Position-Dependent Opacity

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

In Mathematica, opacity specified by Opacity[o] gives an opaque surface where the opacity is independent of the position. For curved surfaces this makes colors appear "flat". If the surface was made from a thin sheet of transparent material, the effective length of the optical path would depend on the angle between the surface normal and the view point. The optical path would be longest where the light rays would hit the surface parallel to its local tangent plane. The upper torus uses a position‐dependent opacity to model a larger absorption; the lower torus uses a constant opacity (equal to the average opacity of the upper image). The position‐dependent opacity results in darker edges and caustic‐like structures around cusp projections.

Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica GuideBook for Graphics, second edition by Michael Trott (© Springer, 2008).
Open content licensed under CC BY-NC-SA


Snapshots


Details

Because the opacity used depends on the view point, rotating the upper graphic interactively yields physically incorrect results that do not correspond to the imitated appearance of a thin transparent sheet.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send