Doodlings

Lest you think I’m doing real work at grad school, mostly it’s about doodling pretty picures...

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ME 471—Finite Elements (spring 2006)

2-D plane strain

Fun bending metal. Aluminum bar on an epoxy layer. The right end is fixed, the left end is subject to a traction of 180 megapascal, about 26,000 psi.

Displacement

Note high stress near joints

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CS 591mh—parallel and numeric computing

Projective ODE Method (fall 2005)

Brusselator equations showing chemical concentration over time.

t=1.2	t=1.3
t=1.4	t=1.5

Wavelets (spring 2005)

Used for signal processing, graphics compression (JPEG 2000), and elsewhere.

“They are not as smooth as they look.” –Strang

Daubechies Φ scaling function

Daubechies Ψ mother wavelet

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CS 519—Scientific Visualization (fall 2005)

Internet2 Delay

Visualization of network delays across the Internet2 networks, using data from the AMP project.

Yosemite Valley

Terrain viz, using elevation data from the USGS. The first texture is from the Yosemite visitors map, the second from Google maps. You can see Half Dome as a white splotch near the top center.

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CS 419—advanced graphics (spring 2005)

Bezier Patches

Bezier patches are defined by Bernstein polynomials, but this uses an iterative algorithm that never actually evaluates the polynomial.

Teapot

Fun house mirror

Photon mapping

Indirect lighting, caustics (focused light), color bleeding

Gathering isn’t working properly. It is less blurry than without gathering, but is adding weird highlights at corners.

With map & gathering	With map	Without map
With map	Without map

Smoothed

Interpolate normals across the surface

Sanded killeroo

Glass killeroo

Hills

Waves

Wood and bumpy surfaces

Textures defined by simple equation plus noise function

Oak killeroo

Displacement map

Add depth-of-field, anti-alias, soft shadows

By shooting many rays through each pixel, we can smooth jaggies and blur out-of-focus objects.

Banchoff 6

Legos

Basic shapes, reflection & refraction

A ray shoots through each pixel, intersecting geometric objects and bouncing off mirrored objects.

Banchoff 6

Glass

CSG Spheres

Ellipsoids