James Arvo (arvo@cs.caltech.edu)


Bidirectional Ray Tracing

Focused Light: This image was generated in 1986, and is of purely historical interest. It was one of the first synthetic images to demonstrate caustics, or brightly illuminated areas due to refraction (as shown here) or reflection. A simple technique for capturing this effect was described in the short paper Backward Ray Tracing that appeared in the notes for the SIGGRAPH `86 tutorial on ray tracing organized by Al Barr. The term "backward" meant "from the light" rather than the traditional method of tracing rays from the eye. This is bad terminology, so please don't propagate it further! It's much better to call it light ray tracing, or even photon tracing. (This image was scanned from an old slide, which introduced a few artifacts.)


Magazine Covers

Here are a couple of images that were used as magazine covers. The image used for the February 1988 edition of the CACM is called
The Six Platonic Solids; it was ray traced in collaboration with Dave Kirk. The cover of the April 1985 edition of Computer Graphics World was also ray traced. The design is by Michael Sciulli. Both images were created at Apollo Computer.


Other Covers

Here are some other book covers that were adorned with ray traced images. These are all from 1987 and 1988.
The Six Platonic Solids appeared on five covers in all, including the back cover of the SIGGRAPH `87 conference proceedings (not shown).


Environment-Sensitive Automata

The vines clinging to the trellis in this image were "grown" algorithmically using the technique described in
Modeling Plants with Environment-Sensitive Automata. The automata sense their surroundings by casting rays, which allows them to detect nearby surfaces and avoid obstacles. So, this image used ray tracing in two distinct ways: as an aid to modeling, and as a rendering technique after the model was created. [1988]


Analytically-Computed Glossy Reflection

Glossy Reclection: This image is from the paper Applications of Irradiance Tensors.... The image depicts a "glossy" or imperfect reflection of a collection of polygons. The reflection was computed analytically using a new technique described in the paper (with more complete details given in my thesis). The reflection corresponds to a Phong exponent of 400. The original data for this stained glass window (designed by Elsa Schmid) is available here, although it is in a rather ad hoc format. It is also available in mgf format. [1995]

See Paul Diefenbach's web page for examples of glossy reflection that were generated with hardware acceleration.


A Range of Glossy Surfaces

Here is a sequence of images depicting glossy reflections. Click on the image for a full resolution TIFF version. The reflections correspond to Phong exponents of 10, 45, and 400, from left to right.


Comparison with Monte Carlo


Lizard with Closeups: These images are also from the paper Applications of Irradiance Tensors.... The middle image is a closeup of the reflection of the Escher lizard, and the image on the far right is the same closeup computed using Monte Carlo. The analytic method was a bit faster, and clearly much better since there are no statistical errors. [1995]


Analytically-Computed Glossy Transmission


Frosted Glass: These images are also from the paper Applications of Irradiance Tensors.... They depict a polygonal butterfly behind two different pieces of frosted glass. The transmitted light was computed analytically at each pixel using Phong exponents of 10 and 65. [1995]


Iso-Intensity Contours for Volume Rendering

Iso-Mesh of Human Pelvis: This mesh was generated from iso-intensity contours computed directly from the volume data of a human pelvis. The contours are solutions of ODEs based on analytically computed image intensity gradients. The mesh, generated using constrained Delaunay triangulation, can be used to reconstruct the image. For details, see the paper Iso-Contour Volume Rendering.

This is a contrived test case called the "urchin". It consists of irregular data organized into 20 radial spines. [1994]


Isolux Contours

These images show directly computed isolux contours and the resulting mesh generated by constrained Delaunay triangulation. The algorithm is described in
The Irradiance Jacobian.... [1994]


Anamorphic Images


These images were created on a pen plotter sometime in the late 70's (I don't remember the year). They are examples of anamorphic images: that is, they are distorted so that the original (undistorted) images will appear when viewed in an unusual manner. The images above are examples of cylindrical anamorphic distortions. If you were to look at the reflection in a cylindrical mirror held to the circle at the top of the image, you would see the original (undistorted) image. A short length of chrome pipe from the hardware store works quite well.


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James Arvo (arvo@cs.caltech.edu)