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3D Representations: Difference between revisions
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===Light Field=== | ===Light Field=== | ||
This is similar to a collection of images. | This is similar to a collection of images.<br> | ||
However, instead of thinking of it as a set of images, each pixel represents the color along a ray in 3D space. | However, instead of thinking of it as a set of images, each pixel represents the color along a ray in 3D space.<br> | ||
Thus, light fields are collections of rays in 3D space. Typically we assume the rays lie in an empty/transparent space until they hit a surface. | Thus, light fields are collections of rays in 3D space which can be modeled using the plenoptic function <math>F: \mathbb{R}^5 \to \mathbb{R}</math>.<br> | ||
See [[Light field]]. | 3-dimensions for the starting point of the ray and 2 dimensions for the direction of the ray.<br> | ||
Typically we assume the rays lie in an empty/transparent space until they hit a surface thus rays can be models as lines which can be defined with 4 dimensions.<br> | |||
See [[Light field]].<br> | |||
===Volume=== | ===Volume=== | ||
A volume is a dense 3D dataset <math>F: \mathbb{R}^2 \to \mathbb{R}</math> where the value at each position <math>(x,y,z)</math> corresponds to a density. | A volume is a dense 3D dataset <math>F: \mathbb{R}^2 \to \mathbb{R}</math> where the value at each position <math>(x,y,z)</math> corresponds to a density.<br> | ||
Volume rendering is used project a 3D volume into a 2D image by sampling the volume along a ray for each pixel in the 2D image. | Volume rendering is used project a 3D volume into a 2D image by sampling the volume along a ray for each pixel in the 2D image.<br> | ||
Also known as a radiance field. | |||
===Signed Distance Field=== | ===Signed Distance Field=== | ||