Anamorphism

Transformation Geometry

• Anamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image

Anamorphism – Is when artists foreshorten and angle linear perspective to deform and change the scale of an object. The image becomes incomprehensible when viewed directly but resolves into a clear picture when looked at from a different vantage point.

There are two main types of anamorphism: perspective (oblique) and mirror (catoptric).

Both perspectival and Mirror anamorphism date back to the Renaissance period.

Perspectival anamorphism - requires the viewer to look at a picture from an unusual angle instead of standing in front of the painting and looking at it straight on.

Mirror anamorphism - a conical or cylindrical mirror is placed on the drawing or painting to transform a flat distorted image into a three-dimensional picture that can be viewed from many angles.

Perspectival anamorphism

Mirror anamorphism

Where is the Math in Mirror Anamorphosis

• Find equation for surface• Define vector from viewer to pixel• Find intersection• Calculate normal vector• Find reflection vector• Determine printing coordinates

The Set-Up

Finding the intersection

Finding the intersection

Finding the Normal Vector

• A normal vector is a vector perpendicular to another object, such as a surface or plane. Often we refer to a unit normal vector as n.

Finding the Reflection Vector

• a Reflection is a mapping from a Euclidean space to itself. The image of a figure by a reflection is its mirror image in the axis or plane of reflection.

Printing the Pixel

• Future work on anamorphs of 3D models will include investigating what can be done with conical and cylindrical anamorphs in combination with their respective reflecting surface and a ray tracing rendering. Anamorphic texture mapping might be interesting to persue also. Other collineations could be explored.

Sources• http://www.thisiscolossal.com/tags/anamorphism/• http://web.ebscohost.com.mu.opal-libraries.org/ehost/pdfviewer/pdfvie

wer?vid=6&sid=b351ca99-9517-4517-af56-cec4428566f7%40sessionmgr113&hid=123

• http://archive.bridgesmathart.org/2012/bridges2012-513.pdf• http://www.washacadsci.org/Activities/Capital%20Science/presentations/

washpresentation.pdf• http://www.roserushbrooke.com/article-anamorphosis.html