Some older references:
An expensive answer:
@InProceedings{mitchell-1992-illumination,
author = "Don P. Mitchell and Pat Hanrahan",
title = "Illumination From Curved Reflectors",
year = "1992",
month = "July",
volume = "26",
booktitle = "Computer Graphics (SIGGRAPH '92 Proceedings)",
pages = "283--291",
keywords = "caustics, interval arithmetic, ray tracing",
editor = "Edwin E. Catmull",
}
A cheat:
@Article{inakage-1986-caustics,
author = "Masa Inakage",
title = "Caustics and Specular Reflection Models for
Spherical Objects and Lenses ",
pages = "379--383",
journal = "The Visual Computer",
volume = "2",
number = "6",
year = "1986",
keywords = "ray tracing effects",
}
Very specialized:
@Article{yuan-1988-gemstone,
author = "Ying Yuan and Tosiyasu L. Kunii and Naota
Inamato and Lining Sun ",
title = "Gemstone Fire: Adaptive Dispersive Ray Tracing
of Polyhedrons",
year = "1988",
month = "November",
journal = "The Visual Computer",
volume = "4",
number = "5",
pages = "259--70",
keywords = "caustics",
}
----------------------------------------------------------------------
Subject 5.10: What is the marching cubes algorithm?
The marching cubes algorithm is used in volume rendering to
construct an isosurface from a 3D field of values.
The 2D analog would be to take an image, and for each pixel, set
it to black if the value is below some threshold, and set it to
white if it's above the threshold. Then smooth the jagged black
outlines by skinning them with lines.
The marching cubes algorithm tests the corner of each cube (or
voxel) in the scalar field as being either above or below a given
threshold. This yields a collection of boxes with classified
corners. Since there are eight corners with one of two states,
there are 256 different possible combinations for each cube.
Then, for each cube, you replace the cube with a surface that
meets the classification of the cube. For example, the following
are some 2D examples showing the cubes and their associated
surface.
- ----- + - ----- - - ----- + - ----- +
|:::' | |::::::
|:::: | | '::
|:' | |::::::
|:::: | |. '
| | | | |:::: | |::. |
+ ----- + + ----- + - ----- + + ----- -
The result of the marching cubes algorithm is a smooth surface
that approximates the isosurface that is constant along a given
threshold. This is useful for displaying a volume of oil in a
Some older references:
An expensive answer:
@InProceedings{mitchell-1992-illumination,
author = "Don P. Mitchell and Pat Hanrahan",
title = "Illumination From Curved Reflectors",
year = "1992",
month = "July",
volume = "26",
booktitle = "Computer Graphics (SIGGRAPH '92 Proceedings)",
pages = "283--291",
keywords = "caustics, interval arithmetic, ray tracing",
editor = "Edwin E. Catmull",
}
A cheat:
@Article{inakage-1986-caustics,
author = "Masa Inakage",
title = "Caustics and Specular Reflection Models for
Spherical Objects and Lenses ",
pages = "379--383",
journal = "The Visual Computer",
volume = "2",
number = "6",
year = "1986",
keywords = "ray tracing effects",
}
Very specialized:
@Article{yuan-1988-gemstone,
author = "Ying Yuan and Tosiyasu L. Kunii and Naota
Inamato and Lining Sun ",
title = "Gemstone Fire: Adaptive Dispersive Ray Tracing
of Polyhedrons",
year = "1988",
month = "November",
journal = "The Visual Computer",
volume = "4",
number = "5",
pages = "259--70",
keywords = "caustics",
}
----------------------------------------------------------------------
Subject 5.10: What is the marching cubes algorithm?
The marching cubes algorithm is used in volume rendering to
construct an isosurface from a 3D field of values.
The 2D analog would be to take an image, and for each pixel, set
it to black if the value is below some threshold, and set it to
white if it's above the threshold. Then smooth the jagged black
outlines by skinning them with lines.
The marching cubes algorithm tests the corner of each cube (or
voxel) in the scalar field as being either above or below a given
threshold. This yields a collection of boxes with classified
corners. Since there are eight corners with one of two states,
there are 256 different possible combinations for each cube.
Then, for each cube, you replace the cube with a surface that
meets the classification of the cube. For example, the following
are some 2D examples showing the cubes and their associated
surface.
- ----- + - ----- - - ----- + - ----- +
|:::' | |::::::
|:::: | | '::
|:' | |::::::
|:::: | |. '
| | | | |:::: | |::. |
+ ----- + + ----- + - ----- + + ----- -
The result of the marching cubes algorithm is a smooth surface
that approximates the isosurface that is constant along a given
threshold. This is useful for displaying a volume of oil in a
|:::: | | '::
