3D Representations: Difference between revisions

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===Light Field===

This is similar to a collection of images.

However, instead of thinking of it as a set of images, each pixel represents the color along a ray in 3D space.

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3-dimensions for the starting point of the ray and 2 dimensions for the direction of the ray.

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.

~~See [[Light field]]. ~~

===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}^3 \to \mathbb{R}</math> where the value at each position <math>(x,y,z)</math> corresponds to a density.

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.

Also known as a radiance field.

Also known as a radiance field. These can be encoded as explicit functions or neural networks.

===Signed Distance Field===

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===Marching cubes===

Marching cubes converts volumes to meshes.

Marching cubes converts volumes or signed distance fields to meshes.

===Reconstruction===

Structure from motion and multi view stereo methods can build point clouds from 2D images.

Meshing, or ~~surface reconstruction~~, works on converting this point clouds into meshes.

Meshing, or [[Surface Reconstruction]], works on converting this point clouds into meshes.

==See Also==

* [[Image-based rendering]]

@@ Line 7: / Line 7: @@
 ===Light Field===
+{{main | Light field}}
 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.<br>
@@ Line 12: / Line 13: @@
 -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===
-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>
+A volume is a dense 3D dataset <math>F: \mathbb{R}^3 \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.<br>
-Also known as a radiance field.
+Also known as a radiance field. These can be encoded as explicit functions or neural networks.
 ===Signed Distance Field===
@@ Line 48: / Line 48: @@
 ===Marching cubes===
-Marching cubes converts volumes to meshes.
+Marching cubes converts volumes or signed distance fields to meshes.
 ===Reconstruction===
 Structure from motion and multi view stereo methods can build point clouds from 2D images.<br>
-Meshing, or surface reconstruction, works on converting this point clouds into meshes.
+Meshing, or [[Surface Reconstruction]], works on converting this point clouds into meshes.
 ==See Also==
 * [[Image-based rendering]]