Using Space Effectively: 3D

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Lecture on Mar 15, 2010




  • Chapter 2, Projection Systems. In Art and Representation. Willats (pdf)
  • Chapter 8: Marginal Distortions. In The Psychology of Perspective and Renaissance Art. Kubovy (pdf)
  • What object attributes determine canonical views? Blanz et al. (html) (pdf) (alt pdf)

Optional Readings

  • Artistic Multiprojection Rendering. Agrawala et al. (html)
  • Automatic View Selection Using Viewpoint Entropy and its Application to Image-Based Modelling. Vázquez et al. (pdf)
  • Artistic Composition for Image Creation. Gooch et al. (pdf)
  • Gallery of Map Projections

Jeffrey Patzer - Mar 15, 2010 11:27:20 am

After reading marginal distortions, I am curious to what the application of the observations would be when used on a display like a computer screen. Since most viewers see a computer at relatively the same distance and angle, and their screens all tend to be within a certain aspect ratio (which is becoming even more standard with HD displays), I wonder if visualizations will have to be as careful when manipulating perspective. Since visualizations will most likely fall within your field of view by a good amount, I think that many of the issues brought up by the article might not too heavily affect a visualization meant to be viewed on a computer.

Zev Winkelman - Mar 15, 2010 01:14:01 pm

I'm relatively new to 3D so some of the language was a bit challenging, but the diagrams in the Willats chapter were very helpful.

Kubovy's marginal distortion paper was an interesting 'view' into how Renaissance Art dealt with 3D. My first reaction was that new electronic media would leave less room for marginal distortions (for better or worse), and result in consistent representations, but on second thought, there's no reason marginal distortions could not be introduced there as well. The special treatment of spheres was particularly 'enlightening'.

The canonical views study was great. The use of technology to provide more dynamic evaluation, the differences between the tasks of picking a "brochure" view and an imagined view, and the differences between familiar and nonsense objects were the most interesting aspects of the study.

The Vázquez et al paper made me think of a scene from the movie 'Enemy of the State'. I wonder if similar algorithms were used.

Stephen Chu - Mar 22, 2010 01:23:30 am

Viewpoint Entropy: The authors chose viewpoint entropy as the criterion to select a set of views adequate for image-based rendering. I don't understand all the math in the calculation of the viewpoint entropy, but it makes sense that the goal is to find a viewpoint where you can see all faces with approximately the same projected area.

Boaz Avital - Mar 23, 2010 03:57:16 am

One of the readings covered this briefly, but I'm interested to know more, amidst all the different ways to represent an image, what is the way that humans see them? Every projection and distortion has situations in which it looks the most natural and situations where it looks completely off. Do people see in a mix of these projections? As shown in the reading and lecture, even a plain, regular photograph may not show exactly what the human eye sees (do we see like a telephoto lens or a 'regular' lens?).

Moving away from the real world, which form of projection would be the best for representing 3d visualizations? If they're spacial, do you want to preserve as much as possible the relationship between elements on every axis, or the relationship between axes? Does it depend on what data you're visualizing, and what different types of data lend themselves to different strategies?

Shimul Sachdeva - Mar 29, 2010 02:31:03 am

Multiprojection images present an interesting concept - although, I wonder how an artist draws the line between what makes sense and what just looks absurd. "The Bounds of Perspective" talks about this aspect and Perkin's laws have simplified the filtering process, albeit primarily for rectangular objects. I was overwhelmed by the numerous examples in the gallery of map projections, each one conveying the same information from a different perspective. Is there a rule of thumb for identifying what kind of projection (parallel vs. perspective etc) and what kind of geometry (primary vs. secondary) is ideal, or is it upto the artist's discretion? I liked the Soriguerola example showed in class.

"Artistic Composition for Image Creation" mentions the importance of golden ratio in formulating compositional principles for artists, which I found to be interesting. The paper also discussed the rule of thirds and fifths, which are useful to know.

Arpad Kovacs - Mar 29, 2010 10:49:23 am

Kubovy's chapter 8 contains an interesting discussion of how the eye's visual field was empirically determined to be approximately 37 degrees, by measuring perceived distortion, reaction times, and line discrimination.

