3D Representations: Difference between revisions

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Ways to represent 3D objects and scenes.

==Representations==

===Collection of images===

Just a set of 2D images. Videos may also fall under this category.

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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.

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.

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>.

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.

===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.

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. These can be encoded as explicit functions or neural networks.

===Signed Distance Field===

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A list of vertices (<math>N \times 3</math>) and triangles (<math>N \times 3</math>).

The current standard representation used in real-time 3D applications.

===CAD Models===

These are vector representations with relationships between objects.

E.g. Object A is left of Object B by 5 centimeters.

==Conversions==

===Volume rendering===

Volume rendering converts volumes to 2D images.

Differentiable volume rendering (NeRF) can convert posed 2D images to neural volumes.

===Ray marching===

Ray marching converts signed distance fields to 2D images.

===Rasterization===

Rasterization converts meshes to 2D images.

===Marching cubes===

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.

==See Also==

* [[Image-based rendering]]

@@ Line 1: / Line 1: @@
 Ways to represent 3D objects and scenes.
+==Representations==
 ===Collection of images===
 Just a set of 2D images. Videos may also fall under this category.
@@ Line 6: / Line 7: @@
 ===Light Field===
-This is similar to a collection of images.
+{{main | Light field}}
-However, instead of thinking of it as a set of images, each pixel represents the color along a ray in 3D space.
+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>
+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>
+-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>
 ===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.<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. These can be encoded as explicit functions or neural networks.
 ===Signed Distance Field===
@@ Line 25: / Line 31: @@
 A list of vertices (<math>N \times 3</math>) and triangles (<math>N \times 3</math>).
 The current standard representation used in real-time 3D applications.
+===CAD Models===
+These are vector representations with relationships between objects.
+E.g. Object A is left of Object B by 5 centimeters.
+==Conversions==
+===Volume rendering===
+Volume rendering converts volumes to 2D images.<br>
+Differentiable volume rendering (NeRF) can convert posed 2D images to neural volumes.
+===Ray marching===
+Ray marching converts signed distance fields to 2D images.
+===Rasterization===
+Rasterization converts meshes to 2D images.
+===Marching cubes===
+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.
 ==See Also==
 * [[Image-based rendering]]