.

matthen:

Cross your eyes, so your right eye is looking at the left image, and vice versa. There will be 3 images and the middle one should be an animation in 3D.  This shows how a Klein bottle can be constructed in three dimensions. The Klein bottle is an interesting mathematical object with no inside, no outside, and no boundary- it is similar to a Mobius band. [my code] [more]

matthen:

Cross your eyes, so your right eye is looking at the left image, and vice versa. There will be 3 images and the middle one should be an animation in 3D.  This shows how a Klein bottle can be constructed in three dimensions. The Klein bottle is an interesting mathematical object with no inside, no outside, and no boundary- it is similar to a Mobius band. [my code] [more]

matthen:

Cross your eyes so that the two images converge to one in the middle. Your right eye will be looking at the left image, your left at the right, you will see 3 images and the middle one will be in 3D! This is the Mathematica spikey shape, and it was the answer to the flat-land problem I set a few days ago. [my code]

matthen:

Cross your eyes so that the two images converge to one in the middle. Your right eye will be looking at the left image, your left at the right, you will see 3 images and the middle one will be in 3D! This is the Mathematica spikey shape, and it was the answer to the flat-land problem I set a few days ago. [my code]