During the course of this reading, I found multiple allusions to Perkin's laws, which I was not familiar with. I found the following definitions in Chapter 7 of Kubovy's book:

  • Perkins's first law: A fork juncture is perceived as the vertex of a cube if and only if the measure of each of the three angles is greater than 90°.
  • Perkins's second law: An arrow juncture is perceived as the vertex of a cube if and only if the measure of each of the two angles is less than 90° and the sum of their measures is greater than 90°.

To clarify this, the image below (reproduced from the text) identifies a cube with a fork-juncture that is smaller 90 degrees, and how it appears distorted compared to the cubes above it.


Credits: Michael Kubovy, Christopher Tyler and WebExhibits

It seems that the main takeaway from this chapter is that rectangular prisms can still be perceived as having right-angles if we use Perkin's laws as rules-of-thumb, but the only perceptually-acceptable projection of a sphere is a circle. Consequently, artists and designers can create aesthetically pleasing images by moving the picture plane parallel to the principle surfaces of represented objects to minimize distortion.

Jonathan Yen - Mar 29, 2010 03:25:45 pm

I'm not sure if I completely understand the relevance of the Psychology of Perspective and Renaissance Art reading. Are there times when we will actually need to deal with angles and actually measure out the angles when we are creating visualizations? My guess is that it doesn't apply to every visualization, but I suppose it helps with the overall understanding of visualization. Kind of brings to mind an interesting tool that some web designers use: PixelStick (

Jon Barron - Mar 29, 2010 10:01:59 pm


I found the explanation of oblique projection as "projection using parallel rays inclined at an oblique angle to the plane of projection" extremely helpful and intuitive, and I'm not sure why the author is so opposed to describing these projections in terms perspective projection. It's especially vexing why the author advocates for poorly-defined, rule-of-thumb methods for making these oblique projections, like "Add a front face to a side face", which is hardly unambiguous.


The two takeaways from this seem to be: Keep everything within 37 by 28 degrees, when using perspective projection, and always project spheres to circles. Not the most actionable advice from an algorithmic perspective, but sound nonetheless.


Neat paper. I was surprised by how loosely clustered a lot of the datapoints were, I would have expected much stronger trends. What I found most interesting was the discovery that novel objects have no canonical views. However, this hardly seems fair, as the novel object they present has no clear orientation. If they had made it clear which direction was up (by giving the object a stand, for example) I'd imagine they would at least see a trend towards perspectives in the upper half of the sphere, which they do see in non-novel objects.

Jaeyoung Choi- Mar 30, 2010 01:58:54 am

Kubovy : The main point seems to be that geometrically correct representation isn't always perspectively satisfactory and there are certain ideas that you should keep in mind (such as sphere should be drawn as circle not ellipsis, Olmer's perspective normale, etc) to achieve that. A. Sanders' experiment to estimate the size of the field encompassed by the stationary eye by measuring reaction time was quite interesting.

Akshay Kannan - Mar 30, 2010 10:33:19 am

I found the discussion on marginal distortions quite interesting. While the constraint of central projection in static images is an issue, interactive visualizations could solve this problem by allowing dynamic panning, zooming, and rotation- similar to the method described in the Blanz paper. Even more interesting would be a system which rather than taking manual input from an input device, could track the position of the eyes of the viewer and reposition the visualization accordingly for their angle. This would not only allow accurate depiction of the graphic from all sides, but also enable a very realistic 3d feeling on a 2d screen.

Priyanka Reddy - Mar 31, 2010 02:13:25 pm

I found this lecture to be very eye-opening. I never really noticed the distortions and projections that are used in graphics before, so that was fun to learn about. I also enjoyed the discussion on what makes an image appear less distorted - it wasn't obvious that the natural image that we see with our eyes would not be the best way to represent the image on paper.

Prahalika Reddy - May 12, 2010 07:26:52 am

The paper on Marginal Distortions talks a lot about "canonical views" that I don't quite understand. I did find it interesting though to read about the results of the different experiments done. It was interesting to read about how the picture people took for brochures differed so much from what their mental image of the picture.

The stuff we discussed during this lecture was intriguing. The different views of the same image were entertaining to see. It was also informational to see all the different types of views that are there and how they actually look when applied to an image.

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